CASSIANO TERRA RODRIGUES

A STUDY ON THE CONCEPT OF SCIENCE IN THE PHILOSOPHY OF CHARLES S. PEIRCE

VOLUME II

Programa de Estudos Pós-Graduados em Filosofia

Pontifícia Universidade Católica de São Paulo

São Paulo

2005

SUMMARY

6. The Problem of Induction and Scientific Method204

7. Experience and Expectation299

8. The Genealogy of Sciences 339

8.1 The most natural scheme possible374

9. Mathematics as the most general science398

10. Conclusion: Ulrich’s Dilemma 439

Bibliography481

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6. THE PROBLEM OF INDUCTION AND THE SCIENTIFIC METHOD

In natural science this rigid method is the Baconian method of induction, a mehod which, if consistently pursued, would have left science where it found it. What

Bacon omitted was the play of free imagination, controlled by the requirements of coherence and logic. The true method of discovery is like the flight of an aeroplane. It

starts from the ground of particular observation; it makes a flight in the thin air of imaginative generalization; and it again lands for renewed observation rendered acute

by rational interpretation.

Alfred North Whitehead, Seção II, Process and Reality.

David Hume, in his Treatise on Human Nature, explicitly

formulated, for the first time, the problem of rational justification of our

inductive inferences. However, he did not use the word “induction”, not

even “inductive reasoning”1. Where the adjective “inductive” would

naturally be used, Hume talks either of arguments or inferences, or yet

reasonings “based on the experience”; or “from causes to effects”; or,

still, “in respect to the question of fact”2. The arguments he discusses

under such denominations, however, are all (with a single possible

exception)3 arguments called inductive. For the Scottish philosopher,

there is no justification for illations because it is impossible to

demonstrate that there is a necessary relation between cause and effect

1 In effect, induction appears only once in the Treatise, in the Appendix, but it seems that there is not the meaning of “argument based on experience”. Cf. HUME (1739-1740), p. 628. 2 Cf. HUME (1739-1740), I: III, section XI; p. 649 seq. (An Abstract of a book lately published entitled A Treatise of Human Nature, etc., wherein the chief argument of that book is farther illustrated and explained); 3 Namely, the class of probable arguments that Hume discuss on section XI of book I, part III, of Treatise, and in the third paragraph of the correspondent section VI of the Enquiry.

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in things. For the question “how is it possible to know that the sun will

rise tomorrow?” the only answer would be: “by habit”; in other words,

the repetition of the past experience leads to the belief that what

always happened, will always happen: “all our reasonings concerning

causes and effects are derived from nothing but custom”4. In other

words, the experience cannot show that the effect is necessarily

contained in the cause, because our sensations do not give us more

than separate and distinctive perceptions, unrelated one from another:

That our senses offer not their impressions as the images

of something distinct, or independent, and external, is

evident; because they convey to us nothing but a single

perception, and never give us the least intimation of any

thing beyond. A single perception can never produce the

idea of a double existence, but by some inference either

of the reason or imagination. When the mind looks

farther that what immediately appears to it, its

conclusions can never be put to the account of the

senses; and it certainly looks farther, when from a single

perception it infers a double existence, and supposes the

relations of resemblance and causation betwixt them.5

Thus, a supposed relation of necessity between cause and effect is

grounded upon the associations of ideas such as it happened in the

past: nothing can warrant that from the existence of a fact B the

existence of a fact A must necessarily obtain, but for the custom of

thinking or imagining that it is so. Therefore, no inferential conclusion

based on experience is necessary, but all are contingent; it is certain

4 HUME (1739-1740), I: IV, section 1.5 HUME (1739-1740), I: IV, section II.

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that we cannot state any necessary relation between two distinct facts;

we cannot state, says Hume, the continuous existence of objects,

distinctly and independently of human nature.6

Hume drives our attention to an existent gap between premises

and conclusions in inductive reasoning, showing the problem of the

rational acceptation of hypotheses on inductive bases by putting in

check the procedure of scientific activity; once science is based in

theoretical verifications inductively obtained, there are no steady

grounds for scientific knowledge7. The problem of causality is exemplar

in this respect. Causality, for Hume, “makes me go from something that

was given to me to an idea of something that was never given to me, or

even that is not givable in experience”, in Deleuze’s words8. Or, in

Hume’s own words:

The only connexion or relation of objects, which can lead

us beyond the immediate impressions of our memory and

senses, is that of cause and effect; and that because ‘tis

the only one, on which we can found a just inference

from one object to another.9

We do not draw the idea of the necessity of the causal relation

from some rational knowledge, but from empirical observation. Things

themselves do not furnish us any bases for such knowledge, but only

our experience of them. Thus, one can conclude that Cesar was

murdered in the senate because it is read in history books about the

6 Idem, ibidem.7 TIDMAN; KAHANE (2003), p. 396; COSTA (1993), pp. 33 seq.8 DELEUZE (1974), p. 62.9 HUME (1739-1740), I: III, section VI.

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murder; one can conclude that the sun will rise tomorrow because one

had always seen the sun rising; in that one feels the hot stone under the

sun, one can infer that the sun is the cause of the heat of the stone.

Hume says:

‘Tis therefore by EXPERIENCE only, that we can infer the

existence of one object from that of another. The nature

of experience is this. We remember to have had frequent

instances of the existence of one species of objects; and

also remember, that the individuals of another species of

objects have always attended them, and have existed in a

regular order of contiguity and succession with regard to

them. Thus we remember to have seen that species of

object we call flame, and to have felt that species of

sensation we call heat. We likewise call to mind their

constant conjunction in all past instances. Without any

farther ceremony, we call the one cause and the other

effect, and infer the existence of the one from that of the

other. In all those instances, from which we learn the

conjunction of particular causes and effects, both the

causes and effects have been perceived by the senses,

and are remembered: But in all cases, wherein we reason

concerning them, there is only one perceived or

remembered, and the other is supplyed in conformity to

our past experience.10

Causality is a relation that allows the surpassing of the given, and

to infer a necessary link that is not in the things themselves, but that is

thought as it were necessary and intrinsic in them. In effect, Hume

postulates the exteriority of relations as to the world: relations of

causality, similarity, contiguity, succession, etc. are creations of human

10 HUME (1739-1740), ), I: III, section VI.

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imagination to explain the world of particular and contingent

experiences, a world constituted of separated and distinct facts11. Thus,

we infer and believe in relations of causality, similarity, etc. because we

habituate ourselves to certain world experience:

The idea of cause and effect is derived from experience,

which informs us, that such particular objects, in all past

instances, have been constantly conjoined with each

other: And as an object similar to one of these is

supposed to be immediately present in its impression, we

thence presume on the existence of one similar to its

usual attendant. According to this account of thins, which

is, I think, in every point unquestionable, probability is

founded on the presumption of a resemblance betwixt

those objects, of which we have had experience, and

those, of which we have had none [...].12

Therefore, the natural sciences would be based upon a series of

beliefs: because experience has always been of a certain character, one

can trust that experience will always be similar to that, in similar

circumstances. Scientific knowledge is, then, restricted to probability,

because the certainty of knowledge results from the verification of the

repetition of a series of events in experience. And this probability, even

so, can only concern to what was empirically given:

Let men be once fully perswaded of these two principles,

That there is nothing in any object, consider’d in itself,

which can afford us a reason for drawing a conclusion

beyond it; and, That even after the observation of the

frequent or constant conjunction of objects, we have no

11 DELEUZE (1974), pp. 60-63.12 HUME (1739-1740), ), I: III, section VI.

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reason to draw any inference concerning any object

beyond those of which we have had experience [...].13

The problem of induction, therefore, can be formulated by Hume

in respect to the success of the scientific method in calculating the

probabilities (in determining the approximate similarities among the

objects), based on the reiterated experience of the past:

Thus not only reason fails us in the discovery of the

ultimate connexion of causes and effects, but even after

experience has inform’d us of their constant conjunction,

’tis impossible for us to satisfy ourselves by our reason,

why we shou’d extend that experience beyond those

particular instances, which have fallen under our

observation. We suppose, but are never able to prove,

that there must be a resemblance betwixt those objects,

of which we have had experience, and those which lie

beyond the reach of our discovery.14

Of course, Peirce understands the problem of induction not only

in Humean terms. His comprehension of induction, differently of

Hume’s, was not informed by the idea of simple enumeration, as we will

see. Nevertheless, the philosophical position grounded on the idea of

the exteriority of relations is essentially contrary to the one he has

assumed. Indeed, Peirce understood the problem of induction also in

Humean terms, meaning that it was relatively to the possibility of

amplified knowledge, and by this way the Humean position could be

refuted. Already in 1869 Peirce stated that the problem of knowledge

could be understood on the basis of the question about the possibility of

13 HUME (1739-1740), I: III, section XII. 14 HUME (1739-1740), I: III, section VI.

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synthesis, explicitly recognizing that his approach comes from Kant’s

philosophy:

According to Kant, the central question of philosophy is

“How are synthetical judgments a priori possible?” But

antecedently to this comes the question how synthetical

judgments in general, and still more generally, how

synthetical reasoning is possible at all [W 2: 267-268,

Grounds of Validity of the Laws of Logic].

To answer this question is, Peirce said, to unlock the door of

philosophy. Early in his writings, he sustained a theory of induction, the

gist of which is the idea of the autocorrecting nature of inductive

reason in the long run. The conceptions of frequency and probability

become gradually more important in his works to ground this idea,

because they show a straight link between the deductive and inductive

inferential processes. These are ideas that, despite the evolution of his

thought, and the improvement of his theories, Peirce has never

abandoned. Accordingly, we will present an interpretation of Peirce’s

theory of induction, starting from his writings in the beginning of his

philosophical career. We will not occupy ourselves with the

development of his ideas in a perspective of historical reconstruction,

but we will show that the strongest theses of his late philosophy largely

occur from the refinement of his early ideas.15

15 ULLIAN (1995), pp. 94-95; RESCHER (1978), p. 17 seq. For a detailed comparison of the Humean and the Peircean theories of induction, as well as for the evolution of the idea of induction in Peirce’s philosophy, cf. BACHA (1999), passim, especially pp. 47 ff., chap. 3: “A evolução histórica do conceito de indução em Peirce”, pp. 114-335.

210

In 1868, Peirce distinguished kinds of valid inferences in

syllogistic terms: apodictic (or deductive) syllogisms, and probable (or

inductive and hypothetical) syllogisms. “An apodictic or deductive

syllogism is one whose validity depends unconditionally upon the

relation of he fact inferred to the facts posited in the premises” [W 2:

215, Some Consequences of Four Incapacities]. That the validity of

deduction does not depend upon the experience of an ulterior

knowledge, but only upon its premises, is a peculiar characteristic of

deduction: either this other knowledge would be in the premises, and

obviously would not be another, or it would be implicit, and the

inference would be incomplete. For this reason, deduction is the only

kind of reasoning that can be called necessary [HL 217]. The truth of

deduction is warranted in a necessary manner in that all the possible

relevant information needed to reach the conclusion is in the premises

[W 2: 175, Questions on Reality, 1868]. Peirce gives two examples of

deductive reasoning:

No series of days of which the first and last are different

days of the week exceeds by one a multiple of seven

days; now the first and last days of any leap-year are

different days of the week, and therefore no leap-year

consists of a number of days one greater than a multiple

of seven.

Among the vowels there are no double letters; but one of

the double letters (w) is compounded of two vowels:

hence, a letter compounded of two vowels is not

necessarily itself a vowel [W 2: 215].

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It is an important conclusion that in all necessarily valid deductive

reasoning from true premises, it is possible to draw only true

conclusions [id.]. As a matter of fact, this position will always be

maintained by Peirce in his writings; see the following passage, from

1903:

In deduction, or necessary reasoning, we set out from a

hypothetical state of things which we define in certain

abstracted respects. Among the characters to which we

pay no attention in this mode of argument is whether or

not the hypothesis of our premisses conforms more or

less to the state of things in the outward world. […] Our

inference is valid if and only if there really is such a

relation between the state of things supposed in the

premisses and the state of things stated in the conclusion

[HL 225].

The principle stated since 1868 remains the same, which says that

true premises yield true conclusions. Now, the agreement with the

concrete facts, so to say, is another problem, that does not affect the

validity of the deduction. All deduction is reasoning starting from the

general to reach the particular, meaning that it is an inference

according to a general rule of drawing particular propositions from

general propositions. For that reason, the necessity of the reasoning is

in that the truth of conclusions depends on the truth of premises [NEM

3/I: 172, Probability and Induction, 1911]. For the same reason,

deduction can be called analytical inference, because the result

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attained cannot be discordant from the rule [W 3: 323-326, Deduction,

Induction, and Hypothesis, 1878].

Notwithstanding, Peirce further recognized that deductively

reached conclusions may not be absolutely valid. Deductions are also

forms of probable reasoning, even when the probability of extracting

false conclusions from true premises is minimal; that is, deductions are

inferences that “in the long run of experience the greater part of those

whose premises are true will have true conclusions.”16 [EP 2: 298,

Nomenclature and Divisions of Triadic Relations, as Far as They Are

Determined, 1903]. In this respect, it may be more correct to say that

there are necessary deductions and probable deductions, meaning that

these deductions are of a certain probability [NEM 3/I: 172].

The first important point we want to emphasize is that the logical

validity of reasoning depends essentially on the obeysance of the rule

for passing from conclusions to premises:

The passage from the premise (or set of premises) P to

the conclusion C takes place according to a habit or rule

active within us. […] The habit is logically good provided

it would never (or in the case of a probable inference,

seldom) lead from a true premise to a false conclusion;

otherwise it is logically bad. [W 4: 165, On the Algebra of

Logic, 1880].

In other words, a good habit of reasoning takes into account a

disjunction of the following form: or the premise is false, or the

16 See CROMBIE (1997).

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conclusion is true. A bad habit of reasoning extracts false conclusions

from true premises [RLT 167].

The second important point to highlight is that, theoretically,

error is impossible in deduction. Nevertheless, two cases of error are

possible: first, since deductions concern mathematical reasonings on

probabilities, the possibility of its application leaves open the possibility

of an error:

Deduction is the only necessary reasoning. It is the

reasoning of mathematics. It starts from a hypothesis,

the truth or falsity of which has nothing to do with the

reasoning; and of course its conclusions are equally ideal.

The ordinary use of the doctrine of chances is necessary

reasoning, although it is reasoning concerning

probabilities.” “Moreover, its application to experience,

or to possible experience, opens the door to probability,

and shuts out absolute necessity and certainty, in toto.

[CP 6.595, A Reply to Necessitarians, 1893].

Second, any mistake can occur in a deduction, and false

conclusions can be obtained starting from true premises, as mentioned

before, resulting from a bad deductive habit or some inattention in

reasoning:

Deduction is really a matter of perception and of

experimentation, just as induction and hypothetic

inference are; only, the perception and experimentation

are concerned with imaginary objects instead of with real

ones. The operations of perception and of

experimentation are subject to error, and therefore it is

only in a Pickwickian sense that mathematical reasoning

can be said to be perfectly certain. It is so only under the

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condition that no error creeps into it; yet, after all, it is

susceptible of attaining a practical certainty.17 [CP 6.595,

A Reply to Necessitarians, 1893].

Until 1878, the typical logical form of deduction is understood by

Peirce as one of a syllogism, the major term of which must be a

universal categorical proposition, and the minor term of which an

affirmative proposition, seen in the syllogism of the first figure (in

Barbara) that could be written like this:

Rule: All beans in this bag are

white.

All S is P.

Case: These beans are from

this bag.

M is S.

Result: These beans are white. M is P.

To pass to the other kinds of reasonings, it is important to keep

this syllogistic form in mind. We shall return to it later. Now, we pass to

the other kinds of reasonings.

Induction and hypothesis are closely linked with each other by

the difference between logical extension, or breadth, and

comprehension, or depth. In other words, the extension of a term or

proposition is composed of all things or events of which the term is

predicable or that the proposition can represent. The comprehension of

a term or proposition, in turn, relates to the characteristics that can be

predicated to any object, which is in principle unknown [W 2: 79, Upon

Logical Comprehension and Extension, 1867]. In both cases, reasonings

17 Pickwick is an allusion to Charles Dickens’ character, in his novel The Adventures of Mr. Pickwick.

215

depend on an absence of knowledge, related to the question of knowing

if certain objects have or not certain characteristics, what question

places two alternatives:

[...] the absence of knowledge is either whether besides

the objects which, according to the premises, possess

certain characters, any other objects possess them; or,

whether besides the characters which, according to the

premises, belong to certain objects, any other characters

not necessarily involved in these belong to the same

objects. [W 2: 215-216, Some Consequences of Four

Incapacities].

This is not a mere terminological distinction, but a distinction

between two distinct domains of facts, because the assertions are made

either according to the objects themselves, in the case of extension, or

according to the predicates, in the case of comprehension. Related to

extension, we have an induction; related to comprehension, a

hypothesis. Both are distinct cases of synthetic inferences, and

respectively result from the generalization of a particular characteristic

of an object for a whole class, and from the supposition of the existence

of a particular case with certain characteristics. This supposition is

derived from the knowledge of a general rule, in order to explain a fact,

which is strange at first view [W 2: 216-217, Some Consequences of

Four Incapacities].

The difference between breadth and depth can be better

understood if we look at the diagram below [W 1: 459, Lowell Lecture

VII, 1866]:

216

Peirce used the idea of breadth to describe the domain of

nomination, or denotation, or reference, or extension, or the

application of terms to “all the real things of which it is predicable […]”;

and the idea of depth, in turn, is linked to that of meaning, connotation,

definition, intension, sense; in sum, “all the real characters (in

contradistinction to mere names) which can be predicated of it” [W 2:

79, Upon Logical Extension and Comprehension, 1867]. Breadth and

depth, extension and comprehension, denotation and connotation, all

are ideas used in defending the thesis that no term, proposition or

argument is neither absolutely determined, nor absolutely

undetermined. The definitions of extension as denotation, and of

comprehension as connotation, according to Peirce, belong to John

Stuart Mill. Kant, in his turn, had already defined the relation between

extension and comprehension in the following way:

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What is denotedSphereExtensionBreadth: wider

narrower

What is contained under

What is connotedContentComprehensionDepth: lower

higher

What is contained in

Every concept, as partial concept, is contained in the

representation of things; as ground of cognition, i.e., as

mark, these things are contained under it. In the former

respect every concept has a content, in the other an

extension.18

Extension and comprehension (content), for Kant, are inversely

proportional, that is, “the more a concept contains under itself, namely,

the less it contains in itself, and conversely”19. Thus, “the more the

things that stand under a concept and can be thought through it, the

greater is its extension or sphere”20, and the less it will be as more

things are contained in the concept itself, because it will be possible to

think of a more restrict domain of objects through it.

To say that a term is absolutely undetermined is the same as to

say that it has absolute depth, meaning that it would designate a

characteristic belonged to all things – and this is impossible:

[…] we have propositions whose subjects are entirely

indefinite, as “There is a beautiful ellipse,” where the

subject is merely something actual or potential; but we

have no propositions whose predicate is entirely

indeterminate, for it would be quite senseless to say, “A

has the common characters of all things,” inasmuch as

there are no such common characters [W 2: 50, On a

New List of Categories, 1867].

A completely determined term is also impossible, because it

would mean that such term would be extended to everything, denoting

18 KANT (1799-1800), Ak. 95.19 Idem.20 Id., Ak. 96.

218

everything, indistinctly, what is the same as saying that it would not

denote anything; in other words, to say that a term has an infinite

extension is the same as saying it does not have any extension. This is

impossible, in the first place, because to determine means to relate:

It is incontestable that difference from anything is

determination in respect to being or not being that thing.

A monkey, in differing from a man, is determined

(negatively) in respect to humanity. Difference, then, in

any respect, is determination in that respect [W 2: 150,

Nominalism versus Realism, 1868].

Secondly, an absolutely determined term would be a “logical

atom”, that is, a ”term not capable of logical division”; a logical atom

“must be one of which every predicate may be universally affirmed or

denied” [W 2: 389, Description of a Notation for the Logic of Relatives,

resulting from an Amplification of the Conceptions of Boole’s Calculus

of Logic, 1870]. Now, such term cannot be imagined neither in the

senses, nor in the thought. On one hand, it cannot be imagined in the

senses because our perception does not give us the knowledge of all the

aspects of an object, so that there will always be something else to

determine. For example, the view of an object does not say anything

about its taste; and neither about its color, nor if its surface is rough or

smooth etc.; some further determination is always possible. On the

other hand, because the logical atom is undetermined in the senses, it

is not possible in thought:

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In thought, an absolutely determinate term cannot be

realized, because, not being given by sense, such a

concept would have to be formed by synthesis, and there

would be no end to the synthesis because there is no

limit to the number of possible predicates. A logical

atom, then, like a point in space, would involve for its

precise determination an endless process [W 2: 390,

Description of a Notation for the Logic of Relatives ...].

Thus, the only way of determining some one thing is to relate it to

another. Terms, arguments, propositions, signs in general are only

determinable in certain ways, and never absolutely: “We can only say,

in a general way, that a term, however determinate, may be made more

determinate still, but not that it can be made absolutely determinate.”

[id.]. For example, “Philip of Macedonia II” can be divided into “Philip

sober” and “Philip drunk”; “Philip of Macedonia II” is interpreted as an

individual term, determined, because it refers to a man in a determined

place in a determined time; but nothing avoids its interpretation as a

general term, in reference to different states of the same Philip in

different moments: a sign is only indivisible, analyzable, complete and

absolutely determinable if the temporal differences are disregarded.21

These remarks open the discussion about the role of

interpretation. The distinction between breadth and depth does not

remain restrict to the differentiations between meaning and reference.

For Peirce, the inverse relation between one and another is not

established in the same way as for Kant. Firstly, we need to remember

21 TIERCELIN (1993b), pp. 278-279.

220

that the distinction between extension and comprehension is extended

also to propositions, and not only to terms or isolated concepts [W 1:

272, Grounds of Induction, 1865]. Secondly, it is possible that two

different terms or propositions have the same extension, but not the

same comprehension, as for example, “Men more than 200 years old”

and “men”22. The whole problem is due to the possibility of increasing

knowledge, that is, to the possibility of knowing more or less. In other

words, the inverse relation between extension and comprehension can

only be defined if it is considered based on the interpretation of

possessed information regarding the objects contained under or in the

concept, that is, regarding everything that is known about the

represented objects: “The sum of synthetical propositions in which the

symbol is subject or predicate, or the information concerning the

symbol” [W 2: 83, Upon Logical Comprehension and Extension].

Now, remember that Kant has differentiated two elementary

kinds of propositions, the analytical and the synthetic ones:

1st Analytical Propositions which are immediately

determinative only of connotation and may be called

connotative

2nd Extensive Propositions which are immediately

determinative only of denotation and may be called

denotative

3rd Synthetic Intensive Propositions which are

immediately determinative both of denotation and

connotation therefore also of information and may be

22 The example is taken from MURPHEY (1993), p. 93.

221

called informative propositions. [W 1: 278, Grounds of

Induction].

The first propositions do not increase knowledge, because the

idea of predicate is already in the idea of the subject. The knowledge

they bring is, then, a mere elucidation, since it occurs from the

decomposition of the concept of the . Now, synthetic judgments amplify

our knowledge, because the idea of the predicate increases the idea of

the subject, adding to it “a predicate which has not been in any wise

thought in it, and which no analysis could possibly extract from it; and

they may therefore be entitled ampliative.” [KrV A 7/B 11]. Extending

the concepts of breadth, depth and information to the propositions,

Peirce, in turn, proposes a division of the propositions into analytical,

intensive synthetical and extensive synthetical:

1st Analytical Propositions which are immediately

determinative only of connotation and may be called

connotative

2nd Extensive Propositions which are immediately

determinative only of denotation and may be called

denotative

3rd Synthetic Intensive Propositions which are

immediately determinative both of denotation and

connotation therefore also of information and may be

called informative propositions [W 1: 278, Grounds of

Induction].

Two ideas are fundamental in order to abandon the Kantian

distinction. First, the key Kantian concept of intensional concepts,

intensionality being understood analytically; that is, the idea of

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representation based on the essential characteristics of objects. We

shall explain it.

The example of analytical propositions given by Kant is: “To

everything x, to which the concept of body (a + b) belongs, belongs also

extension (b)”23. Analytical propositions have only logic predicates to be

extracted from the concept of the subject; in other words, in an

analytical proposition, the concept of the predicate is extracted from

the concept of the subject because the predicate is understood as a

mark [Merkmal], or constitutive note of the subject. So, analytical are

always logically necessary, and in order to distinguish them from

synthetic propositions it would be enough to apply the principle of non-

contradiction: once the idea of the predicate is deduced from that of the

subject, any contradiction between subject and predicate is impossible

[KrV A 7/B 12]. Analytical propositions, then, only give yield formal

knowledge24.

Synthetic propositions, differently, have determinations, and

because of that, they provide material knowledge. The example is: “To

everything x, to which the concept of body (a + b) belongs, belongs also

attraction (c)”25. In other words, the link between subject (a + b) and

predicate (c) is mediated by the reference to an object that has certain

defined characteristics – a synthetic proposition amplifies our

knowledge about an object x because it give us a determination of the

23 KANT (1799-1800), Ak. 111.24 KANT (1799-1800), Ak. 111.25 Id.

223

object that is not in the concept (a + b), mediately conceiving it by

means of the mark that the mark of the predicate has:

If I say, for instance, “All bodies are extended”, this is an

analytic judgment. For I do not require to go beyond the

concept which I connect with “body” in order to find

extension as bound up with it. To meet with this

predicate, I have merely to analyse the concept, that is,

to become conscious to myself of the manifold which I

always think in that concept. The judgment is therefore

analytic. But when I say, “All bodies are heavy”, the

predicate is something quite different from anything that

I think in the mere concept of body in general; and the

addition of such a predicate therefore yields a synthetic

judgment. [KrV A 7/ B 11]..

Thus, through the marks of the objects, Kant distinguishes

between analytical and synthetical propositions. Human knowledge is

possible because it is possible to represent what is common to many

objects as a “ground for knowledge” [Erkenntnissgrund]. The concept

can be defined, therefore, as repraesentatio per notas communes: a

concept has an extension, that is, it is applicable to many objects,

because it represents them by the characteristic marks they have in

common.26 Thus, the extension of a concept, that is, its reference to the

notas communes of the objects, determines its intension, conferring to

it an analytical unity, making possible to recognize the objects as

pertaining to a certain class. Kant says:

A mark is that in a thing which constitutes a part of the

cognition of it, or – what is the same – a partial

26 KANT (1799-1800), Ak. 58 and Ak. 91.

224

representation, insofar as it is considered as ground of

cognition of the whole representation. All our concepts

are marks, accordingly, and all thought is nothing other

than a representing through marks.27

The process by which the marks are conjointly thought informs

the distinction between the ideas of analytical and synthetical, and

therefore between extension and intension of the concepts. Analytical

notes are partial representations of an “effectively given”

representation, in which the defining notes of the determined objects

can be thought under an a priori concept. Synthetical notes, differently,

are representations only of possible representations, that is, they are

thought a posteriori, after a synthesis of many notes. That is why the

first representations are, for Kant, rational concepts, and the latter are

concepts of experience.28 This first conceptual distinction between sorts

of notes allows for a second distinction between coordinate and

subordinate notes:

Marks are coordinate insofar as each of them is

represented as an immediate mark of the thing and are

subordinate insofar as one mark is represented in the

thing only by means of the other. The combination of

coordinate marks to form the whole of a concept is called

an aggregate, the combination of subordinate concepts a

series.29

27 KANT (1799-1800), Ak. 58.28 KANT (1799-1800), Ak. 59.29 Idem. In effect, Kant distinguishes yet three further sorts of notes, namely: affirmative and negative notes; important and fecund notes, sufficient and necessary notes [Ak 59-60]. We will come later to the distinction between affirmative and negative notes.

225

The total sum of the coordinate notes accomplishes the totality of

the concept, which can only be completed in analytical concepts ,

because the synthetic ones reunite only the immediate notes a

posteriori. This is impossible, then, to determinate the extension of

empirical concepts, once the process of subordination can be infinitely

taken forward in experience. In effect, this is the Kantian explanation

for the principle of nota notae nota rei ipsius, that is, the representation

of a representation is the very thing’s representation. In other words, it

is possible to establish the difference between extension and intension

clearly based on that distinction between notes:

Marks are coordinate insofar as each of them is

represented as an immediate mark of the thing and are

subordinate insofar as one mark is represented in the

thing only by means of the other. The combination of

coordinate marks to form the whole of a concept is called

an aggregate, the combination of subordinate concepts a

series.30

Based on the idea of representing what is common among things,

Kant’s conception of representation distinguishes merely formal

knowledge, in which the analytical unity indicates sufficiently the

totality of notes, from material knowledge, in which there is not such

unity, but only the synthesis, by means of the experience, of notes.

Matter and form can consequently be distinguished unequivocally as

what is a posteriori determinable in general, and therefore, empirically,

and the a priori determination itself, which is analytically definable; at

30 Id., ibid.

226

the same time matter and form are inseparable, in that no

determination can exist without something to be determinate [KrV A

266/ B 322]. The combination of many representations, providing more

determinate representations – nota notae nota rei ipsius – is operated

by the copula that links subject and predicate in the proposition. Kant

can state, then, that to judge is to represent representations; that is, to

unify them in a more general concept, what is the same as to synthesize

representations in a process of increasing generalization: “A judgment

is the representation of the unity of the consciousness of various

representations, or the representation of their relation insofar as they

constitute a concept.”31 In this representation of representations, the

matter is the given knowledge, and the form is the “determination of

the way and the manner [Bestimmung der Art und Weise]” da relação

desses conhecimentos na unidade da consciência.32

Another Kantian idea is the logical distinction between

categorical and synthetic propositions. For Kant, the transformation of

hypothetical judgments into categorical ones is impossible, because

their logical natures are completely distinct. Categorical judgments

have matter and form defined by concepts that directly represent

things: the copula is the form that subordinates the predicate to a

subject in a relation of concordance or conflict between them both: “S

is P” or “S is not P”.33 Categorical judgments, consequently, constitute

31 KANT (1799-1800), Ak. 101.32 Id.33 KANT (1799-1800), Ak. 105.

227

the matter of other judgments, by the reason that they affirm things

directly.

Hypothetical judgments, differently, establish a relation of

consequence between two other judgments:

The matter of hypothetical judgments consists of two

judgments that are connected with one another as

ground [Grund] and consequentia [Folge]. One of these

judgments, which contains the ground, is the antecedent

(antecedens, prius), the other, which is related to it as

consequence, is the consequent (consequens, posterius),

and the representation of this kind of connection of two

judgments to one another for the unity of consciousness

is called the consequentia [Consequenz], which

constitutes the form of hypothetical judgments.34

Thus, the formal relation between subject and predicate

expressed by the copula in a categorical judgment stands for the formal

relation of consequence expressed in a hypothetical judgment between

fundament and consequent. What matters in a categorical judgment is

the veracity of the link between subject and predicate; in a hypothetical

judgment, otherwise, what matters is the form of the link between one

proposition and another, so that the veracity of the link between subject

and predicate in each one of them is independent of the formal

correction of each judgment. The fundamental difference is that in the

categorical judgments “nothing is problematic, rather, everything is

assertoric”; in the hypotheticals, “only the consequentia is assertoric”:

There is an essential difference between the two propositions, All

34 Id.

228

bodies are divisible, and, If all bodies are composite, then they are

divisible. In the former proposition I maintain the thing directly, in the

latter only under a condition expressed problematically.35

Peirce assumes a diametrically opposite position to Kant. Firstly,

he also states that the extension of a term or proposition depends on its

comprehension: “The meaning of a term is called its connotation; its

applicability to things its denotation. Every symbol denotes by

connoting” [W 1: 272]. Only by this statement, one can already see how

the discussion is conducted to another direction. In order to apply a

concept or a proposition to a class of objects, it is needed before to

know what the concept or the proposition mean in a defined state of

information; that is, it is necessary first to know which objects they

comprehend, or in Kantian terms, which objects they contain in

themselves, and only then to predicate them, defining an extension:

For a symbol denotes by virtue of connoting and not vice-

versa, hence the object of connotation determines the

object of denotation and not vice-versa, in the sense in

which the subject of a proposition is the term determined

and the predicate is the determining term. Whence if one

of the terms is an object of connotation and the other an

object of denotation, the latter is the subject and not the

former [W 1: 273, Grounds of Induction].

The essential difference from the Kantian paradigm, we can see

by the following passage:

35 KANT (1799-1800), Ak. 106.

229

Now, so far as the object of a symbol contains the thing,

so far the symbol stands for something and so far it

denotes. So far as its object embodies a form, so far the

symbol has a meaning and so far it connotes. Thus we

see that the denotative object and the connotative object

are in fact identical; and therefore an analytic, an

intensive synthetic, and an extensive proposition may all

represent the same fact and yet the mode in which they

are obtained and the relation of the proposition to that

fact are necessarily very different [W 1: 275, Grounds of

Induction].

Now, the merkmale of the objects do not matter anymore;

differences between propositions will not be based upon the

characteristic marks the objects have in common, but on the way of

referring them. The applicability of a concept to a object or to a class of

objects rests on the group of predicates which are possible to attribute

to the concept. Peirce states:

[…] the Sphere of a term is all the things we know that it

applies to or the disjunctive sum of the subjects to which

it can be predicate in an affirmative subsumptive

proposition. The content of a term is all the attributes it

tells us or the conjunctive sum of the predicates to which

it can be made subject in a universal necessary

proposition. The maxim then which rules explicatory

reasoning is that any part of the content of a term can be

predicated of any part of its sphere [W 1: 462, Lowell

Lecture VII, 1866].

Kant’s distinction between matter and form loses its meaning,

once the logical discussion is dislocated from examining the

conformation of matter to form to examining the ways in which it is

230

possible to represent such conformation. This logical operation renews

the Kantian distinction between affirmative and negative notes. By the

affirmative notes, we know what a thing is, by the negative ones we

know what it is not; in other words, negative notes prevent us from

erroneously applying a concept36. If it is the depth of concepts that

define their breadth, so the wider the sphere of concept is, the less

determinate the concept will be. In Kantian terms, therefore, to define

affirmative notes is the same as increasing its sphere, that is, to achieve

a greater degree of generalization. For Peirce, the definition of the

content diminishes extension of the concept, in a process described in

the following manner:

Now this is evidently true. If we take the term man and

increase its comprehension by the addition of black, we

have black man and this has less extension than man. So

if we take black man and add non-black man to its

sphere, we have man again, and so have decreased the

comprehension. So that whenever the extension is

increased the comprehension is diminished and vice

versa. The highest terms are therefore broadest and the

lowest terms the narrowest [W 1: 460, Lowell Lecture

VII].

With the application of the concepts of breadth and extension to

arguments and propositions, the distinction between categorical and

hypothetical judgments loses its meaning:

The forms A -< B, or A implies B, and A ~-< B, or A does

not imply B, embrace both hypothetical and categorical

36 KANT (1799-1800), Ak. 59-60.

231

propositions. Thus, to say that all men are mortal is the

same as to say that if any man possesses any character

whatever then a mortal possesses that character. To say,

‘if A, then B’ is obviously the same as to say that from A,

B follows, logically or extralogically. By thus identifying

the relation expressed by the copula with that of illation,

we identify the proposition with the inference, and the

term with the proposition. This identification, by means

of which all that is found true of term, proposition, or

inference is at once known to be true of all three, is a

most important engine of reasoning, which we have

gained by beginning with a consideration of the genesis

of logic. [*]

[*]In consequence of the identification in question, in S -

< P, I speak of S indifferently as subject, antecedent, or

premiss, and of P as predicate, consequent, or

conclusion.37 [W 4: 170, On the Algebra of Logic, 1880].

A consequence of great importance will be a new conception of

logic. For Kant, logic was “the science of the necessary laws of the

understanding and of reason in general, or what is one and the same, of

the mere form of thought as such”38. Then, logic does not study contents

of knowledge; it is not the study of “real and natural essence of

things”39. As such, logic is an instrument (organon) of knowledge only in

a very straight meaning, being essentially a preparatory technique:

Logic [...], as universal propaedeutic to all use of the

understanding and of reason in general, may not go into

the sciences and anticipate their matter. It is only a

universal art of reason (canonica Epicuri) for making

37 Cf. KANT (1799-1800), Ak. 106, where he states that the ways of linking in the hypothetical judgments are given by the modus ponens and by the modus tollens.38 KANT (1799-1800), Ak. 13.39 KANT (1799-1800), Ak. 61.

232

cognitions in general conform to the form of the

understanding in general, and hence is only to this extent

to be called an organon, which servers of course merely

for passing judgment and for correcting our cognition,

but not for expanding it.40

Already in 1865 Peirce considered the Kantian definition of logic

as the best ever given, till then; although with strong traits of

psychologism, notwithstanding what Kant himself thought, the

definition had already the essence of the one Peirce would adopt [W 1:

306, An Unpsychological View of Logic to which are appended some

applications of the theory to Psychology and other subjects, 1865]. For

the young Peirce of those years, logic should not be understood as a

psychological science; nevertheless, it is not be a science of the laws of

thought either, but a study of symbols – linguistic symbols (words,

propositions, arguments) or not – in general, as symbols can be

expressions of every and any possible thought, and not only as they are

actually thought; logic is universal and does not need to understand

how the mind works in order to understand how symbols represent. So

logic studies the forms of expression of thoughts and their relations to

what they mean, and not thought itself or the constitution of mind,

standing back from any aspect of psychologism: “This manner of stating

the matter frees us at once from all psychological perplexities; and at

the same time we lose nothing, since all we know of thought is but a

40 Id., ibid. Our italics.

233

reflection of what we know of its expression [W 2: 25, On the Natural

Classification of Arguments, 1867].”

If logic is concerned with thoughts, it is only inasmuch as they can

be understood as symbols, that is, in their quality of representations;

then, in Kantian terms, Peirce states in 1865:

In fact, thought may be illogical; it is only correct

thought which is logical. What is this correct thought? It

is thought which represents the intuition. Logic therefore

deals with thought only in so far as the latter is a

representation. And as I said every representation has its

logical relations whether it is actually thought or not. So

that it is more correct to say that logic is the science of

the forms of representation than that it is the science of

the forms of thought [W 1: 322, Logic of the Sciences].

So, logic is restricted to the study of representations inasmuch as

they can be interpreted, that is, insofar as it is possible to understand

them in relation to some object (which can be another representation),

that is, in relation to the information they convey:

The informed breadth and depth suppose a state of

information which lies somewhere between two

imaginary extremes. These are, first, the state in which

no fact would be known, but only the meaning of terms;

and, second, the state in which the information would

amount to an absolute intuition of all there is, so that the

things we should know would be the very substances

themselves, and the qualities we should know would be

the very concrete forms themselves [W 2: 79, Upon

Logical Extension and Comprehension].

234

For Peirce, complete states of essential and substantial

information as extremely imaginary. In truth, it is impossible to know

for sure what is meant, as said before. Nevertheless, there are ways to

define what is meant, though in an uncertain way. To accomplish this

definition it is requisite to abandon the idea of a complete

determination of meaning, an idea which is present, for instance, in the

Kantian presumption that logic deals not with contents. Logic does deal

with contents, informative contents, as it also does deal with the

conditions for the veracity of the information, even though the

possibility of absolute precision or complete demarcation of the domain

of signification is refused. It is illusory to want to begin with precision,

since indetermination is a necessary condition for every interpretation.41

That does not mean it is not possible to have some precision. As a

matter of fact, the new conception of logic as an analysis of expressivity

concerns the very ways of diminishing the indetermination of signs,

through the analysis of the relation between depth and breadth. To

imagine that some degree of indeterminacy is impossible would be

foolishness; the understanding of processes of determination requires

the study of ways to refer to objects. Peirce distinguishes three distinct

ways in which this reference can happen. First, reference to an object

may be direct, so that breadth be defined; second, reference may be

mediated by characters of the objects, so that depth be defined; finally,

reference may be made through a joint determination of connotation 41 We shall see this idea again in the theory of assertion. Cf. TIERCELIN (1993b), p. 279.

235

and denotation, that is, through interpreting the total information or

idea known of the object which is represented [W 2: 83].

We have seen that Kant thought of the relation between extension

and comprehension of a concept as an inverse relation; to Peirce, this

relation depends upon a state of information: if the information about a

term or expression is constant, there is no modification neither of

extension, nor of comprehension; if there can be an increase of

information, either the extension increases and the comprehension

decreases, or vice-versa; and if there is no information, that is, if

nothing is known about the relation of a term or expression with their

representanda, there is neither extension nor comprehension. Then, the

relation between extension and comprehension can be defined by the

formula: Breadth X Depth = Area [id.], which is the same as to say that:

Extension X Comprehension = Information [W 1: 276, Grounds of

Induction]. The reason why is Peirce clearly puts in this way: “The

reason why Extension X Comprehension = Information is that Extension

and Comprehension can only be reckoned by the interpretants, each

interpretant measuring either one or the other.” [W 1: 479, Lowell

Lecture IX, 1866].

Propositions represent facts or objects from a standpoint from

which it will be possible to predicate them with certain attributes. And

the predicate applies to what is represented because it is interpreted as

such in another representation, which is the interpretant. Every

236

representation is a representation of an object from a certain point of

view to an interpretant, which unifies all the information concerning

such object in one conception, interpreting them. The representative

function, therefore, does not depend only upon the material qualities of

the symbol (whether it is spoke or written) or upon its demonstrative

pure application (the definition of its denotation, in an ostensive

gesture, for instance), but chiefly upon the possibility of remittance to

another representation, upon the possibility of its being understood as

such – if a cloud means rain, it is because it is interpreted as a sign of

rain. Even no one in fact interprets it as such, what makes the cloud a

sign of rain, we stress, is the possibility of meaning rain: “And yet if I

take all the things which have certain qualities and physically connect

them with a another series of things, each to each, they become fit to be

signs. If they are not regarded as such they are not actually signs” [EP

1: 40, Some Consequences of Four Incapacities].42

Describing the forms of expressing thoughts and the relations

settled between them and their representanda, Peirce’s logic

simultaneously approaches and distances itself from Kant’s logic, in

some respects which is worth to mention: 1st) logic is universal, but not

because it deals with the rules of the use of the intellect in general, but

because it deals with symbols in general, whatever they may be, in their

capacity of representing their objects in certain ways; 2nd) hence, logic

is not psychological, since it is not interested in the psychological 42 Cf. Hookway (1992), pp. 32-34.

237

apprehension or effective understanding of the symbols, but only to

their capacity of being expressed and interpreted; in other words, logic

deals with the conditions of possibility of meaning, and not with the

actual signification proper of the signs as they are subjectively

understood; 3rd) hence, logic does not study the way in which we

actually think, but which are the formal grounds of our inferences; 4th)

and, consequently, the business of logic is exactly that which was

refused by Kant: the amplification of knowledge. Years later, in 1905,

Peirce Said:

After a series of inquiries, I came to see that Kant ought

not to have confined himself to divisions of propositions,

or ‘judgments’, as the Germans confuse the subject by

calling them, but ought to have taken account of all

elementary and significant differences of form among

signs of all sorts, and that, above all, he ought not to

have left out of account fundamental forms of reasonings.

[EP 2: 424, Pragmatism, 1907].

Deduction, induction, and hypothesis will therefore be objects of

analysis par excellence. Seen from the point of view of the distinctions

between depth, breadth and information conveyed, the three kinds of

reasoning are the subject-matter of exact logic:

Logic (exact): Ger. exakte Logik; Fr. logique exacte; Ital.

logica esatta. The doctrine that the theory of validity and

strength of reasoning ought to be made one of the 'exact

sciences,' that is, that generalizations from ordinary

experience ought, at an early point in its exposition, to be

stated in a form from which by mathematical, or

expository, reasoning, the rest of the theory can be

238

strictly deduced; together with the attempt to carry this

doctrine into practice.43

Inductive reasoning is wider than hypothetical, and the latter are

deeper than the former. Inductive inference is probably true of all

instances of a class of objects, which conclusion results from the

application of the rule to one or more cases known under the terms or

propositions, constituting the universe of known objects. Now,

hypothetical inference is probably true just of one of the instances; we

do not have knowledge of one special instance which is the content of

terms and propositions, it is necessary to figure it out, surmising it,

verifying whether the result fits the rule:

In the former case, the reasoning proceeds as though all

the objects which have certain characters were known,

and this is induction; in the latter case, the inference

proceeds as though all the characters requisite to the

determination of a certain object or class were known,

and this is hypothesis. [W 2: 216].

Let us see Peirce’s examples. Take any piece of writing in English,

called A, of which the number of times that certain letters appear will

be ascertained; insofar we count them, we come to see that some occur

more than others, less and less variably. For example, the number of

times in which the letter “e” occurs makes 11 ¼ percent of the total,

letter “t”, 8 ½ percent of the total, letter “a”, 8 percent, etc. if we find

the same approximate result, say, in more half a dozen other English

43 Entry “Logic (exact)” for the Dictionary of Philosophy and Psychology, edited by James M. Baldwin, 1902. Partially available on-line at: [http://psychclassics.yorku.ca/Baldwin/Dictionary/]. Acessed 13/02/2005.

239

writings, which will be called B, C, D, E, F, G, we will infer that in every

piece of English writing of a certain extension, we will probably find

more or less the same percentage of occurrence to the same letters.

However, if we know of a certain writing H, of which the percentage of

occurrence of the same letters is entirely different, the initial

conclusion loses credibility; if the percentage is the same, the

conclusion gains force. This is one case of induction, in which the

conclusion obtained is valid only if we do not know of any other

different instance from what was analysed [id.].

Consider an analogous instance of a codified writing to decipher.

We find that the code has twenty six characters, one of them occurring

11 ¼ percent of the times in text; another one, which percentage of

occurrence is around 8 ½ percent, and another else, with 8 percent of

occurrences, etc. substituting “e”, “t”, “a”, etc., respectively, for them,

we will see how the code makes sense in English (counting also the

orthographic mistakes). If this piece of codified writing has a

considerable extent, we can say that we have correctly deciphered the

code, with a great probability. Our inference will be valid if we do not

know of any other characteristics peculiar to the code, which are not

peculiar to the English idiom. Otherwise, we will have to take them into

account, to enforce or weaken our hypothesis – and the knowledge of

such other characteristics may, for instance, indicate another way of

deciphering it. [W 2: 217-218, ibid.].

240

Deduction, induction, and hypotheses are then the only three

kinds of valid reasoning, and all thought is of some one of these kinds,

or a combination of them [W 2: 217, Some Consequences of Four

Incapacities, 1868]. This is the basic conclusion Peirce arrives at in

these early writings. The basal difference he in 1868 established

between the three kinds of reasoning is that deduction is a

demonstrative inference that does not increase our knowledge of facts,

for it passes from a general rule, as a premise, to affirm a conclusion

resulting from the analytical unfolding of the relations affirmed in the

premise; induction and hypotheses, differently, are ampliative illations,

different one from another, that increase our knowledge: induction is a

generalization, it proceeds from the verification of a particular

experience to infer a general explanatory rule for such experience;

hypothesis, in its turn, assumes a general rule from the beginning, and

from it seeks to establish relations between particular facts of

experience, otherwise apparently disconnected. Differences are clearer

when we compare them definitions. First, induction:

Induction may be defined as an argument which proceeds

upon the assumption that all the members of a class or

aggregate have all the characters which are common to

all those members of this class concerning which it is

known, whether they have these characters or not; or, in

other words, which assumes that that is true of a whole

collection which is true of a number of instances taken

from it at random. This might be called statistical

241

argument. In the long run, it must generally afford pretty

correct conclusions from true premises. [W 2: 217].

Peirce clears up the definition with the following illustration. If we

have a bag full of beans, white and black, drawing from it a sufficient

number of samples at random, we will be able to approximately

determine the relative number of black and white beans, in a certain

moment, and with a small range for error.

Now, let us remember the syllogistic form of deduction:

Rule: All S is

P.

Case: M is S

Resul

t:

M is

P.

A typical inductive reasoning would have the inverted form of a

deductive syllogism as follows:

Case: These beans are from this bag. M is S

Resul

t:

These beans are White. M is P

Rul

e:

All the beans in this bag are

white.

All S is

P.

An induction can be seen as the deductive inference of the second

premiss, from the conclusion obtained and the particular case affirmed

in the first premises; or, in other words, a probable deduction

consisting in the inference of a general rule from the observation of a

242

result in a certain case [W 3: 328, Deduction, Induction, and

Hypothesis]. Then, deriving the major premiss of a syllogism from its

minor premises, induction is a form of reduction of the multiplicity to

the unity, allowing for an assertion about facts, very likely to be true [W

3: 217]. Induction, amplifying the extension of a certain class of

subjects, amplifies the generality of the conclusion beyond the limits

affirmed in the major premiss of the syllogism, in an operation that

allows to pass from the determination of the existence to the virutality

of the possible, for it reaches a general concept about actual instances;

for such reason we can assure that other similar instances can be

submitted to the same concept44. We will recover this point further on.

Let us see hypothesis:

Hypothesis can be defined as an argument which

proceeds upon the assumption that a character which is

known necessarily to involve a certain number of others,

may be probably predicated of any objects which have all

the characters which this character is known to involve.

[W 2: 217-218].

According to such definition, hypothesis can be defined as the

inference of a minor premiss from two other premises of a syllogism; in

other words, as an inference of a particular instance from a general

rule and the probable result of the application of the rule to the case, in

another kind of the inversion of deduction [W 3: 325-328]. Thus we

44 BACHA (1999), p. 159.

243

have the following formulation of the example of the letters, given

above:

1. Every English writing of some length in which such

and such characters denote e, t, a, and s, has about 11

1/4 per cent of the first sort of marks, 8 1/2 of the

second, 8 of the third, and 7 1/2 of the fourth. This secret

writing is an English writing of some length, in which

such and such characters denote e, t, a, and s,

respectively:

.·. This secret writing has about 11 1/4 per cent of its

characters of the first kind, 8 1/2 of the second, 8 of the

third, and 7 1/2 of the fourth.

2. A passage written with such an alphabet makes sense

when such and such letters are severally substituted for

such and such characters. This secret writing is written

with such an alphabet.

.·. This secret writing makes sense when such and such

substitutions are made. [W 2: 218]

Just as induction, hypothesis also operates a reduction of the

multiplicity to the unity, substituting one affirmation, or a few ones,

which may be linked to other affirmations, for various other

unconnected. Hypothesis can be written as follows:

Rule: All the beans of this bag are white All S is P.

Result: These beans are white. M is P.

Case: These beans are from this bag. M is S.

We then see that through the inversion of the deductive syllogism,

changing the places of subjects and predicates, that is, changing

244

premises, we get different kinds of reasoning. Peirce can conclude then,

in 1883:

Deduction proceeds from Rule and Case to Result; it is

the formula of Volition. Induction proceeds from Case

and Result to Rule; it is the formula of the formation of a

habit or general conception – a process which,

psychologically as well as logically, depends on the

repetition of instances or sensations. Hypothesis

proceeds from Rule and Result to Case; it is the formula

of the acquirement of secondary sensation – a process by

which a confused concatenation of predicates is brought

into order under a synthesizing predicate.45 [W 4: 422, A

Theory of Probable Inference].

We can now proceed to the problem of the validity of induction.

The justification of induction, in Peirce’s early writings, is grounded

upon two basic ideas. The first is that parts make up the whole. To this

idea we will return after examining the second, which is that there is an

independent reality from all subjectivities, a reality possessing some

general features, what ultimately warrants the success of inductions

because it compels opinions to converge in one true final and definite

opinion. If such reality did not exist, no illation would be successful:

Now, since if there is anything real, then [...] it follows

necessarily that a sufficient long succession of inferences

from parts to whole will lead men to a knowledge of it, so

that in that case they cannot be fated on the whole to be

thoroughly unlucky in their inductions. [W 2: 269, id.].

This argument for the validity of induction has a double feature.

First, it puts forward the idea that the inductive method, if sufficiently

45 Cf. BACHA (1999), p. 209.

245

pursued, is successful, to which we will get back further on, for it is a

central idea to validate the thesis of self-correctness of induction.

Second, the argument depends upon the first one, Peirce’s theory of

reality, according to which the real is independent of conceptions,

volitions, or feelings of a certain finite number of people, that it has the

character of remaining the same in the long run, and the character of

being other than the figments of fancy:

And what do we mean by the real? It is a conception

which we must first have had when we discovered that

there was an unreal, an illusion; that is, when we first

corrected ourselves. Now the distinction for which alone

this fact logically called, was between an ens relative to

private inward determinations, to the negations

belonging to idiosyncrasy, and an ens such as would

stand in the long run. [W 2: 239, Some Consequences of

Four Incapacities].

In the 1871 Berkeley review, Peirce contrasts a realist conception

of reality and a nominalist one. Described as the conception that

considers as real something which is outside the mind, constraining our

sensations, and, through them our thoughts, nominalism is refused by

Peirce under the claim that it makes it impossible to recognize any

feature of generality in reality. This nominalist conception of reality,

which is pretty much “familiar, according to him, does not take into

account that universal terms such as man, horse, rose, etc., are real,

that is, that they represent real relations between all individual men,

horses, or roses, independently of how we conceive them; instead,

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nominalism defends that “these classes are constituted simply by a

likeness in the way in which our minds are affected by individual

objects which have in themselves no resemblance or relationship

whatsoever.” [W 2: 467, Fraser’s The Works of George Berkeley, 1871].

To the nominalist, reality is conceived as the efficient cause of our

sensations, independently of any and every conception about it that

might be [W 2: 469, id.]. in short, the nominalist conception, besides

refusing generality to reality, transforms it into a kind of unknowable

thing-in-itself, the cause of our thoughts, yet even so unattainable:

The nominalist must admit that man is truly applicable to

something; but he believes that there is beneath this a

thing in itself, an incognizable reality.[...] The great

argument for nominalism is that there is no man unless

there is some particular man. [W 2: 240, Some

Consequences of Four Incapacities].

The realist conception, on the contrary, is supported by the idea

that “universals must have a real existence”; an universal is not a mere

flatus vocis, inasmuch as it is not a classificatory mental scheme, as a

nominalist could say. Peirce exhibits the problem of universals in the

following terms:

Are universals real? We have only to stop and consider a

moment what was meant by the word real, when the

whole issue soon becomes apparent. Objects are divided

into figments, dreams, etc., on the one hand, and realities

on the other. The former are those which exist only

inasmuch as you or I or some man imagines them; the

latter are those which have an existence independent of

247

your mind or mine or that of any number of persons. The

real is that which is not whatever we happen to think it,

but is unaffected by what we may think of it. [W 2: 467].

The real must be something independent of a finite number of

people, not relative to subjective determinations. As Peirce says, this

conception of reality involves the conception of a community, with

undefined limits, capable of indefinite increase, that, in its general

conceptions, will represent the real and the unreal, remittently

affirming the former, and the same conditions maintained, denying the

latter in the same way [W 2: 239, Some Consequences of Four

Incapacities].

Remaining through an indefinite time in the run of experience,

reality becomes apprehensible in a certain way – in truth, the real has

the power to constraint our opinions: “Where is the real, the thing

independent of how we think it, to be found? There must be such a

thing, for we find our opinions constrained; there is something,

therefore, which influences our thoughts, and is not created by them.”

[W 2: 468, Fraser’s The Works of George Berkeley].

This character of insistence reality has makes that it is forced

against consciousness to be recognized. Such insistence shows itself

under the guise of regularity: the permanence of the real is the

necessary condition to cognoscibility, and also the warranty of the

objectivity of representations, for it assures that our conceptions about

reality are irreducible to subjective whims.46 This general feature of 46 IBRI (1992), p. 30.

248

permanence makes it impossible not to discover the truth about reality,

in an undetermined future:

[...] human opinion universally tends in the long run to a

definite form, which is the truth. Let any human being

have enough information and exert enough thought upon

any question, and the result will be that he will arrive at

a certain definite conclusion, which is the same that any

other mind will reach under sufficiently favourable

circumstances. […] The individual may not live to reach

the truth; there is a residuum of error in every

individual’s opinions. No matter; it remains that there is

a definite opinion to which the mind of man is, on the

whole and in the long run, tending. [W 2: 468-469, id.].

It is possible to say that the continuous duration of the real in

experience is condition sine qua non for the verifiability of hypotheses –

these latter will only be valid if the can predict how reality will continue

in the future. In other words, in our present conceptions we have to

represent now the future regularity of things; and this regularity is

capable of being represented because the world has a certain spatial-

temporal order which remains independently of our will47. Time in this

way is an essential element to the possibility of conceiving reality; in

order it may be possible to pass from the immediate experience of a

single perception to the recognition of relations and meaningful links

between empirical eventos, time is needed. In the course of time, the

regularity of events will show the errors of the initial surmises, driving

47 IBRI (1994), cap. 1: “Da possibilidade do dever ser: o teorema de Alice”, passim.

249

human opinion universally to the truth that will be expressed in the

final opinion:

This final opinion, then, is independent, not indeed of

thought in general, but of all that is arbitrary and

individual in thought; is quite independent of how you, or

I, or any number of men think. Everything, therefore,

which will be thought to exist in the final opinion is real,

and nothing else. [W 2: 469].

The realist, then, will be led to believe in reality as it is

represented in a true representation, that is, in its general features: the

word “man”, for instance, is true only because it means something real

[W 2: 239]. Differently from what Hume claims, the world Peirce

describes is such wherein relations are real, wherein the continuity of

events allows discovering the way one is linked to another through the

logic of induction.

In fact, inductions and hypothesis can be successful in their

generalizations and predictions because reality remains reacting

against our experience: there is a reality, which permanently reacting

against experience, presents general and continuous characters.

Nevertheless, those are not the only features of reality. In the same

writing from 1869 about the laws of logic, Peirce asks whether it is

possible to ground the validity of induction upon and hypothetical order

of nature. How is it possible to answer to the question that the facts of a

certain species are normally true when other facts, of another species,

are also true? In other words, how is it possible to assert that facts of a

250

determined species have specific relations to facts of another species?

An easy answer would be to assume an order of nature:

The usual reply is that nature is everywhere regular; as

things have been, so they will be; as one part of nature is,

so is every other. But this explanation will not do. Nature

is not regular. No disorder would be less orderly than the

existing arrangement. It is true that the special laws and

regularities are innumerable; but nobody thinks of the

irregularities, which are infinitely more frequent. Every

fact true of any one thing in the universe is related to

every fact true of every other. But the immense majority

of these relations are fortuitous and irregular. A man in

China bought a cow three days and five minutes after a

Greenlander had sneezed. Is that abstract circumstance

connected with any regularity whatever? And are not

such relations infinitely more frequent than those which

are regular? [W 2: 264, Grounds of Validity of the Laws

of Logic].

The regularities of the universe, therefore, happen much less than

the irregularities, what leads to the supposition that not everything in

nature has as determined cause; the idea of an order of nature thus

cannot be presupposed, for experience shows us that there are events

that happen without apparent cause, without a necessary connection

with other events, more often than the ones that happen in determinate

ways48. The knowledge of the existence of some minimal order of nature

would be useful only if we could take it as the major premises of

48 In effect, this idea, constitutive of the metaphysical doctrine of chance (tychism), is presented by IBRI (1992), p. 40 ff., as the first ground of Peirce’s fallibilism, the other foundation being evolutionism. We will not deal with such theme in detail. The reader can find more thorough expositions of the subject, and other connected matters, in HAUSMAN (1993); IBRI (1992), pp. 39 ff.; SANTAELLA (1999); SILVEIRA (1984).

251

deductions, as a basis to explain only how knowledge could be made

more or less certain. However, it is not a matter of certainty, but of

increase of knowledge. Knowledge of an order of nature would not

serve to ground a justification of hypothetical and inductive illations,

that is, it does not explain how it possible to increase knowledge. [W 2:

265, Grounds of Validity of the Laws of Logic]49.

Here we have the other basal idea for the justification of

induction, which is that the parts make up the whole. The gist of the

discussion is in the idea that it is possible to ascertain the proportion of

the relations between known and unknown facts. In short, the only valid

justification for grounding the laws of logic must search for its bases in

a theory of probabilities: “The only attempt of this sort, however, which

deserves to be noticed is that which seeks to determine the probability

of a future event by the theory of probabilities, from the fact that a

certain number of similar events have been observed.” [W 2: 267]. The

success of such attempt in its turn depends upon the definition of

probability as “the ratio of the frequency of occurrence of a specific

event to a general one over it.” [id.]. In other words, it is necessary to

determine how many times it is possible that a certain event happens in

the indeterminate future, when it occurred already a certain number of

times. So, to affirm a general proposition about the future course of

49 Peirce’s argumentation is much more detailed. We show here only a sketch of his conclusions, intending to put the arguments forward. About the question of the certainty of knowledge, see CROMBIE (1997), pp. 460-461. We will get back to the idea of order of nature further on.

252

events is to affirm, from the observations made, the existence of a

certain regularity in nature. The idea is that knowledge is justified

when it is inductively tested; it is not the attempt to prove a natural

regularity previously assumed, but the attempt to discover whether

there is any regularity in facts that may be expressed in general terms,

so that it explains the conduct of facts, the actual and the merely

possible ones [EP 2: 316, , 1904]. This problem involves

several difficulties. Let us see, firstly, which are the terms in which the

issue is presented in 1869.

First, the validity of induction depends upon the fact that in the

long run all the members of a collection to which one wants to prove

that it possesses certain features will be drawn at random, and have the

same chance to be draw in the samples:

Out of a bag of black and white beans I take a few

handfuls, and from this sample I can judge approximately

the proportions of black and white in the whole. This is

identical with induction. Now we know upon what the

validity of this inference depends. It depends upon the

fact that in the long run, any one bean would be taken

out as often as any other. [W 2: 268, Grounds of Validity

of the Laws of Logic].

Thus, the characters of the sample can be taken as an index of the

characters of the whole, because the frequency of occurrence of a given

kind is relative to the whole set. It is mainly important that the

probability of being drawn in the samples be equal to all the beans in

the bag; that is valid to all classes of objects. Following this principle,

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whatever member of a class could be subject of a premises, and

therefore, predicable of the quality that one wants to discover so much

as the extant. Inductive reasoning, therefore, “is the same as statistical

inference” [W 2: 268].

This is the essence of the idea of the long run: in processes of

long duration, the character of alterity of reality would warrant that the

possibility of determining a certain range of probabilities is effective, a

range wherein it would be possible to estimate in an approximate

degree the truth, that is, the “order of general relations”50 existent

between the events of the world. Thus, through the remittent

continuation of the method, it is possible to reach closer to a true

representation of the mode of happening of facts.

Peirce gradually passes to emphasize the idea of self-correctness

of induction in his writings. By doing so, he abandons the idea that

inductive reasoning is an ampliative kind of reasoning, reserving all

heuristic power to abduction; the business of induction is to test

hypothetical suggestions only, to assure them prognostic reliability. In

1901, for instance, we see the problem displayed in a much more

explicit way:

Induction […] is not justified by any relation between the

facts stated in the premisses and the fact stated in the

conclusion; and it does not infer that the latter fact is

either necessary or objectively probable. But the

justification of its conclusion is that that conclusion is

50 IBRI (1994), p. 105.

254

reached by a method which, steadily persisted in, must

lead to true knowledge in the long run of cases of its

application, whether to the existing world or to any

imaginable world whatsoever. [HP II: 736, On The Logic

of Drawing History from Ancient Documents].

Therefore, differently from the position assumed in his early

writings, induction is no more seen as a kind of inference that brings

true knowledge about the world, but only as a means to ascertain the

validity of hypothesis experimentally, by remittently confronting them

against experience: “Induction is the experimental testing of a theory.”

[HL 218]. Induction so acquires validity inasmuch as it is capable of

self-correcting its own results:

Induction is a kind of reasoning that may lead us into

error; but that it follows a method which, sufficiently

persisted in, will be Inductively Certain (the sort of

certainty we have that a perfect coin, pitched up often

enough, will sometime turn up heads) to diminish the

error below any predesignate degree, is assured by

man's power of perceiving Inductive Certainty. [EP 2:

443, A Neglected Argument for the Reality of God].

In other words, the issue is to determine, even though in a

provisory way, the probability of getting heads or tails in a throw of a

coin. Let us say that it is asserted that a coin, if thrown 10.000 times,

half the throws will be heads, once 50 of the first 100 were heads. Now,

suppose this conclusion is false. According to the theory, it is possible

then to correct this induction merely by observing more and more

throws, basing the conclusion on the relative frequency of heads in the

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total series of 10.000 throws on the relative frequency in the biggest

available sample in a certain moment. If this experiment is carried on

time enough, in a given moment the correct value will be reached. The

assertion that the process is self corrective is then justified: remittent

applications of the method lead to increasing approximations to truth.

The capacity of self-correctness of the process is due to th

successsive comparisons of the hypotheses with what experience shows

us. If the frequency of occurrence of a property of individuals of the

sample is not proportional to their frequency of occurrence on the

whole set, this difference tends to get clearer in the long run. Thus, by

systematically adjusting the estimations, it is possible to arrive each

time at a more correct measurement.

In truth, it is being asserted that in long run processes the

probability of failure in scientific inquiry can be reduced to very low

levels. It is almost as saying that science is theoretically infallible [CP

7.77-78, c. 1902]51. Let us understand better what means such

infallibility. In the way we have exposed it, everything depends on

determining relations between distinct quantities; nevertheless, one

can never know how much of nature was already discovered, simply

because one does not know how much is yet to be discovered; in a

51 RESCHER (1978), p. 2.

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word, nature is like a infinite collection [W 2: 265] 52. The concept of

collection helps our understanding of the issue:

By a collection, I mean an individual object whose actual

presence in any part of experience consists in the actual

presence of certain other individual objects called its

members, so that if one of them were absent, the same

collection would not be present; and these members are

such that any part of them might logically be present or

absent irrespective of the presence or absence of any

others; and the truth of any predication concerning a

collection consists in the truth of a corresponding

predication concerning whatever members it may

possess, so that taking any universal proposition

whatever, there is a collection having for its only

members whatever independent objects there may be of

which that proposition makes any given affirmation. [HP

II: 742, On the Logic of Drawing History from Ancient

Documents …].

Thus, to say “Every man is mortal” is to say that there is a

collection of all men that there may be; to say “Every man in Mars is

mortal” is to say that there is in Mars a collection of men that, whatever

they may be, they are mortal. The actual existence of men in Mars

implies only the falsity of the assertion, but it does no change the fact

that the collection continues to be a collection [id.]. A collection,

defined in this way, can be called continuous. In other words, it is an

aggregate of independent objects, but such as cannot be taken as the

52 Following some and opposing others of Georg Cantor’s conceptions, Peirce developed a theory of continuity and “multitudes”, which will not be analyzed here. For a detailed comparison of Cantor’s and Peirce’s conceptions, see PARKER (1998), chap. 4: “Infinity and Continuity”.

257

ultimate constituents, because they are all related in such a way that

there is no possibility of isolating the parts without breaking the

collection, that is, without breaking the continuity. The capacity of

being infinitely divided is a necessary condition to define a true

continuity [NEM 3/II: 748, Mathematical Logic, 1902]. It means that in

between each of its members, there are other members. For instance,

think of the series of natural numbers:

1, 2, 3, 4, 5, 6, 7, ... n.

It is always possible to divide the series between a term a and

another, as follows:

1, 1.1, 1.11, 1.112, 1.1121, ..... 1.n, 2, 2.1, 2.11, 2.112, ....,

2.n etc., 3n etc. ...

Or yet, let us separate the series into two distinct ones, of odd and

even integers:

1, 3, 5, 7, 9, ... n

2, 4, 6, 8, ... n

It is clear that the parts are also infinite, the same as the whole

[EP 1: 317, The Law of Mind, 1892]. Therefore, it is impossible to

ascertain the exact quantity of the members of a continuous collection;

but it is possible to ascertain an approximate value to its multitude: “I

use the term multitude to express that character of any collection which

consists in its being as small as whatever collections it is as small as,

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and being as great as whatever collections it is as great as.” [HP II:

743, On the Logic of Drawing History from Ancient Documents …].

Even tough it is the first defining character of a true continuity,

infinite divisibility is not a sufficient condition to define it; with this

concept of continuity, irrational numbers cannot be explained, for

instance. As it is known, irrational numbers can be written as decimals,

but not as fractions. In other words, irrational numbers are numbers

that cannot be expressed as the ratio (whence their name) of two

integers. The discovery of irrational numbers is ancient, and it is

related to problems of defining a number for quantities not measurable

by real integers. A rational number is defined as the quotient of h/k,

where h and k are integers, and k ≠ 0. A rational number, therefore, is

such that represents the ratio between two integers. Thus any rational

number can be represented by a point in a straight line. Let it the set of

rational numbers be Q:

However, there are several quantities, as weight, width, time, the

square diagonal, etc. that are not measurable by integers; to express

them we need fractions, which are not quotients of two integers. It is

then possible to indicate points in a line that do not correspond to any

ratio between two integers, that is, not corresponding to any rational

number. Such points are represented by irrational numbers; they are

259

capable to be written as tithes, or they can be graphically represented

in the line as follows:

The most famous irrational number maybe is the square root of 2,

which cannot be written as a fraction, that is, as the quotient of two

integers:

Other irrational numbers are =3,14159...and e = 2, 71828...,

for instance. is an irrational number because there is no exact decimal

value correspondent to it, since it cannot be expressed as the ration of

two integers; nonetheless, it is possible to apply 3, 1415926...

satisfactorily in various instances.53 r decimal exato que lhe

corresponda, embora seja possível aplicar satisfatoriamente em vários

casos.

53 For the account of rational numbers, we follow EVES (2004), pp. 104-107. See still NEM 3/I: On Continuous Series and the Infinitesimals, n.d., wherein Peirce tries to show that the whole series of rational and irrational numbers is not a continuous series. We will not go deep into this debate here.

260

Now, for the definition of continuity as infinite divisibility,

irrational numbers are a problem, for rational infinitude, though it is

numerable, it is not continuous. As I. Ibri says, “the infinite divisibility

does not warrant continuity, due to the non-existence of irrational

numbers associated to the innumerability of the points of the line.”54 For

such reason, Peirce criticizes the way how Kant defined continuity:

Let us now consider what is meant by saying that a line,

for example, is continuous. The multitude of points, or

limiting values of approximations upon it, is of course

innumerable. But that does not make it continuous. Kant

defined its continuity as consisting in this, that between

any two points upon it there are points. This is true, but

manifestly insufficient, since it holds of the series of

rational fractions, the multitude of which is only

dinumerable. Indeed, Kant's definition applies if from

such a series any two, together with all that are

intermediate, be cut away; although in that case a finite

gap is made. I have termed the property of infinite

intermediety, or divisibility, the Kanticity of a series. It is

one of the defining characters of a continuum. [CP 4.121,

The Logic of Quantity].

As a matter of fact, infinite divisibility, for Kant, is defined in

terms of limits: the points in the line and in space, moments of time are

all approximative limits, “places of the limitation of space and time”, so

that continuous greatnesses do not have minimal parts [KrV A 169/ B

211]. Peirce recognized that in a first moment he neglected such

54 IBRI (1992), p. 65. Our translation; see the original: “a infinita divisibilidade não garante a continuidade devido à não-existência dos números irracionais associados à inumerabilidade dos pontos da linha.”

261

character of the Kantian definition; nonetheless, he maintains the

criticisms, renewed:

His true doctrine is not that space is divisible without

end, but that it cannot be so divided as to reach an

ultimate part as clearly stated in the last paragraph of p.

169. […] To the obvious objection that points are

ultimate parts of lines, Kant begins to make the right

answer, that they are not parts but limits. But that he

does not understand this right can be seen by p. 209

where he speaks of a change as passing through all the

instantaneous intermediate states. He thus looks on the

point as existing in the line, while the truth is they do not

exist in the continuous line, and if a point is placed on a

line it constitutes a discontinuity.55 [NEM 3/2: 780, letter

to Paul Carus, 17 August 1899].

Indeed, Kant says:

Esta é, pois, a lei da continuidade de toda a mudança,

cujo princípio é o seguinte: nem o tempo, nem tão-pouco

o fenômeno no tempo, se compõem de partes, que sejam

as menores possíveis; e, no entanto, o estado da coisa, na

sua mudança, transita por todas estas partes como por

outros tantos elementos, para o seu segundo estado. [KrV

A 209/ B 254].

Now, if the points in a line are limits, and not distinct parts, there

cannot be the passage “thorugh all the infinite degrees of the same

reality, whose differences among each other are all smaller than the

difference between 0 and a” [id.]. In a true continuity, infinitude is not

numerable, as the discrete parts of an aggregate would be. Let us take

a closer look up upon the concept of true continuity. Its second

55 Pages referred to by Peirce are from the first edition (A), from 1781, of the Critic of the Pure Reason.

262

character is that its parts share limits.56 This property is called by

Peirce its Aristotelicity: “I made a new definition, according to which

continuity consists in Kanticity and Aristotelicity. The Kanticity is

having a point between any two points. The Aristotelicity is having

every point that is a limit to an infinite series of points that belong to

the system.” [CP 6: 166, 1903]. Indeed, in the Metaphysics, the

Aristotelian definition of the continuous is the following:

[…] two things are called continuous [] when the

limits [] of each, with which they touch and are kept

together, become one and the same, so that plainly the

continuous is found in the things out of which a unity

naturally arises in virtue of their contact.57

The theoretical basis for such definition are to be found in the

Physics, in the books 5 () and 6 (). In book 5, chapter 3 [226b 18-227b

2], and also in the beginning of book 6 [231ª 21-24], Aristotle lays out a

series of definitions: “Things are said to be in contact when their

extremities are together” [226b 23]. Things can also be in succession in

the following way:

A thing is in succession when it is after the beginning in

position or in form or in some other respect in which it is

definitely so regarded, and when further there is nothing

of the same kind as itself between it and that to which it

is in succession, e.g. a line or lines if it is a line, a unit or

units if it is a unit, a house if it is a house (there is

nothing to prevent something of a different kind being

between).58

56 IBRI (1992), p. 66.57 Book 11 (): 12, 1069ª 5-8.58 226b 34-227ª 5; 231ª 23.

263

And things can also be contiguous: “A thing that is in succession

and touches is contiguous.” [227ª 6]. These definitions prepare the way

for the definition of the continuous:

The continuous is a subdivision of the contiguous: things

are called continuous when the touching limits of each

become one and the same and are, as the word implies,

contained in each other: continuity is impossible if these

extremities are two. This definition makes it plain that

continuity belongs to things that naturally in virtue of

their mutual contact form a unity. And in whatever way

that which holds them together is one, so too will the

whole be one, e.g. by a rivet or glue or contact or organic

union. [227a 7-17].

From this, Aristotle argues in book 6 that this definition of

continuous precludes to conceive of it as something composed of

indivisible parts, i.e., as if it was a line consisting in entire points, or of

atoms:

[...] nothing that is continuous can be composed of

indivisibles: e.g. a line cannot be composed of points, the

line being continuous and the point indivisible. For the

extremities of two points can neither be one (since of an

indivisible there can be no extremity as distinct from

some other part) nor together (since that which has no

parts can have no extremity, the extremity and the thing

of which it is the extremity being distinct). [231ª 26-29].

The continuum cannot be composed of indivisible parts each in

touch with the other because that would be a succession of wholes,

each one whole different from the other; they would not therefore be as

the parts of a true continuum, different and spatially separated.

264

Moreover, a true continuum cannot be composed of successive things,

since between successive things there must be something of a different

kind, while between two points there is always a line, between two

moments of time, there is always a time [231b 8-10].

After all these elucidations, Aristotle gives another important

defining character of continuity, to wit, what Peirce calls Kanticity – the

property of being infinitely divisible:

Moreover, it is plain that everything continuous is

divisible into divisibles that are always divisible; for if it

were divisible into indivisibles, we should have an

indivisible in contact with an indivisible, since the

extremities of things that are continuous with one

another are one and are in contact. [231b 15-18].

[And yet:] By continuous I mean that which is divisible

into divisibles that are always divisible [...].59 [232b 23-

25].

We then see that Aristotle already defined both conditions that,

for Peirce, were necessary and, if taken together, sufficient to define a

true continuity. The Stagirite can, after that, say that multitudes, time,

movement are all continuous greatness: they are either composed of

divisible parts, or they are not continuous. However, differently from

what Aristotle seems to mean, it seems that Peirce does not take having

parts with common limits and being infinitely divisible as logically

equivalent definitions of true continuity. In truth, the interesting point

59 Notice that the Greek could be equally rendered “divided into parts ever divided”, perhaps even more literally. See the original: “” And: “”.

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is that the Peircean definition is parallel to the Aristotelian. In effect,

from what we have seen, the Aristotelian continuum must always be

divisible, so that any parts in which it is divided have the same common

limits. And Peirce’s definition of a true continuity can be expressed in

the following way: true continuity is defined by infinite divisibility,

wherein the parts share common limits.60

We can get a better grasp of the Peircean concept of continuity

going back to the differences between collections. A collection can be

denumeral, for it is impossible to ascertain a precise limit for the

multitude of its parts. In effect, multitude is not the same as numeral

quantity. For instance, a set of three objects and a set of three thousand

objects are both enumerable sets, for it is possible to count the discrete

unities which make up the collection. Any finite collection, for this

reason, is enumerable, for it may have its members discretely

determined. In infinite collections (and, therefore, truly continuous), the

quantity of the members of the collection is not countable, what makes

that they have multitudes, i.e., “That relative character of a collection

which makes it greater than some collections and less than others.” [CP

3.626, Multitude (in Mathematics), 1902]. Multitudes can be defined as

denumeral and abnumeral. The former are enumerable, being the most

basic type of infinite collection, equivalent to the multitude of finite

60 For the account of continuity in Aristotle, we follow Richard T. W. Arthur’s, presented in LEIBNIZ (2001), pp. 347-352. Indeed, this definition of continuum is decisive for the Aristotelian solution for Zeno’s paradoxes. Peirce follows Aristotle in this regard, grounding his own solution also upon the idea of continuity. See, for example, W 2: 207-211, Some Consequences of Four Incapacities; 254-256, Grounds of Validity of the Laws of Logic; NEM 3/I: Achilles and the Tortoise, n.d. See too IBRI (1992), p. 66.

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integers [HP II: 744, On the Logic of Drawing History from Ancient

Documents...]. Abnumeral multitudes are superior to denumeral ones,

that is, they correspond to multitudes with superior degrees of infinity,

i.e., bigger than the multitude of finite integers: “An abnumeral

multitude is one of a denumeral succession of multitudes greater than

the denumeral multitude; each of these being the multitude of the

different possible collections of members of a collection of the next

lower abnumerable multitude.” [id.].

Such infinite divisibility is the first defining character of a true

continuity. Notice that a collection, to be continuous, cannot be a mere

aggregate of distinct parts. Exactly for the fact that there is a relation

between the parts that defines their inclusion in the collection, the

continuity comes from the fact that it is possible to mark distinctions, it

is possible to determine and divide the continuity without the necessity

of defining the collection itself in function of its parts.61 A true

continuity, therefore, is not what has parts, but what can have parts. In

this way, a true continuum has not the distinction between its individual

parts, for such distinction is merely possible, and not actual. 62 Second,

the infinite divisibility is also applicable to the parts of the whole, as the

61 PARKER (1998), p. 87-88. 62 Cf. PARKER (1998), p. 87-88; IBRI (1992), p. 66. As a curiosity, as to this regard, Peirce’s ideas seem to be parallel to Leibniz’s, who says: “Magnitude is that constitution of a thing by the recognition of which it can be regarded as a whole. It also seems that a whole is not what has parts, just what can have parts.” This leads Leibniz to doubt whether a mere aggregate, namely, something really divided, could be called one, that is, a true whole, and not a composite of parts. See LEIBNIZ (2001), pp. 98-99, or edition of the Deutsche Akademie der Wissenschaften, series VI, v. 3, p. 503: Numeri Infiniti; see too Monadology, § 2. We will not go further into the relation of the concepts of continuity for Peirce and for Leibniz; about this subject-matter the reader may go to LEO (2001), passim.

267

numerical series make clear; in this way, there is never a constituting

part which is ultimate and indivisible – there are no atoms. In other

words, we have once more the two necessary conditions for a true

continuity: infinite divisibility and common limits in between the parts.

For that reason, Peirce can say: “all the parts of a perfect continuum

have the same dimensionality as the whole.” [CP 4.642, Some Amazing

Mazes, 1908]. Or, in other words:

If there is room on a line for any multitude of points,

however great, a genuine continuity implies, then, that

the aggregate of points on a line is ‘too great to form a

collection’: the points lose their identity; or rather, they

never had a numerical identity, for the reason that they

are only possibilities, and therefore are essentially

general. They only become individual when they are

separately marked on the line; and however many be

separately marked, there is room to mark more in any

multitude. [HP II: 745, On the Logic of drawing History

from Ancient Documents …].

The distinction between finite and infinite collections is possible

to be a priori logically determined through the application of what

Peirce calls, following Augustus De Morgan, the “syllogism of

transposed quantity”. The application of such syllogism allows for the

determination the multitude of a denumeral collection. See the

following definition of this syllogism:

Syllogism of transposed quantity: a syllogism in which

the whole quantity of one concluding term, or its

contrary, is applied in a premiss to the other concluding

term, or its contrary, by means of a relation of one-to-N

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correspondence. As in the following: Some X's are not

Y's, for every X there is a Y which is Z; hence, some Z's

are not X's. [CP 2.579, Syllogism, 1902].

The validity of conclusion depends upon the adjunction of a

further premise, the one that the class of X’s be a finite collection [W 5:

188, On the Algebra of Logic: A Contribution to the Philosophy of

Notation, 1885]. Another one of Peirce’s example is the following:

Every Hottentot kills a Hottentot;

No Hottentot is killed by more than one Hottentot;

Therefore every Hottentot must be killed by a Hottentot.

[CP 5.662, Thelepathy, 1903].

Of course, Peirce remarks, that to reason in such way about an

infinite collection, as the series of integers, for instance, leads to a

nonsense:

Of collections not enumerable it is not generally true that

the part is less than the whole. Every integer has a

square; and thus there are as many squares as there are

integers; although the squares form but a part of all the

integers.

Take this example:

Every woman marries a man,

For every man there is a woman;

.·.Every man is married to a woman.

The necessity of this plainly arises from the fact that

after every woman has got a husband, the collection of

men is exhausted. To say this, is to imply that for every

quantitative relation it would have a maximum, that is, a

last reached, in any order of running it through. [CP

4.104, The Logic of Quantity, 1893].

269

In another very good humoured passage, the same relation is

explained in the following manner:

Balzac, in the introduction of his Physiologie du mariage,

remarks that every young Frenchman boasts of having

seduced some French woman. Now, as a woman can only

be seduced once, and there are no more French women

than Frenchmen, it follows, if these boasts are true, that

no French women escape seduction. If their number be

finite, the reasoning holds. But since the population is

continually increasing, and the seduced are on the

average younger than the seducers, the conclusion need

not be true. [EP 1: 316, The Law of Mind].

What this reasoning proves is that for finite collections, the whole

is bigger than the parts; for infinite collections, nevertheless, the whole

is not bigger than its parts, as we have seen. From this reasoning,

Peirce can derive the definition of a finite class:

Suppose a lot of things, say the A's, is such that whatever

class of ordered pairs λ may signify, the following

conclusion shall hold. Namely, if every A is a λ of an A,

and if no A is λ'd by more than one A, then every A is λ'd

by an A. If that necessarily follows, I term the collection

of A's finite class. [CP 4.187, Multitude and Number,

1897].

With the application of the syllogism of transposed quantity,

enumerable collections are distinguished from denumeral and

abnumeral ones. Now, to distinguish between these latter, it is needed

to apply a special sort of reasoning, the Fermatian inference, or

mathematical induction [EP 1: 317]. It is this special mode of reasoning

that we will examine in what follows.

270

In what regards the theory of induction, it is possible to formulate

two problematical questions63. First, suppose that half of 10.000 throws

of a coin will actually result heads. If the result is heads exactly in the

5.000 throws, then, by deduction, one may unmistakably know that the

relative frequency of heads compared to all the throws of the whole

series of 10.000 throws should be somewhere in between ¼ (if the

extant throws all turn up tails) and ¾ (is the exatnt 5.000 throws turn

up heads). Hence our prediction, that half of the 10.000 throws will

turn up heads, cannot be overcome by more than ± ¼.

In another case, suppose that after 8.000 throws the relative

observed frequency of heads continues to be ½. At this point, it will be

clear that the relative frequency of heads in the whole series of 10.000

throws must be between ⅖ (if the 2.000 remaining throws all turn up

tails) and ⅗ (if the extant 2.000 throws all turn up heads). Hence our

prediction that half of the 10.000 throws will turn up heads cannot be

overcome by more than ± ⅟10. Thus, it is possible to come gradually

closer to the correct value (whatever it may be), since the biggest

possible error in all our predictions is each time less.

The problem is that the estimations come closer a correct value

because each time bigger portions of the series concern past throws,

and are considered as weight of evidence in the estimations referring to

the probability of the results of the future throws, to which less and

less portions of the series would concern. This problem is still more 63 TIDMAN; KAHANE (2003), pp. 397-398.

271

important in respect to infinite series, for the relative frequency of any

given portion of a infinite series is accordable with any relative

frequency of the whole series. For instance, even that the evidence

comes from a million coin throws turned up heads; the limit of a

supposed infinite series still could be equal to zero. How to assure that

induction is capable of self correctness in this case? The problem is that

in some one moment it is possible to say that the conclusions are

getting closer to a correct measure of the relative frequency.

Peirce himself recognized the problem. 64 In 1910, when reviewing

his article The Doctrine of Chances, published in 1878 [W 2: 276-289],

he recognized the lack of sureness and the impossibility to trust his own

early attempts at solving the problem, expressing himself as follows:

But when [in The Doctrine of Chances] I come to define

probability, I repeatedly say that it is the quotient of the

number of occurrences of the event divided by the

number of occurrences of the occasion. Now this is

manifestly wrong, for probability relates to the future;

and how can I say how many times a given die will be

thrown in the future? [CP 2.661].

Now, it is needed to consider the possibility of the occurrence of

events in an infinite series without definite value, that is, with relation

to an unlimited collection. It seems clear the reason for such

formulation: if the collection is finite, because of the insistence of the

method, in a certain moment the samples would begin to repeat. But, in

the case of a set of objects whose limits are unknown, we would never

64 BACHA (1999), pp. 286 seq.

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know if the samples are being repeated. It is a situation analogous to

the one previously described, as to the order of nature. It is needed,

then, to improve the method. In other words:

For it is plain that, if probability be the ratio of the

occurrences of the specific event to the occurrences of

the generic occasion, it is the ratio that there would be in

the long run, and has nothing to do with any supposed

cessation of the occasions. This long run can be nothing

but an endlessly long run; and even if it be correct to

speak of an infinite “number,” yet / (infinity divided by

infinity) has certainly, in itself, no definite value. [CP

2.661].

To solve this problem two ideas are central: randomness and pre-

designation. It is needed, first, that the samples are fair, that is, that it

is possible the highest degree of randomness in drawing the samples, in

a way that each one of them may happen as many times as any other, as

seen above; and, secondly, one needs to know what one is looking for,

so to be possible to ascertain standards for comparison.

Let us see better these points, taking off from the idea of the long

run. It is from this idea that Peirce defines probability in a non-circular

way. Take the example of a throw of dice, which is essentially the same

of a throw of coins. The probability to obtain any number in a throw is

always 1/6, if the dice are not vitiated. That means that the throws are

independent in between themselves, i.e., to get 5 in a throw is

completely independent of getting 4 or 6 in any other throw. To say that

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the probability of getting 6 is 1/6 in the long run is the same as to say

that of 10.000 future throws, for instance, 1.600 (16%) will turn up 6. in

other words, the long run means “an endless succession of throws in

the order in which they are thrown.” [NEM 3/I: 173, Probability and

Induction, letter to Kehler from 22 June 1911]. Probability, therefore, is

defined as the ratio of frequency that there is between the occurrence

of known facts and the occurrence of unknown facts:

The probability that if an antecedent condition is

satisfied, a consequent kind of event will take place is the

quotient of the number of occasions, ‘in the long run’, in

which both the antecendent will be satisfied and the

consequent kind of event will take place, divided by the

total number of occasions on which the antecedent

conditions will be satisfied. [NEM 3: 174, Probability and

Induction].

The idea of the long run is essential because it links the ideas of

probability and convergence: the method of induction gives us the

possibility of asserting that, in the long run, the frequency of a certain

kind of event would tend to a definite value, which is not yet known; in

other words, the ratio between the number of times in which this event

could occur and the number of times in which the proper occasion for

this happening arises would indefinitely converge towards a limit. The

idea oc convergence is explained as follows:

The word “converge” is here used in a different sense

from that which is usual in mathematics. The common

definition is that a series of values, x1, x2, x3, etc.,

converges toward a limiting value x, provided, after any

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discrepancy ε has been named it is possible to find one of

the members of the series xv such that, for every value of

n greater than v, (xn – x) < ε. This ought to be called

definite convergence. No such member, xn can in the

indefinite convergence with which we have to do, be

fixed in advance of the experiment. Nevertheless, there

will be some such value. [HP II: 745, On the Logic of

Drawing History from Ancient Documents…].

Now, it is possible to discover a ratio, that is, an approximate

proportion of occurrence, a statistical probability: “Objective

probability is simply a statistical ratio.” 65 [NEM 4: 59, Carnegie

Application]. It means that our knowledge is reduced to a merely

probable estimation: scientific discoveries are but attempts to diminish

our errors; that is, from an initial sample, to endeavour in defining the

probable characters of the whole universe, correcting the deviations

through successive qualitative inductions.66 In sum, any and every

scientific assertion can be but probable:

To say, for instance, that the demonstration by

Archimedes of the property of the lever would fall to the

ground if men were endowed with free will is

extravagant; yet this is implied by those who make a

proposition incompatible with the freedom of the will the

postulate of all inference. Considering, too, that the

conclusions of science make no pretense to being more

than probable, and considering that a probable inference

can at most only suppose something to be most

frequently, or otherwise approximately, true, but never

65 Cf. PARKER (1998), p. 171.66 In fact, no scientific affirmation can be more than probable. Peirce vehemently rejects any absolute necessity and truth whatever they might be.

275

that anything is precisely true without exception

throughout the universe, we see how far this proposition

in truth is from being so postulated. [EP 1: 299, The

Doctrine of Necessity Examined, 1892].

Scientific knowledge, therefore, is a way of understanding the

distribution of the characters in the sample with relation to the whole

supposed universe. The idea of pre-designation is important in that

scientific knowledge is grounded in the recognition of how the sample

presents certain qualities. Suppose that a ship be loaded with wheat, as

Peirce says [id.]. This load is stirred up so that the grains are all mixed

up. Samples are equally taken out from the fore, amidships, and from

the aft parts, from larboard as well as from starboard, from the top, half

depth and bottom of her hold, and, after analyzing them: “Then we

infer, experientially and provisionally, that the approximately four-fifths

of all the grain in the cargo is of the same quality.” [EP 1: 301, id.]. The

estimated frequency has nothing to do with some wheat that might

have possibly been hidden in the ship and is not drawn in the sample:

By saying that we infer it experientially, I mean that our

conclusion makes no pretension to knowledge of wheat-

in-itself. […] We are dealing only with the matter of

possible experience – experience in the full acceptation

of the term as something not merely affecting the senses

but also as the subject of thought. [...] By saying that we

draw the inference provisionally, I mean that we do not

hold that we have reached any assigned degree of

approximation as yet, but only hold that if our experience

be indefinitely extended, and if every fact of whatever

nature, as fast as it presents itself, be duly applied,

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according to the inductive method, in correcting the

inferred ratio, then our approximation will become

indefinitely close in the long run; that is to say, close to

the experience to come (not merely close by the

exhaustion of a finite collection) so that if experience in

general is to fluctuate irregularly to and fro, in a manner

to deprive the ratio sought of all definite value, we shall

be able to find out approximately within what limits it

fluctuates, and if, after having one definite value, it

changes and assumes another, we shall be able to find

that out, and in short, whatever may be the variations of

this ratio in experience, experience indefinitely extended

will enable us to detect them, so as to predict rightly, at

last, what its ultimate value may be, if it have any

ultimate value, or what the ultimate law of succession of

values may be, if there be any such ultimate law, or that

it ultimately fluctuates irregularly within certain limits, if

it do so ultimately fluctuate. [ibid.].

We have seen that induction is the kind of inference that allows

for the passage of the particular to the general. In effect, relatively to

this respect, there is the idea of pre-designating the character to be

discovered. Samples are drawn at random, to be examined as to some

specific respect; in the case, of which quality is the wheat. Induction

makes possible to ascertain a general character to the whole cargo

based upon the fact that the samples are of a certain quality. Through

successive sampling a conclusion is reached, that most likely defines

the whole. The procedure can be repeated as many times as wanted.

And in fact, the more it is repeated, the greater assurance the

generalization will attain. Thus, if there is some truth to be discovered,

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it can be affirmed in terms of the general character, which can be

attributed to a whole class or infinite series, from the verification that a

character of the same species in its members to which we had access;

in other words, induction is a reasoning which allows to recognize what

is true of the whole, in recognizing a general true character of the parts

[NEM 3/ I: 182, letter to Kehler].67

The idea of induction as synedoche is from early on present in

Peirce’s writings. Nevertheless, he came to distinguish three different

kinds of induction, to wit, the crude or rudimentary induction,

qualitative induction, and quantitative induction [CP 7.110-130, Lowell

Lectures – VII, 1903]. Each one of these sorts of induction relates in a

different way the particular to the general, and it is worthwhile to

analyse them more thoroughly. It is with the idea of quantitative

induction that Peirce recovers Fermat’s inference, affirming to be

possible to ascertain in a quantitative way certain distinctive qualities,

so to allow the identification of the events in classes.

The first kind of induction is defined in the following way: “By

‘crude’ induction, I mean that inarticulate, unreflective kind usually but

very inappropriately termed (I suppose in imitation of Francis Bacon)

inductio per simplicem enumerationem [induction by simple

enumeration].” [NEM 3/I: 214, On the Foundation of Ampliative

Reasoning, 1910]. In this kind of rudimentary induction “the collection

to be sampled is an objective series of which some members have been 67 BACHA (1999), pp. 298-299; IBRI (1994), p. 108

278

experienced, while the rest remain to be experienced, and we simply

conclude that future experience will be like the past.” [HP II: 748, On

the Logic of Drawing History from Ancient Documents …].

This is the weakest kind of induction [HP II: 749, id.], for it is

based on the absence of knowledge, i.e.: “Rudimentary induction […]

proceeds from the premiss that the reasoner has no evidence of the

existence of any fact of a given description and concludes that there

never was, is not, and never will be any such thing.” [CP 7.111, id.]. It is

a self-correcting method, since the experimental series is not

interrupted; “and if the series of observations skips a single day, that

day may be the very day of the exceptional fact.” [ibid.]. In other words,

the most that crude induction warrants is that there are not enough

evidence yet to abandon the initial hypothesis. An example given by

Peirce deserves to be quoted:

I find myself introduced to a man without any previous

warning. Now if I knew that he had married his

grandmother and had subsequently buried her alive, I

might decline his acquaintance; but since I have never

heard the slightest suspicion of his doing such a thing,

and I have no time to investigate idle surmises, I

presume he never did anything of the sort. I know a great

many men, however, whose whole stock of reasoning

seems to consist in this argument, which they continue to

use where there is positive evidence and where this

argument consequently loses all force. [CP 7.112, Lowell

Lectures – VII, 1903].

279

Notice this is the kind of induction considered by Hume; in fact,

all the generalizations of common-sense are of this kind: “the Sun

raised every day before today; so, it will raise tomorrow as well”. Also

other examples given by Peirce to illustrate this kind of induction point

to the problem in the terms Hume proposed: the one of the Greek man

that watches the flux and reflux of the tides, and the one to the action of

gravitation measured by the oscillations of the pendulum [HP II: 748-

750]. If the problem of induction is considered only from this point of

view, it certainly would not have any way out of the Humean aporia. In

a word, its weak point is in that if positive contrary evidence to the

initial surmise is discovered it must be abandoned. It seems, then, that

the only possible justification to crude induction is the fact that if such

method is pursued uninterruptedly, making continuous observations

one after the other, its mistakes will be corrected. Yet if one single day

the series of observations be interrupted, the reasoning loses its force;

for instance, the day the Greek did not go to see the tide, it may have

changed as to what he had observed before; once reasoning is based on

the continuation of an uninterrupted series of observations, one

interruption can invalidate the whole reasoning.

For if the tide was going to skip a half-day, he [the

Greek] must discover it, if he continued his observations

long enough. This degree of justification and no more he

would have whether he made a dozen trials, or half-a-

dozen, or three, or two, or one only, or even none at all,

the argument would have precisely the same justification

280

in either case. The method would infallibly correct itself,

provided he continued this series of experiments; but not

if he dropped it and subsequently commenced another

series, as would be the case with quantitative induction.

For this induction not being quantitative, does not

conclude that the probability of the tides rising is 1; but

that it rises every half-day without exception. It has

nothing to do with probabilities or improbabilities; and if

the series of observations skips a single day, that day

may be the very day of the exceptional fact. [HP II: 748].

Now, the only conclusion crude induction reaches is that there is

nothing yet to contradict the hypotheses. As it is not a question of

probabilities, there is no reason why to assume the falsity of the

conclusion; but there is not also a higher reason to assume its truth in

the future. In other words, the probability of the conclusion being true

is 50%. This is a method which, relative to “gratuit hypothesis” it

furnishes some degree of assurance; it is impossible not to use it some

time. Even then, it is the weakest kind of induction. [id.].

Another kind of induction is qualitative induction: “This kind of

reasoning may be described […] by saying that it tests a hypothesis by

sampling the possible predictions that may be based upon it.” In more

detailed terms, the process consists in the following steps:

I seem to recognize a […] genus of inductions where we

draw a sample of an aggregate which can not be

considered as a collection, since it does not consist of

units capable of being either counted or measured,

however roughly; and where probability therefore cannot

enter; but where we can draw the distinction of much

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and little, so that we can conceive of measurement being

established; and where we may expect that any error into

which the sampling will lead us, though it may not be

corrected by a mere enlargement of the sample, or even

by drawing other similar samples, yet must be brought to

light, and that gradually, by persistence in the same

general method. [HP II: 750-751].

In general lines, then the process above described is equivalent to

the hypothetical-inductive method of verification of theories.

Phenomena are observed, apparently disconnected, that is, apparently

they do not make up the same collection. Two possibilities are then

open to the inquirer: “In the first place, we may look through the known

facts and scrutinize them carefully to see how far they agree with the

hypothesis and how far they call for modifications of it.” [CP 7.114,

Lowell Lectures VII, 1903]. In other words, we seek to understand new

facts creating general conceptions based upon what we already know.

This is the process of abduction, that is, of creation of explanatory

hypothesis for the facts, and it is formally very much like induction, for

it also starts from the particular to reach the general. Nevertheless, to

take one for the other is to commit a fallacy post hoc, ergo propter hoc

(literally: after that, then because of that), i.e., to confound the cause

with what is not the cause (yet: to affirm the consequent). For instance,

to think that a fact A, when temporally previous to B, only for being

previous, is the cause of B. But A can be previous to B without being its

cause, in the same way that B may come after A without being its

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consequence.68 If this fallacy not committed, the procedure of looking

for the facts we know in the attempt to understand those we do not

know is of a great value to inquiry [ibid.].

The second attempt is not to look at the facts, but to the

hypothesis that we have and to test their capacity to predict what will

happen in the future:

The other line which our studies of the relation of the

hypothesis to experience may pursue, consists in

directing our attention, not primarily to the facts, but

primarily to the hypothesis, and in studying out what

effect that hypothesis, if embraced, must have in

modifying our expectations in regard to future

experience. [CP 7.115, ibid.].

In such way bounded by empirical check, the hypotheses that

better describe the run of experience are continually tested, until the

expectations they created be contradicted by facts. Now, this is the first

step of scientific investigation, for it starts from a surprise in

experience to get to the hypothesis that explains it [CP 2.755, c. 1905].

This reasoning Peirce called retroduction:

The whole series of mental performances between the

notice of the wonderful phenomenon and the acceptance

of the hypothesis, during which the usually docile

68 Aristotle gives the following example for this kind of fallacy: “E.g. the soul and life are not the same; for if coming-to-be is contrary to perishing, then a particular form of perishing will have a particular form of coming-to-be as its contrary: now death is a particular form of perishing and is contrary to life; life, therefore, is a coming-to-be, and to live is to come-to-be. But this is impossible; accordingly, the soul and life are not the same. Now this has not been deduced; for the impossibility results even if one does not say that life is the same as the soul, but merely says that life is contrary to death, which is a form of perishing, and that perishing has coming-to-be as its contrary.” Sophistical Refutations, 167b21-167b36.

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understanding seems to hold the bit between its teeth

and to have us at its mercy, the search for pertinent

circumstances and the laying hold of them, sometimes

without our cognizance, the scrutiny of them, the dark

laboring, the bursting out of the startling conjecture, the

remarking of its smooth fitting to the anomaly, as it is

turned back and forth like a key in a lock, and the final

estimation of its Plausibility, – I reckon as composing the

First Stage of Inquiry. Its characteristic formula of

reasoning I term Retroduction, i.e. reasoning from

consequent to antecedent. [EP 2: 441, A Neglected

Argument for the Reality of God].

The reasoning is called retroduction exactly because the framing

of the hypothesis begins with the observation of a striking fact. Its

logical form is the following:

The surprising fact, C, is observed;

But if A were true, C would be a matter of course.

Hence, there is reason to suspect that A is true. [HL

245].

Every inquiry begins with the observation of something that

appears as striking, something not agreeable to what is expected,

interrupting an habit of expectation. The business of inquiry is to

inquiry into those phenomena, to devise an explanatory hypothesis to

give an account of such “wondering”. Thus, the very first step towards

discovering truth is in the imagination of what this truth could be:

As soon as a man experiences a longing to know the

truth, he begins to imagine what that truth can be. He

very soon finds that [1118] unrestrained imagination is

sure to lead him wrong. Nevertheless, it remains true

that imagination alone, - under proper checks, - can

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possibly suggest the truth. Hence, the second requisite

for the successful pursuit of science, - coming out after

the desire to learn, - is a scientific and fertile

imagination. […] The scientific man dreams of agencies

by which the phenomena of nature might be brought

about. [HP II: 1117-1118, The Chief Lessons of the

History of Science].

According to this, Peirce states:

Tennyson says:

maybe wildest dreams

are but the needful preludes of truth.

But I would dock the maybe. Wildest dreams are the

necessary “first steps toward scientific investigation”.

[HP I: 157, Early History of Science, 1892].

The imagination of hypotheses is the essential first step of

science, in its search for truth. In fact, the retroductive process of

imagining hypotheses is the only one which is endowed with original

heuristic power:

Abduction is the process of forming an explanatory

hypothesis. It is the only logical operation which

introduces any new idea; for induction does nothing but

determine a value, and deduction merely evolves the

necessary consequences of a pure hypothesis.

Deduction proves that something must be; Induction

shows that something actually is operative; Abduction

merely suggests that something may be. [HL 230].

The modus operandi of scientific method is that from imagined

hypothesis it is retroductively possible to reach certain conclusions

necessarily. Notice that abduction itself does not put any necessity on

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the hypotheses it suggests, for they can be used only in a deductive

reasoning in the place of the premises. The conclusion necessarily

obtained from this surmise will be inductively tested in experience, in

order to be possible to discard the conclusions which do not describe

facts properly:

Deduction is the only necessary reasoning. It is the

reasoning of mathematics. It starts from a hypothesis,

the truth or falsity of which has nothing to do with the

reasoning; and of course its conclusions are equally ideal.

[…] Induction is the experimental testing of a theory. The

justification of it is that, although the conclusion at any

stage of the investigation may be more or less erroneous,

yet the further application of the same method must

correct the error. The only thing that induction

accomplishes is to determine the value of a quantity. It

sets out with a theory and it measures the degree of

concordance of that theory with fact. It never can

originate any idea whatever. No more can deduction. All

the ideas of science come to it by the way of Abduction.

Abduction consists in studying facts and devising a

theory to explain them. Its only justification is that if we

are ever to understand things at all, it must be in that

way. [HL 217-218].

As the only justification for the validity of abduction is its capacity

to open new boundaries [NEM 3/I: 206, letter to Kehler], it is needed to

test it in experience. Abductions are like Whitehead’s play of free

imagination, which must made acute by the coherence with facts and

logical consistency. The process of imagining hypotheses and their

following test are characteristic of qualitative induction. Qualitative

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induction thus is the “mix”69 of two processes: the abductive, or

retroductive, the imagining of a hypothesis, and the inductive, the

testing of it. After successive eliminations of explanatory hypothesis

through empirical testing, an explanation will be reached to exhibit the

striking fact as the conclusion of a deductive syllogism. This

explanatory hypothesis finally may be account as plausible [EP 2: 441, A

Neglected Argument for the Reality of God]. In other words: “This kind

of reasoning may be described in slightly different terms by saying that

it tests a hypothesis by sampling the possible predictions that may be

based upon it.” [HP II: 751, On the Logic of Drawing History from

Ancient Documents …]. The development and working out of this

method is tied-linked to the collective practice of science:

One generation collects premises in order that a distant

generation may discover what they mean. When a

problem comes before the scientific world, a hundred

men immediately set all their energies to work upon it.

One contributes this, another that. Another company,

standing upon the shoulders of the first, strike a little

higher, until at last the parapet is attained. Still another

moral factor of the method of science, perhaps even more

vital than the last, is the self-confidence of it. In order to

appreciate this, it is to be remembered that the entire

fabric of science has to be built up out of surmises at

truth. All that experiment can do is to tell us when we

have surmised wrong. The right surmise is left for us to

produce. [CP 7.87, Scientific Method, 1902].

69 RESCHER (1978), p. 3. In fact, Rescher distinguishes abduction from retroduction. In this regard, we follow the account provided by PARKER (1998), p. 175, in its criticism to Rescher.

287

Now we pass to quantitative induction. Take one of its

particularly clear definitions:

This [form of induction] investigates the interrogative

suggestion of retroduction, ‘What is the ‘real probability’

that an individual member of a certain experiential class,

say the S's, will have a certain character, say that of

being P?" This it does by first collecting, on scientific

principles, a "fair sample" of the S's, taking due account,

in doing so, of the intention of using its proportion of

members that possess the predesignate character of

being P. This sample will contain none of those S's on

which the retroduction was founded. The induction then

presumes that the value of the proportion, among the S's

of the sample, of those that are P, probably

approximates, within a certain limit of approximation, to

the value of the real probability in question. I propose to

term such reasoning Quantitative Induction. [CP 2.758, c.

1905].

Quantitative induction seeks to ascertain a quantity, and nothing

more; in other words, it measures the degree of concordance of the

theory with the facts. For such reason, its success is relative to the

amount of extra information not contained in the premises which it is

possible to gather: the probability of its conclusions being true is

proportional to the quantity of positive evidence which is gathered to

prove a theory, “for induction proper consists in judging of the relative

frequency of a character among all the individuals of a class by the

relative frequency of that character among the individuals of a random

sample of that class.” [CP 6.100, Uniformity, 1902]. In this idea the

288

concept of weight of evidence appears, which allows to consider that

the observed frequencies are representative of the actual frequencies.70

Peirce explains quantitative induction in the following manner:

The sample is to be drawn under the guidance of a

precept under which we can enlarge any sample drawn

indefinitely and can also draw an indefinite number of

samples. Now I shall suppose that in some way, no

matter how, we become assured that a relation exists

between four correlates, to wit, the predesignate

character, the precept of sampling, the collection

sampled, and the future course of experience, this

relation being such that, in the long run, the distribution

of the predesignate character in samples drawn under

the precept will be the same as if they had been drawn

strictly at random from an indefinitely large finite

collection composing all our future experience of

members of the same collection. Then, as before, we can

infer inductively the proportional frequency of that

character in future experiences of members of the same

collection; and the induction must approximate

indefinitely, though irregularly, to the true proportion.

[HP II: 746, On the Logic of Drawing History from

Ancient Documents …].

Quantitative induction, to Peirce, is by far the strongest way of

inducing conclusions [NEM 3/I: 183, letter to Kehler]. Firstly, its force

comes from the fact that the procedure could be indefinitely extended,

in a way that a objective probability relative to the occurrence of the

pre-designated character can be defined in fact. Quantitative induction

70 RESCHER (1978), p. 3.

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serves to measure probabilities in a precise way, and it would lead to a

true answer:

Quantitative induction approximates gradually, though in

an irregular manner to the experiential truth for the long

run. The antecedent probable error of it at any stage is

calculable as well as the probable error of that probable

error. Besides that, the probable error can be calculated

from the results, by a mixture of induction and theory.

Any striking and important discrepancy between the

antecedent and a posteriori probable errors may require

investigation, since it suggests some error in the

theoretical assumptions. But the fact which is here

important is that Quantitative Induction always makes a

gradual approach to the truth, though not a uniform

approach. [CP 2.770, c. 1905].

Quantitative induction, therefore, is a mathematical method used

in determining the proportion of the distribution of the qualities

between the members of a collection. The ascertainment of a statistical

ration has this sole function: to distinguish the proportion of specific

classes of events in relation to the whole of possible events.71 If we think

that induction will be indefinitely carried further on by a limitless

community of inquirers, we have that with time given the method

becomes gradually more reliable. Thus, quantitative induction is a safe

method to prove the validity of hypothesis. Peirce, in a certain moment,

says that for etymological reasons he prefers to call this kind of

71 As a matter of fact, the application of mathematical induction in the operation of distinguishing denumeral from abnumeral collections works as a criterion to distinguish classes of potency 0 א , i.e., capable of being defined by the series of cardinal numbers, from classes fo higher potency. Cf. PARKER (1998), chap. 4 supra cit., passim; CHAUVIRÉ (1984), pp.353-354.

290

reasoning adduction, meaning the process of putting in discussion, the

process of bringing to the center of the discussion the problematic

cases and theories [NEM 3/I: 190, letter to Kehler].72 Remember that

the idea of probable deduction means the deduction of a probability:

through a deductive process, a certain probability is proved certain. In

quantitative induction a similar process happens, with the difference

that the new knowledge suggested is confirmed by abduction, just

because adduction consists in taking the hypothesis further on, putting

it forward, that is, it consists in advancing knowledge, by the

application of the hypothesis to future cases:

The induction adds nothing. At the very most it corrects

the value of a ration or slightly modifies a hypothesis in a

way which had already been contemplated as possible.

Abduction, on the other hand, is merely preparatory. It is

the first step of scientific reasoning, as induction is the

concluding step. [HP II: 752, On the Logic of Drawing

History from Ancient Documents …].73

With this interpretation of the inductive method, Peirce can

present an account of scientific inquiry whose chief merit lies in

explaining how science advances combining moments of interruption

with continuity. Quantitative induction is only one kind of induction,

and induction proper is characteristic of only one stage of inquiry. From

72 Cf. the following: “Yet the bringing forward of instances is just the characteristic of the kind of reasoning or argumentation called ‘induction’. In view of this, I intend to take seriously into consideration, in view of my conception of the essential nature of such reasoning being as different from that of all who preceded me as it is, whether I ought not to have a different word for what I mean and call it adduction.”73 PARKER (1998), pp. 172-173, asserts that induction, differently from deduction, brings new knowledge too. For this quotation, we see it is not exactly like this.

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this point of view, the experimental test of hypotheses is a way of

monitoring scientific procedure as a whole, so that the self-correctivity

of induction may be stretched out to the whole process. In other words,

scientific method proceeds to use statistical instruments to ascertain a

probabilistic truth, which is the only truth possible of being ascertained.

74

The difference between abduction and induction is crucial. While

the first has as its starting point the facts, and it seeks a theory to

explain them, induction, on the contrary, starts from an explanatory

hypothesis to seek the facts to support it:

Abduction makes its start from the facts, without, at the

outset, having any particular theory in view, though it is

motivated by the feeling that a theory is needed to

explain the surprising facts. Induction makes its start

from a hypothesis which seems to recommend itself,

without at the outset having any particular facts in view,

though it feels the need of facts to support the theory.

Abduction seeks a theory. Induction seeks for facts. [HP

II: 752, On the Logic of Drawing History from Ancient

Documents…].

For this reason, the inductive and the abductive methods differ

one from another being each one the inverse of the other, in an

analogous way as the syllogistic forms of hypothetical and inductive

reasonings were opposed in Peirce’s early writings. Here, specifically,

the logical forms of hypothesis and induction are not opposed, but

inductive reasoning and the very process of imagining hypothesis: “In

74 RESCHER (1978), chap. 1, passim; DELANEY (1995), p. 116.

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abduction the consideration of the facts suggests the hypothesis. In

induction the study of the hypothesis suggests the experiments which

bring to light the very facts to which the hypothesis had pointed.” [id.].

To Peirce, it is necessary to give up the idea of a completely

certain and absolute knowledge of the world. There is no strictly

infallible knowledge, there is only a very high degree of probability that

certain theories will continue to foresee the course of events. Certainty

is not and cannot be the standard of knowledge. In effect, his account of

the history of scientific thought is centered on the idea of probability,

that is, in the idea that it is possible to ascertain a percentage of truth

for real synthetical general propositions about the future, grounded

upon the presently available evidence [NEM 3/I: 139, Probability]75. The

infallibility of modern science, mentioned in the beginning, is therefore

restricted to a matter of probability – the only certainty we can have is

in short the measure of our own ignorance. However, we should not

because of that begin to believe, as Hume did, in the impossibility of

knowing the truth, even it is a provisional and approximate truth.

From this idea, it is possible to say that no revolution in science

happens simply all of a sudden, as if it was out of the blue. If, as Gaston

Bachelard says, the only way to make science advance is to attack

established science, changing its constitution76, it is impossible that this

attack comes from outside science itself. As a matter of fact, remember

75 Cf. NEM 3/I: 143, The Concept of Probability, Peirce’s account of Phyrro’s philosophy, and the role of Pascal to the history of western thought. 76 BACHELARD (1984), p. 31.

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what was said before: to refute a mathematician, it is needed to do it

mathematically.

In all sciences revolutions are possible; nevertheless, such

revolutions can only happen if they take as a starting-point the

conceptual marks already existent, as Mario Bunge says77. If we take

the picture of the philosophy of scientific inquiry Peirce offers, we could

even say that there is no possibility of being different, since the

abductive process of creating hypothesis, even though it is not

submitted to strict rules78, is always an attempt to recognize the

surprise and novelty within the boundaries of known conceptual

schemes. Thus, to use another expression of the Argentinean

philosopher, we could say: “There are no revolutionaries without roots,

no revolutions in a conceptual void.”79.

Now, according to the scheme proposed by Peirce, wherein the

procedures of abduction, induction, and deduction are intimately

connected, it is possible to say that the test of theories leads to

revolutions. In this way, at the same time that a Bachelardean rupture

épistémologique implies the abandonment of previous conceptual

marks, it also opens new fields of investigation, even whether it

maintains old conceptual bases. In fact, Peirce’s opinion seems to be

just that when he says: 77 BUNGE (1985), pp. 45 ff. In effect, Bunge’s remarks are very similar in spirit to those of Peirce. What follows is an attempt to think in Peircean terms the ideas presented by the Argentinean philosopher. 78 IBRI (1994), pp. 110 ff.79 BUNGE (1985), p. 47: “No hay revolucionarios sin raíces, ni revoluciones en un vacío conceptual.” Our translation.

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We cannot ordinarily hope that our hypothesis will pass

through the fire of induction, absolutely unmodified.

Consequently, we ought not to conclude that it is

absolutely correct, but only that it very much resembles

the truth. Insofar as further induction will modify it, as it

must be expected that it will do, if it is not to meet with

downright refutation, it can hardly fail that the

modification should come about gradually. [HP II: 751,

On the Logic of Drawing History from Ancient

Documents …].

Now, instead of supposing facts are incomprehensible, it is

needed to suppose that, notwithstanding they are striking, they

reconcilable with what is known about other facts. In a certain moment,

the quantity of strinking facts – unforeseen facts – will be so much that

it will force a modification of the theory [id.]. Even if enough evidences

are not gotten, so as to demand a modification of the conceptual

scheme, there is no possible return to the same point as before; either

because the striking facts, if they happen again, will then not be as

striking as at first anymore, and they will be in a certain way already

incorporated to the theory, or because they have already led to the

search for another similar facts, to gather enough evidence to abandon

the theory, for instance80. In fact, there are two ways of suggestion

whereby abduction and induction make knowledge advance:

The mode of suggestion by which, in abduction, the facts

suggest the hypothesis is by resemblance, – the

resemblance of the facts to the consequences of the

80 Now, according to BUNGE (1985), p. 48, this is the most important contribution of Thomas Khun. For a comparison between Khun’s and Peirce’s ideas, cf. ROSENTHAL (1994), pp. 13 ff.

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hypothesis. The mode of suggestion by which in induction

the hypothesis suggests the facts is by contiguity, –

familiar knowledge that the conditions of the hypothesis

can be realized in certain experimental ways. [HP II: 752-

753].

Therefore, to know is also to recognize. In every field of inquiry

and investigation there is the tension between tradition and change,

between invention and recognition. Anyway, the confrontation with

experience is the motive for modifications, whether in the conceptual

re-framing of theories already existent, to accommodate new facts,

whether in the invention of new theories. However, the confrontation

with experience does not say exactly what must be done, not even how

it should be done. This is a decision we ourselves have to take – a

pragmatic decision, which has to be based in the interactive context of

the world surrounding us.81 This idea will be remembered further on, in

the conclusion of this work.

81 ROSENTHAL (1994), p. 14.

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7. EXPERIENCE AND EXPECTATION

Como poderíamos colocar nossa esperança total no tempo presente, sujeito a todas as instabilidades?

Murilo Mendes, § 527, O Discípulo de Emaús82

A Eternidade está longe(menos longe que o estirão

que existe entre o meu desejoe a palma de minha mão).

Um dia serei feliz?Sim, mas não há de ser já:

a Eternidade está longe,brinca de tempo-será.

Manuel Bandeira, Tempo-Será83

According to Peirce, every thought is a continuous interpretation

of signs, and to interpret is to infer. To infer in turn means to consider a

proposition as true in its statement: “Confining ourselves to science,

inference, in the broadest sense, is coextensive with the deliberate

adoption, in any measure, of an assertion as true.” [HP II: 722, On the

Logic of Drawing History ...]. As we have seen, there are three

fundamental forms of inference: deduction, induction, and abduction

[CP 3.516]. Thought itself s a sign, the whole mind is a sign: “we must

conclude that the mind is a sign developing according to the laws of 82 “How could we put all our hope in present time, subject to all instabilities?” Our translation. 83 “Eternity is far/ (less than the stretch/ that exists between my wish/ and the palm of my hand)/ Will I be happy one day? / yes, but not now it will be: / Eternity is far/ plays of time-will-be.” Our translation.

297

inference.” [W 2: 240, Some Consequences of Four Incapacities]. In this

way, always projected to the future, all thought leads to the formation

of convictions and habits, which are settled in a horizon of experience

and expectation. In effect, we also saw that to each kind of inference

there corresponds a logical modality: the business of deduction is to

establish necessary reasonings, that of induction to establish probable

reasonings, and to abduction the task is to delimitate an expectation:

What, then, is the end of an explanatory hypothesis? Its

end is, through subjection to the test of experiment, to

lead to the avoidance of all surprise and to the

establishment of a habit of positive expectation that shall

not be disappointed. [HL 250].

After the initial definition of the hypothesis, its experimental

verification will say whether the initial expectations were justified. And,

being disappointed, the habit of thinking must be modified, that is, the

initial hypothesis should be abandoned, in favour of another that

renders facts intelligible. This process of modifying hypothesis happens

through establishing new hypothesis, i.e., it always happens as to open

new fields of experience and expectation, making it possible to infer

other abductive reasonings. So, abduction being a process of framing

explanatory hypotheses [HL 230], the link with Peirce’s pragmatism is

evidently essential. Peirce in fact comes to say that all the ideas of

science were originated through abductions, to the point that ““if we

are ever to understand things at all, it must be in that way” [HL 218].

The abductive process of establishing a hypothesis begins with the

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recognition of a striking fact, to which an intelligible explanation has to

be provided. Not that this fact is an irregular fact; rather, the surprise

is caused by an unpredicted regularity. Indeed, “nobody is surprised

that the trees in a forest do not form a regular pattern, or asks for any

explanation of such a fact. So, irregularity does not prompt us to ask for

an explanation.” [HP II: 724, On the Logic of Drawing History…]. Why

should we expect that irregularity would be surprising to us, when

everywhere in nature we see irregularities? The process of abduction

begins when an unexpected regularity is noticed:

Before dismissing irregularity, I may note, as aiding to

clear the matter up, that a breach of an existing

regularity always stimulates a demand for an

explanation; but where, having expected regularity, we

only find irregularity without any breach of regularity, we

are only induced to revise our reasons for expecting

anything. Irregularity, be it noted, cannot be expected, as

such. For an expectation is, in every case, founded upon

some regularity. For the same reason, merely not finding

regularity where no particular regularity was expected,

occasions no surprise. [HP II: 724-725, On the Logic of

Drawing History…].

Every inquiry and interpretation arises from the observation of a

phenomenon which breaks habits of expectation of the inquirer. This

surprising irruption of a fact in need of explanation marks the first step

in search of a general conception which renders the fact intelligible, so

that it influences the internal logic of the process in delineating an

empiric-expectative horizon:

299

Now what an explanation of a phenomenon does is to

supply a proposition which, if it had been known to be

true before the phenomenon presented itself, would have

rendered that phenomenon predictable, if not with

certainty, at least as something very likely to occur. It

this renders that phenomenon rational, - that is, makes it

a logical consequence, necessary or probable. [HP II:

725].

In short, abduction is a process of adopting a hypothesis which is

suggested by facts. The hypothesis has to say that the facts will very

likely happen in a certain manner, so that it is adopted. Its

characteristic logical form is that of a modus ponens in reverse, so to

say:

The surprising fact, C, is observed;

But if A were true, C would be a matter of course.

Hence, there is reason to suspect that A is true. [HL

245].

The logical form of the modus ponens can be written like this84:

p qp q

Abduction, differently, is a reasoning from the consequent to the

antecedent, a retroduction, therefore; that is, it is the logical conclusion

of the consequence C to the premise still unknown A, which acquires

the status of hypothetical explanation or provisional theory to render C

intelligible. It may be written in the following logical form:

qp p q

84 PARKER (1998), p. 174.

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Thus, the role of abduction may be said to be to furnish a

”virtual” antecedent premise {CP 2.759, c. 1905]. 905]. Of course, this

idea of inverting logical implication gives abduction a highly

problematic character. The lack of logical sureness for the illation in

synedoque is the highest. However, we have seen that this lack of

sureness can be counterbalanced by the inductive testing of hypothesis,

in a strategy of application of the pragmatic maxim. In effect, the

anticipatory state prepared by abduction perfectly agrees with the

spirit of the pragmatic maxim: “It is a state of mind in which a man

seems to have ground for expecting certain things, and yet has

evidence that those expectations may e falsified.” [HP II: 732, On the

Logic of Drawing History …]. Thus, the development of the rational

purport of a hypothesis, taken as criterion of evidence, holds well

because the maxim works out as a method that relates the probability

and plausibility of the hypothesis with its character of being a possible

description of experience. As a matter of fact, the inductive test of

hypotheses has exactly the function of verifying their effectiveness in

the prediction of future events:

I have already explained to you briefly what these three

modes of inference, Deduction, Induction, and Abduction,

are. I ought to say that when I described induction as the

experimental testing of a hypothesis, I was not thinking

of experimentation in the narrow sense in which it is

confined to cases in which we ourselves deliberately

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create the peculiar conditions under which we desire to

study a phenomenon. I mean to extend it to every case in

which, having ascertained by deduction that a theory

would lead us to anticipate under certain circumstances

phenomena contrary to what we should expect if the

theory were not true, we examine the cases of that sort

to see how far those predictions are borne out. [HL 249].

The formal inadequateness of abduction is softened through using

the pragmatic maxim as a rule of caution and prudence in the adoption

of hypotheses, in a process Peirce calls the logic of abduction:

If you carefully consider the question of pragmatism you

will see that it is nothing else than the question of the

logic of abduction. That is, pragmatism proposes a

certain maxim which, if sound, must render needless any

further rule as to the admissibility of hypotheses to rank

as hypotheses, that is to say, as explanations of

phenomena held as hopeful suggestions; and,

furthermore, this is all that the maxim of pragmatism

really pretends to do, at least so far as it is confined to

logic, and is not understood as a proposition in

psychology. For the maxim of pragmatism is that a

conception can have no logical effect or import differing

from that of a second conception except so far as, taken

in connection with other conceptions and intentions, it

might conceivably modify our practical conduct

differently from that second conception. [id.].

The maxim is then nothing but a rule to ascertain whether

hypotheses can serve as general descriptions of facts, and, hence, as

guides to fine-tune future conduct. Thus, the meaning of any

hypothesis, term or conception is restricted to the different ways of

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guiding conduct that the adoption as true of one or another hypothesis

could cause; if there is no difference on the influence over conduct,

then there is no difference at all of meaning between the conceptions.

With this, any possibility of some ultimate and inscrutable residuum of

meaning, echoing resonances of the Kantian thing-in-itself, is excluded

from pragmatism.85

Abduction, from which it is possible to draw necessary

conclusions, effects a double transposition: from an experienced

temporal relation, one at once infers through abduction the analogy

between a logical relation in the inward domain of consciousness and a

causal relation in the domain of outward experience. According to

Apel86, then, abductive inference is then the projection of a logical form

characteristic of the successive temporal elements of its inward

experience over the causally determined outward experience of the

world. Abductive inference therefore has to be always immerse and

unfolding within a broader argumentative connexion. At the same time

it makes the attainment of plausibility for hypotheses possible, the

process also gains heuristic potency, going beyond the limits of factual

experience:

[…] if pragmatism is the doctrine that every conception is

a conception of conceivable practical effects, it makes

conception reach far beyond the practical. It allows any

flight of imagination, provided this imagination ultimately

85 IBRI (2003), p. 12.86 APEL (1995a), pp. 104 f.; APEL (1995b), p.65.

303

alights upon a possible practical effect; and thus many

hypotheses may seem at first glance to be excluded by

the pragmatical maxim that are not really so excluded.

[HL 250].

The link between true theories and conceivable practical bearings

in Peirce’s pragmatism appears as the creation of habits of conduct

capable of orientating future conduct, so that there may be a

convergence between the form of the concept and the course of

possible experience in the future. In truth, the projection of forms over

experience has a twofold sense: on the one hand, it is a way of

ascertaining the verisimilitude of hypotheses with facts; on the other, it

is a way of mediating the construction of ideals of conduct, the latter

being rationally understood.87

The tension preciously mentioned between the life of science,

which asserts nothing as definitely certain, and the commitment of the

scientist with the continuation of inquiry reappears here: it seems that

the scientist does not in fact have practical beliefs, but only theoretical

beliefs. It is decisive because of this to know what are the objectives

when propositions are asserted, for everything resumes in knowing

which are the expectations involved in the assertion of the truth of the

theories. Were we to investigate into the truth of a hypothesis, would

we be disappointed in discovering its falsity? In other words, would we

want to put to test the beliefs we adopted from the suggestion of a

hypothesis? If the supreme aim of scientific inquiry is to reach truth,

87 Idem, p. 10-11; IBRI (2000a).

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even if a vague and uncertain truth, the answer must be: yes, we would

like to test our beliefs, even because we want to attain a less vague and

more precise truth.

Uma hipótese, stricto senso, não é ainda uma crença.

Paralelamente a essa idéia, crenças, enquanto hábitos de conduta

operativos e eficientes, são naturalmente testadas cotidianamente.

Let us recover the line of the argument up to now. On the one

hand, Peirce holds there is no place for beliefs in science. Here, it

seems there is a problem with the concept of belief. True theories in

science are beliefs of the community of inquiry. However, that does not

mean that they are ultimate, or absolutely certain. There are, therefore,

beliefs in science, though they are not final beliefs. In this sense, we

restate, beliefs are not ultimate or final beliefs. To propose a theory as

valid does not mean to accept its truth as definite: all we can say is that,

up to the moment, no one doubts it as a valid description of facts, but it

may as well be that in the future this theory is replaced for a better one,

and the provisional truths it affirms now may be, either better

formulated and understood, or simply refuted, with the continuation of

inquiry. We have seen that for Peirce beliefs meant dispositions to act

in a certain way in situations of vital crises. On the other hand, it is

necessary to trust in the cognitive capacity of inquiry carried on in the

long run. In the process of inquiring, the scientist must not take up

definite beliefs. Nevertheless, so to engage in the process of inquiring,

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the scientist needs to believe he or she will be successful. Now, let us

remember what Peirce understands as “belief”:

I use the word belief to express any kind of holding for

true or acceptance of a representation. […] its principal

element is not an affair of consciousness at all; but is a

habit established in the believer’s nature, in consequence

of which he would act, should occasion present itself, in

certain ways. [NEM 4: 39, Carnegie Application].

Thus, belief is a habit of conduct of the individual, which he

deliberately adopts, to act satisfactorily in certain given practical

circumstances. Belief is a habit of conduct of which one is aware, a

habit against which one does not fight, and that can be contracted by

an act of will: contrarywise to other habits, which are acquired only by

the repetition of an action under the circumstance, “belief may be, and

commonly if not invariably, is contracted, by merely imagining the

situation and imagining what would be our experience and what our

conduct in such a situation” [idem]. This simple exercise of fancy would

suffice, according to Peirce, to settle the habit and to determine

conduct in case the actual situation comes to happen. Belief, therefore,

is something inscribed in the soul of a person, whether by the repetition

of certain actions, whether by an exercise of strenght of will.

Differently, a doubt is a problem of consciousness:

It is an uneasy feeling, a special condition of irritation, in

which the idea of two incompatible modes of conduct is

before the doubter’s imagination, and nothing

determines him, indeed he feels himself forbidden, to

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adopt either and reject the other. [NEM 4: 40, Carnegie

Application].

Doubt, because it is an irritation, forces the search for its

appeasement, that is, it fights against the satisfcation of belief,

compelling to recover it. Therefore, it is not the exact opposite of belief,

but it is a quite different state of mind. Peirce says they are

physiologically different, for they affect different parts of the human

being. Nevertheless, imagination also can suggest a doubt: “The most

important character of doubt is that no sooner does a believer learn

that another man equally well-informed and equally competent doubts

what he has believed, than he begins by doubting it himself.” [NEM 4:

41, idem]. It is not needed actually to find someone in the same

circumstances, to fancy the possibility of someone being in doubt is

enough to cause doubt:

Indeed, it is not necessary that one should actually meet

with a man who doubts; for such is the influence of

imagination in such matters that as soon as a believer

can imagine that a man, equally well-informed and

equally competent with himself, should doubt, doubt

actually begins to set in, in his own state of feeling. [id.,

ibid.].

Thus, the believer may not abandon his or her belief, that is, it

may keep the same habits of conduct, but they inevitably will not be

considered as certain and as indoubitable as before. This is the first

step toward their abandoment, and, according to Peirce, this will

happen with time given, since experience provides evidence for that. To

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such situation a corolarial is added, which is that if there is no real and

actual doubt as to some belief, the believer cannot see no reason as to

how to doubt it. That does not mean, however, that it is impossible to

question beliefs:

It thus appear that it is one thing to question a

proposition and quite another to doubt it. We can throw

any proposition into the interrogative mood at will; but

we can no more call up doubt than we can call up the

feeling of hunger at will. [ibid.].

Here it is essential to get a clear grasp of the difference between

beliefs and doubts, for upon such difference all the following

argumentation depends. Belief may be acquired by an act of will: the

self-convincement can lead us to consolidate hard to change habits of

conduct. Doubt, on the contrary, is independent of any act of will. That

is why they are regarded even as physiologically different by Peirce.

Doubt needs a concrete occasion to arise in one’s mind: if I do not see

any reason why I should doubt, why should I doubt? The imagination of

another person, equally informed and competent, who doubts the same

things I believe, is not an act of will, but the recognition that doubt is

possible. The important here (to be recovered further on) is that true

beliefs are capable of being doubt in face of contrary evidence. 88 And, in

case the contrary evidence is strong, showing that doubt can exist, an

exercise of self-criticism is unavoidable, in the course of which one may

or may not come to truly doubt one’s beliefs. What matters is that the

88 MISAK (1994b), p. 744.

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genuine believer, before the mere possibility of doubt, seeks as fast as

possible to get rid out of the doubt. Thus, even before one begins to

doubt, it is possible to question a proposition without in fact doubting it.

In other words, the recognition of the possibility of doubting maybe

does not lead to the abandoment of beliefs, but, it will at least lead to

their relativization: not throwing them away, indeed, but not

considering them as if they corresponded to absolute truths or

fundaments.

Let us get back to the distinction between practical and

theoretical beliefs. In the text Reason’s Rules, above quoted, Peirce

discusses the concept of truth, connecting it in contradistinction

between the two kinds of beliefs. Practical beliefs, according to him,

can be described as “habits of deliberate behaviour”. They are,

therefore, beliefs in the full sense, beliefs that determine the conduct,

according to the definition we just presented. To have a habit of

deliberate behaviour means to act or to have a tendency to act, in

general, in a certain way every time a certain occasion arises. The

example given is the one of the proposition “anthracite is a convinient

fuel”:

Now to say that a man believes anthracite to be a

convenient fuel is to say no more nor less than that if he

needs fuel, and no other seems particularly preferable,

then, if he acts deliberately, bearing in mind his

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experiences, considering what he is doing, and exercizing

self-control, he will often use anthracite. [CP 5.538,

Reason’s Rules].

The simple example, in fact, is full of details, which are worthy of

detailing. There is a practical situation which, imposing itself, demands

intervention: the man needs fuel. This situation does not need a special

intervention, no special fuel is demanded. The situation is similar,

therefore, to the one of the apple pie: there is a certain general purpose

which needs to be accomplished, and a kind of fuel is enough to solve

the problem; it is, therefore, an undetermined situation. To accomplish

this purpose, Peirce clearly says what it is needed to do. First, to

deliberate about what it is needed to do; this deliberation unmistakenly

makes its way through the calling for past experiences in similar

circumstances, and, next, through the consideration of the situation at

hand, that is, the comparison between what one knows by experience

and what appears as a sudden fact. Thus, the new actual fact is

interpreted accordinf to the general patterns of what was previously

lived, and acquires sense in so far as it can be taken in homology of the

same general nature as what is already known. In the end, it is needed

to control the action to act according to what is known, and not only

now, but also from now on.

By the example, this general determination of a way of acting

happens because the past experience shows that, in circumstances of a

certain sort, certain lines of action are preferable to others. But it may

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be that past experience never had happened in fact, that is, concretely

happened. According to the definition of belief, such link between the

attention to past memories and the present purpose, together with

selfcontrol, can be made in imagination. The example is clarifying and

explains in detail the process:

But habits are sometimes acquired without any previous

reactions that are externally manifest. A mere

imagination of reacting in a particular way seems to be

capable after numerous repetitions of causing the

imagined kind of reaction really to take place upon

subsequent occurrences of the stimulus. In the formation

of habits of deliberate action, we may imagine the

occurrence of the stimulus, and think out what the

results of different actions will be. One of these will

appear particularly satisfactory; and then an action of the

soul takes place which is well described by saying that

that mode of reaction ‘receives a deliberate stamp of

approval.’ The result will be that when a similar occasion

actually arises for the first time it will be found that the

habit of really reacting in that way is already established.

[CP 5.538].

Even though the assent, or “endorsement”, is not essential, that is

generally linked to practical beliefs. Practical beliefs, thus, involve an

act of assertion, that is, an assumption of responsibility before the

effects that a certain manner of conduct may have. It does not matter

which the conditions are, to act according to a practical belief is to

deliberately act according a previously settled standard, whther by

effectively past experience, whether by means of mental

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experimentations, to which the same endorsement is given. The chief

notion is the one of the temporal anteriority of that which bases the

decision to act following a certain pattern; to this base Peirce gives the

name of experience: “experience means nothing but just that of a

cognitive nature which the history of our lives has forced upon us.” [CP

5.539]. experience thus in its strong sense is characterized as the

cognitive outcome of living, source of concepts that have the force for

shaping human conduct, both present and future conduct. 89 This

definition of experience is highly important, and to it we shall return

other times from now on.

Theoretical beliefs, in turn, are more complicated. In the

sequence of the argumentation, Peirce comes to admit that theoretical

beliefs are indirectly practical beliefs. However, they are not only this.

Theoretical beliefs have a different status; the determination of a

general way to our actual future general conduct is not questioned, but

how this could happen. In the case of practical beliefs, if I believe the

proposition “Anthracite is a convenient fuel” is true, I will act so that to

use anthracite as a convenient fuel in certain circumstances. In the case

of theoretical beliefs, normative commitment is different: it is possible

that I believe in a proposition without establishing a definte habit of

conduct based in it; at the same time, it is possible to question a

proposition without discarding it for good, that is, without putting it

into doubt in a first moment. 89 Cf. IBRI (1992), p. 5.

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The first important thing to notice is that the distinction between

two kinds of practical beliefs, “those which are expectations, and those

which are not even that.” [CP 5.539, Reason’s Rules]. This discussion is

strategically important in so far as it involves the concept of experience.

First, we must notice that experience has teh character of fact; linked

to the past, for it is its outcome, experience inevitably imposes itself:

Laconically speaking, experience is esse in praeterito.

[…] Some fact there is. All experience compels your

acknowledgment. What, then, is the fact that is present

to you? Ask yourself: it is past. A fact is a fait accompli;

its esse is in praeterito. The past compels the present, in

some measure, at least. [CP 2.84, Minute Logic, 1902].

Imposed as it is, experience means effort, and brings with itself

the mark of duality between Within and Without: “a sense of effort and

the experience of any sensation are phenomena of the same kind,

equally involving direct experience of the duality of the Without and the

Within.” [CP 5.539]. Though Peirce adimts that every sensation carries

with itself the feeling of this duality, in the sensation of physical effort

this feeling is characteristically present, for there is no effort without

resistance to this effort. The duality then remains clearly and strongly

marked, and it is a clear sign of the reality of the outward world. To

Peirce, to deny this is of a foolishness characteristic of those who

ingenuous ideaists. He gives an ironic illustration to highlight this

point. Suppose an idealist philosopher comes wandering in the streets,

absorbed in musements about the doubtful existence of the external

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world. Suddenly, a drunk man punches the philosopher in the eye,

taking him out of this speculative world. This “unexpected” is a direct

experience of the duality that makes it impossible to neglected the

reality of the external world. “Experience”, Peirce says, “invariably

teaches by means of surprises.” [EP 2: 194, The Seven Systems of

Metaphysics, 1903]. The chief point is the contrast between an inward

mental state before the experience of this brute fact and the state of

sudden surprise after the same experience. The calm expectation of the

inward state was broken by duality, and the brute unexpected fact

replaced it by a state of surprise.

The difference between practical and theoretical beliefs, with this,

is formulated in the following terms: “In the light of these remarks, we

perceive that there is just this difference between a practical belief and

an expectation so far as it involves no purpose or effort; namely that the

former is expectant of muscular sensation, the latter of sensation not

muscular.” [CP 5.539]. Both are therefore expectations, and all

expectation is an anticipation of experience, to which assent is given or

not. A practical belief, hence, as a determined habit of action, is but the

expectation that the action shall happen in a certain way, if the

occasion arises in a certain way. Thus, in determining a general habit of

conduct, practical beliefs always involve the approvement of what is

expected, for they are entirely based upon what was deliberately

established as a pattern to be followed. It in this exact point that the

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illustration works: only by means of a surprise a genuine doubt has its

origin [EP 2: 348, Issues of Pragmaticism]. From the moment in which

something surprises me, so to change my inward peace of mind, it is

impossible to return to the same state as before. Even if I wanted to

doubt my positions and theories, before something external comes to

awake my attention, I would not get to doubt, for I would always be

immerse in what I already knew. In this sense, a belief is related to the

truth of its assertions, in a threefold commitment, referring to what can

be expected, to the circumstances under which it is possible to expect

and to the interpretation of the assertion of the belief:

The expectancy consists in the stamp of approval, the act

of recognition as one's own, being placed by a deed of

the soul upon an imaginary anticipation of experience; so

that, if it be fulfilled, though the actual experience will, at

all events, contain enough of the unexpected to be

recognized as external, yet the person who stands in

expectancy will almost claim the event as his due, his

triumphant “I told you so” implying a right to expect as

much from a justly-regulated world. A man who goes

among a barbarous tribe and announces a total eclipse of

the sun next day, will expect, not only “his” eclipse from

Nature, but due credit for it from that People. [CP 5.540].

When future experience happens according to what was

anticipated, our expectations are confirmed, and we feel rewarded by

facts. There is not, then, any surprise, and we feel satisfied. That

happens both in the case of practical beliefs and in the case of

theoretical beliefs. The example of the eclipse shows the point very

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well. To predict a solar eclipse is to make a scienctific assertion that

also brings expectations.

However, scientific expectations are a little different. It is possible

to question a proposition, as we have seen, but without putting it in

doubt. In other words, it is possible to hold up judgment in relation to

the truth value of certain propositions. This advisable exercise of

methodeutics, as Peirce says, is exactly what determines the specific

difference of theoretical beliefs. With “ca das crenças teóricas. “As to

purely theoretical beliefs not expectacious, if they are to mean

anything, they must be somehow expectative.” [CP 5.541]. At the same

time that to affirm a proposition means, to the scientist, a different

thing than to assert a proposition giving to it full assent, to believe that

things should happen in a certain way is different than believing that

things must happen in a certain way, in which they will happen.

Theoretical beliefs are grounded in past experience, they also can be

determined in fancy and they also have an expectational character, jsut

like practical ones. But, differently from the latter, they do not concern

the past, for they do not deal directly with experience, with the fait

accompli, but with what is expectable from experience in the future;

thus, they cannot concern a well determined manner of conduct, they

have to be connected to the future, that is, to ways of acting that are

not yet fully determined; they report themselves to the future without

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fixed commitments, therefore. The expectation they create is the one

that future events may come to happen to confirm or refute theories:

The word “expect” is now and then applied by careless

and ignorant speakers, especially the English, to what is

surmised in regard to the past. It is not illogical

language: it is only elliptical. ‘I expect that Adam must

have felt a little sore over the extraction of his rib,’ may

be interpreted as meaning that the expectation is, that so

it will be found when the secrets of all hearts are laid

bare. History would not have the character of a true

science if it were not permissible to hope that further

evidences may be forthcoming in the future by which the

hypotheses of the critics may be tested. A theory which

should be capable of being absolutely demonstrated in its

entirety by future events, would be no scientific theory

but a mere piece of fortune telling. On the other hand, a

theory, which goes beyond what may be verified to any

degree of approximation by future discoveries is, in so

far, metaphysical gabble. [CP 5.541].

As pointed out, to propose a scientific theory does not mean a

commitment with its truth. It means indeed to rely upon the capacity of

the theory to predict the future run of events, but a contingent future,

which may or may not happen as predicted. The scientist expects that,

if he lives time enough, or if inquiry continues indefinitely, his or her

beliefs would be confirmed. In this expectation there is not necessarily

any volition, but only an attitude of awaiting. As we said before, the

scientist waits to know, in an attitude that seeks to prevent every

striking occasion. In truth, the scientist seeks to anticipate surprise,

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anticipating the novelty. In this awaiting attitude, the scientist has to be

aware, observing in distance every detail.

This observing attitude, of detached awaiting, connected to a

craving to learn, is not easy to adopt. This cold detached attitude, not

mixing emotional involvement and inquiry, is decisive to reach truth.

Because it is an attitude, any one could adopt it; but even for scientists

it is difficult to get to maintain coldness and not being taken by

personal individual passions. This is something Peirce warns:

But veracity apart, do these people suppose that they can

make any pure observation unaffected by fancy passion

or accidental moods or states of the nerves? The most

trained scientific observers cannot do that; and as for

those who are undisciplined and who are unaware of this

weakness of human nature, especially when they are

dealing with a subject as momentous as the other world,

they are incapable of any approximation to it. A physician

won’t prescribe for himself. And if he has too much

interest in the matter to keep his observations cold,

ought not any ordinary person to e regarded as

incompetent to keep cool when an immortal destiny is in

question? [W 2: 345, Whewell].

If experience shows to the scientist enough for doubting the

theories, the scientist must draw assent out of them. If he, on the

contrary, seeks to defend them against all contrary evidences, the

scientific spirit is put aside, and the scientist will be more like the

practical man, who needs certainties to act hic et nunc; or closer to the

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professor, who needs to know to teach; or even of the religious man,

who is attached to dogmas.

Science, thus, would be the least conservative of human practices,

because it does not admit anything as definitely settled. At the same

time, it is possible to say that it is the most prudent of all practices,

since what the scientist does in the laboratory is only to test

hypotheses, to construct reasonings upon what has already been

proved, to test again, and so forth, avoiding to assert anything as a

categorical definite truth, for experiments may as well result otherwise

than expected. The scientist, because always trying before (and, in our

practical life, the chances to try before are reduced), is always trying to

prove redundancy, and seeking to avoid surprises: “But the influence of

the mind upon observations is not necessarily evil. It may almost be

said that we can only see what we look for.” [idem]. And, as we know,

even that one does not always find what one was looking for, that must

not be a reason for sadness. Someone, another inquirer, another being

or investigative mind will find.

Such parallel between decisions in science and decisions in

practical life brings another problem: to adopt science as a mode of life

is a practical decision of vital importance. Would not it be possible to

ask, then, whether in taking up this decision, one would make it acting

on the ground of full belief, that is, according to what was said,

adopting something which is out of place in science? In other words,

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the problem presented is that taking up the life of science is a vital

decision – but the life of science does not assume anything as vital! As

we will see further on, Peirce frequently points out that it is reasonable

to act based on what we do not believe, but that we hope to be true.

Remember the pragmatic maxim, in one of its late formulations:

Pragmatism is the principle that every theoretical

judgment expressible in a sentence in the indicative

mood is a confused form of thought whose meaning, if it

has any, lies in its tendency to enforce a corresponding

practical maxim expressible as a conditional sentence

having its apodosis in the imperative mood. [HL 110].

In this context, the meaning of a proposition will be expressed by

another proposition to describe all the phenomenal empirical

occurrences virtually predicted by the first proposition. The meaning of

a proposition is therefore given by a set of hypothetical propositions,

not in the indicative mood, but in the subjunctive mood, which express

a law or willingness to act according to a habit-belief, making up its

ultimate interpretation, yet provisional and incomplete:

I deny that pragmaticism as originally defined by me

made the intellectual purport of symbols to consist in our

conduct. On the contrary, I was most careful to say that it

consists in our concept of what our conduct would be

upon conceivable occasions. [CP 8.208, letter to Signor

Mario Calderoni, c. 1905].

In total agreement with this form of presenting the pragmatic

maxim, there is the idea expressed in 1878, about the difference

between doubt and belief:

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Belief does not make us act at once, but puts us into such

a condition that we shall behave in a certain way, when

the occasion arises. Doubt has not the least effect of this

sort, but stimulates us to action until it is destroyed. [W

3: 247, The Fixation of Belief, 1877].

Doubt justly prompts to action. People act because they believe in

the efficacy of their actions. Belief, from this standpoint, is seen as a

habit of mind that determines conduct, as a rule of action. This habit is

shaken when an unpredicted striking situation arises, demanding a

change in attitude. The unquiet state caused by doubt demands to be

dismissed, as soon as possible, and it becomes the mobile of action: it is

necessary to inquiry to end doubt. The pragmatic maxim establishes

how doubt would be dismissed if certain conditions were settled:

But [pragmatism asserts], that the total meaning of the

predication of an intellectual concept is contained in an

affirmation that, under all conceivable circumstances of a

given kind (or under this or that more or less indefinite

part of the cases of their fulfillment, should the

predication be modal) the subject of the predication

would behave in a certain general way – that is, it would

be true under given experiential circumstances (or under

a more or less definitely stated proportion of them, taken

as they would occur, that is in the same order of

succession, in experience). [CP 5.467, Pragmatism, c.

1905].

To say “A diamond is hard” (or to say that it has any other

property) is to say that the diamond is subjected to the law, i.e., to a

general mode of determinate conduct, and that, for that reason, it is to

say that in the future it is expectable that the diamond shows certain

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characters; in other words, if the diamond be scratched one day, it may

not come to be damaged – if it be damaged, that will be a surprise,

which will lead to inquiry into the causes of such unforeseen

occurrence. In other words, the rational purport of a word, expression

or sign lies only in its influence over the conduct of life [EP 2: 332,

What Pragmatism Is]. It is not a mere criterion for verification,

therefore; rather, it is a criterion for ascertaining meaning –

independently of experiential verification, the reality of the hardness of

the diamond is expressed in a proposition which is true, general, and

conditional: “if a substance of a certain kind should be exposed to an

agency of a certain kind, a certain kind of sensible result would ensue,

according to our experiences hitherto.” [EP 2: 357, Issues of

Pragmaticism]. Thus, it is possible to conclude that the meaning of a

habit of action will depend upon the manner how a real objective

possibility can be actualized90, that is, in the way how some one subject

passes from possible immateriality to the concretion of action in

experience, driven according to a general rule to the future, in a

prospective movement which goes from dýnamis to

enérgeia.

In the parallel between science and morality, we can single out

points of contact. Science also concerns individuals. Even though a

moral code concerns the customs of a community, it is to individuals

who follow folkloric rules of conduct that it is directed; the individuals 90 MAGALHÃES (1984), p. 186; IBRI (1992), pp. 99 ff.

322

must behave in a certain way. In the same way, the Peircean definition

of science, with its strongly ethical exigencies, also imposes some lot of

moral commandments over individual scientists. We must notice,

mainly, the weight given to the cooperation among individuals: they

must put aside all personal beliefs, considering them as provisional, for

the sake of the Will to Learn [CP 6.3, The Logic of Events, 1898]; they

must share the results attained in their particular investigations; they

must, above all, remain open to criticisms and to submit their studies to

the criticisms of other inquirers, for the sake of discovering truth, as

well as to be ready to criticize and evaluate other researches when

needed. Science, therefore, naturally comes to be a public activity. It is

not only to address the problem of how individuals behave, but of which

are the ends they choose to themselves, in what regards the conduct of

their lives in an inquiry that seeks to discover something independent of

them. A scientist is someone who does not have personal commitments

to block the discovery of a truth of universal value, that is, “one that

goes toward enlarging the system of what is already known.” [EP 2: 48].

This cooperation among individuals makes science a public activity,

which main feature is to be a living and ever changing process:

But if I am asked to what the wonderful success of

modern science is due, I shall suggest that to gain the

secret of that, it is necessary to consider science as

living, and therefore not as knowledge already acquired

but as the concrete life of the men who are working to

find out the truth. Given a body of men devoting the sum

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of their energies to refuting their present errors, doing

away with their present ignorance and that not so much

for themselves as for future generations and all other

requisites for the ascertainment of truth are insured by

that one. [CP 7.50, probably c. 1882]

The public agreement and sharing of theories, results,

conclusions, and methods is considered by Peirce as of central

importance to science as he understands it. This agreement is not

limited to human life though. The consensus on scientific truth has to

be really universal:

And the catholic consent which constitutes the truth is by

no means to be limited to men in this earthly life or to the

human race, but extends to the whole communion of

minds to which we belong, including some probably

whose senses are very different from ours, so that in that

consent no predication of a sensible quality can enter,

except as an admission that so certain sorts of senses are

affected. [W 2: 470, Fraser’s Works of George Berkeley,

1871].

Science, in this way, has as its basis for evaluation only and

exclusively a reality that is independent of subjective vicissitudes. It is

fundamental to emphasize the communicative dimension of science: if it

aims at discovering a truth about a reality, which is independent of our

human conceptions, it is a necessary consequence that this true be

valid also to other beings that are not humans. For instance, if it is true

that fire burns, this truth must be verifiable also in such cases, wherein

human sensibility is not at stake: the truth of the proposition must

describe a factual occurrence truly universal, capable of being

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perceived by all beings – humans, vegetable, aliens, or of whatever

other nature. That is what would allow truth to be communicated

beyond the limits of human consensus.

Let us keep two main ideas, namely, that the scientific inquiry,

such as thought by Peirce, should work on the supposition that its

representations are valid because in first place they describe well the

manner of occurrence of facts, that is, it is a realist conception of

science, wherein reality imposes itself and determines the sign; in

second place, because every scientist must be immersed in a

community of inquiry to the point of being able to work on at and

develop other inquiries different from his or her own, with methods

which are not properly his or hers, but always keeping the same aim of

discovering truth, regardless its further use. In other words, if there is

not the pure wish to learn, there will not be genuine science – and, we

could say that, if there really are scientists devoted to this genuine

search, there is science:

Science consists in the sincere and thorough search for

truth according to the best available methods. Its only

quite indispensable condition is the absolute single-

hearted energy with which it works to ascertain the

truth, regardless of what the character of that truth may

be. It is not science if it is not an intelligently directed

research. But it will come to be so if it is absolutely

sincere and highly energetic. These dispositions will

generate the intelligence required. It is not science, if it

is not a well-informed research. But sincerity and energy

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will bring about study. It is not science if it does not

invent cunning ways… [NEM 4: xix, s/d].

It can be said that it would be foolishness to exclude from the

scientific community, for instance, those whose aim is to improve

people’s lives. If the true will to learn is present, sooner or later the

study will be genuinely scientific, just as the practical utility of its

discoveries may be, in one way or another, sooner or later, also found.

That does not change the fact, though, that science has as its aim above

all others the discovery of truth, this being its supreme value, in face of

which all the others have to be considered collateral, and because of

which all inquiry is possible to become really scientific. Peirce steadily

affirms:

True science is distinctively the study of useless things.

For the useful things will get studied without the aid of

scientific men. To employ these rare minds on such work

is like running a steam engine by burning diamonds. [CP

1.76, Lessons from the History of Science, 1896].

The point is that the discovery of truth is the only thing of

supreme interest of the genuine scientist. Peirce does not say that the

summum bonum of scientific inquiry has not value – in fact, it is the

most valuable. He says that the inquiry and the Will to Learn must be

taken in genuine science as having a value per se – as ends in

themselves, and not because they make us reach something else, or

because of other things we can make or discover through them. It a

study of the useless that reveals an “interest by disinterest”91, a

91 BOURDIEU (2003), p. 31

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disinterested interest. Peirce was completely contrary to any kind of

scientific utilitarianism; for him, questions of practical utility should be

“put out of sight” by the scientist [RLT 113]. For instance, take the

particularly interesting following passages:

To demand that man should aim at the stability of British

society, or of society at large, or the perpetuation of the

race, as an ultimate end, is too much. The human species

will be extirpated sometime; and when the time comes

the universe will, no doubt, be well rid of it. […]. I do say,

however, that truth is truth, whether it is opposed to the

interests of society to admit it or not – and that the notion

that we must deny what it is not conducive to the

stability of British society to affirm is the mainspring of

the mendacity and hypocrisy which Englishmen so

commonly regard as virtues. I must confess that I belong

to that class of scalawags who purpose, with God's help,

to look the truth in the face, whether doing so be

conducive to the interests of society or not. Moreover, if I

should ever attack that excessively difficult problem,

“What is for the true interest of society?” I should feel

that I stood in need of a great deal of help from the

science of legitimate inference; and, therefore, to avoid

running round a circle, I will endeavor to base my theory

of legitimate inference upon something less questionable

– as well as more germane to the subject – than the true

interest of society. [EP 2: 60-61, Pearson’s Grammar of

Science].

What to do with the resulting knowledge from scientific inquiry is

an important question, but secondary, given the nature of the scientific

practice. The question about the utility or practical usefulness cannot

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be taken as the primordial problem according to which we should

concentrate our efforts. That would prevent deviations of purposes, for

instance, as it is seen in the very common conceptual confusions

between science and technology, broadly understood as the application

of the results of the research; but technology cannot be taken as an end

in itself. 92

The political dimension is here, as it is easy to notice, extremely

important. Mainly in Pearson’s book review, Peirce directs hard

criticisms to the way science is made in his days, criticisms that could

very well be kept nowadays:

The worst feature of the present state of things is that

the great majority of the members of many scientific

societies, and a large part of others, are men whose chief

92 According to our knowledge, Peirce rarely uses the word “technology”. However, we believe that the context of the discussions is clear enough to support our account. See, for instance, the context in CP 7.279, undated, wherein he uses “technique” in opposition to creative work; this, however, is not enough to say that technological work is necessarily and exclusively an ideological work directed to make money, for instance. The problem is not of technique in itself, but of the applications made of it, that is, what technique is desired for; for such reason, we prefer to contrast Peirce’s conception of science to the idea of technology. In first place, because technology, differently from mere technique, has heuristic potency, for it involves the formulation of theories, as the name itself points out, linking logic and technique; in second place, because contrarily to science, in the Peircean sense, technology directs its power to the discovery of previously determined ends. Technology, then, can lead to unforeseen discoveries, but its ultimate aim is not the discovery of the new. Furthermore, nowadays, technological ends, if not entirely, in great part are determined by the productive process. Cf. APEL (1995), pp. 192-193; HAACK (1997), pp. 241-261; SANTAELLA (1992), p. 109, makes an interesting remark: “In fact, it would be incurably ingenuous nowadays to ignore the increasing incorporation of the sciences by the hungry jaws of the productive process, a process from which result small differences between the mode of life of a great part of the scientists and the life of CEO’s of big corporations, for instance.” [Seria, de fato, de uma ingenuidade incurável ignorar atualmente a crescente incorporação das ciências às famintas mandíbulas do processo produtivo, de que resultam pequenas diferenças entre o modo de vida de boa parte dos cientistas e a vida de executivos de grandes empresas, por exemplo.].” Our translation.

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interest in science is as a means of gaining money, and

who have a contempt, or half-contempt, for pure science.

Now, to declare that the sole reason for scientific

research is the good of society is to encourage those

pseudo-scientists to claim, and the general public to

admit that they, who deal with the applications of

knowledge, are the true men of science, and that the

theoreticians are little better than idlers. [EP 2: 60-61,

Pearson’s Grammar of Science].

Science as a market business, technique and science as ideology,

these are dear themes to the 20th century, themes Peirce in the 19th

century was aware of. The business of scientific inquiry, science’s

autonomy in relation to the broader social context, wherein science is

inserted and to which it pertains, hypocrisy found where it is not

expected to be found, against all of this Peirce proposes sincerity,

single-heartiness and obstinacy, as the power of what is genuine and

simple. With vigorous statements he attacks the ideologically forwarded

confusion between science, as inspirited by a pertinacious desire to

learn the truth, whatever it is to be learnt, and the application of the

results of the inquiry, guided by undeclared or suspicious interests. He

also condemns the political-ideological discourse that takes advantage

of this confusion to justify itself to the “general public”, when in fact it

is supported by economic motives. In fact, the relations of force and the

concentration of money and power in scientific production are due to

the fact that the social world of science depends, to its survival as

research in the contemporary world, upon economic decisions that are

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taken outside its own limits – and such economic decisions give power

and prestige to certain agents inside the scientific community. This is

something Peirce attacks when he speaks about “making science as a

means to make money”: to direct the researches to vindicate the

pretensions of validity of an ephemeral society, or, what is worst, to

make money, this is but another form, maybe one of the worst forms of

utilitarianism, individualism and immediaticism, in vogue since the

beginning to the capitalist industrial society, which transforms science

in a myth, a mere ideology at the service of the justification of a

perverse technocratic system. In short, two aspects of a myth of science

can be refuted on the grounds of Peirce’s position: first, the illuminist

illusion that necessarily unites epistemic progress with social progress;

second, the idea that the means of access to the scientific production

have to be necessarily restricted to channels for distributing

technology. Science as a collective activity is communicative, and the

means of access to it should be overtly public; the production of

technological objects is only one way, among many others, of having

access to scientific production, contrary wise to what may seem, when

inquiry is subordinated to the straight interests of private social groups.

The Peircean conception of science appears as a conceptual

alternative to think the autonomy of the scientific activity in relation to

the external forces and pressures over it, pressures which try to reduce

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the inquiring activity to a productive activity. In other words, the

internal coherence of the scientific “social group”, according to Peirce,

is given by the fidelity to the phenomena, and not by the fidelity to the

community, whatever it is. This is the only way to make genuine

science, and not science for the advancement of society, mean it

whatever it may mean. The internal coherence thus appears to

scientists as a consequence of the unity of aims, methods and spirit

characteristic of their fidelity to phenomena. This is a problem which is

inherent to scientific production: it is always made by a certain group of

people with a certain interest – yet the result of the researches do not

necessarily have to always be a grotesque and direct answer to the

needs of their authors. Inquiry will always be, because of that unity,

theoretical and empirical; the concepts cannot, for such reason, be

discussed in themselves, but always in regard to what they try to

describe – what interests in this discussion is to put the aims in doubt.

There is this long passage wherein Peirce discusses the relation

between efficient and final causality in science, that is, in what manner

the adoption of diverse means can lead to the same conclusion:

One man may investigate the velocity of light by studying

the transits of Venus and the aberration of the stars;

another by the oppositions of Mars and the eclipses of

Jupiter's satellites; a third by the method of Fizeau; a

fourth by that of Foucault; a fifth by the motions of the

curves of Lissajoux; a sixth, a seventh, an eighth, and a

ninth, may follow the different methods of comparing the

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measures of statical and dynamical electricity. They may

at first obtain different results, but, as each perfects his

method and his processes, the results are found to move

steadily together toward a destined centre. So with all

scientific research. Different minds may set out with the

most antagonistic views, but the progress of investigation

carries them by a force outside of themselves to one and

the same conclusion. This activity of thought by which we

are carried, not where we wish, but to a foreordained

goal, is like the operation of destiny. No modification of

the point of view taken, no selection of other facts for

study, no natural bent of mind even, can enable a man to

escape the predestinate opinion. This great hope is

embodied in the conception of truth and reality. The

opinion which is fated to be ultimately agreed to by all

who investigate is what we mean by the truth, and the

object represented in this opinion is the real. That is the

way I would explain reality. [W 3: 273, How to Make Our

Ideas Clear, 1878].

Those who engage in scientific inquiry must trust that if the

inquiries are carried on long enough they will reveal a truth to us.

Because the real will always be there, insisting, remaining, and

directing our questions; it is certain that a given time will come when

we will not be able to disagree with it. We trust truth will be reached

one day because all other reasonings from all other investigators

support ours, for they also are directed by the real; we also know that

reasonings are the result of ages of experience, attempts, mistakes and

corrections. Of course, we may be wrong. But, in the scientist the will

to learn lives, the will to discover truth – and even that there are

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reasons to doubt this will, we should not give up trying, for that would

mean the assumption that there is nothing else to seek, nothing to

search for, that is, it would mean to assume that everything is already

in our hands.

The man of science has received a deep impression of the

majesty of truth, as that to which, sooner or later, every

knee must bow. He has further found that his own mind

is sufficiently akin to that truth, to enable him, on

condition of submissive observation, to interpret it in

some measure. As he gradually becomes better and

better acquainted with the character of cosmical truth,

and learns that human reason is its issue and can be

brought step by step into accord with it, he conceives a

passion for its fuller revelation. He is keenly aware of his

own ignorance, and knows that personally he can make

but small steps in discovery. Yet, small as they are, he

deems them precious; and he hopes that by

conscientiously pursuing the methods of science he may

erect a foundation upon which his successors may climb

higher. This, for him, is what makes life worth living and

what makes the human race worth perpetuation. [EP 2:

58, Pearson’s Grammar of Science].

The passage above indicates that science is prospective, it is yet

an unfinished work: opposed to the recognition of the esse in praeterito,

science views an esse in futuro which is unknown [CP 2.148, Minute

Logic, 1902]. As Apel says, “the world cannot be known or explained

merely by its previously fixed, lawful structure, but must rather

continue to be developed as a historical, social world of institutions and

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habits for which we must assume responsibility”93. In the passage above

we also see more details to help to understand the scientific attitude:

first, the scientist waits, looking ahead to the possible confirmation of

the theories, hoping his or her inquiry is a small contribution to a

broader inquiry, with a supreme objective: to bring human mind in

agreement with the universal cosmic mind. The scientist’s most sincere

belief is to be able to construct a step above which others may climb, to

reach a higher point, in the future. For that reason, the scientist has an

anticipatory attitude: the truth is thought of as a project yet to be

accomplished. Now, to think truth as a future project still yields room

for manipulations, and the criticisms Peirce directs to pseudo scientists

go straight to this point: we have to assume responsibility on what we

help to create, a responsibility to the future generations, to the

perpetuation of the species. Who produces knowledge? To whom? In

the name of what? With what means – technological, economic? All such

questions deepen the criticisms to the ideological manipulation of

science. To Peirce, the word science “embodies the epitome of the

intellectual development” of human being; the conception of scientific

inquiry concerned primarily and ultimately with a heuristic activity,

teleonomically oriented to a truth we do not know, works in a way to

counterbalance the conception of science as a rational and

systematized knowledge, which is certain and directed to a determined

objective, oriented to the past, therefore. 93 APEL (1995a), p. 193.

334

Peirce’s writings, thus, show to be very important for us. They

remind us that even if we take everything we know as our ground,

absolute certainty in any subject-matter is impossible. Even we find

some definite experience about some subject-matter he says “reasoning

will, from the nature of its rules, be able to draw some inference from

it, whether with great or little confidence.” [W 2: 353, Rules for

Investigation, 1869-1870]. For that reason, we can never have any

pretension to the necessity, universality and absolute certainty of our

propositions. The base of knowledge will always be cultural, historically

built during the centuries – a provisional ground, therefore.

We cannot, therefore, throw this knowledge away and go seeking

for unquestionable grounds, which are certain, indubitable, and

absolute. Inquiry always begins with some kind of disagreement, and it

is exactly to reach agreement that it begins, looking for the reasons of

the disagreement. It does not matter how provisional our knowledge is,

it is all we have, and at the same time it is only what we have. As it is

not absolutely certain, we can only hope to be in the right track, even

though we know our track is not the only track – remember nothing is

vital in science, not even science itself. Therefore, it may take a long

time, but inquiry will be released from the instabilities of the present –

of the immediate practical aims, circumstantial political pressures, and

religious dogmas. Inquiry carried on long enough would reverse any

and every opinion, putting truth always in the future: the opinions of

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now are always provisional, and we have to put up with it. The long

time inquiry may last is long only for us, human beings, if we consider

the duration of the universe. The time of truth for the inquiry, as in

Bandeira’s poem, never is – will be.

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8. THE GENEALOGY OF THE SCIENCES

Der Mann war noch nicht auf der Welt, der zu seinen Gläubigen hätte sagen können: Stehlt, mordet, treibt Unzucht – unsere Lehre ist so stark, daß sie aus der

Jauche eurer Sünden schäumend helle Bergwässer macht; aber in der Wissenschaft kommt es alle paar Jahre vor, daß etwas, das bis dahin als Fehler galt, plötzlich alle Anschauungen umkehrt oder daß ein unscheinbarer und verachteter Gedanke zum Herrscher über ein neues Gedankenreich wird, uns solche Vorkommnisse sind dort

nicht bloß Umstürze, sondern führen wie eine Himmelsleiter in die Höhe. Es geht in der Wissenschaft so stark und unbekümmert und herrlich zu wie in einem Märchen.

Robert Musil, Der Mann ohne Eigenschaften.

The aim of every classification of the sciences is to settle an order,

in things and in the thought of things. When one tries to classify

sciences in a certain point of their evolution, this undertaking gives a

faithful yet provisional image of the scientific knowledge of that age.

The classification, by making it possible to be conscious of our

knowledge through such inventory, also works as a spatial-temporal

map of the intercrossing of the cultural ideas of a given period. The

value of a classification of the sciences, however, goes far beyond that

of a mere inventory or “table of contents”, no matter how complete it

may be. The very fact that the classification depends on logical criteria,

which by nature may be objective or subjective, already gives us an

initial idea of the obstacles posed to the classifier, difficulties which are

rarely found in other types of classification, as the preparation of a

catalogue, for instance. Therefore, an effort which is successfully

brought about may serve to lead us to discover the connexions and

analogies between the different fields of knowledge, in a certain time,

within a given social-historic more or less well defined period. The

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classification of the sciences, therefore, is a picture of a moment of a

civilization. Nevertheless, history and stasis are repealing concepts – all

history is a process in continuous development, an incomplete and very

problematic attempt of reconstructing something which does not exist,

for its very object, when it is past, can only be viewed with the eyes of

the present; and, when one tries to make the history of the present, the

present is no more. We are, hence, obliged to consider the study of

sciences and their classification essentially as a historic process, which

is subject to changes and hence in continuous development.

All such previous considerations, in what regards our present

work, can be summed up in the following way. The question about the

possibility of a classification of the sciences can be understood in a

twofold ways: the first, relative to the normative stress of a general

classification of the sciences, for it is needed to say how sciences should

be organized one in relation to the others; the second, in relation to the

inevitable descriptive task that such a classification has to involve.

Thus, a classification of the sciences is possible only if it concretely

accounts for what each particular science is, and how it is produced.

Peirce could not be satisfied with some abstract definition of science,

for as a scientist himself, he knew that abstract definitions could be

sooner or later overcome, due to new discoveries, fusions of methods

and even to criticisms.

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To look at what really happens with scientists, when in the

process of investigation, is the key to the classification of the sciences

he offers. Thus, we have to understand what we previously said in the

following way: even though some may conduct scientific inquiries

without the exclusive wish to learn, it would be foolish to put them

aside and say that they do not make part of the scientific community,

because, in fact, that is what happens. He states this because he

considers a mistake of other classifications to try to classify the possible

sciences, and not the present ones; i.e., to attempt at a classification of

which sciences will be in the remote future:

Many of these schemes introduce sciences which nobody

ever heard of; so that they seem to aim at classifying, not

actually existent sciences, but possible sciences. A

somewhat presumptuous undertaking is that of

classifying the science of the remote future.94 [EP 2: 115,

On Science and Natural Classes].

This is a mistake we consider a consequence of what Peirce

himself knew very well to be the case, i.e., that even though there is a

classification to establish limits and demarcations, “boundary lines in

some cases can only be artificial” [EP 2: 125, id.]. In not recognizing

this, the classifications commit the mistake of in general imposing

limiting and abstract definitions with the purpose to fix precise

94 The same idea, slightly modified, appears in the following passage: “But there is one monstrous fault that seems to be common to all published classifications; namely, it is that they attempt, apparently, upon a basis of experience to pronounce upon what sciences are the only ones possible. I shall not venture upon that attempt, but shall confine myself to the sciences that either exist, or whose birth seems to be promised.” [MS 655: 16, Quest of Quest].

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domains, exactly where it is impossible to draw a clear and precise

demarcation line. The way sciences develop, the mode scientists

effectuate their investigations breaks up classificatory lines, showing

the impossibility of the absolute determination of the limits of human

knowledge – for it is a fact that there is a transmission of knowledge

from generation to generation, resulting in a continuous progress in our

knowledge of the world, what means that at least an increase of

meaning there is in the concepts used. Here we have again the idea

that science is a public communicative activity, wherein it is impossible

to separate the individual work from the collective work of all: “what

we mean by science is the sum of human activity at any epoch in the

path of discovery” [N 1: 156, 1892].

Now, if science is made of collaborations between scientists, if

science means the sum of human activities in the pathway of Discovery,

the classification of the sciences has to take into account the

intercrossing of activities that renders impossible the definite

distinction between one science and another: the work in one science

implies the work in all the others. The development of science happens

by means of collaborations between scientists, through dialogues and

argumentations, acquaintance with what was done before to the

recognition of one’s own work as a part of a bigger work; hence,

boundaries frequently would be very easily blurred, because science

constantly changes: ““Science is not a fixed, unchangeable body of

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propositions.” [N 2: 213, 1899]. Thus, the historic development of

science is understood by Peirce as a process by means of which each

individual inquirer adds something, the small it may be, to the universal

investigation:

The man of science has received a deep impression of the

majesty of truth, as that to which, sooner or later, every

knee must bow. He has further found that his own mind

is sufficiently akin to that truth, to enable him, on

condition of submissive observation, to interpret it in

some measure. As he gradually becomes better and

better acquainted with the character of cosmical truth,

and learns that human reason is its issue and can be

brought step by step into accord with it, he conceives a

passion for its fuller revelation. He is keenly aware of his

own ignorance, and knows that personally he can make

but small steps in discovery. Yet, small as they are, he

deems them precious; and he hopes that by

conscientiously pursuing the methods of science he may

erect a foundation upon which his successors may climb

higher. This, for him, is what makes life worth living and

what makes the human race worth perpetuation. [EP 2:

58, Pearson’s Grammar of Science, 1901].

The way, then, to avoid an arbitrary schematization would be to

propose a classification based upon what in fact happens in scientific

inquiry; in other words, a natural classification is needed, because it is

related to the way how science is made, that shows the degrees of

interdependence and specificity among sciences.

What is the precise status of such classification? Let us see its

conditiones sine quibus non. At the same time that, to reach a natural

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classification it is imperative to consider science as it is presently made,

it is also needed to look a little bit ahead, not to lose sight of the

possible development of the sciences: “our classification ought to have

reference to the science of the future, so far as we are now able to

foresee what the future of science is to be” [CP 7.56, Of The

Classification of the Sciences. Second Paper. Of the Practical Sciences,

c. 1902]. This reference to the future, of course, can only be to the close

future – science, as we said above, changes, and this makes it

impossible to foresee its development in a very distant future:

[…] it is plainly important that our notion of science

should be a notion of science as it lives and not a mere

abstract definition. Let us remember that science is a

pursuit of living men, and that its most worked

characteristic is that, when it is genuine, it is in an

incessant state of metabolism and growth. [EP 2: 129, On

Science and Natural Classes].

Therefore, the presumption to try to look very far, to the remote

future, is a vain presumption, when it is the case to understand

scientific knowledge. Thus, the first thing a natural classification of the

sciences is not, it is not a classification of the sciences in the distant

future, simply because these future sciences are yet to be – they do not

exist. To try to classify sciences in this ways would be a methodological

lethal mistake, in so far as science is an activity brought about by living

people, and nothing warrants they remain in creative stasis; on the

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contrary, they are in constant mutation, for they make part of life in

movement.

There are several statements in Peirce’s writings on the necessity

of a natural classification that would classify the different objects of the

different sciences in the present state of inquiry, as well as the activity

exerted by scientists in their practice; furthermore, it could also give a

brief view of their possible developments in the next future. Such

classification, in this way, accounts for the temporal development of the

sciences, chiefly accounting for how they became what they are, and

what they might likely turn out to be, only in the very close future.

According to Peirce, a natural classification of the sciences necessarily

has to show sciences in their historic development, as if it was “a

classification which displays, in a useful way, the principal general

relations which we have learned from observation concerning the more

important resemblances and differences of the objects classified” [N 3:

170, 1904]. It cannot be a forced classification, that is, a classificatory

model imposed over the facts. The scope of a natural classification is

“to embody the chief facts of relationship between the sciences so far

as they present themselves to scientific and observational study.” [MS

1334: 11/12]. In other words, the classification of the sciences should

be an “usefully expressive diagram of the meaningful inter-relations” of

the sciences [NEM 4: 227].

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Related to the way how science is produced, the classification

proposed by Peirce will be such a diagram, wherein all the science s

may be simultaneously seen, wherein all scientific activities will be

presented in communication one with another. In his logical notebook,

on 5 September 1906, Peirce wrote on his concept of a diagram. The

purpose of a diagram is:

[...] to represent certain relations in such a form that it

can be transformed into another form representing other

relations involved in those first represented and this

transformed icon can be interpreted in a symbolic

statement. It is necessary that the Diagram should be an

Icon in which the inferred relation should be perceived.

[…] No other kind of sign can make a truth evident. For

the evident is that which is presented in an image,

leaving for the work of the understanding merely the

Interpretation of the Image in a Symbol. [MS 339 D:

544].

Without going further in deep semiotic discussions, for it is not

our aim, we can say that the general idea shown in the passage above is

clear enough. The diagram must be vague enough to allow further

interpretation, that is, it must be vague enough to make us see its scope

in the way it pictures certain logical relations; however, it must have

sufficient precision to present, as a picture, the relations the objects

classified entertain one another. In Santaella’s words, the Peircean

classification of the sciences is like a true “cartography” of the

sciences95. The diagram, therefore, has an abstract generality that

95 SANTAELLA (1992), p. 101.

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pictures the structural homologies. It is this same abstract generality

that makes it possible to be open to the representation of processes in

development, once the diagram represents relations in a way that can

be transformed; it is a “mobile and dynamic diagram, flexible to the re-

adaptations demanded by the passage of time” 96. In the case of the

classification of the sciences, it means that a natural classification

would have to be sufficiently clear to show the relations of

interdisciplinarity, dependence and evolution among the sciences,

putting to light the historic-temporal dimension of scientific enterprises.

Thus, the diagram of the classification of the sciences would make

the relations of dependence among the sciences evident; such relations

would not be necessarily relations of hierarchy. In presenting the

relations between the various scientific activities in an evident manner,

the diagram of the classification shows how it is possible in the various

ways of approaching the objects to work with the various sciences at

the same time. The diagram, then, makes it possible to pass from the

plan of simultaneity to the plan of sequentiality. By its form of display,

the diagram makes us see the relations, without putting them into a

96 Idem, ibid. Santaella also says, continuing: “The Peircean classification of the sciences, far from working only as a classification in the strict sense, in fact serves as a guide, chart of orientation for those who wish to thread, with some accuracy, the dense forest of the sciences. [A classificação peirciana das ciências longe de funcionar apenas como uma classificação em sentido estrito, serve, na realidade, como guia, carta de orientação para aqueles que desejam percorrer, com alguma acuidade, a espessa floresta das ciências.]” (1992), p. 101.

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hierarchy, however, leaving thus the interpretations of such relations

undetermined.97

In general lines, the nature of a natural classification of the

sciences is then defined: it has to be a representative diagram of the

inter-relations of the sciences, vague enough to allow further

interpretation and change if needed (therefore, we do not need a

classification of the sciences to tell us what to do with our knowledge,

even because it is already used before classifying the sciences), for it

must show where sciences come from, and whereto they may develop in

the close future; it must be also precise enough so that we do not lose

sight of the relations of dependence and overlapings among the various

scientific domains.

Nevertheless, it is not only this. It also necessary to understand

what is a natural class. According to Peirce, the classification will be

natural only if it is a classification of objects capable of some kind of

description, which is the only possible way to correspond to real

empirical objects. This implies that objects must have some common

character in common capable of description, i.e., this common

character will be like a criterion to put them under a determined class,

and not under another. For Peirce, the only possibly natural

classification would be one that would consider the objects from the

97 For more details on the concept of diagram, see. EP 2: 207, The Three Normative Sciences, 1903; 212, The Nature of Meaning, 1903; 303, New Elements (), c. 1904; LEO (2002), pp. 56 ff.; IBRI (1994), pp. 124 ff.

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point of view of their aims, what they must be, in a word, from the

standpoint of their final causes:

A class, of course, is the total of whatever objects there

may be in the universe which are of a certain description.

What if we try taking the term "natural," or "real, class"

to mean a class of which all the members owe their

existence as members of the class to a common final

cause? This is somewhat vague; but it is better to allow a

term like this to remain vague, until we see our way to

rational precision. [EP 2: 117, On Science and Natural

Classes].

This is the principle that informs Peirce’s classification of the

sciences. In effect, to him, “Every classification has reference to a

tendency toward an end. If this tendency is the tendency which has

determined the class characters of the objects, it is a natural

classification.” [NEM 4: 65, Carnegie Application]. About aiming at

ends, Peirce declares98:

[…] we must understand by final causation that mode of

bringing facts about according to which a general

description of result is made to come about, quite

irrespective of any compulsion for it to come about in this

or that particular way; although the means may be

adapted to the end. The general result may be brought

about at one time in one way, and at another time in

another way. Final causation does not determine in what

particular way it is to be brought about, but only that the

result shall have a certain general character. [EP 2: 120,

On Science and Natural Classes].

98 From this point on, we follow the account given by HULSWIT (2002), pp. 76 ff.

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It is important to notice that in the passage above the concept of

final cause is not defined, but only that it is said what is the process of

final causation, i.e., how the process comes about to a final cause.

According to what was said above, it is a process of actualization of a

certain general form to which events must come to agree [N 1: 200,

1893]. We find what Peirce means by final cause in another passage:

“Now, what is a ‘final’ cause? It is merely a tendency to produce some

determinate kind of effect having some relation to the destiny of

things.” [EP 2: 464 n., An Essay toward Improving Our Reasoning in

Security and in Uberty, 1913]. Final causes, then, are not something

actually and concretely existent, but rather a mere possibility that the

facts come to unfold in a certain way with a view to a certain kind of

end:

By a tendency to an end, I mean that a certain result will

be brought about, or approached, and in such a way that

if, within limits, its being brought about by one line of

mechanical causation be prevented, it will be brought

about, or approached, by an independent line of

mechanical causation. […] An end is an intellectual idea

[…]; every intellectual idea governing a phenomenon

produces a tendency toward an end. [NEM 4: 65; 66].99

Now, we have seen that final causes, to Peirce, are general forms

to which events tend in a defined process. They determine the sort of

events that are being caused now by efficient causes. And the process

of actualization of forms acquires sense just by the tendency the facts

99 Cf. SANTAELLA (1999), for a more thorough discussion on the processes of final causation in nature.

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have to conform to certain ends. This is the meaning in saying that

independent lines of mechanical causation run to the same end: it is

possible to attain the same general aims through several lines of action.

The discussion here is about what is normally called teleological

process, i.e., processes that tend to a final ideal state. The emphasis of

Peirce’s writings is not over the determined manner in which events

happen; we have just seen, it is possible that different lines of action

lead to the same final result. The emphasis is in attaining one final

state, and not another. Once this final state is achieved, it is not

possible to go back, for it is not possible to reverse the lines of

mechanical causation that have acted; in other words, it is not possible

to change the efficient causes because they were actualized already.

This leads us to another character of processes of final causation, such

as Peirce understands them, which is that of being irreversibly oriented

toward a certain direction:

Those non-conservative actions which seem to violate the

law of energy, and which physics explains away as due to

chance-action among trillions of molecules, are one and

all marked by two characters. The first is that they act in

one determinate direction and tend asymptotically

toward bringing about an ultimate state of things. If

teleological is too strong a word to apply to them, we

might invent the word finious, to express their tendency

toward a final state. The other character of non-

conservative actions is that they are irreversible. [RLT

220].

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As Putnam says, this reveals Peirce’s commitment to an

irreversible conception of time; in other words, we can say that the past

is definitely determined, the future is undefined, and the present is a

state of absolute now [RLT 96]. Finious processes, then, are those

wherein there is a tendency to a general determined end, not being

possible to explain the process by the indication of which forces operate

in it, that is, only by indicating its efficient causes: it is also needed to

indicate how these forces work together in bringing about certain

specific effects and not others, for lines of mechanic causation may

vary, but the result obtained must always be of the same general kind.

The fact that the means to produce these specific effects may be

different is acceptable only if we think of a general regulative idea

directing the whole process, which is what Peirce means with the final

cause of the process..

We can come to a closer understanding of all of this if we look to

some examples given by Peirce. One of them is about gases. One cannot

explain the diffusion of gases, according to Peirce, only with the

concept of force:

Take, for example, the phenomenon of the diffusion of

gases. Force has very little to do with it, the molecules

not being appreciably under the influence of forces. The

result is due to the statistics of the equal masses, the

positions, and the motions of the molecules, and to a

slight degree only upon force, and that only insofar as

there is a force, almost regardless of its character, except

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that it becomes sensible only at small distances. [NEM 4:

66, Carnegie Application].

Therefore, there are several other factor to influence the

behaviour of gases, and the fact that a gas is composed of “molecules

distributed according to a statistical law” indicates that the

phenomenon of the diffusion of gases is like a irreversersible

phenomenon, with a tendency to occur in one direction and not in

another, i.e., a tendency to achieve a certain end in a certain way

(according to that statistical law); which tendency, “if hindered, within

certain limits, it will, when freed, recommence in such way as it can.”

[id.]. Another example is the one of the falling stone, which in falling

hits a horizontal elastic surface, coming back in the opposite direction,

upwards, until the point wherefrom it started to fall, in the same

velocity of the fall: “Whatever motion conservative forces can effect the

very reverse of that motion they are equally capable of effecting.” [RLT

220]. This does not mean that the process is reversible, but only that

action and reaction are explained according to the same laws,

according to the same general tendencies to occur in a certain

determined way. The movement of the stone, when hindered by an

elastic surface, does not suddenly ends, but, keeping the same general

characters, happens in the reverse order.

The illustration of the lamps is the best to clear up the relation

between final and efficient causes. Lamps are products thought of by

human beings with the main purpose of providing light – which kind of

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light, directed to what specific place, coloured or not, more or less

shining or more or less dim, flashing or statical, electric or fire-lit – all

such questions are secondary, which the particular circumstances will

help to ascertain. In fact, it is easier to classify objects one already

knows the final causes, that is, objects which finalities are already

known, that is, that to which they were made for. If I want an object to

fulfill a defined function, I know how should act to obtain the desired

result. Human creations, possibly with the exception of artistic

creations, have all a defined role, and their final causes are determined

by their usefulness. The general purpose of a lamp, no one doubts, is to

provide illumination, and that is enough to give us a natural class:

“lamps form a true, real, and natural class, because every lamp has

been made and has come into being as a result of an aim common and

peculiar to all lamps.” [EP 2: 117, On Science and Natural Classes]. In

fact, the example of lamps lets us see how it is with all human product

with a defined function100.

The example of the lamps is clarifying not only because of the

utility of the lamps, but because it contrasts products made by human

beings to fulfill a defined function and things in nature: animals, plants,

stones, mushrooms, viruses; whatever it may be, nothing in nature has

a humanly defined. We, human beings, do not know a priori which the

designs of nature are, and an attempt to classify natural objects

100 One should notice that Peirce is not concerned in this discussion with artistic objects, as we may understand them today, as objects that do not need to have an utilitarian function.

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according to which purposes they were created is impossible, unless we

know the final causes operating in nature (supposing nature has any

final causes, of course). Peirce says: “In regard to natural objects,

however, it may be said, in general, that we do not know precisely what

their final causes are.” [id.]. in this sense, to speak about purposes of

natural objects is not appropriate, for it may as well be that natural

objects do not have an a priori defined purpose, but that they build

their purposes up unconsciously, in so far as they develop and tend to

actualize a certain end.101

The illustration given, this time, is the one of the animals that

have legs:

The use of legs is clear to us, having them ourselves. But

if we pass the animal kingdom in review, we see that in

the majority of branches there are no such organs of

locomotion; while in the others they are present

throughout some whole classes, are absent throughout

others; and in still others are sometimes present,

sometimes absent. [id.].

The conclusion we can draw is that to have legs is a means of

locomotion that can be connected to the possibility of a form; that “two

animals of the same order could not differ in respect to using

101 We will return to this point ahead. Cf. SANTAELLA (1992), p. 112: “[…] Peirce preferred this term final causation or ideal causation to the term purpose, because the latter could be mistaken by intentionality, which merely is the conscious variation of final causation. Not only causation can be unconscious, one of the cases in which the purpose is unknown, but it may as well be a case of purposes not specifically human, as it is with natural objects. [Peirce preferia esse termo causação final ou causação ideal ao termo propósito, porque este pode ser confundido com intencionalidade que é meramente a variação consciente da causação final. Não apenas a causação pode ser inconsciente, um dos casos em que o propósito é desconhecido, mas pode também não ser uma questão de propósitos especificamente humanos, como é o caso dos objetos naturais.]” Our translation. For more details, see SANTAELLA (1999), p. 501-503.

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legs.”[ibid.] But we cannot assert that to have legs is in fact linked to

the possibility of a definite form, because we also see that animals with

legs “do not form a natural group; for they are not separated from all

others in any other important particular.” [ibid.] Therefore, regarding

nature, all we can do is to risk, for we do not previously know which its

purposes are, whether exist or not. Our knowledge of nature is based

upon observations we generalize, and everything we do is to construct

hypotheses that can come to be refuted by future experience. The

upshot of this argumentation leads us to conclude we cannot attain

absolute logical exactness: “We thus get a tolerably clear idea of what a

natural class is: it will amply suffice for our present purpose; though we

can hardly hope that it will turn out to be logically accurate.” [ibid.].

The idea of a general class, therefore, is a vague idea. Vagueness,

in this context, is a necessary character of natural classes, if we

remember that differently from all natural things, human objects are

(almost) all made having in sight some sort of actualization. Their

classification a fortiori is not difficult, because it is possible to know a

priori their purposes, meaning, before attempting to classify them, we

already know what the objects to be classified were made for.

This is the exact point concerning the sciences: it is perfectly

possible to obtain a natural classification of the sciences,

notwithstanding the unavoidable vagueness of our natural classes,

because sciences are, more or less in the same way as lamps, human

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creations; and as such they also serve to human wishes, no matter how

vague such wishes may be: “We also see that, when an object has been

made with a purpose, as is, of course, the case with the sciences, no

classes can be more fundamental nor broader than those which are

defined by the purpose.” [EP 2: 117/118]. Purposes are general and

vague, for they are “operative desires”, according to Peirce. They direct

our efforts towards getting a certain kind of event or thing which is

desired. Thus, that which is desired never is something completely

determined, but something vague and general; even though the fact

that I want is a single and determined fact, that which is the object of

my desire, as Hulswit says, “is of the nature of an idea, or general type”

102 . Peirce gives a delicious example for this claim, one could say. An

apple pie is desired. Not this or that pie, but a certain type of pie, made

of a certain kind of pastry, a certain kind of fruits. The more varied the

degree of generality is, and the more we wish a especial pie made of a

especial type of apple, by an especial particular cook, even then the

object of our wish remains of a general nature. We have an idea of what

kind of pie we want, and the final pie, that pie, made and cooked

according to our idea, ends to satisfy the general specifications of our

will to eat the apple pie. However, if someone eats the pie before, our

desire can be satisfied with another pie; as Peirce says, “Desire is not a

reaction with reference to a particular thing; it is an idea about an idea,

102 HULSWIT (2002), p. 77.

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namely, the idea of how delightful it would be for me, the cook's

master, to eat an apple pie.” [CP 1.341, c. 1895]103.

Back to the sciences, this vagueness will allow to classify them

without imposing limits and boundaries arbitrarily restrictive between

them, because what this operative desire makes is to create a broad

enough class to include the various kinds of objects that could satisfy 103 The passage is deliciously interesting, and deserves to be transcribed in full: “Let us examine the idea of generality. Every cook has in her recipe-book a collection of rules, which she is accustomed to follow. An apple pie is desired. Now, observe that we seldom, probably never, desire a single individual thing. What we want is something which shall produce a certain pleasure of a certain kind. To speak of a single individual pleasure is to use words without meaning. We may have a single experience of pleasure; but the pleasure itself is a quality. Experiences are single; but qualities, however specialized, cannot be enumerated. There are some two dozen kinds of metals well known to me. I remember to have examined lumps of those qualities. But it is only the limitation of experience which attaches that number; there is simply no end to the metallic qualities I can imagine. I can imagine an infinite variety between tin and lead, or between copper and silver, or between iron and nickel, or between magnesium and aluminum. An apple pie, then, is desired – a good apple pie, made of fresh apples, with a crust moderately light and somewhat short, neither too sweet nor too sour, etc. But it is not any particular apple pie; for it is to be made for the occasion; and the only particularity about it is that it is to be made and eaten today. For that, apples are wanted; and remembering that there is a barrel of apples in the cellar, the cook goes to the cellar and takes the apples that are uppermost and handiest. That is an example of following a general rule. She is directed to take apples. Many times she has seen things which were called apples, and has noticed their common quality. She knows how to find such things now; and as long as they are sound and fine, any apples will do. What she desires is something of a given quality; what she has to take is this or that particular apple. From the nature of things, she cannot take the quality but must take the particular thing. Sensation and volition being affairs of action and reaction relate to particular things. She has seen only particular apples, and can take only particular apples. But desire has nothing to do with particulars; it relates to qualities. Desire is not a reaction with reference to a particular thing; it is an idea about an idea, namely, the idea of how delightful it would be for me, the cook's master, to eat an apple pie. However, what is desired is not a mere unattached quality; what is desired is that the dream of eating an apple pie should be realized in Me; and this Me is an object of experience. So with the cook's desire. She has no particular apple pie she particularly prefers to serve; but she does desire and intend to serve an apple pie to a particular person. When she goes into the cellar for the apples, she takes whatever bowl or basket comes handy, without caring what one, so long as it has a certain size, is clean, and has other qualities, but having once selected it, into that particular bowl she intends to put some apples. She takes any apples that are handy and seem good; but having taken them she means to make a pie of those apples. If she chances to see some others in the kitchen, on her return from the cellar, she will not use them for the pie, unless for some reason she changes her mind. Throughout her whole proceedings she pursues an idea or dream without any particular thisness or thatness – or, as we say, hecceity – to it, but this dream she wishes to realize in connection with an object of experience, which as such, does

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the desire. The specification of an individual object, in an individual

occasion, happens when there is the intermediary element of will, that

is, our desire becomes clearer and more specific when we begin to

focus our attention upon an object or thing we want above everything

else, and consequently the classes may come to be narrowed. Purposes,

then, are like general desires, they can always be made more and more

specific, insofar as we go pursuing them, trying attain them. The

example of the lamps is once more clarifying. First, one thinks of a lamp

because one wants “economic lighting”. After thinking of some ways to

get economic lighting, it is needed to choose again one further thing in

each thought way – for instance, if we decide by combustion or by

electricity; once it is decided by electricity, if we want burning lamps or

fluorescent lamps, and so forth. Desires, as Peirce says, are in this way

vague, variable and have “longitude”:

[…] while a certain ideal state of things might most

perfectly satisfy a desire, yet a situation somewhat

different from that will be far better than nothing; and in

general, when a state is not too far from the ideal state,

the nearer it approaches that state the better. [EP 2: 118-

119, On Science and Natural Classes].

It is better to have something to satisfy the desire than nothing,

we could say, Besides, one solution can be good from one point of view,

and bad from another: “A brighter lamp than that I use would, perhaps,

possess hecceity; and since she has to act, and action only relates to this and that, she has to be perpetually making random selections, that is, taking whatever comes handiest.”

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be more agreeable to my eyes; but it would be less so to my pocket, to

my lungs, and to my sense of heat.” [id.]

The conclusion of all these arguments is important. Be the natural

classes as precise as they may be, there will always remain a certain

vaguensess, a certain degree of variability and a certain adjustment of

objects that could be better fit in another classification, which is lacking

at the moment, but it may be found further on. It is impossible then to

draw an exact line of demarcation between natural classes. Even if we

knew the purpose of each object classified, the conclusion would remain

the same, because our desires, as vague and general, are not exactly

correspondent to a specific object, for we do not need this or that object

to satisfy them, but only an object of a certain kind will suffice:

[...] the objects actually will cluster about certain

middling qualities, some being removed this way, some

that way, and [until that] at greater and greater removes

fewer and fewer objects will be so determined. Thus,

clustering distributions will characterize purposive

classes. [EP 2: 119].

When we specify more and more, this does not mean we have

reached the last and ultimate degree of particularization, because more

straight classes would still be possible; that means we can only know

how broad were our previous classes, but not how fine are our actual

ones.

One important conclusion for a classification of the sciences is

that, as we will see in detail, sciences are in constant relation with their

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areas of acting and they mingle with one another. In this sense, a broad

line of research for one science may as well be a more specific field to

another. A very precise and clear line of separation could not be traced

between them, even if we knew a priori the ends – the final causes – of

their objects, for a further specification could still happen; but, as we do

not know a priori the final causes in every case, we have to deal with

vagueness and some sort of logical inaccuracy [id.].

The most important is yet to be said. In trying to say what a

natural classification of the sciences is to be, Peirce has in view the fact

that, in defining a science as an activity performed by living persons,

united to accomplish a common purpose, he was aware that he could

not force any abstract definition above the sciences, because that would

mean to impose a classificatory model in the same artificial way that

every other attempt he had criticized. It is important to understand

classes, therefore, as ideas corresponding to some existence; in his own

words, it is important to understand classes as ideas of final causation

related to the efficient causation, that is, the idea of a process directed

to an end, allied to a process of actualization of means to reach that

end.

Peirce still gives the following description of the process of

efficient causation:

Efficient causation […]is a compulsion determined by the

particular condition of things, and is a compulsion acting

to make that situation begin to change in a perfectly

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determinate way; and what the general character of the

result may be in no way concerns the efficient causation.

[EP 2: 120, On Science and Natural Classes].

The difference between final and efficient causation is cleared up:

the latter is a process not directed to a special end, but it is driven by

mere blind compulsion.

The example given is that of a shooter aiming at a bird flying in

the sky. To hit the aim, the shooter does not aim at the bird itself, but a

little ahead, figuring out the velocity, the rout of the bird’s flight, the

time the bullet is to take to hit the moving aim. Thus, the shot has as

finality to hit the bird. However, the moment the bullet leaves the rifle,

the efficient causation commences, that is, the force of the powder

begins to act pushing the bullet in a certain direction. If the bird

changes its route with a loop in the air, the bullet continues in the same

direction as before, without looping to hit the bird. Efficient causation,

therefore, is a mere compulsive power, and has nothing to do with the

result; it only obeys orders blindly [id.].

We said that final causes and purposes are not, according to

Peirce, exactly the same; he himself says it explicitly: “it is a very

common mistake to think that a ‘final cause’ is necessarily a purpose”,

and the reason why one should not think like this is the following:

[…] we must understand by final causation that mode of

bringing facts about according to which a general

description of result is made to come about, quite

irrespective of any compulsion for it to come about in this

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or that particular way; although the means may be

adapted to the end. The general result may be brought

about at one time in one way, and at another time in

another way. Final causation does not determine in what

particular way it is to be brought about, but only that the

result shall have a certain general character. [ibid.].

Final causation, differently from efficient causation, is relative to

the attainment of an aim: an end or finality. Its result is not specified; as

we said, just a kind of result is indicated, a kind of apple pie, not this or

that special apple pie. Final causation, thus, is of the same form as a

law, that is, it has the power of driving the blind and compulsive

efficient process which produces a particular fact hic et nunc so that

this fact be produced in a certain way, and not in another; it is similar

to a summon, a calling for parts to convene in a convocation; or it is the

aim of the shooter, who directs the shot in a certain sense. As the aim

to be attained is always ideal, the result may vary, depending on the

means used to get it. Now, it is impossible an idea without something to

actualize it, it is impossible to achieve an end without using any means,

it is impossible to think of an aim or purpose to be achieved without a

process to bring it about; that is, “Final causality cannot be imagined

without efficient causality” [EP 2: 121], in Peirce’s words.104

104 HULSWIT (2002), p. 80, says that efficient causation is a dyadic relation, between two individual concrete facts, while final causation is a triadic relation, among the general final cause, the concrete efficient cause and the concrete effect: “The production of the individual effect (B) by the individual efficient cause (A) is determined, or mediated, by the general final cause (C’).” Of course, the result (C) will not be exactly as the ideal result thought of. The same idea is defended by SANTAELLA (1999), pp. 502-503, though in other terms: “Hence, the key to final causality is in the concepts related to Thirdness: continuity, law, mind, law of mind, and habit. However, as Peirce’s categories are omnipresent and interrelated […], considering final causality as Thirdness in isolation from Secondness or efficient causality would be as

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What that may mean we will be able to see after analyzing both

concepts of causation more in detail:

Efficient causation is that kind of causation whereby the

parts compose the whole; final causation is that kind of

causation whereby the whole calls out its parts. Final

causation without efficient causation is helpless; mere

calling for parts is what a Hotspur, or any man, may do;

but they will not come without efficient causation.

Efficient causation without final causation, however, is

worse than helpless, by far; it is mere chaos; and chaos is

not even so much as chaos, without final causation; it is

blank nothing. [EP 2: 124, On Science and Natural

Classes].

Remember that a natural class is a class of objects grouped

according to a common character they have; for that, they make up a

determined set. To cause a factual process, by the passage above, is to

compose a set of conjoined elements according to a common character.

Efficient causation, thus, is nothing but an aggregation of objects

according to a common character: they can, however, be grouped

otherwise, for the fact they have something in common is not enough to

make a whole out of them, it means only that they may make up a set.

Final causation, in turn, is the calling up of those common characters as

defining characters of the parts of a whole, ordered exactly in function

of this common. A natural class, therefore, would be that through which

we could see how the final causation operates together with efficient

causation – the class exhibits the idea that ordains the set of classified

serious a mistake as it would be to isolate both from Firstness, the category of chance and feeling.”

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things; that is, the criterion used for classifying must be one such as to

show how the process of coming-to-be of the objects was brought about.

It is only possible to say the reason why things happened as they did

after all the process of efficient causation has passed; only in this way it

is possible to show how things came to inherit the nature they

inherited. A natural classification, then, would have to present the

genealogical structure of what is to be classified – wherefrom it came,

whereto it may develop in the next future, and, most important, in

regard to this development, the reason why it developed in this way,

and not in that way.

This is possible because objects of a class, as Peirce says, derive

their existence from an idea that the class exhibits. This derivation has

a precise meaning: “What I mean by the idea’s conferring existence

upon the individual members of the class is that it confers upon them

the power of working out results in this world, that it confers upon

them, that is to say, organic existence, or, in one word, life.” [EP 2: 124,

On Science and Natural Classes]. When we look at a natural class, in

this sense, we should understand why it is a way to classify those

things, for we would understand, thus, which is the living principle

common to all the individuals of that class. The idea shown in the

natural classification, then, would be an idea of the final cause that

gives coherence to the set, in its turn understood in terms of how its

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parts became its parts, in a process described as the causal

actualization of this outcome.

Let us recover the reasoning. On the one hand, in the case of non

human productions, we will be able to affirm only the final cause of a

process after we understand its genetic process, for only then we will

have comprehended how things came to be. In the case of human

productions, on the other hand, it is not quite so: we know which is the

final cause, but in the same way there remains to know how it was

attained, that is, we have to explain why we have to do with this final

cause, and not with any other final cause: to know how things happened

and which were the initial reasons of their happening in the way they

did – this knowledge helps us to better understand our own purposes.

A natural classification of the sciences, therefore, should provide

a description of how sciences are created and why they are created in a

certain way, and not in others. The important point would be to give

one interpretation of the process of creation of sciences, the process of

generating guiding scientific principles. This is explained, in a very

characteristic Peircean way, from the the very etymology of the word

“nature”, in a passage which deserves to be transcribed in its full:

Every class has its definition, which is an idea; but it is

not every class where the existence, that is, the

occurrence in the universe of its members is due to the

active causality of the defining idea of the class. That

circumstance makes the epithet natural particularly

appropriate to the class. The word natura evidently must

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originally have meant birth; although even in the oldest

Latin it very seldom bears that meaning. There is,

however, a certain sub-conscious memory of that

meaning in many phrases; just as with words from

[phýsis], there is the idea of springing forth, or a more

vegetable-like production, without so much reference to

a progenitor. Things, it may be, [phýetai]

spontaneously; but nature is an inheritance. [EP 2: 121,

On Science and Natural Classes].

As he says in the beginning, it is not that each particular

individual should have its existence directly caused by the defining idea

of the class, but that a natural class, if it is to be a genuine natural

class, will express the general idea of the process of becoming of its

members. In the essay where he displays such ideas, Peirce first

explains that processes like those of final and efficient causation

operate in nature conjointly, to contrast them with process we humans

ourselves create. The most important difference between natural

evolution and human production is that a final cause does not

necessarily need to be a purpose, but can be a tendency, as we said

above [EP 2: 122; 464]. Now, it is important to remember also that in

regard to living processes, which can change at any moment, once the

efficient cause is yet operating, it is impossible to state that the

classification is absolutely definite, since the efficient cause, as an

external compulsive factor, can change the original tendency of a

process. A natural class, therefore, must express the idea or ideas,

which are present in the genesis of the objects it classifies conjointly

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with the idea (or ideas) that influence the process of development of

what is classified. This is exactly the scope of the Peircean classification

of the sciences: to display how sciences are Born one from another, how

it is that they spontaneously spring forth in the investigative practice,

and how they go modifying themselves in their interaction among

themselves and with what they investigate.

Now, how it is in the text, things may be brought about

spontaneously, but they inherit their nature. As with the sciences, the

inherited nature, the characteristic mark of each of them, is an idea,

generated by the distinctive idea of another science: “In considering the

classification of sciences, however, we have no need of penetrating the

mysteries of biological development; for the generation here is of ideas

by ideas.” [EP 2: 122, On Science and Natural Classes]. There is no

other possibility, because in fact “sciences are, in part, produced one

from the others” [EP 2: 126, On Science and Natural Classes]. This is

an extremely important problem:

All natural classification is then essentially, we may

almost say, an attempt to find out the true genesis of the

objects classified. But by genesis must be understood,

not the efficient action which produces the whole by

producing the parts, but the final action which produces

the parts because they are needed to make the whole.

Genesis is production from ideas. [EP 2: 127, On Science

and Natural Classes].

If a science is produced from others, how to distinguish them?

The mixing of one science up with another is no reason to abandon the

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attempt of a natural classification, because the question on the

precision of boundaries is not at stake. It is possible very successfully to

draw the lines between a class and the other quoting examples:

The descriptive definition of a natural class, according to

what I have been saying, is not the essence of it. It is only

an enumeration of tests by which the class may be

recognized in any one of its members. A description of a

natural class must be founded upon samples of it or

typical examples. [id.].

The emphasis in the generation of an idea by another is more

important for the classification of the sciences in so far as we may want

a natural classification. In describing how one science springs forth

from the ideas of another, we can also see which ideas and principles

inspirit it; in other words, we can see better to which purposes it comes

to answer, why it was produced. The genealogical feature of the

classification, therefore, must be the most important and the only one

upon which we can ground any attempt to establish a natural

classification of anything:

Now genealogical classification, among those objects of

which the genesis is genealogical, is the classification we

can most certainly rely upon as being natural. No harm

will be done if, in those cases, we define the natural

classification as the genealogical classification; or, at

least, that we make the genealogical character one of the

essential characters of a natural classification. It can not

be more; because if we had before us, ranged in

ancestral order, all the intermediate forms through which

the human stock has passed in developing from non-man

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into man, it is plain that other considerations would be

necessary in determining (if it admitted of determination)

at what point in the series the forms begin to merit the

name of human. [EP 2: 126].

This is how it should be with any intended natural classification:

every natural classification has to be a genealogical classification. The

main task, therefore, of a classification of the sciences, in so far as it is

a natural classification of human products, is in showing how sciences

are brought about – that is, from which ideas they spring forth – and

why they are brought about – that is, to which general desires they give

an answer. In other words, so we do not overlook the motive why we

want the sciences, it is necessary to seek for the origins of sciences.

And, in fact, according to Peirce, science is itself a search for origins:

I remember the days when a pronouncement all the rage

was that no science must borrow the methods of another;

the geologist must not use a microscope, nor the

astronomer a spectroscope. Optics must not meddle with

electricity, nor logic with algebra. But twenty years later,

if you aspired to pass for a commanding intellect, you

would have to pull a long face and declare that “It is not

the business of science to search for origins.” This maxim

was a masterpiece, since no timid soul, in dread of being

thought naive, would dare inquire what “origins” were,

albeit the secret confessor within his breast compelled

the awful self-acknowledgment of his having no idea into

what else than ‘origins’ of phenomena (in some sense of

that indefinite word) man can inquire. [EP 2: 437, A

Neglected Argument for the Reality of God].

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In peircean terms, a natural classification would describe

processes of efficient causation, displaying the genesis of each science –

that is, describing which final causes operate in sciences. And the

description of the final causes of a science is a means to understand the

problems it tries to solve:

It may be difficult to understand how this is true in the

biological world, though there is proof enough that it is

so. But in regard to science it is a proposition easily

enough intelligible. A science is defined by its problem;

and its problem is clearly formulated on the basis of

abstracter science. This is all I intended to say here

concerning classification, in general. [EP 2: 127].

The genealogy of the sciences, in the end, by showing from which

ideas sciences are generated, would show how they became what they

are in trying to answer specific problems; to solve certain problems is

the end of every science, that is, every science is created to solve

certain problems. Now, in the exercise of an inquiry, there are

problems that arise for which we do not have answers within the

standards wherein we are. Then, it is needed to establish new

parameters and to begin a new inquiry, having as its background the

general ideal of the previous inquiry; the new problem, however, sets

new aims to be attained, and this defines its specificity. The importance

of certain problems defines the specificity of a science, for it indicates

whereto apply, in practice, the precepts it brings with itself. In general

terms, to ascertain the purposes of the sciences is to understand which

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problems it tries to solve. Once this is understood, we are capable of

understanding the general idea that caused the occasion for the arising

of that precise investigation, seeing, then, where that problem, and,

therefore, where that science came from:

So then, a natural class being a family whose members

are the sole offspring and vehicles of one idea, from

which they derive their peculiar faculty, to classify by

abstract definitions is simply a sure means of avoiding a

natural classification. […]After all, boundary lines in

some cases can only be artificial, although the classes are

natural […]. [EP 2: 125, On Science and Natural Classes].

A last remark before we pass to the other stage. The definition of

a science is possible by means of the definition of its problem. We have

seen that this problem is linked to the general purpose for which a

science is wanted, and such purpose is born from the practice of

another science; we have also seen that purposes are of a general

nature, like general desires, which never completely specify the objects

that may satisfy them, but only the kind of such objects. This

affirmation is a refusal of the idea that sciences are defined by their

objects of study. In truth, it is exactly the opposite: the generality of

purposes of a science allows understanding how a certain object can be

studied by it. The object, so, does not define the investigation, rather it

is the investigation that defines how the objects can be studied, for the

objects may exhibit peculiar characters of more than one class.

Therefore, there is no essence in the objects that determines our way to

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approach them. If we do not get to interpret an object with certain

means of study and inquiry, this is not a problem of the object, but of

our means, that can be changed. So, the classification of the sciences is

a classification of the ways to interpret objects; this idea is from the

very beginning present in Peirce’s thought. Remember a passage we

have already quoted:

Most of the classifications of the sciences which have

been proposed rest upon a classification of the things

which they treat. This method is objectionable for two

reasons: first that many sciences treat of everything, as

the science of mechanics, that of geometry, that of

chemistry, and so forth; second because the classification

of things needs to rest upon a classification of sciences.

The first great division of things is according to their

functions and hence it is that the homologies or

likenesses which pervade a whole kingdom of nature as

mouths, stomachs, and locomotive apparatus among

animals are functional homologies. Now the function of a

thing in itself considered cannot be determined;

whatever it does or is it is its function to do or be. Hence

any division of the functions of things is only a division of

different sciences which ask different questions about

things, and thus the classification of things rests finally

on the classification of sciences. [W 1: 486-487, Lowell

Lecture IX, 1866].

This is the reason why Peirce states that the objects form groups

according to their classes and purposes: the same objects may be

studied by different sciences, from different perspectives, without this

being an epistemological problem of defining limits between one

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science and another. There is no need to settle precise limits for each

science, defined regions for acting, for the actual present problems had

their origin in other problems, what makes the will to demarcate

precise boundaries an idealist illusion; as H. Pape says, what counts as

an object pertaining to a class or another never can be decided upon

purely theoretical grounds.105 Thus, for Peirce, the only natural

classification of the sciences, as we said, is the one that takes into

account science as a living thing, in straight connexion with practice:

“What is a science as a natural object? It is the actual living occupation

of an actual group of living men. It is in that sense only that I presume

to attempt any classification of the sciences.” [MS 1334: 13].

8.1. THE MOST NATURAL SCHEME POSSIBLE

We can now see how the general classificatory scheme sketched

by Peirce for the sciences is organized. The scheme was adopted and

adapted from Louis Agassiz, with whom Peirce studied fossils

classification in his youth [EP 2: 118]106. The organization is according

to the generality of the divisions, in the following way:

105 PAPE (1993), p. 584. Cf. PARKER (1998), p. 35: “Classification, then, does not look for essential features of objects (i.e., characteristics that are necessary and sufficient for a thing’s inclusion in a class) because there is no essence that makes a thing what it is. Rather, it is a combination of a general ‘desire’, vague specifications for satisfying it, and various limitations on the resources available to meet those specifications that make a thing what it is.”106 See BRENT (1998), pp. 60 and 364.

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Branches are characterized by the plan of structure;

Classes, by the manner in which that plan is executed, as

far as ways and means are concerned; […] Orders, by the

degrees of complication of that structure; […] Families,

by their form, as determined by structure; […] Genera, by

the details of the execution in special parts; Species, by

the relations of individuals to one another and to the

world in which they live, as well as by the proportions of

their parts, their ornamentation, etc. [EP 2: 128, On

Science and Natural Classes].

There is still a last division, “variety” of science, “a study to which

men devote their lives, but not, in the present stage of development of

science, so numerously as to justify exclusive societies and journals for

it” [NEM 4: 16, Carnegie Application]. The variety of a science, thus,

concerns more individual researches, the specialization to which each

inquirer dedicates him or herself.

Such organization in levels comes from the more general to the

more particular, aggregating objects “according to the ideas from

which their existence results” [id.]. furthermore, each level of

generality has its specific character. Sciences are divided in:

Branch: the branches divide the sciences according to their

fundamental purpose. In this way, the most general division is between

theoretical science, the purpose of which is only and exclusively in the

knowledge of “God’s truth”, and the practical sciences, oriented “to the

uses of life” [MS 1334: 22].

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Sub-branch: sub-branches mark a modification in the general

purpose. Thus, the sub-branches of theoretical sciences are the

sciences of research, or heuretic, and the sciences of review, or

retrospective, or synthetical philosophy.

Class: are marked by the peculiarity of their observations, that is,

by the characteristic marks of their kind of research. Thus, for instance,

mathematics is a classe of the sub-branch of heuristic sciences, which

can be divided in three sub-classes, namely, mathematics of logic,

mathematics of discrete series, and mathematics of continua and

pseudocontinua.

Order: sciences divided according to the difference in

conceptions, or according to the intellectual distinct character of each

of them, even though they are within the range of a same general

research, appertain to distinct orders. Thus, for instance, in the

subclass of the normative sciences, esthetics, ethics, and logic are

different orders that study different ways of understanding the duality

existing in our encounter with brute fact.

Family: it is the division under which scientists who deal with the

same subject-matters aggregate, within the same inquiring range, but

with different skills. For instance, in the same order of general physics,

the studies of dynamics and optics constitute different families, because

they are equally pursued by physicists, but physicists with different

skills.

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Genus: they are the divisions in which it is possible to have

disinformation on the part of the inquirers regarding specific details; as

for instance, in the family of physic-chemistry, the study of particles

(neutrons, protons, and electrons) is related to, but different from the

study of anti-particles (antineutrons, antiprotons, and positrons).

Species: within the same genus of inquiry, a species would be the

division formed by the groups and societies more specific, so that every

student may be able to pass from one species to the other. One

illustration, in the genus of the study of the particles of the matter, the

study of leptons and the study of bosons constitute different species.

Variety: finally, the minutest study, the most specialized division

of science. Maybe we could say that, inside the study of leptons, to keep

the example, we have the varieties that study the electrons, the

neutrinos, the quarks etc., within the species of the study of bosons, the

varieties dedicated to the photons, gravitons, etc. 107.

The classification of the sciences is to be arranged in such a way

that the most abstract and general sciences appear genealogically

before the more specific, ones, since the more general ones provide

principles and the more specific are source of data, examples and

information to the antecedent. This is stated in the following passage:

107 The sources consulted for the presentation of the divisions are: NEM 4: 16-17, 1902; EP 2: 258-262, 1903; and mainly CP 1. 238-272, 1902, wherein the reader will find several examples of Peirce himself. However, he does not come deep to the level of specialization of genus, species and varieties to indicate all the sciences in these levels of specificity.

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The different sciences help one another, and that in

multiform ways. No rules can be laid down as to where a

science shall seek help; far less as to where it shall not.

Yet in a general way the sciences are related like the

rungs of a ladder. That is to say, some sciences are

broader than others, look over a wider range of facts, but

look less into details. The general rule is that the broader

science furnishes the narrower science with principles by

which to interpret its observations while the narrower

science furnishes the broader science with instances and

suggestions. [NEM 4: 227, Of the Place among the

Sciences of Philosophy and of each Branch of It, c.1904-

1905].

The relation is not revertible, that is, a more abstract science

cannot derive its principles from a less abstract. The organization, then,

must begin from the science that provides more principles, i.e., the

most basic, because from it all the other sciences will draw principles,

to it all the other sciences will run when facing a problem they do not

know how to solve. It is important to stress that a science can only

furnish principles or data to the other; two sciences cannot help one

another mutually in the same way; there may be information exchange,

methodological loans, but two sciences cannot simultaneously provide

principles to one another, for the reason why “no two things can

depend upon each other in the same way.” [MS 693A: 27, Reason’s

Conscience]. In effect, it is the desire to learn that leads the scientist to

become interested in a greater range of objects, so that the movement

always tends to a bigger generalization:

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Science arises from a genuine and heart-felt, and not

from a fictitious, interest in the objects studied; and

consequently, its birth comes in the study of some single

object. […] So a man, from watching a few stars, will at

length proceed to draw up a catalogue of all the stars he

can see with his naked eye. Next, he procures a

telescope, and he or his successor makes a larger

catalogue, and then some imitator of him with a still

better telescope is able to make a still larger catalogue.

At last, the telescope comes to show so many millions of

stars that from studying individual stars, the astronomers

pass to considering classes of stars, of clusters, and of

nebulae. In this way, every study of individual objects,

which includes to all intents and purposes, a study of all

objects of precisely the same nature, tends to pass into a

study of classes each composed of differing objects.

Meantime, students are becoming interested in parts of

the objects which have similar functions. The

ornithologist becomes interested in wings; and does not

limit this interest to bird’s wings, but extends it to bats’

wings, to the fin’s of flying fish, and to the still more

different wings of insects. Another man will become

interested in the formation of valleys; still another in the

formation of laws. In this way, the study of kinds of

structure, or the comparison anatomy of all sorts of

classes, tends to pass into an interest in the different

ways in which uses are subserved, or kinds of functions

carried on; that is to say, in comparative physiology. [MS

693A: 27-29].

Not every scientist begins to study in this way, in the same way

that not every science arises as Peirce there describes, from the study

of more particular things, to be later on transformed into a study of

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classes. It is important to notice how he describes the process of

generalization, though, in a way that each science becomes more

general because it tends to embrace more and more objects under its

wings [MS 693A: 32]. These objects are not collected at random, as if

there was no better reason but the scientist’s curiosity; as a matter of

fact, the scientist’s curiosity is guided by the interest in generalizing,

and each object is incorporated as an object of study because it makes

it possible to achieve a higher degree of generalization. In fact, the only

interest a science can have in facts of another science is with a view to

generalization:

When one science furnishes another with a fact, what

causes the latter science to be interested in that fact?

Evidently because it hopes and expects to be able to

utilize that fact as one of the foundation stones of a

generalization. Then the science for which this fact is a

result is plainly a more special kind of science than the

science for which the same fact is a mere datum, or

premises. [MS 693B: 96, Reason’s Conscience].

This idea agrees with what was said before about the creation of

habits of expectation and about the functioning of perception: as no

percept is perceived in isolation, we have the formation of perceptual

judgments viewing generalization, i.e., viewing to say what would be

perceived in analogous circumstances to the ones of the present, so

that it is possible to predict, even though very roughly, the general form

of future experience. In the same way, all knowledge can be understood

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in the same key, since its proper cognitive value is due to observations

made of present facts with the purpose to anticipate future facts:

Nothing, however, can be called knowledge which might

not be applied to anticipating the characters of future

experiences. Such anticipations must be founded on

general rules, and these can only be the fruit of

generalizations. Consequently, if science is to advance at

all, it must do so by passing from the study of the

characters [to that of] classes of things. [MS 693B: 106-

107].

A good classification, then, would be more than a mere icon of

relations; rather, it would be a diagram through which we could see the

inter-relations of dependence between the sciences, and consequently

which is the most general and which the most concrete, or more

specific in its domain of inquiry. Furthermore, for the fact that the

classification is described as a ladder in which each rung is also a

smaller ladder with its own rungs, each of them also of the same

nature, the possibility of smaller and more specific subdivisions is

extended ad infinitum, in the same way as the ladder leads to the sky,

as in the beautiful metaphor given in Robert Musil’s passage in the

epigraph. As a matter of fact, Peirce says:

A good classification is a diagram usefully expressive of

significant interrelations of the objects classified. The

best classification of sciences is a ladder-like scheme

where each rung itself is a ladder of rungs; so that the

whole is more like a succession of waves each of which

carries other waves, and so on, until we should come to

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single investigations. [NEM 4: 227/228, Of the Place

Among the Sciences of Philosophy...].

Thus, the organization according to the scheme of logical

dependence has a precise reason why, which is, every knowledge

begins with the knowledge of an undefined class of objects, vaguely

understood, and tends to generalize to a knowledge of a general class;

and from these classes, to the sub-branches, and from the sub-

branches, to the branches of sciences, in a tendency to generalization

each time broader. In this process, every science has the three rungs of

theoretical science, retrospective science and practical science

conjointly [NEM 4: 228]. A possible arrangement of the scheme could

be displayed in the following way108:

A. Branch: Theoretical Science

A.1. Sub-branch: Science of Discovery, heuretic or heurospude.A.1.1. Class: Mathematics

A.1.1.i. Subclass: mathematics of logicA.1.1.ii. Subclass: mathematics of discrete series A.1.1.iii. Subclass: mathematics of continua and

pseudocontinua.A.1.2. Class: Philosophy, or cenoscopy

A.1.2.i. Subclass: Categorics, phenomenology or phaneroscopy

A.1.2.ii. Subclass: Normative sciencesA.1.2.ii.a. Order: AestheticsA.1.2.ii.b. Order: EthicsA.1.2.ii.c. Order: Logic

A.1.2.iii. Subclass: MetaphysicsA.1.2.iii.a. Order: General metaphysics, or

ontologyA.1.2.iii.b. Order: Psychic or religious metaphysicsA.1.2.iii.c. Order: Physical metaphysics

A.1.3. Class: Special science, or idioscopyA.1.3.i. Subclass: Physical sciences

108 Cf. NEM 4: 17, for a different position of practical science. In this regard, we follow here the classification presented in EP 2: 258, 1903; MS 1334: 20 ff., 1905; MS 655: 18, 1910.

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A.1.3.i.a. Order: NomologicalA.1.3.i.b. Order: ClassificatoryA.1.3.i.c. Order: Descriptive

A.1.3.ii. Subclass: Psychic SciencesA.1.3.ii.a. Order: NomologicalA.1.3.ii.b. Order: Classificatory

A.1.3.ii.c. Order: Descriptive

B. Branch: Science of review, retrospective science or taxospude

C. Branch: Practical science, the arts or prattospude

With this, we can see that Peirce tries a kind of classification

wherein the genealogy of the sciences can be pictured with some

clarity. The sciences of discovery, placed above all the others, furnish

the more general problems, of which all the more specific arise. The

reason why is that they are directed to the discovery of truth only for

truth’s sake, in the name of nothing else. The restrospective sciences

concern in their turn the classification of such knowledge, its

sytematizing, arranged in a digest to make it useful, i.e., to make it the

matter for the practical sciences, to apply it to the uses of life. But, as

Peirce states that every science also contains the three branches, this

actually means that all inquiry joins three distinct ways of making

science in one inquiry, insofar that it is impossible to separate theory

and practice; in other words, it is impossible to separate the intention

to discover from the intention to apply, because the relation between

the sciences is defined by means of the final purpose to which they are

directed – to know for what?

This idea becomes clearer when we look at the specificities of the

different branches of the sciences, to wit, heuretic science, sciences of

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review, and practical science. Let us see in detail how they are one

from another distinguished.

1. Science, whose main aim is to discover truth for truth’s own

sake, is called “science of Discovery” or, what is the same, “heuretic

science”; this is for Peirce the most primordial signification of science,

because it concerns only and exclusively with the discovery of truth,

and with nothing else [HO II: 825, Reason’s Conscience; EP 2: 372, The

Basis of Pragmaticism in the Normative Sciences]. Such conception

belongs to the first and more general branch of the classification and

will be remembered further on.

2. The second branch is that of the sciences of review, or

retrospective sciences, which seek to form a systematized digest of the

whole or of part of human knowledge, using whatever science of

discovery has brought to light and filling up its gaps according to their

own purposes, by means of proper investigations. This is science is

Coleridge’s sense, and embraces all the way from Comte’s Cours de la

Philosophie Positive, Spencer’s Synthetic Philosophy, passing by von

Humboldt’s Kosmos, and all the dictionaries and digests, up to scholarly

books and popular presentations, according to Peirce [EP 2: 372; MS

655: 19]. We see here that Peirce does not exclude from the

classification the Aristotelian-romantic conception we saw in the

beginning. The systematization of knowledge is necessary, and has its

well defined place in the domain of scientific inquiry.

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3. The third branch of the classification is the branch of practical

sciences, concerned mainly with the circumstantiated utility of the truth

sought, and not with its “august nature” [EP 2: 372]. In Peirce’s words,

practical science is “the theory of the arts, [it] is that science which is

selected, arranged, and further investigated in details as a guide to the

practice of an art.” [NEM 4: 191]. Here, it is interesting to make a little

exercise of etymology. In this particular context, Peirce uses the word

“art” differently from its use nowadays, approaching the early

etymological sense of it. The word comes from the Latin ars, used to

translate the Greek “” [techné], from which come the words (and

some of the sense too) “technique” and “technology”, for instance. The

meaning of the term is better understood if we get back to Aristotle:

All art [] is concerned with coming into being, i.e.

with contriving and considering how something may

come into being which is capable of either being or not

being, and whose origin is in the maker and not in the

thing made; for art is concerned neither with things that

are, or come into being, by necessity, nor with things that

do so in accordance with nature (since these have their

origin in themselves). Making and acting being different,

art must be a matter of making, not of acting.109.

Such conception of téchné, as it is clear, concerns the production

of some object whose existence is contingent. It is not necessary that

this object exists, and the choice between it existing or not is due to

whom is going to make it. Techné, therefore, has to do with the

109 Nichomachean Ethics, VI, 1149a 4.

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capacity to create an artificial object, as the shoe-maker makes a shoe

that does not need to be necessarily of that very form. As H. Murachco

says:

is, before everything, practical possession of the

necessary processes to execute this or that deed; it is the

practical ability, handicraft or potential ability that is

named talent. From this meaning others derive, by

metaphor or methonymy: knowledge of the means,

articulation of such means, expedient, ability, cunning,

tricks, and even office and business. But it is not wit; it is

an aprenticeship […]110.

The objects made through some art are, hence, the outcome of a

determinate ability of some artisan, who deliberately endeavours to

accomplish a specific type of production. Thus, we see that, for such

reason, it is an activity with an interest in a particular end, which is the

production of a specific object, and a fortiori contingent objects,

through a just the same specific practice.

Cicero, for example, still reports such use of the word, joining

besides the idea of creation, in his De Natura Deorum: “Zeno thinks

proper to each art to create and to bring about” 111. And it is in this

110 MURACHCO (1998), p. 13. Our translation; see the original: “é, antes de tudo, a posse prática de processos necessários para executar este ou aquele ato; é a habilidade prática, manual ou a habilidade potencial que chamam de talento. Deste significado derivam outros por metáfora ou metonímia: conhecimento dos meios, articulação desses meios, expedientes, habilidade, artifícios, artimanhas e até ofício e atividade. Mas não é o engenho; é um aprendizado [...].”111 “Zeno [...] censet enim artis maxume proprium esse creare et gignere”, De Natura Deorum, book 2, section 22, paragraph 57. Available on line at URL: [http://www.thelatinlibrary.com/cicero/nd2.shtml#57]. Acessed on 10 April 2005; see too Academica priora 2, 7, 22; De Officiis 2, 3, 12 seq. Cf. still Charlton T. Lewis and Charles Short, A Latin Dictionary: “ars, artis, f. [v. arma] , skill in joining something, combining, working it, etc., with the advancement of Roman culture, carried entirely beyond the sphere of the common pursuits of life, into that of artistic and scientific action, just as, on the other hand, in mental cultivation, skill is applied to morals, designating character, manner of thinking, so far as it is made known by external

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sense that Peirce also uses the word “art”, specifying, however, that an

art produces things with a view to a practical necessity. A sign of this is

that, for instance, in distinguishing the three kinds of scientific inquiry

listed above, the notion of art is straightly connected to the idea of

utility, while the notion of heuretic science, in its turn, as the name

itself says, is related to the idea of discovery, and not to the one of

production, without immediate relation to what is to be done with what

is discovered. This relation to a determined end to be produced is

clearly expressed by Peirce in the following passage:

When a general purpose is quite fixed and settled, as, for

example, that dwellings must be made warm in winter, a

skill is gradually developed in accomplishing that

purpose. If the operations required to accomplish the

purpose are complex, and if the purpose itself is

complicated with secondary considerations that vary

considerably on different occasions, it becomes desirable

that the skill in accomplishing it, which already involves

a good deal of special information, and as such is called

an art, should be guided by a general theory of the

relation of means to the purpose in question. This theory

of an art is a practical science. [HP II: 831, Reason’s

Conscience].

An art is an ability to effectuate something, accompanied by the

special information needed to such effectuation, i.e., by the technical

knowledge needed to the accomplishment of the task. The bridge

actions (syn.: doctrina, sollertia, calliditas, prudentia, virtus, industria, ratio, via, dolus). I. Skill in producing any material form, handicraft, trade, occupation, employment ()”. Acessed on 05 May 2004, at URL: [http://www.perseus.tufts.edu/]. In fact, such notion of or ars still echoes in our idea of artisanship.

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between practical sciences and the ancient conception of techné or ars,

therefore, is just the idea of how to perform the application of such

special knowledge to attain a pre-designed end. Practical sciences

determine the directioning of a specific activity, in a practical defined

context, toward the accomplishment of a specific aim. By itself a

technique is unable to perform the connection between means and

ends. As Ibri says, “the technique that provides the success of a

practice has not in itself, so to say, heuristic power to new pathways”112.

This heuristic power, in the peircean classificatory scheme, as we have

seen, is majorly confined to the domain of the sciences of discovery,

what would distance him from the use reported by Cicero. 113

Nevertheless, within the range of arts as techniques, it is more

important to know which are the more adequate ways to attain an aim

previously ascertained, and this is settled by practical sciences.

It may seem so that practical sciences do not concern discoveries

at all, contrary to what we said before. It is not so. Remember that, as a

matter of fact, the supreme aim of any and every science is to inquiry

and investigate to discover. The difference is in the modality of such

discoveries; it is in the end ascertained to the inquiry:

It is true that all scientific men are engaged upon nothing

else than the endeavor to discover. This is true of the

taxospudists and the prattospudists as much as of the

heurospudists. But the difference is that the

112 IBRI (1998), p. 154113 Notice Peirce does not use “technology” in this context.

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prattospudists endeavor to discover for the ultimate

purpose of doing, and the taxopudists endeavor to

discover for the purpose of applying knowledge in any

way, be it in action or more especially in cognition. [MS

1334: 21-22].

Hence it is also an aim of practical sciences to investigate truth,

with a view to accomplish something by means of applying the

knowledge in specific circumstances. That is why practical sciences are

considered as the theory of an art, for they try to discover the best

procedure to actualize a specific purpose, bridging between means and

ends, what the art-techniques cannot do by themselves. And, as it also

seems clear to us, it is one of the aims of theoretical sciences to

discover with a view to what is to be done with knowledge, even though

not for any immediate practical applicability. One of the aims, not the

highest, nor the greatest, nor the ultimate; in fact, theoretical sciences

envisage knowledge as an end in itself, and not as a means to other

accomplishments.114

In general lines, these are the differences between each specific

kind of science. There is to notice once more that they are not dry

114 If we believe in what Nietzsche says, this is a historic novelty of great importance. In The Gay Science, book III, § 123, he states: “‘Die Wissenschaft ist Etwas von zweitem Range, nichts Letztes, Unbedingtes, kein Gegenstand der Passion’, – dieß Urtheil blieb in der Seele Leo's zurück: das eigentlich christliche Urtheil über die Wissenschaft! Im Alterthum war ihre Würde und Anerkennung dadurch verringert, dass selbst unter ihren eifrigsten Jüngern das Streben nach der Tugend voranstand, und dass man der Erkenntniss schon ihr höchstes Lob gegeben zu haben glaubte, wenn man sie als das beste Mittel der Tugend feierte. Es ist etwas Neues in der Geschichte, dass die Erkenntniss mehr sein will, als ein Mittel.” If Nietzsche evaluates such novelty positively or negatively, this is a theme we will not develop here. However, we can briefly mention that, in dealing with what is called will to truth, the German philosopher asks exactly for the assumptions and aims of scientific knowledge, in an analogous reflection to Peirce’s: truth for what? To whom?

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separations. Each type of investigation and inquiry has its determined

objectives, but that does not mean that the range of heuretic sciences is

completely separate from the range of the sciences of review, or from

the practical sciences. Thus, not forgetting the inter-relations, we have

the differences in purposes clear between sciences concerned with

discovering truth, sciences concerned with the organization and

systems of knowledge, and sciences concerned with practical

application of what we know, even though all inquiry often combines

the three purposes when carried on.

Through Peirce’s scheme, we see that the sciences would

gradually tend more and more to a higher degree of generalization and

abstraction, for if the more general and abstract sciences are on the

top, in the condition of sources of principles, once the more specified

problems of the more concrete sciences are resolved, there would

remain the more general ones to busy us. The general orientation of

scientific inquiry, then, converges toward a supreme aim, which Peirce

describes as the discovery of the truth of God: “I recognize two

branches of science: Theoretical, whose purpose is simply and solely

knowledge of God's truth; and Practical, for the uses of life.” [CP 1.239,

1902]. As a matter of fact, even when inquiry is of the highest branch,

some practical accomplishment is always envisaged:

The widest division among the sciences is into the work

of Discovery, the work of Systematizing knowledge, and

the work of planning how to apply knowledge to the

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attainment of a special purpose, - or the science of

discovery, the science of review, and practical science.

Almost every discoverer has made some pretty extensive

studies of the science of review, though it is a common

vanity to pretend to be a stranger to it; and the majority

of scientific men do some work in the way of practical

science. [MS 693B: 80].

Practical sciences are linked precisely to the investigation into the

best way to use the already discovered and systematized knowledge to

solve specific problems. And the sciences of review also envisage to

discover ways of applying knowledge. Thus, theoretical sciences

envisage discovery, pure and simply discovery; the sciences of review

would be those that would investigate the conditions of possibility of

actualization of theory in practice, for they are busied with what is to be

done with our knowledge; they thus bridge between the discovery of

something new and its actual utility. As Peirce himself says, little can be

done with knowledge not yet systematized and organized, in this way

indicating the practical need of organizing our theoretical discoveries.

And practical sciences, in their turn, discover the diverse possible uses

of the obtained knowledge, in straight link with heuristic practice.

There is not, therefore, a hierarchy between the several kinds of

science, once new discoveries can arise from practical applications, and

vice-versa. There is, indeed, a differentiation as to the ultimate aims of

inquiry: to investigate to discover, or to investigate to apply the

knowledge. The application of knowledge must result as a natural

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outcome of the genuine interest in learning, and not as an a priori

requisite of inquiry.

Finally, some last remarks on the applicability of knowledge. It

would be ingenuity to say that scientists investigate without any

interest in the applicability of their discoveries. In fact, knowledge is

valid only if it can be adapted, in some sense, to the accomplishment of

human interests: “Knowledge is a plastic, applicable stuff – a putty

whose solid part, the barytes or the lead, is the percepts, of which more

and more is worked up in the oil of reflection.” [MS 693B: 113]. Science

is understood as a form of human activity capable of transforming the

environment which we live in according to our interests. Now, it is an

essential constitutive part of such pragmatist conception of science that

there is harmony between the aims of this inquiring activity and the

means available to us to actualize them, to make them concrete. In this

way, the questioning of the objectives with which this activity is

pursued appears under the form of the reflective questioning of the

responsibilities taken up in the inquiry, since all knowledge is an

attempt to anticipate unrealized possibilities:

Indeed, the idea of knowledge is very imperfectly

realized as long as it is confined to existent individuals. A

lifeless mummy is a knowledge that cannot be applied, -

and [it is a] metaphysical mummy at that, a mummy of

straw. But how can there be any practical application to

the past [?] The future is the practical part of life.

Applicable knowledge, the only knowledge deserving the

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name, is the anticipation of future percepts. Now that

which is in the future only is not among the things that

now exist. Hence in order to realize the idea of

knowledge the man of science must broaden the scope of

his study by adding to the cash collection of existing

things to which he has heretofore limited it, the

corresponding classes of things that are to be. [MS 693B:

115-116].

Our imperfect knowledge of the possibilities of the future is the

only way we have to leave the immediate and limited range of our

concepts and thoughts. This is so because our knowledge depends,

above everything, on the interpretations it receives. Remembering the

distinction between depth and breadth, we can say that to Peirce the

meaning of a concept is related to the way in that the concept is

interpreted: a sign means its object because, within a certain

informative context, it is interpreted as a representation of the object.

In other words, a sign acquires meaning because it informs something

about its object, thus creating with such operation a rule for

interpretation, according to which it can be understood – in one word, it

creates a habit of possible conduct to say how the sign will be able to

be interpreted [MS 693B: 100].

Of course, science in this way understood cannot give answers to

the instabilities of the present. However, the scientific activity carried

on in the long run can lead to the determination of habits of expectation

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that function as hypothetical imperatives of prudence, to prevent us

from surprises:

Our first imperfect knowledge of what is to come to pass

is virtually based upon a state of execution which, if it

were formulated would appear as an assumption that

nothing very surprising is going to occur. I say it is

virtually based on this state of expectation; for no

conclusion is actually based upon an assumption not

deliberately adopted. Now the state of expectation is not

a proposition at all; far less has it been deliberately

embraced. Uncontrolled, uncriticized, and merely

subconscious actions of the mind form no part of

reasoning and are not subject to logic. It is simply a fact

that so we think, and that a state of mind brings about a

belief which is related to a possible formulation of that

state of mind as a conclusion to the premises. [MS 693B:

116-117].

Science, consequently, we repeat, is based on a whole “cultural”

background we do not put into doubt. The creation of meanings and

habits of expectation seems to be, for Peirce, the only way to leave the

unavoidable domain of common-sense beliefs, and to fly higher flights,

to dream wilder dreams, in his own words. The assertion of the

propositions in the scientific community thus allows for their

interpretation from an external point of view, external to their own

rationale, since the whole group of background assumptions is not

exactly the same for all inquirers, even though there is a common

experience being constructed and shared. However, because of the own

nature of the logic of abduction, allowing for the specification of what

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the practical results of a given hypothesis may be if it is taken as true, it

is exactly the biggest problem to know how the construction of such

facticity is brought about in the practice of inquiry, and how is it

possible to favour one interpretation instead of another; and even to

decide which theories count as valid interpretations and which do not

count. One of the conclusions to be drawn from Peirce’s theory of

assertion is that every speech act threefold, i.e., someone utters an

assertion and simultaneously makes reference to what is talked about,

for another. Discourse, whatever it is, is therefore at once referential,

intentional, and self-reflective, and the identification of a new meaning

can itself only be constructed collectively, by at least two: a speaker

and a hearer (who can be the same person). Language, therefore, is

understood by Peirce for the first time as communication, that is, as

interaction. The possibility of interpretation is not anymore given by the

capacity of the other to understand the references mentioned by the

speaker, but by the capacity to share the same experience (and, hence,

because of this, to be able to understand references), that is, by the

capacity to interact within certain worldly context.

In fact, the link between pragmatism and ethics is not fortuitous.

The pragmatic maxim is not only a logical maxim to clarify concepts,

but also a moral maxim. This seems clear when Peirce states the

following: “Pragmatic anthropology, according to Kant, is practical

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ethics. Pragmatic horizon is the adaptation of our general knowledge to

influencing our morals.” [CP 5.1, Pragmatic and Pragmatism, 1902].

The reference to Kant is unequivocal in indicating the ethical

purport of pragmatism, and agrees with the idea presented before, that

the essential nature of knowledge is its capacity to mould to the ends to

which we want it. As a matter of fact, in refusing William James’

interpretation of the pragmatic maxim, Peirce says:

In 1896 William James published his Will to Believe, and

later his Philosophical Conceptions and Practical Results,

which pushed this method to such extremes as must tend

to give us pause. The doctrine appears to assume that the

end of man is action – a stoical axiom which, to the

present writer at the age of sixty, does not recommend

itself so forcibly as it did at thirty. If it be admitted, on

the contrary, that action wants an end, and that that end

must be something of a general description, then the

spirit of the maxim itself, which is that we must look to

the upshot of our concepts in order rightly to apprehend

them, would direct us towards something different from

practical facts, namely, to general ideas, as the true

interpreters of our thought. [CP 5.3, Pragmatic and

Pragmatism].

Now, this is exactly the key idea of the classification of the

sciences: to direct knowledge to the accomplishment of ends, which are

of the nature of general ideas. And the description of the process of

how ideas can influence conduct and even to produce facts is not only

the other side of the question, for future conduct is guided by ideas

themselves. The construction of ideals of conduct, therefore, appears to

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be the ultimate aim of human actions. All knowledge, in short, is based

in an interest, even if this interest is interested in itself. Science, in

Peirce’s thought, appears as a prospective activity, directed towards

the discovery of the self-development of [phýsis], i.e., to the most

supreme possible aim, for it is entirely directed to the domain of what is

merely possible. Thus, science is also an activity of confrontation, for it

is not content with the existent, and seeks the reality of what is not yet.

This reality, however, only reveals itself in so far as science is

produced. Consequently, action appears as an actualized mode of a kind

of general conduct, that is, as a constant adaptation of human beings to

a reality in continuous evolution, by means of the application of

knowledge to the accomplishment of the general ends that are being

built. New fields of experience go arising, new interactions happen,

new revolutions are prepared, always related to other interests: it is

necessary to begin the inquiry with all the concepts and prejudices we

have. This process of constructing ourselves can only be hinted at here.

We hope that in the conclusion of this work these remarks get clearer.

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9. MATHEMATICS AS THE MOST GENERAL SCIENCE: FORM OF EXPERIENCE AND CATEGORIES

Se Deus fosse à escola aprenderia somente matemática.Murilo Mendes, Conversa Portátil115

Mathematics is thought moving in the sphere of complete abstraction from any particular instance of what it is talking about.

Alfred North Whitehead, Science and the Modern World

Mathematics is, in a certain sense, the mother of all sciences. It is

the first of the heuretic sciences, the one immediately preceding

philosophy, and for such reason we will examine it here. Placed on the

top of the classification of the sciences, it makes up the first class of the

sciences of discovery, the most abstract and general heuretic science,

the one that makes the supremest discoveries. Because it is the most

abstract of the sciences, we can say it is the most basic one, that from

which all the sciences borrow principles, taking its own principles from

no other; it is a self-founding science. Because it is the most general

science, its discoveries concern the discoveries of all other sciences, at

the same time in that they do not concern any special state of things. In

other words, mathematics does not concern the nature of reality.

Hence, it “never can be positive science, that is, science of the real.”

[MS 283: 155], though it is a heuretic science. That does not mean

mathematics cannot be an experimental science, for it is possible to

make experiments by merely observing a geometrical figure.

Mathematics is not concerned with the truth of fact because its

115 “If God went to school He would learn only mathematics.” Our translation.

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conclusions are purely hypothetical, depending only and exclusively on

the diagrams and formal constructions used in proofs and calculi: “it is

the only one of the sciences which does not concern itself to inquire

what the actual facts are, but studies hypotheses exclusively” [RLT

114], Mathematical truths, therefore, must have a different

epistemological status than the truths discovered by positive sciences.

Notwithstanding, to rescue philosophy from the lawless rovers of the

sea of literature, giving it the sureness of reasoning it has lost, it is

necessary to mirror it in mathematical thought:

Philosophy requires exact thought, and all exact thought

is mathematical thought. [NEM 4: x, Detached Ideas on

Vitally Important Topics, 1898]

[And:] My special business is to bring mathematical

exactitude, - I mean modern mathematical exactitude

into philosophy, - and to apply the ideas of mathematics

in philosophy.

I don’t mean to shackle anybody with any condition other

than that they should work at the rendering of philosophy

mathematically exact and scientifically founded on

positive experience of some kind. [NEM 4: x-xi, letter to

F. Russell, 23 September 1894].

To understand what it means for Peirce to bring mathematical

precision and accuracy of reasoning to philosophy, furnishing this latter

with scientific exactness and groundings, it is necessary to understand

the definition of philosophy and the place it occupies in the

classification of the sciences. It is not a case of quantifying or

mathematizing philosophy, but only to explicit how formal homologies

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are established between the two sciences. Peirce says philosophy

should be based on some positive experience. The precise meaning of

this is in the requirement that philosophy should be knowledge of real

things, in opposition to the mathematical knowledge, which should be

merely hypothetical. Thus, two senses can be attributed to the word

“philosophy”:

Two meanings of the term ‘philosophy’ call for our

particular notice. The two meanings agree in making

philosophical knowledge positive, that is, in making it a

knowledge of things real, in opposition to mathematical

knowledge, which is a knowledge of the consequences of

arbitrary hypotheses; and they further agree in making

philosophical truth extremely general. [EP 2: 372, The

Basis of Pragmaticism on the Normative Sciences].

The meanings of philosophy are:

a) Philosophy understood as cenoscopy, that is, as a positive

science, for it rests upon the most general familiar

experience, “and does not search out occult or rare

phenomena”; this meaning, according to Peirce, is more

proper to philosophia prima than what is usually called

ontology;

b) Philosophy understood as sythetical philosophy, or

philosophia ultima, that is, a science that seeks to provide

the results obtained by the different special sciences with

a general sense, which results from the organized

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reunion of such results that no one of the special sciences

can alone provide. [EP 2: 372-373]. 116

To Peirce, these two meanings are neither opposed, nor

complementary; they are just different. In the classification of the

sciences, cenoscopy would come before idioscopy, that is, the special

sciences. The terms “cenoscopy” and “idioscopy”, Peirce says he took

them from Jeremy Bentham [HL 151; EP 2: 373]. The words are, in fact,

adaptations of Greek words, [koinoscopia] and

[idioscopia], respectively. means exactly “look up upon

the common”; , “look up upon the particular”.117 Special sciences

are special just because of this: they offer a fragmented view of reality,

i.e., they concentrate upon phenomena taken individually, or upon

specific groups of phenomena, and do not venture upon remarking

about the nature of the totality of being. This is the very task of

cenoscopy: “The business of cenoscopy is to construct, as best as one

may, a true comprehension of the omne, - and if possible, of the totum, -

of being and of non-being, and of the principal divisions of this omne.”

[EP 2: 374, The Basis of Pragmaticism on the Normative Sciences]. In

other words, the main business of cenoscopy, though not the only one,

is to provide us with an universal conception of the world: “Its principal

116 “For one of them [the meanings of the term philosophy], which is better entitled (except by usage) to being distinguished as philosophia prima than is ontology, embraces all that positive science which rests upon familiar experience and does not search out occult or rare phenomena, while the other, which has been called philosophia ultima, embraces all that truth which is derivable by collating the results of the different special sciences, but which is too broad to be perfectly established by any one of them.”117 Cf. CP 1.241-242, editor’s notes 1 and 2.

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utility, although by no means its only utility, is to furnish a

Weltanschauung, or conception of the universe, as a basis for the

special sciences.” [HL 151]. To attain this total view of the universe,

cenoscopy should rest upon the total experience of the world, rather

than in some special experience:

Cenoscopy is not to resort to special experience, or only

upon the most exceptional occasions, in order not to

break the discussion of one question. There is no

veritable exception. To say that cenoscopy is not to resort

to special experience is to say it is to be science in the

seminal condition. [EP 2: 374].

Thus, cenoscopy should begin its inquiries scrutinising everything

experience shows us that is universal and pervasive, general and

evident. The method of cenoscopic inquiry, as the very name says, rests

upon the careful observation of all manifestations of usual experience:

“Philosophy is positive science, in the sense of discovering what really

is true; but it limits itself to so much of truth as can be inferred from

common experience.” [EP 2: 259, An Outline Classification of the

Sciences]. In effect, the philosophical inquiry, to Peirce, has a positum

– our common-sense experiences:

Class II [of heuretic sciences] is philosophy, which deals

with positive truth, indeed, yet contents itself with

observations such as come within the range of every

man's normal experience, and for the most part in every

waking hour of his life. Hence Bentham calls this class,

coenoscopic. These observations escape the untrained

eye precisely because they permeate our whole lives, just

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as a man who never takes off his blue spectacles soon

ceases to see the blue tinge. Evidently, therefore, no

microscope or sensitive film would be of the least use in

this class. The observation is observation in a peculiar,

yet perfectly legitimate, sense. If philosophy glances now

and then at the results of special sciences, it is only as a

sort of condiment to excite its own proper observation.

[CP 1.241]

In the beginning, the biggest difficulty in philosophical inquiry is,

indeed, to cope with the certainties of common-sense, which are

extremely vague and general, such certainties as expressed in

propositions such as “fire burns”118. Such experiences inform our world

view, before any scientific world view. For such reason, it is very

difficult to observe critically common-sense beliefs, for we consider

them natural, when in fact they are beliefs, as falsifiable as any other;

thereby the necessity to have high attention and critique in cenoscopy:

The method of cenoscopic research presents a certain

difficulty. In commencing it we are confronted with the

fact that we already believe a great many things. These

beliefs, or at least the more general of them, ought to be

reconsidered with deliberation. This implies that it

should be conducted according to a deliberate plan

adopted only after the severest criticism. Each criticism

should wait to be planned, and each plan should wait for

criticism. Clearly, if we are to get on all, we must put up

with imperfect procedure. [EP 2: 373].

This description of philosophy as the second theoretical science of

discovery, in order of generality, answers a series of questions as to the

118 TIERCELIN (1993b), pp. 11-15.

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nature of philosophical activity. A clear feature of Peirce’s definition of

philosophy is that any person can have access to philosophical inquiry.

Differently from special sciences, as physics or biology, for instance,

whose procedures several times require the use of budgets if special

observations, the observations of philosophy consider as data the most

usual and common experiences of everyday life:

I have already explained that by Philosophy I mean that

department of Positive Science, or Science of Fact, which does

not busy itself with gathering facts, but merely with learning

what can be learned from that experience which presses in

upon every one of us daily and hourly. It does not gather new

facts, because it does not need them, and also because new

general facts cannot be firmly established without the

assumption of a metaphysical doctrine; and this, in turn,

requires the cooperation of every department of philosophy; so

that such new facts, however striking they may be, afford

weaker support to philosophy by far than that common

experience which nobody doubts or can doubt, and which

nobody ever even pretended to doubt except as a consequence

of belief in that experience so entire and perfect that it failed

to be conscious of itself; just as an American who has never

been abroad fails to perceive the characteristics of Americans;

just as a writer is unaware of the peculiarities of his own style;

just as none of us can see himself as others see him. [HL 207-

208].

The starting point for philosophy is the here-and-now of every

human being, the world of common-sense of which there are no reasons

to doubt, because one does not perceive it can be doubted, being

immerse in it as we are. Thus, any person also could put to test the

conclusions of a philosophical inquiry, to confirm or to refute its

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veracity.119 Therefore, the only reliable method for the confirmation of

the conclusions of cenoscopy is the inductive method, because it is the

method that raises the possibility of generalization to the infinite [EP 2:

373]. If the conclusions of philosophy consider from the start and

concern the most usual and general experience, their force is to be in

the possibility of being plainly universal, with the minimal probability of

exceptions. Thus, philosophical inquiry turns ab ovo to life, and not to

books: “Certainly, in philosophy what a man does not think out for

himself he never understands at all. Nothing can be learned out of

books or lectures. They have to be treated not as oracles but simply as

facts to be studied like any other facts.” [HL 139].

Then, in sum, philosophy can be understood as the science of the

clash with experience, the science that seeks to render experience

intelligible in its most disturbing and resistant features, as well as in its

most universal and quotidian features. Each of its subclasses is defined

by the characteristic manner of understanding the world of experience.

In first place, there comes phenomenology:

This must be a science that does not draw any distinction

of good and bad in any sense whatever, but just

contemplates phenomena as they are, simply opens its

eyes and describes what it sees […]. This is the science

which Hegel made his starting-point, under the name of

the Phänomenologie des Geistes – although he

considered it in a fatally narrow spirit, since he restricted

himself to what actually forces itself on the mind and so

119 HANTZIS (1987), p. 292; TIERCELIN (1993b), p. 9.

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colored his whole philosophy with the ignoration of the

distinction of essence and existence and so gave it the

nominalistic and I might say in a certain sense the

pragmatoidal character in which the worst of the

Hegelian errors have their origin. I will so far follow

Hegel as to call this science Phenomenology although I

will not restrict it to the observation and analysis of

experience but extend it to describing all the features

that are common to whatever is experienced or might

conceivably be experienced or become an object of study

in any way direct or indirect. [HL 120].

Therefore, phenomenology is not the science only of what

appears, but of what seems to be in a certain way. It is not a matter of

interpreting experience to understand what is it that it says about the

reality of the outward world, but to inspect experience itself, resting

upon the observation and the description of its most essential

elements.120

The normative sciences make up the second subclass of

cenoscopy; they can be briefly defined by means of “the analysis of the

conditions of attainment of something of which purpose is an essential

ingredient.” [CP 1.575, Minute Logic]. Because they are inquiries into

the ways for attaining certain ends, these sciences are called

normative, because they settled the conditions for controlled action,

that is, according to a norm, to the fulfillment of such ends. That is why

they distinguish between what ought to be and what ought not to be

[EP 2: 259, An Outline Classification of the Sciences].

120 IBRI (1992), p. 13; HANTZIS (1987), p. 294.

404

Finally, metaphysics is the third subclass of philosophy, being the

science that seeks to give an interpretation of the universe of mind and

matter [id.], that is, it is the science that seeks to say what is reality in

its most general features and characteristics [EP 2: 375]. For Peirce,

the situation of metaphysics in his time was lacking rigour and scientific

parameters: “But in its present condition it is, even more than the other

branches of cenoscopy, a puny, rickety, and scrofulous science.” [id.].121

The only science philosophy borrows principles from is

mathematics. Therefore, philosophy must analise the data of common

experience according to mathematical criteria. How is it possible? The

answer to this question lies in the answer of another: what is the form

of experience? Remember what was already said on the nature of

experience: it is defined by Peirce as the cognitive final outcome of

living:

Experience may be defined as the sum of ideas which

have been irresistibly borne in upon us, overwhelming all

free-play of thought, by the tenor of our lives. The

authority of experience consists in the fact that its power

cannot be resisted; it is a flood against which nothing can

stand. [CP 7.437, Grand Logic, c. 1893].

According to such definition, mental hallucinations, ilusions,

imaginations of everyt sort and kind also make up experience, which is

121 We will leave the divisions of philosophy for now. For a more detailed account, the reader can look up, for instance, about phenomenology, the works mentioned in note 8 below. On the normative sciences: MCCARTHY (1980); PARKER (2003); PARRET (1994); POTTER (1967); SANTAELLA (2000); SHERIFF (1994), cap. 5: “Esthetics, Ethics, and Logic”; SILVEIRA (2003). On metaphysics: HAUSMAN (1993), passim; HOOKWAY (1998); IBRI (1992), passim; IBRI (2003).

405

not reduced, then, only to the notion of “sensible perception” [CP 6.492,

c. 1896]. But there is another characteristic, namely, compulsiveness,

which was already mentioned. See the following passgem where once

more the link between the idea of experience and expectation is

clarified:

We live in two worlds, a world of fact and a world of

fancy. Each of us is accustomed to think that he is the

creator of his world of fancy; that he has but to

pronounce his fiat, and the thing exists, with no

resistance and no effort; and although this is so far from

the truth that I doubt that much the greater part of the

reader’s labor is expended on the world of fancy, yet it is

near enough the truth for a first approximation. For this

reason we call the world of fancy the internal world, the

world of fact the external world. In this latter, we are

masters, each of us, of his own voluntary muscles, and of

nothing more. But man is sly, and contrives to make this

little more than he needs. Beyond that, he defends

himself from the angles of hard fact by clothing himself

with a garment of contentment and of habituation. Were

it not for this garment, he would every now and then find

his internal world rudely disturbed and his fiats set at

naught by brutal inroads of ideas from without. I call

such forcible modification of our ways of thinking, the

influence of the world of fact, experience. But he patches

up his garment by guessing that those inroads are likely

to be and carefully excluding from his internal world

every idea which is likely to be so disturbed. Instead of

waiting for experience to come at untoward times, he

provokes it when it can do no harm and changes the

government of this internal world accordingly. [EP 2:

406

369-370, The Basis of Pragmaticism in Phaneroscopy,

1906].

Experience has a clear power to shape conduct, as well as to

modify it. It is by means of clashing with the outward world of fact that

we get to create habits of expectations, so that we are not anymore

surprised by the “brutal inroads” from the ideas of outside. Thus, linked

to the idea of “outward clash” [W 5: 225, An American Plato],

experience is the coup that fecunds consciousness and begins

knowledge [EP 2: 374]. In other words, experience has an unavoidable

feature of constraint:

[…] the concept of experience is broader than that of

perception, and includes much that is not, strictly

speaking, an object of perception. It is the compulsion,

the absolute constraint upon us to think otherwise than

we have been thinking that constitutes experience. Now

constraint and compulsion cannot exist without

resistance, and resistance is effort opposing change.

Therefore there must be an element of effort in

experience; and it is this which gives it its peculiar

character. [CP 1.336, Phaneroscopy or the Natural

History of Concepts, c. 1905]

For such reason, experience is characteristically a factor of

modification of consciousness. Now, in truth, as Peirce himself asserts,

experience teaches us to foresee the general future mode of conduct of

events, and not only by means of external sensible perception. Not

restricted to the actual object of perception, experience also has the

feature of possibility; so, it is not reduced to merely actual and physical

407

compulsions. Contents of thoughts can also exert compulsion and

change the course of thinking:

Experience is double, as much as reality is. That is, there

is an outward and an inward experience. Under the latter

head ought particularly to be reckoned a mathematical

experience, not usually so called, which has compelled

the development of pure thought to take a determinate

course. [CP 7.440, Grand Logic].

Now, if philosophy is the attempt to conceive a Weltanschauung

grounded on the observation of experience, to ask for the form of

experience is to ask for the way how knowledge begins. In other words,

it is necessary to explain how mental content in general can be

organized and structured. Philosophy, then, is defined as a search for

the primordial constitutive elements universally present in every

experience. To Peirce, such elements are its universal categories of

firstness, secondness, and thirdness.122 The passage above suggests that

the determination of such universal features of experience can be made

mathematically, in a way that it becomes possible to project abstract

forms over reality. Thus, mathematics can be conceived by Peirce as an

activity of construction of general structures or models that can be

combined with any sort of experience.123 It would so be possible to

isolate a basic framework, relatively simple, universally applicable to

122 Cf. TIERCELIN (1993b), p. 15 and especially chap. 1: “Pour une analyse logique des produits de la pensée”; HOUSER (1990), p. 4. We will not see here in detail each of Peirce’s categories. The literature about the subject is extense. We briefly indicate: APEL (1995a), pp. 109-110; DE TIENNE (1996), passim; IBRI (1992), cap. 1: “A Fenomenologia: as categorias da experiência”; ROSENTHAL (1994), chap. 4: “Pragmatic experimentalism and the derivation of the categories”.123 HOUSER (1990), pp. 3-4; APEL (1995a), p. 119-120.

408

experience, that would reveal its ubiquitous form. In effect, the

examination of omnipresent experience presupposes mathematics:

This science of Phenomenology is in my view the most

primal of all the positive sciences. That is, it is not based,

as to its principles, upon any other positive science.

Phenomenology […] if it is to be properly grounded, be

made to depend upon the Conditional or Hypothetical

Science of Pure Mathematics, whose only aim is to

discover not how things actually are, but how they might

be supposed to be, if not in our universe, then in some

other. [HL 120-121].

Then, there is put the problem of the mathematical and the

phenomenological forms of the categories: does experience has a

mathematical or a phenomenological form? If the principles of

phenomenology are in pure mathematics, then phenomenology must be

able to give an account of every and any kind of experience, or better,

form of experience, including one that is not familiar to us in this world,

but indeed of all possible experience in any possible world. We can

fancy two possibilities, to wit: if, on the one hand, the categories of

experience are conceived as kinds of relations, experience will

essentially possess a mathematical form; if, on the other hand,

categories are kinds of consciousness, experience essentially is

phenomenological. As a matter of fact, Peirce adopted both accounts,

saying it is possible a mathematical as well as a phenomenological

extraction of the categories. The problem of the form of experience,

seen as a problem of the relationship between mathematics and

409

phenomenology can thus be understood as the problem of the

conditions of possibility for projecting mathematical forms over

experience 124. This problems goes back to the remote begnnings of

history of science and philosophy, at least to Pythagoras, and we can

suspect Peirce had it in mind when he wrote the following:

Pythagoras may be said to have originated the whole

science of physics by observing a connection between the

intervals of the tones of strings and the weights which

stretched them. This probably belonged to the secret

doctrine; for as it has come down to us, it is so totally

wrong that the least experiment would show it. Yet

without experiment the idea could not have arisen.

Namely the statement made is that the ratios of weights

12 : 6, 12 : 8, 12 : 9 are respectively an octave, a fifth,

and a fourth. Now the true ratios are precisely the

square roots of these. Evidently, Pythagoras must have

known the truth. It is a historical fact then that he was

the father of physics. No small glory that.

[…]

Pythagoras thought that numbers were the substance of

things. What he meant, I do not believe he knew or

thought he knew. It was his highest aperçu. He felt he

could not quite grasp it. [HP I: 176-177, Early History of

Science].

Peirce sought to unite all these elements in a realist conception of

mathematics as heuretic science. What he himself thought of

Pythagoras’ thought maybe is the following:

124 APEL (1995a), p. 120 ff.; HOUSER (1990), p. 2; PARKER (1998), pp. 103 ff.

410

A state of things is an abstract constituent part of reality,

of such a nature that a proposition is needed to represent

it. […]

A mathematical form of a state of things is such a

representation of that state of things, without definitely

qualifying the subjects of the samenesses and diversities.

It represents not necessarily all of these; but if it does

represent all, it is the complete mathematical form. Every

mathematical form of a state of things is the complete

mathematical form of some state of things. [EP 2: 378,

The Basis of Pragmaticism in the Normative Sciences].

From the quotation above we can grasp the aim of mathematical

inquiry: to represent in a general and abstract manner all possible

forms of states of things, no matter whether existent or not. According

to such idea, we can quote the following Peircean definition of

mathematics:

The first is mathematics, which does not undertake to

ascertain any matter of fact whatever, but merely posits

hypotheses, and traces out their consequences. It is

observational, in so far as it makes constructions in the

imagination according to abstract precepts, and then

observes these imaginary objects, finding in them

relations of parts not specified in the precept of

construction. [CP 1.240, A Detailed Classification of the

Sciences]. 125

125 See LUCAS (2003), p. 143. For the interpretation of Peirce’s philosophy of mathematics, we basically follow HOOKWAY (1992), pp. 192 ff. and MURPHEY (1993), chap. 12: “Pure Mathematics”. For a detailed discussion of Peirce’s philosophy of mathematics as well as his mathematics, the reader can consult RLT 1-54, the introduction written by Ketner and Putnam; besides, see MURPHEY (1993), pp. 183-288, and PARKER (1998), chapters 3: “The Mathematics of Logic: formal aspects of the categories” and 4: “Infinity and Continuity”; cf. also HOUSER (1990); JOSWICK (1988); TIERCELIN (1993a); KERR-LAWSON (1997).

411

In other words, the mathematician is not concerned with the

positive truth of what in fact is, but only with his or her hypothetical

truth, that is, with what could or could not be necessarily concluded

from the imaginary hypotheses constructed. Mathematics, therefore, is

the science that seeks to define pure possibilities. The mathematician

first frames hypotheses, and next observes what necessarily it is

possible to conclude as consequence from such constructions. After

that, it is possible to generalize the conclusions obtained to every

occasion possible of being described in the terms of the imagined

hypotheses. Mathematical knowledge, thus, is purely hypothetical:

Modern science, even from the first, took away from

demonstratively certain knowledge much of its luster;

and mathematicians who alone produce such knowledge,

now see clearly that such knowledge can only be

knowledge of hypothetical states of things, or say of the

implications of arbitrary hypotheses; and never can be

positive science, that is, science of the real. [MS 283:

155, 1906].

Therefore, the imaginary constructions of mathematics can be

applied to any situation of fact, any actual occasion, because they can

be applied to some situation of fact.

Already in 1885, in On the Algebra of Logic: A Contribution to the

Philosophy of Notation, Peirce recognized a difficulty in defining the

scientific status of mathematics:

It has long been a puzzle how it could be that, on the one

hand, mathematics is purely deductive in its nature, and

412

draws its conclusions apodictically, while on the other

hand, it presents as rich and apparently unending a

series of surprising discoveries as any observational

science. Various have been the attempts to solve the

paradox by breaking down one or other of these

assertions, but without success. [W 5: 164].

Shortly after, Peirce tells the key to solve this dilemma, to wit, a

correct understanding of the nature of deduction. We have seen that

deduction is the only form of necessary reasoning. In mathematics,

there are two kinds of deduction, theorematical and corollarial

deduction:

My first real discovery about mathematical procedure

was that there are two kinds of necessary reasoning,

which I call the Corollarial and the Theorematic, because

the corollaries affixed to the propositions of Euclid are

usually arguments of one kind, while the more important

theorems are usually of the other. The peculiarity of

theorematic reasoning is that it considers something not

implied at all in the conceptions so far gained, which

neither the definition of the object of research nor

anything yet known about could of themselves suggest,

although they give room for it. Euclid, for example, will

add lines to his diagram which are not at all required or

suggested by any previous proposition, and which the

conclusion that he reaches by this means says nothing

about. I show that no considerable advance can be made

in thought of any kind without theorematic reasoning.

When we come to consider the heuretic part of

mathematical procedure, the question how such

suggestions are obtained will be the central point of the

discussion. [NEM 4: 49, Carnegie Application].

413

Now, “reasoning essentially consists in the observation that

where certain relations subsist certain others are found” [W 5: 164].

What the distinciton between the two forms of deductive reasoning

shows is that mathematical reasoning is not only the observation of

what is evident in a formal representation of a state of things, but it is

also a constructive activity of such representations, by means of

observing and modifying other representations. This is the heuristic

part of mathematics, the one that makes us see something not implied

in the premisses, clearly involving an abductive reasoning.126 We can

take yet another passage, wherein the difference between the two kinds

of deduction is expressed in other terms:

A Corollarial Deduction is one which represents the

conditions of the conclusion in a diagram and finds from

the observation of this diagram, as it is, the truth of the

conclusion. A Theorematic Deduction is one which,

having represented the conditions of the conclusion in a

diagram, performs an ingenious experiment upon the

diagram, and by the observation of the diagram, so

modified, ascertains the truth of the conclusion. [EP 2:

208, Nomenclature and Divisions of Triadic Relations].

Mental experiments, according to the quotation above, are the

same as observations of the diagram. In corollarial deduction, the

procedure starts from the observation of a diagram such as it is,

without any modification, to affirm the conclusion. The conclusion,

therefore, is necessarily obtained only from what is expressed in the

126 CROMBIE (1997), p. 465 ff.

414

diagram, without any further adjunction to the conclusion.

Theorematical deduction, in turn, modifies the diagram to discover new

relations not evident in its initial form of presentation. Thus, it is the

process whereby the truth of mathematical conclusions is ascertained

“by performing a variety of experiments in our imagination.” [NEM 4:

xiv, s/d].

Such definitions of mathematics in Peirce’s works abound. One of

them says the following:

The first [science of discovery] is mathematics, which

does not undertake to ascertain any matter of fact

whatever, but merely posits hypotheses, and traces out

their consequences. It is observational, in so far as it

makes constructions in the imagination according to

abstract precepts, and then observes these imaginary

objects, finding in them relations of parts not specified in

the precept of construction. This is truly observation, yet

certainly in a very peculiar sense; and no other kind of

observation would at all answer the purpose of

mathematics. [CP 1.240, A Detailed Classification of the

Sciences, 1902].

The quotation above shows very well the link between the

theorematical and the corollarial processes in mathematical reasoning.

Once more there appears the idea that the mathematician is not

concerned with the positive truth of what actually is, but only with what

could or could not be necessarily concluded, from the imaginary

hypotheses framed. By showing the intertwinement of the moments of

creation of formal models and of deduction of the conclusions

415

necessarily implied in such models in the mathematical procedure,

Peirce relates two distinct ways of defining mathematics:

relaciona duas maneiras de definir a matemática:

[...] it is an error to make mathematics consist exclusively

in the tracing out of necessary consequences. For the

framing of the hypothesis of the two-way spread of

imaginary quantity, and the hypothesis of Riemann

surfaces were certainly mathematical achievements.

Mathematics is, therefore, the study of the substance of

hypotheses, or mental creations, with a view to the

drawing of necessary conclusions. [NEM 4: 268, On

Quantity].

In this way, Peirce follows the definition of mathematics given by

his father Benjamin Peirce, according to which mathematics is the

science that draws necessary conclusions, in contradistinction to logic,

which is the science of drawing necessary conclusions:

The philosophical mathematician, Dr. Richard Dedekind,

holds mathematics to be a branch of logic. This would not

result from my father's definition, which runs, not that

mathematics is the science of drawing necessary

conclusions – which would be deductive logic – but that it

is the science which draws necessary conclusions. [CP

4.239, Minute Logic].

Notwithstanding, if we focus on the definition of mathematics, we

will be able to conclude that, in a certain sense, mathematics is logic, or

at least, that logic is a constitutive part of the mathematical procedure.

In fact, the most important difference between logic and mathematics is

in the interest of each science. Take for instance the following passage:

416

For my part, I consider that the business of drawing

demonstrative conclusions from assumed premisses, in

cases so difficult as to call for the services of a specialist,

is the sole business of the mathematician. Whether this

makes mathematics a branch of logic, or whether it cuts

off this business from logic, is a mere question of the

classification of the sciences. I adopt the latter

alternative, making the business of logic to be analysis

and theory of reasoning, but not the practice of it. [CP

4.134, The Logic of Quantity, 1893].

On the one hand, the logician is not concerned with this or that

special hypothesis, unless that in studying it, it brings him some new

information on the nature of reasoning. On the other hand, the

primordial interest of the mathematician is focused on the hypotheses

taken individually, and in how it is possible to pass necessarily from the

premises to the conclusions in each case; the interest of the

mathematician, therefore, is in the effectiveness of the methods of

reasoning, for their capacity of being extended to other unknown

instances; mathematics deals with the possible generalization of the

hypotheses, rather than with sinuosities of reasoning. For instance,

Peirce says:

The logician does not care particularly about this or that

hypothesis or its consequences, except so far as these

things may throw a light upon the nature of reasoning.

The mathematician is intensely interested in efficient

methods of reasoning, with a view to their possible

extension to new problems; but he does not, qua

mathematician, trouble himself minutely to dissect those

417

parts of this method whose correctness is a matter of

course. [CP 4.239].

This point is clarified if we look up at how each scientist considers

logical algebra:

The mathematician asks what value this algebra has as a

calculus. Can it be applied to unraveling a complicated

question? Will it, at one stroke, produce a remote

consequence? The logician does not wish the algebra to

have that character. On the contrary, the greater number

of distinct logical steps, into which the algebra breaks up

an inference, will for him constitute a superiority of it

over another which moves more swiftly to its conclusions.

He demands that the algebra shall analyze a reasoning

into its last elementary steps. Thus, that which is a merit

in a logical algebra for one of these students is a demerit

in the eyes of the other. The one studies the science of

drawing conclusions, the other the science which draws

necessary conclusions. [Id.].

So, logic seems to be interested in the “rhetorical” character of

reasoning, aiming at explicating every step – and not only the necessary

ones – of reasoning from premises to conclusions. Indeed, rhetoric is an

essential part of the Peircean conception of logic. Since the method of

science proceeds pragmatically and experientially, scientific activity

necessarily involves the adoption of methods of inquiry that are public

and dialogical. That is why it is important to define a theory of assertion

that, overcoming the difficulties of modern philosophy, allows for an

evaluation of speech as a way of attributing and claiming

responsibilities to the members of the inquiring community. And this, of

418

course, leads to an amplification of the domain of rhetoric in the context

of inquiry. Thus, logic widely conceived as semiotics would have three

orders:

All thought being performed by means of signs, logic may

be regarded as the science of the general laws of signs. It

has three branches: (1) Speculative Grammar, or the

general theory of the nature and meanings of signs,

whether they be icons, indices, or symbols; (2), Critic,

which classifies arguments and determines the validity

and degree of force of each kind; (3), Methodeutic, which

studies the methods that ought to be pursued in the

investigation, in the exposition, and in the application of

truth.127 [EP 2: 260, An Outline classification of the

Sciences].

These three divisions of logic constitute what Peirce calls the

philosophical trivium, wherein the rhetoric purport of each of them is

manifest; as in the case of speculative grammar, which studies several

other ways of uttering assertions, besides verbal expressions: "such as

algebra, arithmetical figures, emblems, gesture-language, manners,

uniforms, monuments, to mention only intentional modes of

declaration.” Speculative grammar, thus, is the study of the modes of

signifying, in general [EP 2: 19, Of Reasoning in General]. The

discipline Peirce calls speculative rhetoric is also straightly linked to

the study of the ways to be used in meaning something: ““An art of

thinking ought also to recommend such forms of thinking as will most

economically serve the purpose of Reason. […] Since this is the general

127 For a good succinct introduction to the theme of rhetoric in Peirce’s thought, see LISZKA (2000).

419

foundation of the arte of putting propositions into effective forms, it has

been called speculative rhetoric.” [id.].

Mathematics, differently, rests upon the principle of parsimony in

its procedures, what is just the application of Ockham’s razor to

reasoning. It is not the business of mathematicians to seek to evaluate

or to classify reasonings, developing all the steps, saying which is the

beautiful reasoning, or the most effective; mathematics, as an

experimental science over diagrams, seeks only to study the possible

hypothetical consequences, in a tied relation with what the pragmatical

maxim declares:

Consider what effects, which might conceivably have

practical bearings, we conceive the object of your

conception to have. Then, our conception of these effects

is the whole of our conception of the object. [W 3: 266,

How to Make Our Ideas Clear].

The definition of mathematics as the study of what is true of

hypothetical state of things is more frequent in Peirce’s writings. Such

definition justifies why the truth values of mathematical sentences do

not matter so much: the mathematician admits as object of study every

and any hypothesis, without being interested in knowing whether they

are true or not. Very often the mathematician constructs a

mathematical form following the indications given to him or her by

other scientists, who find themselves in an aporetical situation without

understanding the relations the objects entertain in a certain state of

things:

420

Now a mathematician is a man whose services are called

in when the physicist, or the engineer, or the

underwriter, etc., finds himself confronted with an

unusually complicated state of relations between facts

and is in doubt whether or not this state of things

necessarily involves a certain other relation between

facts, or wishes to know what relation of a given kind is

involved. He states the case to the mathematician. The

latter is not at all responsible for the truth of those

premises: that he is to accept. The first task before him is

to substitute for the intricate, and often confused, mass

of facts set before him, an imaginary state of things

involving a comparatively orderly system of relations,

which, while adhering as closely as possible or desirable

to the given premises, shall be within his powers as a

mathematician to deal with. This he terms his hypothesis.

That work done, he proceeds to show that the relations

explicitly affirmed in the hypothesis involve, as a part of

any imaginary state of things in which they are

embodied, certain other relations not explicitly stated.

[NEM 4: 267, On Quantity].

Hence, it makes no sense to distinguish sharply between pure and

applied mathematics.128 Once the mathematician constructs hypotheses

grounded upon a suggestion from experience, he or she has in sight

some application of the models devised. There is a demand that the

mathematician be capable to imagine models simple enough to work

with them. Then, it is his or her task to simplify the relations to the

most to try to find those that are the most elementary. There is no

metaphysical reason behind this; as the mathematical procedure is

128 TIERCELIN (1993a), pp. 41-45.

421

marked by the parsimony of reasoning, the safest way of avoiding

mistakes is also the easiest way to discover necessary relations, to wit,

to simplify and to reduce the relations to the absolutely essential. Thus,

what the mathematician does is to imagine a highly abstract model of

simplified relations, yet still capable of expressing the relations of the

facts. This high degree of abstraction allows for the generalization:

All features that have no bearing upon the relations of

the premisses to the conclusion are effaced and

obliterated. The skeletonization or diagrammatization of

the problem serves more purposes than one; but its

principal purpose is to strip the significant relations of all

disguise. [CP 3.559, The Logic of Mathematics in

Relation to Education, 1898].

The mathematician, then, makes two different things. First, he or

she imagines a hypothesis, represented in the form of a highly abstract

diagram of the state of things, representative only of its most essential

relations, without caring about whether the representation will or will

not correspond to the actual reality. Second, the mathematician begins

to draw necessary conclusions from such relations, conclusions not

explicit in the diagram. Mathematical necessity, therefore, comes from

the logical connexion settled between premises and conclusions. The

mathematician adopts hypotheses, conclusions, rules, and goes on to

verify which state of things necessarily follows from another.

Mathematics thus defined is purely formal, and concerns only the

possibility of application of its models to the actual reality:

422

Now the feature of mathematics which separates it

widely both from Philosophy and from every special

science is that the mathematician never undertakes (qua

mathematician) to make a categorical assertion from the

beginning of his scientific life to the end. He simply says

what would be the case under hypothetical

circumstances. [NEM 4: 208, Reason’s Conscience].

The hypothetical character of its assertions, besides

distinguishing it from the positive sciences that state factual truth,

warrants the very necessity of the conclusions: the interest of the

mathematician is uniquely for the form of relations. Mathematics,

consequently, opens a vast field of structural possibilities.129 The special

circumstance embodying what was mathematically ascertained is

merely contingent. To know if a given form can de facto be applied to

an actually existent state of things is a scientific question that each

scientist must resolve according to his or her needs. The mathematician

only defines the question de jure, that is, to the mathematician is due

solely the work with structures likely to be applied, which result in

certain necessary conclusions.130

It is important to notice the possibility of deducing necessary

conclusions from mathematical propositions; this is the very nature of

mathematical inquiry:

The first of these [three divisions of heuretic science]

comprises the business of finding out what might and

more especially what could not, be true under described

129 HOUSER (1990), p. 4; KERR-LAWSON (1997), p. 79.130 KERR-LAWSON (1997), id.

423

circumstances, without asking whether or not such

circumstances ever really occur. To my apprehension,

this precisely defines mathematics [...]. [MS 1338: 6, c.

1906].

The meaning of mathematical terms and propositions, in this way,

is confined to their form of expression in mathematical signs: “The

meaning of a mathematical term or sign is its expression in the kind of

signs in the imaginary or other manifestations of which the

mathematical reasoning consists. For geometry, this [expression] is [in]

a geometrical diagram.” [NEM 2.251]. However, this does not mean

that mathematical truths are defined by their use in determined

contexts, or that they are determined by some linguistic convention. It

is the importance of the modus operandi, that is, the way how

demonstrations are made and the application of the very mathematical

demonstrative procedures to the hypothetical diagrams that gives

mathematics its sureness:

I certainly think that the certainty of pure mathematics

and of all necessary reasoning is due to the circumstance

that it relates to objects which are the creations of our

own minds, and that mathematical knowledge is to be

classed along with knowledge of our own purposes. [HL

227].

The meaning of mathematical constructions is not given ab ovo,

but it is defined by demonstration: to reason is not only to use

meanings, it is not merely to operate signs, but it is also to construct

424

them, to manipulate signs in a certain way to determine them and to

suggest certain interpretations.131

The Peircean definition of mathematics, in short, has two main

characters; to wit:

1st, mathematics does not concern a special range of entities, as

every other science depending upon it in the classification of the

sciences. In other words, it is not defined neither by means of the

specificity of its objects, nor by the nature of its propositions, nor even

by the kinds of truths it may exhibit; mathematics has nothing to say

about the truth of fact because it is a science dealing with hypothesis

and abstractions; in a more traditional language, one could say that

mathematics is a science, the objects of which are entia rationis [EP 2:

352].132

2nd, according to his father Benjamin Peirce, mathematics is the

science that draws necessary conclusions. Indeed, every necessary

reasoning is mathematical reasoning [NEM 4.47]. This second

characteristic raises the problem of the definitions of a mathematical

ontology.133 What would be the nature of such entia rationis? Would they

be purely arbitrary conventions, since they do not refer to actual

reality? Or would they be purely analytical propositional systems, or

even tautological systems? If it be so, why then to insist in the practical 131 As a matter of fact, this is linked to the theme of self-controlled thinking, which is an essential subject for the definition of logic as normative science. See TIERCELIN (1993a), p. 34.132 TIERCELIN, (1993a), pp. 30-31133 For the supposed Platonism of such conception, a subject we are not able to deep here, see TIERCELIN (1993a); KERR-LAWSON (1997).

425

side of mathematics, that is, over the possibility of application of

mathematics to problems of the positive sciences?134 In short, this is

question of how to connect Peirce’s indeterminist realism with his

conception of mathematics. As a matter of fact, fallibilism in

mathematics is problematic for Peirce, who several times asserts that

error in mathematics is due only to a blunder in reasoning [CP 1.149, c.

1897; 7.108, 1892; 1.248, 1902; NEM 4: 210, 1904]. Therefore, there is

no problem for him to think of the necessity of mathematics as perfectly

compatible with an ideal system, wherein one can reason about possible

cases (and, therefore, undetermined instances), and also about actual

cases.

Finally, it is time now to justify the epigraphs. First, it seems clear

to us that Whitehead adopts a conception of mathematics that is

substantially almost the same as Peirce’s. Take, for instance, the

following statement:

The point with mathematics is that in it we have always

got rid of the particular instance, and even of any

particular sorts of entities. So that, for instance, no

mathematical truths apply merely to fish, or merely to

stones, or merely to colours. So long as you are dealing

with pure mathematics, you are in the realm of complete

and absolute abstraction. All you assert is, that reason

insists on the admission that, if any entities whatever

have any relations which satisfy such-and-such purely

134 In fact, see how TIERCELIN (1993a), p. 31, presents the problem: “If one accepts the notion of applied mathematics as something which is needed by all sciences, what is to warrant that such idealizations have the objective validity which justifies their being used by these other sciences?”

426

abstract conditions, they must have other relations which

satisfy other purely abstract conditions.135

In a very similar way Peirce also insists upon the unavoidable and

abstract character of mathematical conclusions:

The mathematician does not “rely” upon anything. He

simply states what is evident, and notes the

circumstances which make it evident. When a fact is

evident, and nobody does or can doubt it, what could

“reliance” upon anything effect? [NEM 4: 209, Reason’s

Conscience].

In this way, the evidence of the mathematical diagrams forcefully

obliges the mathematician to recognize the necessity of the

consequences. However, Peirce does not understand mathematical

relations as abstract relations of sets of things, whatever might be,

differently from Whitehead:

Thus, in considering the relations of the number ‘five’

with the number ‘three’, we are thinking of two groups of

things, one with five members and the other with three

members. But we are entirely abstracting from any

consideration of any particular entities, or even of any

particular sorts of entities, which go to make up the

membership of either of the two groups. We are merely

thinking of those relationships between those two groups

which are entirely independent of the individual essences

of any of the members of either group.136

Whitehead speaks in terms of groups of particular things. This is

an important detail, for it should be notices that Peirce does not say

that in mathematics we deal with any groups or sets of objects. In fact,

135 WHITEHEAD (1962), p. 31. 136 Our italics. WHITEHEAD (1962), p. 30.

427

the domain ot the Peircean mathematical ontology may very well go

beyond sets, for mathematical objects do not exist, but are merely

imaginary. Therefore, there is no reason why to be constrained to sets

or to relations between sets. Peirce strongly emphasizes the necessity

of mathematical conclusions; but on their applicability, the only thing

one may affirm is that they might or might not be actualized. Algebra

indeed does not want to say anything besides its own forms:

The algebraic system of symbols is a calculus; that is to

say, it is a language to reason in. Consequently, while it

is perfectly proper to define a debt as negative property,

to explain what a negative quantity is, by saying that it is

what debt is to property, is to put the cart before the

horse and to explain the more intelligible by the less

intelligible. To say that algebra means anything else than

just its own forms is to mistake an application of algebra

for the meaning of it. [CP 4.133, The Logic of Quantity,

1893].

In fact, the true mathematical objects are the very forms of

relations, or, as N. Houser says, the “relational structures” 137.

Generalizing the various relations we find in the actual world, giving

them a substantive form, the relations abstracted from all accidentality

become the objects of mathematical inquiry. Mathematics, then,

acquires the status of a formal logic of relations. Maybe the most

meaningful discovery of mathematics, from this point of view, be that

there are three fundamental forms of relation: monadic (1), dyadic (2),

and triadic (3). Here we have the famous Peircean thesis of the

137 No que segue, seguimos a interpretação de HOUSER (1990), pp. 5 seq.

428

essential irreducibility of the triad, and the reducibility of all other

higher relations ((4), (5), (6), etc.) to the triad. Triads combine both

dyads and monads, and dyads combine monads, that is, (2) and

(1) are present in (3), and (1) is present in (2). In the same way that a

triad, however, cannot be reduced to a dyad, that is, a dyad cannot

represent the same relations that a triad can; and every other relations

of higher order than three can be reduced to the triad. Thus, in (4)

there is (3) and (1), and in (5) there is (3) and (2), and in (9) there is ((3)

x (3)], and so forth. [EP 2: 364, The Basis of Pragmaticism in

Phaneroscopy].

Monads, dyads, and triads make our set of fundamental

categories of relations. The relation of one category containing another

that is exhibited is better understood as the presence of the inferior

relation in the superior one, in a structural manner, as if a part-to-whole

relation. In examining a diagram, the mathematician sees that monads

are structurally elementary, i.e., that they are firsts. Dyads,

consequently, depend on monads, i.e., they necessarily contain them;

and the same is true for triads as to dyads. The three essential forms of

relation therefore correspond to being structurally first, second or third

in mathematics. Through hypostatical abstraction, i.e., the abstraction

that permits the passage from an individual to entis rationis [CP 4.235,

The Simplest Mathematics, 1902; 4.549, Prolegomena to an Apology of

Pragmaticism], the mathematician comes to the categories of firstness,

429

secondness, and thirdness. This group of categories, because they are

extremely formal, is applicable to any triads, whether possible or

actual. Thus, we can know a priori which will be the form of experience,

once it is possible to know what will always be the relations of

dependence to be found in experience.138

“[Abstraction] may be called the principal engine of mathematical

thought.” [CP 2.364, Quantity, 1902] With such affirmation, we have

another way of defining mathematics. An abstraction is “but an object

whose being consists in facts about other things” [NEM 4: Logic of

History, c. 1901]. Mathematical notions, such as collections and

numbers, are the outcomes of abstraction, which cannot be confounded

with generalization:

[Abstraction] consists of seizing upon something which

has been conceived as a [winged word], a

meaning not dwelt upon but through which something

else is discerned, and converting it into an

[non-winged word], a meaning upon which we

rest as the principal subject of discourse. Thus, the

mathematician conceives an operation as something

itself to be operated upon.139 [CP 1: 83, Lessons on the

History of Science].

138 HOUSER (1990), p. 6.139 The image of the winged words Peirce might have borrowed from Homer, who in the Iliad, book I, lines 197-204, describes the encounter of Achilles and Pallas Athena with these words: “Rearing behind him Pallas seized his fiery hair - / only Achilles saw her, none of the other fighters - / struck with wonder he spun around, he knew her at once, / Pallas Athena! The terrible blazing of those eyes, / and his winged words went flying: “Why, why now?/ Child of Zeus with the shield of thunder, why come now?/ To witness the outrage Agamemnon just committed? / I tell you this, and so help me it’s the truth - / he’ll soon pay for his arrogance with his life!” Robert Fagles’ translation.

430

When operations are submitted to other operations in

mathematics, what is done is an abstraction. The abstractive operation

renders possible to take an object as the subject upon which

experiments are made, and from it to infer conclusions about other

objects.140 For instance: “A particle is somewhere quite definitely. It is

by abstraction that the mathematician conceives the particle as

occupying a point.” [NEM 4: 11]. Abstraction, then, defines a fixed

signification – a word without wings – to serve as bedrock for the

understanding of other objects. It is, in fact, an operation for isolating

general relations.

There are two elementary kinds of abstraction, precisive and

hypostatical141: e a hipostática:

With this preface, we may proceed to consider hypostatic

abstraction; that is, abstraction in the sense in which we

speak of abstract nouns, as contradistinguished from

precisive abstraction, which consists in concentrating

attention upon a particular feature of a supposed state of

things. [HP 2: 739, On the Logic of Drawing History].

Precisive abstraction, as it is clear, is only an act of attention, in

which certain aspects are noticed, others neglected. In hypostatical

abstraction, an individual object is taken as an ens rationis, that is, an

entity whose being consists in some other fact; its logical peculiarity is

in that the subject of the conclusion is not expressed in the premises,

140 SHORT (1997), p. 296.141 Do not confound hypostatical abstraction with the operation of prescision. See W 2: 50-51, On a New List of Categories, 1867. We will not explain the latter here; it is explained in detail in our Masters dissertation. See RODRIGUES (2001), pp. 85 ff.

431

and yet the conclusion remains necessary [CP 4.463, On Existential

Graphs, Euler’s Diagrams, and Logical Algebra, 1903]. Peirce’s

favourite illustration for hypostatical abstraction is taken from the third

intermezzo of Molière’s Le Malade Imaginaire142. Molière describes an

oral examination, wherein a doctor in medicine asks a graduate student

which are “the cause and the reason” for opium putting people to sleep.

Confident and full of certainty, the bachelor answers back in his best

Latin: “Quia est in eo virtus dormitiva”, that is, “Because there is in it a

force that makes people sleepy.” He is then applauded by the choir and

accepted in the body of doctors. Molière was satirizing, criticising the

pretension to explain everything with beautiful though empty words,

what in truth one does not know how to explain. For Peirce, even such a

declaration can provide some knowledge, since it asserts that there is

an explanation for the fact, besides the very fact: “For it does say that

there is some peculiarity in the opium to which sleep must be due; and

this is not suggested in merely saying that opium puts people to sleep.”

[CP 5.534, Pragmatism; NEM 4: 11]. In other words, hypostatical

abstraction allows for the formulation of a general conception of a

reality that even though it is manifested in the individual phenomena, it

is not neither exhausted in it nor explicit:

But hypostatic abstraction, the abstraction which

transforms ‘it is light’ into ‘there is light here,’ which is

142 O texto desse intermezzo está disponível, em francês, em hipertexto em vários sítios da Internet. Nós o acessamos em URL: [http://www.eleves.ens.fr/home/sray/moliere/maladimg.html], 18/04/2005.

432

the sense which I shall commonly attach to the word

abstraction (since prescission will do for precisive

abstraction) is a very special mode of thought. It consists

in taking a feature of a percept or percepts (after it has

already been prescinded from the other elements of the

percept), so as to take propositional form in a judgment

(indeed, it may operate upon any judgment whatsoever),

and in conceiving this fact to consist in the relation

between the subject of that judgment and another

subject, which has a mode of being that merely consists

in the truth of propositions of which the corresponding

concrete term is the predicate. Thus, we transform the

proposition, ‘honey is sweet,’ into ‘honey possesses

sweetness.’ ‘Sweetness’ might be called a fictitious thing,

in one sense. But since the mode of being attributed to it

consists in no more than the fact that some things are

sweet, and it is not pretended, or imagined, that it has

any other mode of being, there is, after all, no fiction. The

only profession made is that we consider the fact of

honey being sweet under the form of a relation; and so

we really can. [CP 4.235, The Simplest Mathematics].

Now, it is not merely to suppose entia rationis; hypostatical

abstraction leads us to see non-evident relations, leads us to discover

that the virtus dormitiva of opium must be actually real, since opium

puts us to sleep. The virtus dormitiva, therefore, taken separately from

the fact that opium makes people sleepy, is put as an entity – that is

why such abstraction is called hypostatical.143

Regarding the question of how to give content to abstract forms

and relations, this can only be answered with a minute study of Peirce’s

143 SHORT (1997), p. 296.

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phenomenology, what will not be done in this work. We can however

briefly approach the subject. The most important point, now, is that,

while mathematics gives other sciences formal principles,

phenomenology, being an investigation of the [pháneron], must

provide empirical principles to the categories. As the study of what

seems to be, Peircean phenomenology also does not concern itself with

the precise ontological status of its object:

I propose to use the word Phaneron as a proper name to

denote the total content of any one consciousness (for

any one is substantially any other), the sum of all we

have in mind in any way whatever, regardless of its

cognitive value. This is pretty vague: I intentionally leave

it so. I will only point out that I do not limit the reference

to an instantaneous state of consciousness; for the clause

“in any way whatever” takes in memory and all habitual

cognition. [EP 2: 362].

In this way, the limitations of our metal faculties are not a

problem to phenomenology. Its business is to provide a general

description of everything that may in some way or another be present

to consciousness, inwardly or outwardly. Therefore, it is its business to

make an inventory of the most universal features of experience, i.e., to

give mental content to the abstract forms of mathematics. 144 A fuller

development of such points we reserve for a further occasion. We can

conlcusively add that the categories inform the whole natural

classification of the sciences, in a way that the division between

144 HOUSER (2000), p. 8; IBRI (1992), cap. 2

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heuretic, retrospective and practical sciences corresponds to the

characters of being first, second and third of the phenomenon; in the

same way, purposes are defined according to the cateogries: discovery

is first regarding the organization of knowledge, for it is not possible to

organized what is unknown; and application is third, mediating between

“pure” discovery and organization. The categories also appear,

therefore, operating in the definition of the scientific method: to

abduction corresponds the category of firstness; to induction,

secondness; to deduction, thirdness. Indeed, the development of the

theory of categories appears as a decisive factor for redefining the

three kinds of reasoning as the three stages of inquiry145. A thorough

and deeper account of the matter demands a study of the manner how

phenomenological experience is organized according to the aspects of

being first, that is, possible, second, that is, having the character of

alterity, and third, that is, mediating between human beings and their

environment.146

Finally, we should notice the extremely artistic feature of

mathematics, justifying thus the first epigraph, by Murilo Mendes. As a

matter of fact, as mathematics is an activity depending largely upon

imagination, proximities with art are not few. Also the poet, for

instance, constructs possible worlds, devising imaginary hypothesis.

Take the following quotation:

145 Cf. KENT (1987); SANTAELLA (1992). 146 ROSENTHAL (1994) pp. 160 ff.

435

Modern mathematics is highly artistic. A simple theme is

chosen, some conception pretty and charming in itself.

Then it is shown that by simply holding this idea up to

one’s eye and looking trough it, a whole forest that

before seemed a thick and tangled jungle of bushes and

briers is seen to be in reality an orderly garden. [HP I:

492, The Century’s Great Men in Science].

The difference between mathematics and poetry is not in

imagination, but in the necessity obtained with mathematical

conclusions – in art, there is not and there is no need to be any

necessity in reasoning. But it seems that the most evident similarity is

not of mathematics with poesy, but – with music! Mathematics,

according to Peirce, is like music: the development of a theme, in an

unforeseen order. The reference to Bach is unequivocal: “The

intelligent listening to a fugue of Bach is certainly more like reading a

piece of higher mathematics that the lesson of the schoolboy in

elementary geometry is like the higher geometry.” [NEM 4: xiv]. Maybe

the creation of mathematical hypotheses is like writing the scores of the

divine music of the spheres.

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10. CONCLUSION: ULRICH’S DILEMMA

believe it or notthis very if

is everything you gotPaulo Leminski

What thou lovest well remains, the rest is dross

What thou lov’st well shall not be reft from theeWhat thou lov’st well is thy true heritage

[…]The ant’s a centaur in his dragon world.

Ezra Pound, The Pisan Cantos, LXXXI

É o que eu digo, se for... Existe é homem humano. Travessia. ∞147

João Guimarães Rosa, Grande Sertão: Veredas

We can go back to the tension between the life of science that

asserts nothing as definite, and the commitment of each scientist with

the continuation of inquiry, as formerly presented: it seems the scientist

has no practical beliefs, but only theoretical beliefs. It is decisive to

know what are the aims when propositions are uttered, distinguishing

the act of merely saying from what is done in saying what is said, for

everything is resumed in knowing which are the expectations envolved

in the assertion of the truth of theories. If the truth of a hypothesis is

investigated, would the scientist be disappointed to discover its falsity?

In other words, would the scientist like to put his or her beliefs to test?

If the supreme aim of scientific inquiry is to reach the truth, even 147 Leminski’s poem was originally written in English. Guimarães Rosa’s book was translated into English with the title The Devil to Pay in the Backlands. The epigraph is the last sentence of the book, and it means: “That’s what I say, if it is… There exists human man. Traversion. ∞” Our translation.

437

though it is vague and inaccurate, the answer is: “yes”, the scientist

wants to test beliefs, even because he or she wishes for a truth less

vague and more accurate. However, it is possible that the scientist

begins to feel like Ulrich, the main character of Robert Musil’s The Man

Without Qualities148. In the novel, ambiented in the immediately pre-

First World War Europe, Musil pictures Ulrich as a “modern” man, who

living in a world dizzingly changing, in morals, in religion, in science, in

technology, in society, finds nothing permanent, the reason why Ulrich

lacks perspective; despite his good material conditions, Ulrich cannot

find a place to occupy in the world of modernity. Differently from

previous generations, in the modern world pictured by Musil, a person

cannot get or acquire “qualities”149, for all rigid certainties were

replaced by transitory truths; nothing remains the same and the sense

of a vanishing reality becomes imponent: there is no stability, but only

an acelerated process of changing takes place, impelled by the

application of scientific knowledge in the creation of new technologies

that modify ever more the way of human life. With the ever renewing of

the material aspect of society, and the simultaneous difference between

those countries that in a higher stage of economic development lead the

wordly technical progress, and those that being in a lower level of

148 For a connection between Peirce and Musil, see FINLAY (1990). The connections we propose here, however, are not exactly the same as the ones proposed by Finlay, whose main aim is to put forward a “discourse of knowledge” for contemporaneity as an alternative to what she calls the post-modern project, trying to recover the link (which was lost, according to her) between ethics, politics and the “discourse of knowledge”; such attempt, Finlay seeks to build upon Robert Musil’s literature, Peirce’s semiotics, and Werner Heisenberg’s physics.149 The German word “Eigenschaften” carries more resonances and ambiguities, and can be rendered as “characteristics”.

438

wealth try to keep up with such changes, the vital experiences –

“experience of space and time, of the self and others, of life’s

possibilities and perils” – shared by men and women all over the world

become diluted in a sensation of estrangement and vertigo:

To be modern is to find ourselves in an environment that

promises us adventure, power, joy, growth,

transformation of ourselves and the world – and, at the

same time that threatens to destroy everything we have,

everything we know everything we are. The

environmental experience of modernity can be said to

unite all mankind. But it is a paradoxical unity, a unity of

disunity; it pours us all into a maelstrom of perpetual

disintegration and renewal, of struggle and

contradiction, of ambiguity and anguish. To be modern is

to make part of a universe, wherein, As Marx said, “all

that is solid melts into air”.150

Marx and Engels statement, in the Communist Manifest, shows a

state of mind very peculiar to modernity, and sums up the disturbing

sensation of loss of references, caused by the subtle change of the

material conditions of society, in the so called “epoch of the

bourgeoisie”:

150This is taken from BERMAN (1986), p. 15. Some more from the continuing of this reasoning is interesting to what we are trying to say: “The maelstrom of modern life has been fed from many sources: great discoveries in the physical sciences, changing our images of the universe and our place within it; the industrialisation of production which transforms scientific knowledge into technology, creates new human environments and destroys old ones, speeds up the whose tempo of life, generates new forms of corporate power and class struggle; immense demographic upheavals, severing millions of people from their ancestral habitats, hurtling them halfway across the world into new lives; rapid and often cataclysmic urban growth; systems of mass-communication, dynamic in their development, enveloping and binding together the most diverse people and societies; increasingly powerful nation states, bureaucratically structured and operated, constantly striving to expand their powers; mass social movements of people, and peoples, challenging their political and economic rulers, striving to gain some control over their lives; finally, bearing and driving all these people and institutions along an ever-expanding drastically fluctuating capitalist world market. In the twentieth century, the social processes that bring this maelstrom into being and keep it in a state of perpetual becoming, have become known as ‘modernization’.” BERMAN (1982), pp. 15-16.

439

Constant revolutionising of production, uninterrupted

disturbance of all social conditions, everlasting

uncertainty and agitation distinguish the bourgeois

epoch from all earlier ones. All fixed, fast-frozen

relations, with their train of ancient and venerable

prejudices and opinions, are swept away, all new-formed

ones become antiquated before they can ossify. All that is

solid melts into air, all that is holy is profaned, and man

is at last compelled to face with sober senses his, real

conditions of life, and his relations with his kind.151

It is the velocity of such radical transformations that make Ulrich,

Robert Musil’s man without qualities, fell deep the bewilderment and

the disintegration, recognizing himself to be untimeous to the epoch he

is living in. It is the insight of such fragmentation that characteristically

distinguishes the art we call modern, for instance. Musil’s novel focus

just on these aspects. Ulrich’s world is put together as a world of

appearances that seems to be the substitute for another world also

made up of appearances:

Was ist also abhanden gekommen? Etwas Unwägbares.

Ein Vorzeichen. Eine Illusion. Wie wenn ein Magnet die

Eisenspäne losläßt und sie wieder durcheinandergeraten.

Wie wenn Fäden aus einem Knäuel herausfallen. Wie

wenn ein Zug sich gelockert hat. Wie wenn ein Orchester

zu spielen anfängt. Es würden sich schlechterdings keine

Einzelheiten haben nachweisen lassen, die nicht auch

früher möglich gewesen wären, aber alle Verhältnisse

hatten sich ein wenig verschoben. Vorstellungen, deren

Geltung früher mager gewesen war, wurden dick.

Personen ernteten Ruhm, die man früher nicht für voll

151 MARX; ENGELS (1848), p. 5 of the S. Moore translation.

440

genommen hätte. Schroffes milderte sich, Getrenntes lief

wieder zusammen, Unabhängige zollten dem Beifall

Zugeständnisse, der schon gebildete Geschmack erlitt

von neuem Unsicherheiten. Die scharfen Grenzen hatten

sich allenthalben verwischt, und irgendeine neue, nicht

zu beschreibende Fähigkeit, sich zu versippen, hob neue

Menschen und Vorstellungen empor. Die waren nicht

schlecht, gewiß nicht; nein, es war nur ein wenig zu viel

Schlechtes ins Gute gemengt, Irrtum in die Wahrheit,

Anpassung in die Bedeutung. Es schien geradezu einen

bevorzugten Prozentsatz dieser Mischung zu geben, der

in der Welt am weitesten kam; eine kleine, eben

ausreichende Bemeingung von Surrogat, die das Genie

erst genial und das talent als Hoffnung erscheinen ließ,

so wie ein gewisser Zusatsz von Feigen- oder

Zichorienkaffe nach Ansicht mancher Leute mit

einemmal waren alle bevorzugten und wichtigen

Stellungen des Geistes von solchen Menschen besetzt,

und alle Entscheidungen fielen in ihrem Sinne. Man kann

nichts dafür verantwortlich machen. Man kann auch

nicht sagen, wie alles so geworden ist. Man kann weder

gegen Personen noch gegen Ideen oder bestimmte

erscheinungen kämpfen. Es fehlt nicht an Begabung noch

an gutem Willen, já nicht es ist, als ob sich das Blut oder

die Luft verandert hätte, eine geheimnisvolle Krankheit

hat den Kleinen Ansatz zu Genialem der früheren Zeit

verzehrt, aber alles funkelt von Neuheit, und zum Schluß

weiß man nicht mehr, ob wirklich die Welt schlechter

geworden sei oder man selbst bloß älter. Dann ist

endgültig eine neue Zeit gekommen.152

152 MUSIL (1999), chapter 16: “Eine geheimnisvolle Zeitkrankheit”, pp. 57-58.

441

Ulrich, then, seeking a life directed by values minimally constant,

turns to science, and exactly to the most abstract of them, mathematics.

Let us see:

Und so hat es auch schon damals, als Ulrich

Mathematiker wurde, Leute gegeben, die den

Zuzammenbruch der eupäischen Kultur voraussagten,

weil kein Glaube, keine Liebe, keine Einfalt, keine Güte

mehr im Menschen wohne, und bezeichnenderweise sind

sie alle in ihrer Jugend- und Schulzeit schlechte

Mathematiker gewesen. Damit war später für sie

bewiesen, daß die Mathematik, Mutter der exakten

Naturwissenschaft, Großmutter der Technik, auch

Erzmutter jenes Geistes ist, aus dem schließlich Giftgase

und Kampfflieger aufgestiegen sind.

In Unkenntnis dieser Gefahren lebten eigentlich nur die

Mathematiker selbst und ihre Schüler, die Naturforscher,

die von allendem so wenig in ihrer Seele verspürten wie

Rennfahrer, die fleissig darauf los treten und nichts in

der Welt bemerken wie das Hinterrad ihres

Vordermanns. Von Ulrich dagegen konnte man mit

Sicherheit das eine sagen, dass er die Mathematik liebte,

wegen der Menschen, die sie nicht ausstehen mochten.

Er war weniger wissenschaftlich aus menschlich verliebt

in die Wissenschaft.153

Ulrich seeks for science. First, by the passage above, we see he

does not share the belief that science (mathematics, in this case)

necessarily leads to the production of technical means for anihilating

life. He does not either thinks of science as an actiity closed in itself,

narrow sighted, without any concern regarding the wider horizon of the

153 Idem, chapter 11: “Der wichtigste Versuch“, p. 40.

442

cultural and historical context of human life. Ulrich, in this sense,

neither was a scientist like a ciclist, who only had eyes for the whell of

the runner ahead; nor he was a fake humanist, denouncing the crimes

of technique: he was someone “humanly in love with science”, someone

who had become a mathematician because he was in love with it, and

took the decision to oppose the demonizing image of mathematics as

the cause for all the bad thing in the world, opposing in this way its

obscurantist adversaries:

Man braucht wirklich nicht viel darüber zu reden, es ist

den meisten Menschen heute ohnehim klar, daß die

Mathematik wie ein Dämon in alle Anwendungen unseres

Lebens gefahren ist. Vielleicht glauben nicht alle diese

Menschen an die Geschichte vom Teufel, dem man seine

Seele verkaufen kann; aber alle Leute, die von der Seele

etwas verstehen müssen, weil sie als Geistliche,

Historiker und Künstler gute Einkünfte daraus beziehen,

beseugen es, daß sie von der Mathematik ruiniert bilde,

der den Menschen zwar zum Hernn der Erde, aber zum

Sklaven der Maschine mache.154

This image causes the impression that “all the evils of our time” –

“evilness, the incredible coldness of hear, greed, cruelty, and violence”

(to name just a few) – would result from the increasing influence of

mathematics in practical life, through technology produced according

to the rules of capitalist industrial production. This judgment seems to

Ulrich as quite mistaken, for it leads to the idea of the nature of science

as a cold specialized activity, unconnected from the wider context of

154 Id.,ibidem, p. 39-40.

443

human life – as if the scientist was a bicicle runner. In truth,

apassionate dedication is needed in science, it is needed to make it a

form of life. If this idea is put aside all the transformative and

sublimatory power of science is lost. Ulrich muses:

Wenn man statt wissenschaftlicher Anschauungen

Lebensanschauung setzen würde, statt Hypothese

Versuch und statt Wahrheit Tat, so gäbe es kein

Lebenswerk eines ansehnlichen Naturforschers oder

Mathematikers, das na Mut und Umsturzkraft nicht die

größten Taten der Geschichte weit übertreffen würde.155

Ulrich is successful in science, and not just a little, if we trust

what the narrator tells us. Talented, he becomes a hope, and gets some

acknowledgment. However, he soons perceives that the life of science

will not bring him what he hopes for. Signs of his delusion appear when

he faces difficulties in obtaining recognition for his efforts, due to the

hierarchical bureaucracy of the scientific academy; Ulrich then sees

that “even in the kingdom of truth only older wises are admired, upon

whom the obtaining of a masters or of the chair in the unversity

depends.”156 But the last drop to convince him to give up one more

attempt to become a man with qualities comes from the news on a

genial horse in the races:

Und eines Tag hörte Ulrich auch auf, eine Hoffnung sein

zu vollen. Es hatte damals schon die Zeit begonnen, wo

man von Genies des Fußballrasens oder des Boxrings zu

sprechen anhub, aber auf mindestens zehn geniale

155 Id., ibid., p. 40. 156 Ibid., p. 33, chapter 8.

444

Entdecker, Tenöre oder Schriftsteller entfiel in den

Zeitungsberichten noch nicht mehr als höchstens ein

genialer Centerhalf oder großer taktiker des

Tennissports. Der neue Geist fühlte sich noch nicht ganz

sicher. Aber gerade da las Ulrich irgendwo, wie eine

vorverwehte Sommerreife, plötzlich das Wort “das

geniale Rennpferd”. Es stand in einem Bericht über einen

aufsehenerregenden Rennbahnerfolg, und der Schreiber

war sich der ganzen Größe des Einfalls vielleicht gar

nicht bewußt gewesen, den ihm der Geist der

Gemeinschaft in die Feder geschoben hatte. Ulrich aber

begriff mit einemmal, in welchem unentrinnbaren

Zusammenhang seine ganze Laufbahn mit diesem Genie

der Rennpferd stehe. Denn das Pferd ist seit je das

heilige Tier der Kavallerie gewesen, und in seiner

Kasernenjugend hatter Ulrich kaum von anderem

sprechen hören als vonPferden und Weibern und war

dem entflohn, um ein bedeutender Mensch zu werden,

und als er sich nun nach wechselvollen Anstrengungen

der Höhe seiner Bestrebungen vielleicht hätte

nahefühlen können, begrüßte ihn von dort das Pferd, das

ihm zuvorgekommen war.157

Now, how is it possible to have some quality in a world where

horses for races are genial? The ideal of “genius and greatness” of the

“antique” world one day Ulrich knew was replaced, in the scale of

modern values, by the quantifiable and measurable objectivity of a

horse race – or a boxing fight: “the sport and the objectivity deservingly

advanced” 158. The hurry, the “impetus”, the “velocity” and the “frauds”

of the modern world fatally hit Ulrich’s image of the world. That

157 Ibid., p. 44, chapter 13.158 Id., ibid.

445

induces him to conclude that also the scientific life, to which he

dedicated himself with sincere perseverance, leads to nowhere in the

modern world. The “pleasure in the power of mind”, the “expectation”

that is as “a kind of undefined imperious right on the future” is worthy

of nothing in this world; as a matter of fact, “he did not know very well

whereto he would be led with such strength; one could do everything or

nothing at all with it, to be a savior of the world or a criminal.” 159 The

spiritual preparation offered by science was substituted for the

preparation of muscles; and this appears to Ulrich as decadence, and

even as a useless and stupid illusion, once no adventure comes to make

such athletic preparation useful. Ulrich’s disenchantment is then

expressed by the narrator:

Seine Meinung war, man befinde sich in diesem

Jahrhundert mit allem Menschlichen auf einer

Expedition, der Stolz verlange, daß man allem unnützen

Fragen ein “Noch nicht“ entgegensetze und ein Leben

mit Interimsgrundsätzen, aber im Bewußtsein eines Ziels

führe, das später Kommende erreichen werden. Die

Wahrheit ist, daß die Wissenschaft einen Begriff der

harten, nüchternen geistigen Kraft entwickelt hat, der

die alten metaphysischen und moralischen Vorstellungen

des Menschengeschlechtes einfach unerträglich macht,

obgleich er an ihre Stelle nur die Hoffnung setzen kann,

daß ein ferner Tag kommen wird, wo eine Rasse geistiger

Eroberer in die Täler der seelischen Fruchtbarkeit

niedersteigt.

159 Ibid.

446

Das geht aber nur so lange gut, wie man nicht

gezwungen wird, den Blick aus seherischer Ferne auf

gegenwärtige Nähe zu richten, und den Satz lesen muß,

daß inzwishcen ein Rennpferd genial geworden ist.160

Now, it seems clear to us that Ulrich’s image of science resembles

in several respects Peirce’s concept of science. We focus the following

contact points:

1) Science is an activity that has to be sincerely practiced. In

effect, just as Musil links Ulrich’s passion to mathematics, we can think

that the revolutionary power of science comes exactly from its being

practiced with the wholehearted frame of mind of sincerity and honest

attitude. Science practice sincerely allows for a synoptic view of the

whole of human life, making it possible a better grasp of the particular

and the individual.

2) Hence, opposed to the idea of specialization and individuation

of knowledge and reason, scientific life would be an alternative to the

“dryness of inward life, the monstrous mix of sensitiveness to the

details and indifference to the whole.”161

3) The life of science, transforming all beliefs and old habits,

builds an upward pathway, “as a stairway to heaven”. Its wildest

dreams allow us to think differently, rendering scientists (and all

present mankind, we could say) accountable as to the future. Science,

then, is a prospective activity.

160 Ibid., p. 46.161 Ibid. p. 40-41, chapter 11.

447

4) This prospective character of science renders all present

certainties instable and provisional; in their places it sets up the hope

that, in future, in the long run, truth shall be discovered, and the

present effort of inquiry will be waged.

Now, to know if the life of science is worthy of living is to answer

to the question about the conformation of means to ends. Science

viewed as a projective activity, as an open inquiry, has not an

immediate end, a practical objective given beforehand; judging by the

status of mathematics in the classification of the sciences, the supreme

aim aimed at appears in such a way that science may be understood as

a practice of inventing possibilities, distinguished from technique, to

which the ends are ab ovo defined. Examining the image of science

conveyed by Ulrich’s metaphors, we see that the similitude to Peirce’s

concept of science is not so big as it may seem.

Musil pictures the spirit of an age quite according to the

diagnosis made by Max Weber. In his writing Wissenschaft als Beruf,

Weber points out to the fact that, in the 20th century, science is brought

about as a vocation through specialization. The technical-scientific

process of rationalization reached by humanity puts the question on the

possibility of the scientist being conscious about his or her own activity,

within the context of the industrialist capitalism of the early 20th

century. Weber states Ulrich’s dilemma in an exemplary way, in terms

of the opposition between the ever more specialized scientific work and

448

the sense of science, as the projective activity towards the universal. In

effect, to Weber, the “sense” of the scientific work is opposed to the

artistic. While in art the artist’s realizations remain without ever aging,

science is directed to its own overcoming:

Jeder von uns dagegen in der Wissenschaft weiß, dass

das, was er gearbeitet hat, in 10, 20, 50 Jahren veraltet

ist. Das ist das Schicksal, ja: das ist der Sinn der Arbeit

der Wissenschaft, dem sie, in ganz spezifischem Sinne

gegenüber allen anderen Kulturelementen, für die es

sonst noch gilt, unterworfen und hingegeben ist: jede

wissenschaftliche »Erfüllung« bedeutet neue »Fragen«

und will »überboten« werden und veralten. Damit hat

sich jeder abzufinden, der der Wissenschaft dienen will.

[...] Wir können nicht arbeiten, ohne zu hoffen, dass

andere weiter kommen werden als wir. Prinzipiell geht

dieser Fortschritt in das Unendliche. Und damit kommen

wir zu dem Sinnproblem der Wissenschaft.162

It could not be made more explicit: the end of all is to walk

towards the overcoming [Überholung] of the actual stage, and it is

towards this surpassing that science is also directed. More: one could

say that science drives such overcoming.

Apparently, nothing Weber says is foreign to what we have

already seen Peirce saying. And, as a matter of fact, the idea that

science is directed to the future, that its conclusions are mere probable

hypotheses, that everything can be changed all of a sudden, are dear

ideas to both authors. However, there is an essential difference.163 To

162 WEBER (1995a), p. 17.163 Besides several others we will not try to unfold in this work, as for instance, the difference in the treatment each one gives of scientific progress, an expression Weber uses more characteristically than Peirce, one

449

Weber, science is an activity unconnected from the world of value – the

scientific work, in contradistinction to every other elements of culture,

is conceived by Weber as the accomplishment of western Reason in its

highest degree of technological development; in the capitalist world of

the 20th century, science for Weber is settled in a domain of axiological

neutrality, what results in the demystifying of the world, to the

elimination of “magic”, effected through the “increasing rationalization

and intellectualization”:

The growing intellectualization and rationalization do not

mean therefore a growing general knowledge of the

general conditions of our life. Their meaning is quite

different: they mean that it is known or believed that at

any moment that it is wanted it is possible to know; that,

therefore, there are not occult and unpredictable powers

around our lives, but rather that on the contrary

everything can be dominated through calculus and

prediction. This means only that the magic is excluded

from the world. On the contrary to the savage, to whom

there are such powers, we do not nave anymore to use

magical means to control or to make spirits peaceful.

This is accomplished due to technical means and to

prediction. Such is in essence the meaning of

intellectualization. 164

The separation between to be and must be, as H. Marcuse says,

leads to the weberian conception of science showing just the opposite

of what Weber intended: “an attempt to ‘freed’ science, in order to put

should notice. For an account in more detail of Max Weber’s thoughts, see for instance, HABERMAS (1991), cap. II: “Max Weber’s Theory of Rationalization”.164 WEBER (1995a), p. 19.

450

it into conditions of accepting obligatory values, the origin of which

rests precisely outside it.”165 In such way, two dimensions of human life

are isolated one from another: the one of the questions of value and the

one of the questions of technique. Scientific rationality is seen from a

very individualistic and deterministic point of view, according to the

pattern of a technical rationality oriented towards specific aims,

characterized by a distinct “purposive rational action”, in Habermas’

famous expression166. And such ends, we may add, are particular and

directed towards immediate accomplishments, justifying the idea that

the only certainty or scientific belief is the one of the certain knowledge

and of the domination through calculus and prediction. Scientific

neutrality, contrary to Weber’s pretension, cannot be sustained, given

Weber’s own account of the development of the worldly capitalism:

The pure philosophical and sociological conception

established outside the circle of values is converted in

the course of its own development into a criticism of

those same values. And the inverse is equally valid: pure

and value-void scientific concepts reveal their own

system of tacit values. They are converted into a criticism

of data, in the light of what such data impose to the man

and to the world. “What ought to be” reveals as “what

is”. It is the inexhaustible dynamics of the concept that

uncovers it.167

165 Marcuse’s text “Industrialization and capitalism in the work of Max Weber”, was used in the Portuguese edition of Wissenschaft als Beruf: O Político e o Cientista, pp. 9-44; this quotation is from p. 10. See bibliography for complete references.166 HABERMAS (1991), p.145-146.167 MARCUSE, op. supra cit., pp. 11-12.

451

Now, according to our judgment, Ulrich’s dilemma is valid within

this context of industrial capitalism of the early 20th century, such as

describe by Weber. The world Musil pictures in The Man Without

Qualities is such that, on the one hand, the Weberian description of the

process of scientific rationalization is valid and brought about by the

development of the capitalism; on the other hand, the criticisms made

to it cannot offer in alternative to this model of technical rationality

another conception of science. No wonder Ulrich feels lost, fascinated

as he was for science.

The establishment of science as a market business, technique and

science as ideology, so to say, are dear themes to the 20th century. For

instance, to sum up, remember the words of the Brazilian geographer

Josué de Castro:

It happens that these scientists can find payment only

when their works are interesting to someone, whether

the industry, the private initiative or the State. Now, in

this last century of western culture, the State, the

institutions and the bosses have deviated their interests

to the problems of economic exploration, problems of

production and wealth creation, becoming in general

disinterested of human problems. Almost only seeing

man as a machine for production, as a gear of their

technical economicism.168

168 CASTRO (1968), p. 143. Our translation; see the original: “Acontece que estes cientistas só encontram pagamento quando os seus trabalhos são do interesse de alguém, seja este alguém a indústria, o particular ou o Estado. Ora, neste último século de cultura ocidental, o Estado, as instituições e os patrões desviaram os seus interesses para os problemas de exploração econômica, problemas de produção e de criação de riquezas, desinteressando-se em geral pelos problemas humanos. Quase que só vendo o homem como máquina de produção, como uma engrenagem de seu economismo técnico.”

452

According to Josué de Castro, the “mechanicist and utilitarist”

western civilization, because of its “eager desire for dominating the

powers of nature through technique to enslave them”, in truth, “ended

in enslaving man to this technique”169. Notice there is not, to Josué de

Castro, as there was to Max Weber, an idea of strictly separating the

world of values and the world of technique, for the fact that there is not

a condemnation of all science and all technique. The Brazilian

geographer in fact urges for a change in perspective, a better

application of the scientific knowledge, according to the historical

perspective:

The discoveries in the field of atomic energy are rapidly

employed in the destruction of the world, but the

discoveries that are conductive to the salvation are

crawling in marasmus for which there is no explanation…

Something has to change, so that we can steadily affirm

we live in a scientific age. Meanwhile, science has been

only a myth – the new myth in which the most ardent

hopes of a great part of mankind are concentrated.170

Now, according to our account, such statements go very well

along Peirce’s, showing the back door of a myth of science: a door that

opens to the utilitarianism of profits disguised in the highest human

aims. Remember Peirce’s criticisms to Karl Pearson, who claimed that

science should serve society. In the way we understand, there is no

169 Id., p. 141. Our italics.170 Id., ibid., our translation; cf. the original: “As descobertas no campo da energia atômica são rapidamente aplicadas na destruição do mundo, mas as descobertas que conduzem à salvação, se arrastam num marasmo sem explicação... Alguma coisa precisa mudar, para que possamos afirmar com convicção que vivemos numa era científica. Por enquanto, a ciência tem sido apenas um mito – o novo mito no qual se concentram as mais ardentes esperanças de uma grande parte da humanidade.”

453

substantial difference between Peirce’s claims and the idea of the

redirection scientific applications defended by Josué de Castro. Not that

our geographer had read Peirce. And, more that showing Peirce as a

precursor – as if he was only one more precursor – we want to show the

historical persistence of certain problems, to make the critical value of

Peirce’s thought come to the surface; problems of today that he, in the

19th century, was already well aware of.

We have already pointed out some connexions between ethics and

pragmatism; this latter understood as a definition of a horizon of ends.

The idea of horizon in Kantian philosophy has to do with the illuminist

ideal of the possibility of self-determination of mankind. The pragmatic

horizon is defined by Kant in terms of the influence of a given

knowledge on our moral conducts [Sittlichkeiten], indicating that the

convergence between human knowledge and ends depends on a

determination of the will: for what ends we want to converge? 171 The

answer to this question, according to Kant, involves the answer to the

three questions of essential interest for human reason: what can I

know? What should I do? What could I licitly wait? [KrV A 805/ B 833].

This three questions define de domains of metaphysical speculation, of

morals, and of religion, respectively, and can be resumed in one

anthropological question: what is man? 172

171 KANT (1799-1800), Ak. 40-41.172 Id., Ak 25.

454

As a matter of fact, a more detailed account of the connexions

between pragmatism and Kantian morals would have to deal more

thoroughly with Kant’s anthropology, what it is impossible for us to

accomplish here, as just now mentioned. However, some comments can

be done, in order to get a more light upon the issue. It is in the

Anthropology that the ideas of horizon and pragmatic imperative

appear in a more defined way, linked to the idea that the human being

is simultaneously a sensitive natural being [sinnlichen oder

Naturwesens] and a rational being endowed with freedom [eines

vernünftigen, mit Freiheit begabten Wesens]. What makes an

anthropology characteristically pragmatic is the fact that the reflection

“on what man makes, can, or should make of himself as a freely acting

being [frei handelndes Wesen]”.173 The anthropology from a pragmatic

point of view, in this way, is “knowledge of the world” with the purpose

of understanding the human being as a natural being and as “citizen of

the world” 174. It is interesting that human freedom is seen as the ability

to actually interact within a context of play:

Let it be remarked that such anthropology, understood as

knowledge of the world, that has to be continued after

school, is not yet properly called pragmatic so long as it

contains extended knowledge of the things in the world,

such as animals, plants, and minerals in various lands

and climates. It is properly pragmatic only when it

incorporates knowledge of Man as a citizen of the world.

173 KANT (1798), Ak. 119, Vorwort.174 Id., ibid., Ak 120.

455

– Hence even knowledge of the races of man, which are

regarded as products of the play of Nature, is not yet

pragmatic, but only theoretical knowledge of the world.175

For such reason, there are two distinct senses of the human

situation in the world, that are knowing the world, in which situation

human beings are as simply spectators, and having the world, in which

situation human beings enter into play.176 Human freedom for acting in

this play is so plain that they get to exert power over nature,

dominating; and the radical character of human freedom conduces to

the manifestation of a tendency to overwin the freedom of other human

beings, taking them as means to attain private particular ends:

“Controlling the inclinations of other people in order to direct and

manage them according to one’s own intentions, almost amounts to

being in possession of them as mere instruments of one’s own will.”177

Because of such radical aspect of human freedom, Kant even defines a

notion of semiotica universalis, that is, a general and natural theory of

signs, opposed to the civil theory of signs, with the purpose of studying

the character [Charakter] of human beings in their interactive play with

nature and other human beings.178 Human freedom is defined in the

175 Id., ibid. Translation slightly modified; see the original: „Eine solche Anthropologie, als Weltkenntnis, welche auf die Schule folgen muß, betrachetet, wird eigentlich alsdann noch nicht pragmatisch gennant, wenn sie ein ausgebreitetes Erkenntnis der Sachen in der Welt, z. B., der Tiere, Pflanzen und Mineralien in vershciedenen Ländern und Klimaten, sondern wenn sie Erkenntnis des Menschen als Weltbürgers enthält.. – Daher wird selbst die Kenntnis der Menschenrassen als zum Spiel der Natur gehörender Produkte noch nicht zur pragmatischen, sondern nur zur theoretischen Weltkenntnis gezählt.“176 Id., ibid.177 id., ibid., § 84, Ak. 271. Nossa tradução: „Denn anderer Menschen Neigungen in seine Gewalt zu bekommen, um sie nach seinen Absichten lenken und bestimmen zu können, ist beinahe ebensoviel als im Besitz anderer, als blößer Werkzeuge seines Willens, zu sein.“178 Ibid., § 89, Ak. 285.

456

Anthropology, then, as the capacity to pass from the state of nature to

the state of freedom, and critical philosophy seeks to explain this

passage.

Let us go back to Ulrich. Where is his dilemma after all?

According to our account, it is possible to understand it as a lack of

horizon, or better as the lack of understanding his horizon:

Ganz das gleiche ist mit der Liebe der Fall, auf die der

Mensch in der ungeheuerlichsten Weise vorbereitet wird,

und schileßlich entdeckte Ulrich noch, daß er auch in der

Wissenschaft einem Manne glich, der eine Bergkette

nach der anderen überstiegen hat, ohne ein Ziel zu

sehen. Er besaß Bruchstücke einer neuen Art zu denken

wie zu fühlen, aber der anfänglich so starke Anblick des

Neuen hatte sich in immer zahlreicher wervdende

Einzelheiten verloren, und wenn er geglaubt hatte, von

der Lebensquelle zu trinken, so hatte er jetzt fast alle

seine Erwartung ausgetrunken.179

As a matter of fact, the dilemma appears now even more clearly,

when Ulrich perceives he is “more distant from what he wished to be

than he felt when he was young, if he ever knew what he wished.” 180

The character’s perplexity is well described by the narrator: Ulrich

recognizes in himself “all the capacities and qualities that his time high-

praised”, but, at the same time, he is completely unable to apply

them.181 Ulrich’s dilemma, therefore, such as we understand it, is in his

incapacity to define a pragmatic horizon to allow, in a general way,

179 MUSIL (1999), p. 46-47, chapter 13.180 Id., p. 47.181 Id., ibid.

457

shaping present conduct, having in sight the aimed ends, which can be

then seen as regulative ideals.

It seems to us also that the proximity of pragmatism with certain

respects of the ideal of the Kantian philosophy is plain. The difference

would be, on our account, in that Peirce, grounded in his semiotic

theory of the thought-sign, abandons the distinction among the

different uses of reason (the speculative and the practical), unifying all

the interests in one single horizon. In fact, the schematism of the

categories in the first Critic sought to solve the problem of how to

understand the scission between the grounding of the conditions of

validity of knowledge and the question of the rational validation of

knowledge; in other words, the schematism was concerned with how to

explain the application of the categories to the experience, and then

completing the transcendental deduction.

Peirce is quite aware of such problems. With his philosophy of

mathematics, it is clear that he abandons the way Kant deals with the

issue of the schematism. There being no further separation between the

faculty of imagination, which produces the schemes, and the rational

faculty of judgment, which applies the schematized concepts to

experience, there is no more the separation between distinct uses of

reason, the practical and the speculative, as there was for the

philosopher from Königsberg. In Kantian terms, one could say that the

sign’s function of meaning forces the understanding to translate and

458

interpret experience remittently, involving the recognition of the

regularities and the functioning of thought in the semiosis of the

interpretants, unifying the uses of reason, subject and object, in one

domain of meaning, continuous creation, and interpretation of signs.182

In this way, as the supreme ends of morality, metaphysics and

religion are not anymore distinct one from another, the answer to the

problem of defining horizons depends upon the logical coherence of the

thought of all mankind, such coherence being obtained only with the

adhesion and the trust of each individual in the collective inferences, in

a thoroughly and always self correctable process of induction, as we

have seen. Thus, as in Leminski’s poem, everything one has is an if, a

mere if – a hypothetical imperative, like a precept of prudence

[Ratschläge der Klugheit] to guide the conduct in the definition of

means to attain a supreme finality of all rational beings, such as Kant

says in the Groundworkings of the Metaphysics of Morals183. Now,

pragmatism could only be guided indeed by a hypothetical manner of

putting the ends, since the criticism to Kant’s logic showed it was

impossible to distinguish between categorical and hypothetical

propositions. Besides, the attunement of pragmatism with the idea of

the agreement of individual interests with the interests of the

community of inquiry demands that there is no a priori determination of

182 ROSENTHAL (1990), pp. 197.183 KANT (1785), Ak. 415-416. In the Anthropology, the maxims of prudence are identified with the techno-practical reason [technisch-praktischen Vernunft]. Cf. KANT (1798), § 84, Ak. 271. We do not intend with such brief remarks to exhaust the theme of the relations of Peirce’s pragmatism and Kant’s pragmatic anthropology, but only to suggest it, opening the way for a a possible recollection of it in a further occasion.

459

the domain of ought to be, once the ideally aimed truth would be

fallible, because it is semiotically mediated.184

In such way, a consideration on politics from a Peircean

perspective has to embrace the idea of the communicative activity of

science, so that possible to privilege public and collective means for

questioning the assertions and the results of inquiry. In this way, it

cannot deal with the relation between theory and practice privileging

the role to the first over the second, or vice-versa, for that would mean

to submit one to the authority of the other, blocking the way of inquiry.

In his criticisms to Karl Pearson’s ideas, as well as to what he used to

call the Gospel of Greed [EP 1: 357, Evolutionary Love, 1893], we see

that Peirce’s clear concern on the insubordination of theory to practice

is unfolded in two directions: first, theory should not be submitted to

practice because the immediate (and imediaticist) concerns of the

individual or of a finite community are not ultimate, in the widest sense

of such word; they may be vital for the individual, but that does not

mean that they are ultimate and final to the collectivity; second, inquiry

(and not the application of its results) is teleonomically oriented to the

future, and it does not need always follow the aims and objectives

defined by present society, whatever it is.185 That is, then, how the ideas

of truth as a regulative ideal and the idea of the definition of a

pragmatic horizon converge.

184 SILVEIRA (1980) and (2000).185 ANDERSON (1997), p. 227.

460

The idea of truth, as a sign of a general nature to which inquiry

would converge in the long run, is not an affirmation that the

affirmations of a finite group of research will be true, in case this group,

which is indeed competent, follow its investigations for a certain span

of time. Truth in Peirce’s philosophy is defined in terms of the

correspondence between sign and its object, independently of any

sociologically or ideologically limited opinion, since such

correspondence is not actualized, because it is defined in terms of its

possibility of actualization, if inquiry is carried indefinitely, by the right

methods.

The correlation between the conceptions of reality and truth is

central. Take the following passage:

A figment is a product of somebody's imagination; it has

such characters as his thought impresses upon it. That

whose characters are independent of how you or I think

is an external reality. There are, however, phenomena

within our own minds, dependent upon our thought,

which are at the same time real in the sense that we

really think them. But though their characters depend on

how we think, they do not depend on what we think those

characters to be. Thus, a dream has a real existence as a

mental phenomenon, if somebody has really dreamt it;

that he dreamt so and so, does not depend on what

anybody thinks was dreamt, but is completely

independent of all opinion on the subject. On the other

hand, considering, not the fact of dreaming, but the thing

dreamt, it retains its peculiarities by virtue of no other

fact than that it was dreamt to possess them. Thus we

461

may define the real as that whose characters are

independent of what anybody may think them to be. [W

3: 136-137, How to Make Our Ideas Clear].

The difference between fiction and reality is confirmed in the

absence of an objecting object in fiction. Reality has the character of

alterity, of being an opposite to thought, what settles the conditions

minimally necessary of the criteria by means of which to define what is

a true representation, from the point of view of the conformity with

facts. Effectively, the difference between fiction and reality is entirely

understood by the fact that, in objecting to consciousness, reality has

the power of shaping conduct and fixing belief: “The only effect which

real things have is to cause belief, for all the sensations which they

excite emerge into consciousness in the form of beliefs.” [id.] Fiction

does not settle beliefs, for it is lacking the being permanent of alterity,

which is an essential characteristic of the exterior object to the

representation:

The being of a sign is merely being represented. Now

really being and being represented are very different.

Giving to the word sign the full scope that reasonably

belongs to it for logical purposes, a whole book is a sign;

and a translation of it is a replica of the same sign. A

whole literature is a sign. The sentence “Roxana was the

queen of Alexander” is a sign of Roxana and of

Alexander, and though there is a grammatical emphasis

on the former, logically the name “Alexander” is as much

a subject as is the name “Roxana”; and the real persons

Roxana and Alexander are real objects of the sign. Every

sign that is sufficiently complete refers to sundry real

462

objects. All these objects, even if we are talking of

Hamlet’s madness, are parts of one and the same

Universe of being, the “Truth”. [EP 2: 304, ].

As fictional objects are constructed by the sign, that which is said

of the object is not different from the way how it is said; form of

presentation and form of representation are therefore confounded. In

the representations of reality it is otherwise, for such amalgam does not

exist: the way how to say is defined by the object of what something is

said. Thus, science, whose truth depends on the real, is as a matter of

fact an activity that tries to discover the behaviour of the object, so that

inquiry is continuous with reality, and in its limit-horizon, in the long

run, the permanence of the real will lead us to think that the object is in

such way, and not otherwise. In other words, the object is a

determining subject of our representations, so that the continuation of

inquiry will arrive at a representation of a general nature, which is

structurally isomorphic to the conduct of the object, representing it

independently of whatever particular and subjective idiosyncrasies in

an icon. In other words, experience, because it objects, is also subject

of thought; it is experience that makes us think, that conduces us to

think in the existence of things because things react against us, shaping

our conduct, making us conscious of ourselves:

We are continually bumping up against hard fact. We

expected one thing, or passively took it for granted, and

had the image of it in our minds, but experience forces

that idea into the background, and compels us to think

463

quite differently. You get this kind of consciousness in

some approach to purity when you put your shoulder

against a door and try to force it open. You have a sense

of resistance and at the same time a sense of effort.

There can be no resistance without effort; there can be

no effort without resistance. They are only two ways of

describing the same experience. It is a double

consciousness. We become aware of ourself in becoming

aware of the not-self. The waking state is a consciousness

of reaction; and as the consciousness itself is two-sided,

so it has also two varieties; namely, action, where our

modification of other things is more prominent than their

reaction on us, and perception, where their effect on us

is overwhelmingly greater than our effect on them.186 [CP

1.324, Lowell Lecture III, 1903].

As we can see by the passage above, there are no absolute

dichotomies between subject and object, since experience appears as

architect of its own representation. In fact, it is experience that allows

us to give the step from appearing to being, and vice-versa, also the

step that goes from the recognition of an existence different from ours

to the representation of such existence:

When we say that a thing exists, what we mean is that it

reacts upon other things. That we are transferring to it

our direct experience of reaction is shown by our saying

that one thing acts upon another. It is our hypothesis to

explain the phenomena, – a hypothesis, which like the

working hypothesis of a scientific inquiry, we may not

believe to be altogether true, but which is useful in

enabling us to conceive of what takes place. [CP 7.534,

On Topical Geometry, in General].

186 Cf. IBRI (1992), pp. 27-28 e (1999).

464

[And yet:] Whatever exists, ex-sists, that is, really acts

upon other existents, so obtains a self-identity, and is

definitely individual.187 [EP 2: 343, What Pragmatism Is].

The application of the pragmatic maxim to the metaphysical

debate on the nature of truth and reality fortifies the connexion

between the effective practice of science and its orientation to the

general future truth. If, as Peirce claimed in 1878, the method of

science is the best to fix beliefs, it is needed to conciliate the idea that

the practice of science is essentially revolutionary with the adoption of

a living belief, and at the same time, a belief which is regulative of

conduct, even though it is only provisional. In other words, we cannot

take science as an ideology, for this would justify the Weberian image

of technical rationality, making us remain in the perplexity of Ulrich’s

dilemma. The philosopher should look to our quotidian practices and to

attempt at discovering which account of truth would be more adequate:

“We must not begin by talking of pure ideas, – vagabond thoughts that

tramp the public roads without any human habitation, – but must begin

with men and their conversation.” [CP 8.112, Josiah Royce’s The World

and the Individual, 1900]. This anchorage in common experience of

human beings refuses all and any possible axiological neutrality of

science – as a matter of fact, all and any possible inquiry, in so far as it

is a collective effort having its start interhomines should take into

187 On the issue of experience as subject causing representations, see IBRI (1992), pp. 27-28; (1999), passim; (2003b), passim.

465

account all presuppositions, principles, hypotheses, sentiments,

emotions, prejudices, and instincts, from the beginning:

Although inquiry is to be an inquiry into truth, whatever

the truth may turn out to be, and therefore of course is

not to be influenced by any liking for pragmatism or any

pride in it as an American doctrine, yet still we do not

come to this inquiry any more than anybody comes to any

inquiry in that blank state that the lawyers pretend to

insist upon as desirable, though I give them credit for

enough common-sense to know better. [HL 118].

Thus, every form of thought brings with itself historical and social

presuppositions that are unavoidable, and it is the duty of inquiry to put

them to test, and if it is the case of a requirement of the experience of

reality, to refute them. The contrast showed is circumscribed between a

sincere attitude and a fake attitude. Two postures are compared: first, it

is needed to know which responsibilities can be assumed in the

execution of an illocutionary assertive act; second, as the quotation

above makes it clear, which are the responsibilities de facto assumed,

when someone engages in an inquiry. In other words, it is needed to

remember that there is no place so profound or sublime enough where

from we could look to the inquiry without ideological assumptions, as if

reality under questioning was not also our reality; because it is, it is

fundamental that there are various ways to make the communicative

interaction of science possible with every other spheres of life. The

continuity between common-sense and science in Peirce’s philosophy

teaches us that the assumptions and beliefs of common-sense make up

466

the only bedrock upon which it is possible to question assertions,

theories, and taking conscience. Thus, the definition of truth that does

not refer to belief, to doubt, to experience, is a void definition of truth –

a mere transcendental figment, with no relation to whatever human

effective practice.188

Nor even because of this it is necessary to assume any relativism

or historicism, whose results would equally lead to the presupposition

of a Weberian Wertfrei Wissenschaftliche Theorie. Let us get back to

the experience of inquirers that seem to be the more relevant to the

problem – the proofs they have pro and contra hypotheses. On the one

hand, if we stay with the Weberian idea of scientific rationality, the

chasm between theories of which we can have some evidence of being

truth and reality becomes insurmountable and unbearable. On the other

hand, the theory of truth as correspondence also does not reveal to us

what we can expect from a true hypothesis, and therefore it also would

not be capable to guide us in our actions and inquiries. We could have

all proofs and evidences for a hypothesis, and yet it would not be true.

If truth is the aim of inquiry, then, according to the correspondence

between being and being represented, the inquirers do not have any

rule to follow for conducting theur inquiries. The aim, Peurce says, is

not “readily comprehensible” 189 [CP 1.578, Minute Logic, c. 1902]. How

could one aim at a kind of truth that transcends and transforms

188 MISAK (1994a), pp. 360 ff. 189 Cf. MISAK, idem, p. 362.

467

experience? How could an inquirer develop means to attain such aim?

Peirce states:

Yet the logician will never be scientifically or safely

equipped for his explorations until he knows precisely

what it is that he is seeking. The whole doctrine of logic

depends upon that to a degree one could hardly foresee.

The best way will be to go back to the beginning and

inquire what it is that we can be content to wish for

independently of any ulterior result. [id.].

With such statements, Peirce intends to establish the link

between truth and inquiry that, as we can see, was lost of sight by

transcendental philosophy. The pragmatic interpretation of assertions

that aim at truth concerns the common and collective experience that

informs the beginning of inquiry, and thus offers a conception of truth

that can be a regulative ideal for inquiry. The separation between the

sphere of public morals and private morals disappears, once ethics has

to be based on the most basic practical life. Peirce says:

Ethics as a positive science must rest on observed facts.

But it is quite a different thing to make it rest on special

scientific observation, and still more so to base it upon

scientific conclusions. The only solid foundation for ethics

lies in those facts of every-day life which no skeptical

philosopher ever yet really called in question. [N 3: 51,

Ethics: Descriptive and Explanatory, 1901].

The enrooting in the facts of everyday life involves that every

knowledge that intends to say something about our present historical

reality cannot assume beforehand any critical detachment, but rather it

should recognize that it is a part of this historical moment. That does

468

not prevent to attain some minimally degree of autonomous criticism.

Moreover, since inquiry begins, it is possible and often desirable to give

up was already done in face of empirical requirements and constraints.

Obviously, it is not that all accumulated experience is to be abandoned;

even we come to discover that we are not on the right track, the

experience of error leads us to change and to seek to correct ourselves;

in more Peircean terms, the error causes a doubt that requires its own

annihilation.

From Peirce’s philosophy, we can say that every collective project

of constructing an axiological regulative horizon presupposes the

openness of all ways of inquiry, for truth is seen as a human value to be

semiotically developed and worked up ad infinitum. It equally

presupposes the identification of the individual values with the

collective values, as we have previously emphasized. Even knowing to

be accomplishing small, little fragments without apparent relation one

with another, just like Pound’s ant, the individual can trust the

collective work of all other ants of the colony, for they also confront

dragons.

According to Peirce, “To say that a proposition is true is to say

that every interpretation of it is true.” [CP 5.569, c. 1906]. This is, in

fact, another way of saying that the interpretation of a proposition

enables us to define, yet in a uncertain and provisional way, what it is

possible to expect from a true belief: if we begin to inquiry into p, we

469

would discover that p would not find any sort of negative experience

against it, continuing to be permanently true. Then, we could predict

that, if inquiry was carried on further enough, the object represented in

the proposition p would lead us unavoidably to believe that p. In other

words, there would be no doubts as to the veracity of p. A true belief,

therefore, is such that it resists doubt, even with the continuation of

inquiry and investigations. The pragmatic view is that reality is the

“object” of true beliefs – it is what true beliefs Express, it is that about

which they concern. Reality is that over which beliefs would be fixed, in

the final opinion reached in the long run.

Thus, it makes no sense to suppose, as Karl Pearson did, that the

truth value of a proposition would lie in its conformity or contrariety to

the norms and interests of the accepted society. Such affirmation would

have as result only the closure of ways of inquiry, even because it would

be rather difficult to ascertain what is or what is not the true interest of

society [EP 2: 60-61]. Peirce then can say what is the hope that should

guide the actions of the individuals, in the present:

Our hope, however, in endeavoring to make a

measurement extremely precise, is that there is a certain

value toward which the resultant of all the experiments

would approximate more and more, without limitation.

Having that hope, the Berkeleyan theory is, that

whenever we endeavor to state the distance, all that we

aim at is to state as nearly as possible what that ultimate

result of experience would be. We do not aim at anything

quite beyond experience, but only at the limiting result

470

toward which all experience will approximate, – or, at

any rate, would approximate, were the inquiry to be

prosecuted without cessation. [CP 8.112, Josiah Royce’s

The World and the Individual]

Such affirmation is linked to the idea that it not needed to regard

the life of common-sense as the only and inescapable bedrock for

critical action and reflection. The continuity between sentiments and

inquiry, such as it is configured in the critical common-sensism, does

not impose contingent determinations to inquiry. Even the provisional

beliefs of science have the power to guide conduct. The defense of

freedom to inquiry, relative to the social and historic pressures of the

present, has as a possible consequence the outcome that inquiry

purports not only the knowledge of truth such as it would be in the long

run, but that it might come to be applied, in a way that a true belief

would have practical conceivable bearings to the conduct, even tough

these bearings are not necessary and intrinsic to the definition of

truth.190 Thus, yet provisionally, the genuine spirit to learn can take the

individual inquirer to the right way to eliminate his or her doubts – it

can take, but one does not know if in fact it will lead. However, it is

certain that inquiry leans to the future, not being limited to the actual

present.

Remember that Peirce’s critical common-sensism can be

criticized, what does not contradicts the idea that science can refuse,

all of a sudden, all its beliefs, in function of a revolution in experience.

190 ANDERSON (1997), p. 233.

471

As a matter of fact, the starting condition of enrooting in common-sense

does not prevent that science be – science! The knowledge that results

from scientific inquiry can be always partial, limited, provisional,

because it is semiotically mediated, incomplete – but for the same token

it will always be a knowledge turned to possible interpretation and to

possible communication. The way inquiry turns back over its own

presuppositions necessarily implies the recognition of the fallible and

incomplete character of its assumptions.191 Finally, we want to indicate,

for a further development, the idea that the continuity between

instincts and rationality is the key to the discovery of the fundaments of

abduction:

Every concept, doubtless, first arises when upon a

strong, but more or less vague, sense of need is

superinduced some involuntary experience of a

suggestive nature; that being suggestive which has a

certain occult relation to the build of the mind. We may

assume that it is the same with the instinctive ideas of

animals; and man's ideas are quite as miraculous as

those of the bird, the beaver, and the ant. [CP 5.480, A

Survey of Pragmaticism].

The abductive suggestions are of an instinctive nature, and come

to human mind as the lume naturale Peirce praised so much. It is this

continuity between human mind and nature that grounds the refusal of

the substantial duality between matter and mind, subject and object,

theory and practice.192 This continuity, however, does not warrant that

191 Id., ibid.192 ANDERSON (1997), p. 232; IBRI (1999), p. 287-288.

472

we obtain truth, but it is only the first step of inquiry, as we have seen,

for instinctive suggestions must be experientially tested [RLT 112].

Now, what interests us here is that such continuity leads to the

continuous reformulation of the terms in which experience happens, at

the same time that it is adopted as norm for action that guides conduct.

If it is the task of inquiry to test the hypotheses suggested by instinct, it

is necessary to begin to experiment, practicing inquiry in an effective

way. And such infinite process always recommences, leading to the

necessity of abandoning the ideas of absolute necessity, mechanicism,

and determination.193

Ulrich’s dilemma appears because he cannot in the beginning of

the novel unify the various dimensions of his experience. And, in truth,

the view of this unity characterizes the beginning of scientific activity.

It is in the Play of Musement that we envisage a peculiar harmony

between the universe of possibility, the universe of actual fact, and the

universe of mediation, in straight connexion with the categories of

firstness, secondness, and thirdness, that the view of the universal

leads us to inquiry on the hypothesis of its reality: “Let the Muser, for

example, after well appreciating, in its breadth and depth, the

unspeakable variety of each Universe, turn to those phenomena that

are of the nature of homogeneities of connectedness in each; and what

a spectable will unroll itself!” [EP 2: 438, A Neglected Argument for the

Reality of God]. The Play of Musement, in sum, makes it possible the 193 Id.; Ibri (1992), cap. 4: “Idealismo Objetivo e Continuum”.

473

view of the reality of thirdness, understood as a harmonic congruence

of the three universes of experience, such a congruence appearing so

perfect that it would seem to us supremely admirable.194

The inextricability in science of the three stages of inquiry

provides a “solution” for Ulrich’s dilemma, a solution that does not

solve all the tensions, but incorporates them to it. 195 Remember that

abduction is characterized by the opening of new possibilities of

experience; in other words, abduction gives us the suggestion of

horizons in possible experience, horizons that will be always

overwhelmed, given the nature of scientific activity proper. There is no

more, as there was for Kant, a sharp distinction between what is

outside our horizon and what is beyond the horizon196; in fact, we can

say that for Peirce there is not what is outside human horizons, since

the incognizable is impossible, and therefore it does not exist:

[…] all our conceptions are obtained by abstractions and

combinations of cognitions first occurring in judgments

of experience. Accordingly, there can be no conception of

the absolutely incognizable, since nothing of that sort

occurs in experience. But the meaning of a term is the

conception it conveys. Hence, a term can have no such

194 On the subject of esthetics in Peirce’s thought, as science of the ascertainment of the conditions of possibility of what is de per se admirable, cf. BARNOUW (1988) and (1994); SANTAELLA (2000); SILVEIRA (2003).195 We remember that Musil’s novel is an unfinished work. Not even because of this Ulrich remains all the time in the aporetical situation we have described. The way the dilemma is resolve in the novel, we will not say it here, inviting the reader to the experience or the ecstasy of such discovery.196 KANT (1799-1800), Ak. 42.

474

meaning. [W 2: 208, Questions Concerning Certain

Faculties Claimed for Man].

Peirce can say, then, that there is a cognizable reality behind

every human conception; nothing therefore can be outside or beyond

the reach of knowledge, what does not mean that it is possible to

exhaust knowledge. The identification of being and cognoscibility

assures only the possibility of constructing knowledge, without

determining its necessity, completeness or absolute certainty. In fact,

from the Peircean account of scientific method, we have reasons to

affirm that nothing is outside or beyond human horizons, for nothing is

outside the range of possible experience, even thought the possibility of

transforming experience, overcoming horizons and going beyond them,

is in a certain sense unavoidable. At least this tension remains.

After all this way, it appears it is possible to conclude that the

task of philosophy, as the inquiry of human life and its forms of life, will

always be unfinished, as long as there is human life. There is the

famous passage where Peirce says that human beings actually are

signs:

Without fatiguing the reader by stretching this

parallelism too far, it is sufficient to say that there is no

element whatever of man's consciousness which has not

something corresponding to it in the word; and the

reason is obvious. It is that the word or sign which man

uses is the man himself. For, as the fact that every

thought is a sign, taken in conjunction with the fact that

life is a train of thought, proves that man is a sign; so,

475

that every thought is an external sign, proves that man is

an external sign. That is to say, the man and the external

sign are identical, in the same sense in which the words

homo and man are identical. Thus my language is the

sum total of myself; for the man is the thought. [EP 1: 54,

Some Consequences of Four Incapacities].

In the quotation, Peirce says that human beings do not exist in a

determinate way, for if a human being is a sign, its truth depends upon

how it is going to be interpreted from now on. The complete and

definite actualization of the human being, therefore, is merely a

possibility, for it depends on an esse in futuro. For the same reason,

man is a sign, as Peirce says, it is “a symbol [that] is an embryonic

reality endowed with power of growth into the very truth, the very

entelechy of reality.” [EP 2: 324, ]. Entelechy is not

[enérgueia], it is not exhausted hic et nunc in the present, but it is the

perfect realization of a process whose end is inherent to the process

itself. The affirmation that man is an end in itself is, in this way,

reformulated to make human ends coincide with the self-development

of reality itself. But this end in itself is unattainable by the individual

alone; as all symbols, human beings mutually depend on each other to

affirm themselves as such – human beings are altogether projected to

the experience of the world:

We can now see what judgment and assertion are. The

man is a symbol. Different men, so far as they can have

any ideas in common, are the same symbol. Judgment is

the determination of the man-symbol to have whatever

476

interpretant the judged proposition has. Assertion is the

determination of the man-symbol to determining the

interpreter, so far as he is interpreter, in the same way.

[id.].

Human beings, therefore, cannot live isolated one from another,

for their nature is oriented to the mutual interpretation and sharing of

common experiences. In truth, if a human being is not affirmed and

interpreted within a defined practical context such as it is with the

proposition, a human being then is little more than a mere empty form,

lacking realization. As symbols are the only signs capable of growing,

also human beings are conjointly projected into a collective endeavour

of undefined limits, oriented towards the asymptotical approach of

reality. Now, human truth, however, is not fixed or delimited.

An equally interesting less known affirmation is that a human

being is not a vortex, but a wave: “A man is a wave, but not a vortex.”

[EP 2: 124, On Science and Natural Classes]. A vortex is a fluid in

continuous rotation, a whirlpool with a defined center, in constant and

stable velocity. A wave is otherwise a form assumed by the parts of a

body that are out of equilibrium, always in movement and changing

places, in a constant and chaotic tension, so to propagate this tension to

all parts of the body, “while preserving more or less the same form and

other characteristics”. The human being in consequence never is

perfectly stable, and it always changing, always tensioned and

intentioned outwards, to the other, to the future.

477

Just as for Guimarães Rosa, the human being according to Peirce

is movement and instability, a continuous signifying – crossing-

prophecy: “Man is nature’s first essay towards the production of an

intellectual animal. He is not that, but is a prophecy of it, perhaps.” [W

1: 9, Private Thoughts principally on the conduct of life, 18 June 1867].

478

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