Peirce's Concept of Knowledge in 1868

Peirce's Concept of Knowledge in 1868Author(s): Richard SmythSource: Transactions of the Charles S. Peirce Society, Vol. 26, No. 3 (Summer, 1990), pp. 309-323Published by: Indiana University PressStable URL: http://www.jstor.org/stable/40320289 .

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Richard Smyth

Peirce's Concept of Knowledge in 1868

Peirce's reputation as a brilliant but idiosyncratic philosopher is hard to reconcile with his frequent comments about philosophy as a collective enterprise. In particular, Peirce began his essay, "Some Consequences of Four Incapacities," by stressing the importance of agreement in philosophy: "In sciences in which men come to

agreement, when a theory has been broached, it is considered to be on probation until this agreement is reached. . . We individual- ly cannot reasonably hope to attain the ultimate philosophy which we pursue; we can only seek it, therefore, for the community of

philosophers."1 But immediately upon these ecumenical senti- ments comes a concept of knowledge which might appear highly sectarian or even idiosyncratic. My purpose is to show that on this occasion, at least, Peirce's reputation is undeserved and that his concept of knowledge in 1868 reflected a higher degree of consensus than has previously been recognized. If my analysis of his

essay is correct, Peirce made a fundamental conjecture in logic which throws an entirely new light on the relationship between Kant and the Leibnizian rationalists. At the very point where we

anticipate epistemological disagreement, Peirce's insight (if such it

be) allows us to postulate an unexpected harmony of views between rationalism, Kantianism and Peircean pragmatism.

My analysis is centered on the second, only, or Peirce's four

epistemological theses. A complete analysis of his concept of

knowledge would require equal attention to the other three. The second, by itself, only gives us an idea of what the act of knowing is. An act of knowing is never an immediate cognition; it is always an act of reasoning. This thesis gives us no direct information about the objects of knowledge and it gives us no direct information about the subject or subjects of knowledge. More important- ly, it conveys no "procedural" information in epistemology. By "procedural" as opposed to "substantive" information in episte-



310 Richard Smyth

mology I mean information about how to settle questions about our concept of knowledge. I believe that here, too, Peirce was in agreement with the best opinion of his day. Before turning to the main, substantive point, let us briefly review his procedures, as summarized by his first and third theses.

Peirce's epistemology in the 1868 series is often described as anti-Cartesian and anti-empiricist.2 That is the case in regard to the substance of his opinions. However, it is also true that Peirce used John Stuart Mill's own procedure and standard to build his case against all forms of intuitionism.3 Peirce's 1868 series came at the end of a long controversy over our powers of intuition - a debate that had James and John Stuart Mill, Bain and Bowen on one side and Hamilton, Cousin, Mansel and McCosh on the other. Mill's party - descendents of Hume's phenomenalism -

argued that we only have intuitive cognitions of the (actual or possible) contents of our own minds. Hamilton's party - descendents of Reid's common sense school - believed that we also know physical objects by intuition. If Cousin can be classed with the Hamiltonians in this dispute, then perhaps we also know God by an intuition. The procedure that Peirce employed against all versions of intuitionism was the one that Mill had demanded when he said that we cannot settle which powers of intuition we have by an appeal to intuition. Instead, we must employ the scientific method, which involves trying out hypotheses in order to determine which hypothesis about our cognitive powers can best explain what we do know. As I have argued elsewhere, this procedure sets up "inexplicable" as a term of reproach, and, since it is a term which Mill was forced to use quite frequently, it sets him up as a target of his own standards of criticism in epistemology.

How do Peirce's procedural assumptions compare to those of Descartes? In a well-known passage in the first Kritik Kant classifies Descartes's position as problematic idealism which maintains that only one empirical judgment is indubitable - the "I exist," which is known on the basis of inner experience (B274-5). Peirce's first epistemological thesis in "Some Consequences" ex-



Peirce's Concept of Knowledge in 1868 311

plicitly contradicts Dcscartcs's approach by making all our knowledge of the internal world rest on hypothetical reasoning from our knowledge of external facts. And his second thesis, denying the existence of intuitive knowledge, is expressly anti-Cartesian also. Nevertheless, Peirce's relation to Descartes is more complex than it first appears to be.

After setting out his first two epistemological theses, Peirce explains what they mean for our hypothesis about the mental. Among the modifications of consciousness which we must assume are processes of cognition, construed as acts of valid reasoning. He outlines this hypothesis on the basis of a procedural commit- ment which is clearly Cartesian: "The class of modifications of consciousness with which we must commence our inquiry must be one whose existence is indubitable. . . ."4 But in place of Des- cartes's indubitable "I think," Peirce says we cannot doubt there is mental action which conforms to the formula of valid reasoning. Why is the existence of this kind of cognition indubitable? Although Peirce gives no answer in this essay, it is not inconceiva- ble that he had begun to develop the more elaborate Cartesian strategy which appears to be one strand in his defense of the method of science in "The Fixation of Belief."5 Whether or not that is so, he has clearly set a procedural standard for our hypotheses in "Some Consequences" which is Cartesian, rather than anti-Cartesian.

However, what concerns us at present is one part of the substance of Peirce's view of knowledge in 1868. In the standard analyses of knowledge, the paradigmatic act of knowledge is an act of judging (or believing). Such an act is typically said to constitute knowledge if it is true and if the one who judges possesses an objective ground for the judgment. Since we are only con- cerned to compare Peirce with the Leibnizian and Kantian tradi- tions, we need not canvas all the possible variants on this analysis - believing or asserting substituted for judging; subjective grounds or warranted assertability substituted for objective grounds, and so on. The point I wish to make is that, by constru-



312 Richard Smyth

ing the act of knowing as an act of valid reasoning and by making an additional and crucial assumption about the logical implications of each claim about validity, Peirce was justified in asserting a virtual consensus between the rationalists, Kant and himself.

The first step toward this community of opinion results from the way Leibniz's principle of sufficient reason had come to be in- terpreted in the logic texts available to Kant. For example, Gotts- ched's Erste Grilnde der Vernunftlehre tells us that the principle of sufficient reason means that we can always give a sound demonstration of every true proposition.6 He and Baumgarten agree that the principle might be stated in the following form: Whatever we do know a posteriori we might know a priori.7 We must be clear about what the term a, priori meant to these authors. While it is generally understood that they used a posteriori as a synonym of "empirical," it is sometimes implied that the term "a priori" ap- plies to what comes first, or "before all experience." Literally, it means what is from or out of what is first. Lambert explains the term in his Neues Organon in this way: "The words a priori^ & posteriori^ indicate a certain ordering according to which one thing is before or after another in a series. . . . They generally refer to the order in the nexus of our knowledge. For where we must have the premises before we can draw the conclusion, the premises precede the conclusion and the latter follows a priori."* Whatever is a priori as knowledge is from or out of some prior concept or principle, and is gotten from it by a valid act of the understanding. What it comes from might even itself be empirical.

If one proposes to compare this conception of a priori knowledge with Peirce 's conception of knowledge as a process of valid reasoning, several objections will immediately be raised. First, for the rationalists and for Kant, some knowledge is not a priori at all; it is immediate empirical knowledge. Secondly, in their conception of a priori knowledge what the rationalists mean by valid reasoning is deductive reasoning, whereas Peirce claims that some valid reasoning is synthetic. Both of these objections will be disposed of in due course, but it is important at the outset to realize




how dose the preceding explanation of a priori knowledge brings this species of knowledge to what Peirce conceives all knowledge to be. The difference is no greater than that between a process and any product of the process conceived and defined as such. Or, if the matter is viewed from the standpoint of formal logic, the difference is no greater than that between fathering and being a father, or between any relation and one of its relata, conceived as such. That is, when a priori is explained as Lambert explained it, Peirce's concept of knowledge is virtually the same as earlier con- ceptions of a priori knowledge as "cognitions logically determined by preceding cognitions."

It will be objected that for the rationalists and for Kant knowledge which is logically determined by prior acts of cognition con- stitutes only one species of knowledge; some knowledge which we might have had a priori we do have as immediate empirical knowledge. However this objection founders on a combination of two points: the procedural agreement which Peirce has borrowed from Mill and a substantive assumption about unconscious cognition which he has borrowed from Leibniz. The procedural point is that the voice of individual conscience is not to be regarded as decisive in settling questions about our knowledge. Instead, we are to subject the matter to scientific reasoning and we are to give a preference to the simplest hypothesis about knowledge. If we find ourselves committed to the existence of one species of cognition, we should not admit a second species, unless absolutely driv- en to that necessity. Now all that Kant's testimony, or the rationalist's testimony, about the existence of immediate, empirical cognitions proves is that they are not conscious of any prior cognitions from which the given judgments have been derived. But if we admit the possibility of unconscious judgments and reasonings, their testimony on the point ceases to be conclusive.

Is there any necessity for assuming concepts or judgments in our minds which we are not directly conscious of? In answering this question, we must remember, first, that the principle of conti-

nuity was, for Leibniz, an immediate corollary of the principle of



314 Richard Smyth

sufficient reason and, secondly, that the rationalists had interpreta- tions of both principles which construe them as hypotheses about cognition. We know something when we understand it - where (as Aristotle said) the mark of the one who knows is that the person can explain why what is so is so. Thus, for example, Wolff explains a reason as "that through which one can understand why something is."9 A reason in this sense is some concept of the object of knowledge; and the principle of sufficient reason can be stated as a principle about the possibility of giving a first-figure demonstration of any truth about the object, in which the demonstration sets out from an adequate concept of the subject matter. On this interpretation, the existence of a reason, postulated by the principle, comes to mean the existence of a predicate, MM," which was called "the reason," which mediates between the terms "S" and "P" in true, affirmative judgments that S is P. So, for Lambert, it is the existence of this intermediating term which is asserted by the principle that everything has a reason why it is as it is.10 Now, since the whole continuous series of middle terms whose existence the principle requires us to posit as the content of our concept of the subject matter cannot be supposed to be given through our conscious acts of cognition, it seems to follow that, if everything true can be known a priori^ there are aspects of our cognitions of which we are not immediately conscious. The particular point to be stressed here is that this argument found in classical rationalism is very similar to the argument for unconscious cognitions which Peirce gave early in the 1868 series and which is likewise based upon the assumption of continuity in our representations. The upshot of the argument is that there can be no justification for admitting the existence of immediate, empirical judgments. We are trying out the hypothesis that we have a priori knowledge and we find that that hypothesis allows an explanation of why people believe and assert that some knowledge is immediate, empirical knowledge. Moreover, this explanation is such that it extends the possibility of consensus to include some empiricists - namely, to those empiricists who agree that reason-




ing can result in knowledge and that their own opinions about the immediacy of knowledge are not infallible.

There is still the other, more formidable objection to the claim to a consensus about Peirce's analysis of knowledge. When the rationalists speak about the a priori they mean that which is logically determined from what is prior through a process of analytic or deductive reasoning. Peirce wishes to include synthetic reasoning. In order to advance a second step toward a community of opinion, we must take a fresh look at what Kant intended when he divided knowledge into synthetic and analytic judgments. In twentieth-century philosophy there is a distinction between types of truth (or occasionally, types of proposition) which has often been confused with Kant's distinction between types of knowledge, or justified truths. Kant's analytic-synthetic distinction assumes a relation to a ground, and classifies on the basis of that relationship. In dividing analytic judgments from those which are synthetic, Kant asks whether what the given judgment predicates of its subject matter is contained in the concept of the subject matter. What does he mean by "concept of the subject"? It is easy to assume that he means that term in the judgment which is the logical or grammatical subject- term. However, that is not what it meant in eighteenth-century logic in the context of a discussion of u priori knowledge. It meant the adequate reason from which the given predication could be derived as a priori knowledge. Thus, after Wolff had defined the reason as that through which one can understand why something is, he says, "For as long as a thing has a reason why it is, one can know it, that is, one can conceive it . . ."n One's concept of a subject matter could be, and for Lambert certainly was, as complex as the collec- tion of axioms that set forth our concept of Euclidean space.

There is a passage from Kant's reply to Eberhard which con- firms the point which has just been made and which is instructive for students of Peirce's logic. "A reason, taken generally, is that through which something else, that is, something different, is de- terminately posited. . . . The reason, therefore, must always be



316 Richard Smyth

something other than the consequence. He who can produce as a reason nothing but the given consequence shows that he knows (or the matter has) no reason. This difference is either merely logical (in the mode of representation) or nal in the object itself. Now it is real difference which is required for synthetic judgments."12 A close reading of this passage will confirm the following: First, Kant's distinction between the analytic and synthetic presupposes that the judgments in question are ones that have grounds or reasons, and his distinction classifies on the basis of that relationship. Secondly, Kant's distinction is virtually identical to a perfectly sound classification of types of reasoning. Does the conclusion of the reasoning follow by changes in the premises which merely affect the way the subject matter is represented, and which make absolutely no change in the subject matter represented. (Does every model of the premises constitute a model of the conclusion?) If so, the reasoning is deductively valid, or analytic. If, on the other hand, the subject matter of the conclusion is real- ly, not merely verbally, different from the subject matter of the premises, the validity of the reasoning is that of probable or synthetic reasoning. The only difference between this way of repre- senting the problem and Kant's is that Kant believed that there is synthetic knowledge which is not a priori at all. However, that difference has already been disposed of. Even if it had not, Kant would have to agree with Peirce's claim that the key to the lock on the door of philosophy is in the solution to the question about how synthetic reasoning is possible. The questions 'How are synthetic judgments a priori possible?' and 'How is valid synthetic reasoning possible?' differ as little as 'How are effects possible?' and 'How is effecting possible?'

Whatever the intrinsic merits of this reading of Kant's analytic- synthetic distinction, it does focus attention on some aspects of Peirce's argument which might otherwise go unnoticed. In "Some Consequences," after defining a syllogism as any complete, simple and valid argument, Peirce introduced his concept of synthetic or probable reasoning as follows: "But a syllogism whose




validity depends partly upon the non-existence of some other knowledge is a probable syllogism."13 Unless we read this closely, recognizing that it professes to be a definition, we might think that the reference to the "non -existence of some other knowledge" involves a statement of one of the conventional criteria for valid inductions and abduction. The criterion would require us, in evaluating the reasoning, to take account of the full state of our information. However Peirce's statement is an attempt to tell us what this type of reasoning is. What he tells us is, in effect, that synthetic reasoning is ampliative reasoning or reasoning through which our knowledge of the subject matter is increased. Moreo- ver, if we postulate a Kantian background for the explanation, we can appreciate exactly why the definition is couched in the nega- tive. It will be recalled that, when Kant contrasts general logic and its explanation of deduction with transcendental logic and its explanation of the synthetic a priori^ he emphasizes the fact that with the former we can abstract entirely from any cognitive relation to the object. General logic "... abstracts from all relation of knowledge to the object and considers only the logical form in the relation of any cognition to any other cognition" (B79).

The validity of deduction is independent of the existence or non-existence of knowledge of the object because it only involves substitutions or changes in our representations. By contrast - Peirce is saying - the validity of probable reasoning is not independent of the existence or non-existence of knowledge. It can in fact be distinguished from deductive reasoning in just this Kantian way: it is reasoning whose validity does depend upon the non- existence of knowledge about the subject matter of the reasoning. Ampliation means prior ignorance. If the conclusion of the reasoning could be justified as a mere transformation of our prior concept of the subject matter of the reasoning, the reasoning would be deductive and analytic. The object of reasoning would not have to be brought into the picture at all to validate the reasoning - the connection could be made without reference to our cognitive relation to the object. This explanation of Peirce's view



318 Richard Smyth

of the difference between the two types of connection is consistent with his discussion in the Berkeley review of the function of the hypothesis that there are material objects. The epistemological function of this hypothesis is to account for the fact that at present we are ignorant of something and can therefore be surprised by what we come to know. The material object supplies an "other than directly intellectual connection" between our representations. Kant's discussion of the difference between analytic and synthetic connection and of the indispensable role of the object of knowledge in synthesis clearly lies behind Peirce's analysis in both pas- sages.

My effort to bridge the gap between Kant and Peirce would seem to have the effect of widening the gap between the latter's concept of knowledge and the rationalist's position. Such is the conventional wisdom about the relation between these two epistemological systems. However, after Peirce has introduced and illus- trated his different species of reasoning, he makes a point which potentially has enormous significance. He says that, while it is true that there are three distinct species of reasoning, all reasoning is of one genus and can always be given one general form. The schemata which he then produces to illustrate this point are extremely puzzling, because they appear to reduce each of the three forms to a species of deduction. What is Peirce doing here?

My conjecture is that he is exhibiting the possibility of such a reduction. I construe him in the following way: He says (in reference to simple and complete reasonings) that if the subject is changed by the reasoning, this schema will always be possible: M is P and (by the rule we can always add to accomplish the reduction) Every S is an M, therefore S is P. If the predicate is changed in the original reasoning, we have this schema: S is M and (by the rule we add as a second premise) whatever is M is P, therefore S is P. If both are changed, then the following schema will always be available: The state of things represented in P (the premise) is real and (by the rule we add as premise) the state of things represented in P is every state of things such as is represented by C




(the conclusion), therefore, the state of things represented in C is real. Clearly, each of these schemata (as I have construed them) converts the original reasoning into a deduction, so, Peirce con- cludes, "All valid reasoning, therefore, is of one general form; and in seeking to reduce all mental action to the formulae of valid inference, we seek to reduce it to one single type."14

There may be other, better ways to construe this difficult passage. However, it makes perfect sense if we attribute a certain conjecture to Peirce - a conjecture that will allow us to see how non-deductive inferences can always be reconstructed as valid de- ductions. The conjecture, or major insight if it is true, is that counterparts to the deduction -theorem hold for all reasoning, in- cluding induction and abduction. The deduction theorem (for simple inferences, in Peirce's sense) tells us that if we assume that "P, therefore CH is a valid deduction, then we can conclude from the validity of the reasoning that "if P, then C" is true and can add that truth to our stock of assertions. Peirce's insight appears to be this: If we assume that a form of reasoning is valid, then we must as a consequence of that assumption about validity be committed to the truth of some equivalent, corresponding generalization. But if so, and if we add the generalization to our stock of assumptions, the given reasoning can always be replaced by a valid deduction. For the sake of argument, let us assume that this conjecture is true. How does it bear on the rationalist's appraisal of Peirce's analysis of knowledge? Clearly, it has the effect of trans- forming every dispute about knowledge he has with the rationalist into a dispute about what is or is not true. For Peirce the claim that a certain probable reasoning is valid entails the claim that the

corresponding principle is true. Furthermore, Peirce must agree that in every case where the principle is true the conclusion of the reasoning can be known a priori by deduction from our concept of the subject matter of the reasoning, just as classical rationalism maintained. On the other hand, Peirce would also agree that in every case in which the principle is not true, what he claims to be valid, synthetic reasoning is not actually valid. While it is clear



320 Richard Smyth

that this result leaves room for disagreement between Peirce and the rationalist about what in fact is true, there is no longer any significant disagreement about this that results from differences in their analyses of knowledge.

Peirce's treatment of epistemology in 1868 seems to be written from a standpoint which is defensive about synthetic or merely probable reasoning. Now, as a matter of historical fact, those rationalists who were followers of Leibniz were not necessarily hos- tile to probable reasoning. However there was in Peirce's day and there continues to be today a species of pure deductivist who is sceptical about the validity of all reasoning which is not deductive. Peirce's essay gives an interesting insight into the relation between his claim that there is valid synthetic reasoning and the pure deductivist's claim that every ampliative argument is a fallacy. Peirce's response to the deductivist is that, in every case in which a reasoning is held to be fallacious because of the invalidity of the operation underlying the inference, the person who makes that charge is committed to the claim to knowledge of the falsity of the corresponding principle. If the claim to the validity of the inference is equivalent to claim to the truth of the corresponding generalization, knowledge that the inference is a fallacy is equivalent to knowledge that the generalization is false. Peirce's discussion of fallacy in "Some Consequences" establishes the basis for a counter-attack against pure deductivism: deductivism's scepticism about the validity of non-deductive reasoning conceals a dogma- tism about matters of fact - matters of fact which, were they as- sumed to be otherwise, would lead the deductivist to precisely the same conclusion as the non-deductivist and by reasoning which the deductivist approves. In fact, the appropriate historical target for this line of counter-attack would have been John Stuart Mill, rather than the earlier Leibnizians.

If we assume that the 1868 series was written from a standpoint which was defensive about experimental reasonings, we can understand more clearly how matters developed in the 1877-8 series on the logic of science. In 1868 Peirce, in effect, says that if



Peirce's Concept of Knowledge in 1868 ill

one has reservations about synthetic reasonings, then one merely has to suppose that one's concept of the subject matter is strengthened by the addition of certain material generalizations in order to reach the same conclusions by 'safe' deductive reasoning. And regardless of the psychological process by which one happens to reach the conclusions, whatever we do know, we can know a priori by deduction, just as the rationalists imagined. However, this entire line of reasoning could be reversed, if we were able to assume a lack of any doubt or reservation about our scientific reasonings. If we feel a greater confidence in them than we feel in our ability to spell out deductively what is involved in our concept of a given subject matter, then we can work the equivalence in the opposite direction. The pragmatic way to look at the task of clarifying the deductive implications of the concept is to think of those implications in terms of the corresponding procedures of experimental reasoning. On this view of Peirce's reasoning, the contents of "The Fixation of Belief," which establishes our confidence in the methods of science, are a strategic necessity for the reasoning in "How To Make Our Ideas Clear." The latter essay then turns the 1868 defense on its head.

If the preceding suggestion is correct, Peirce's new, pragmatic way of clarifying concepts and principles necessarily continued to presuppose the earlier, rationalistic way of conceiving truth and reality. Pragmatism's concept of truth embodied the consensus Peirce had forged in 1868 between his major predecessors - es- pecially Kant and the rationalists. In regard to the process of knowing, these earlier epistemologists certainly disagreed with Peirce and with one another. But, unless we give psychology an undue weight in our analysis of validity and of truth, the Kantian or Peircean who believes in the validity of operations involving synthesis will believe in the truth of results which can be viewed in just the way the rationalist stipulated as appropriate in claiming that whatever is true can be known & priori and, of course, that whatever is known a priori is true. This permits a definition of



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truth. Truth just is what results from the operations of valid reasoning. The truth results either directly, as the principles whose truth is equivalent to the validity of the scientific reasonings, or indirectly, as the sum of the particular, logical consequences of those principles. If this is pragmatism's concept of truth, it consti- tutes a remarkable 'Aufhebung' that transcended and cancelled a difference between Leibniz and Kant.

University of North Carolina at Chapel Hill

NOTES

1. Charles S. Peirce: Writings (Bloomington, 1984), Vol. II, p. 212.

2. Cf. Timothy L. Alborn, "Peirce's Evolutionary Logic: Conti- nuity, Indeterminacy, and the Natural Order," Transactions of the Charles S. Peirce Society, 25 (Winter, 1989), pp. 4-5.

3. Here I summarize the argument in w Peirce's Examination of Mill's Philosophy," Transactions, 21 (Spring, 1985).

4. Peirce, p. 214. 5. Cf. "Why Be Logical?" Transactions, 24 (Fall, 1988). 6. J.G. Gottsched: Erste Griinde der Vernunftlehre (Leipzig,

1766), p. 56. 7. Thus, Gottsched says, "Since anything which is true must

have a reason why it is true rather than false, it follows that anything which is true can be demonstrated; that is, it can be justified through the indication of a reason that it must be true. Now, since each truth is a proposition and since each proposition taken together with its reason yields a syllogism, it follows that one can prove any truth at all with formal syllogisms." Cf. Baumgarten in Kant: Gesammelte Schriften, (Berlin: Academy of Sciences, 1955), Vol. XVII, p. 27)

8. Johann Lambert: Neues Organon (Leipzig, 1764), Vol. II, p. 412.

9. Christian Wolff: Vemünftige Gedanken von Gott, der Welt, und der Seek des Menschen (Frankfurt, 1736), p. 15.

10. Lambert, Vol. I, p. 156.




11. Wolff, p. 36. 12. Kant, Vol. XI, pp. 34-5. 13. Peircc, p. 215. 14. Peircc, pp. 220-221.



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Peirce's Concept of Knowledge in 1868