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William of Ockham’s The Sum of Logic
Stephen Read
Published online: 12 July 2007
� Springer Science+Business Media B.V. 2007
William of Ockham’s Summa Logicae is a classic of ana-
lytical metaphysics, using a typical fourteenth century lo-
gic treatise to defend a reductionist ontology.1 For
Ockham, everything is an individual, and this is to be
shown by the correct logical analysis of language, rein-
terpreting Aristotle’s Categories as a taxonomy of the
many ways in which terms can be predicated. The ultimate
basis is the attribution of an individual quality to an indi-
vidual substance. This theory of the signification of terms is
then extended to an account of the truth-conditions of
propositions and the truth-preservation of arguments, but
always with the reduction to individuals as the key. This
classic work in the logical analysis of language still con-
tains lively insights for contemporary scholars.
Much of Part I of the Summa Logicae is taken up with
the notion of the signification of words. Indeed, like
Wittgenstein’s Philosophical Investigations, it opens with a
quotation from Augustine, in this case coupled to another
from Boethius reporting Aristotle’s three-fold division of
language from the start of his De Interpretatione. Terms
and the propositions of which they are composed are of
three types, written, spoken and mental: and ‘‘these con-
ceptual terms and the propositions composed from them
are those mental words which St Augustine in De Trinitate
XV said are of no language, because they remain only in
the mind and cannot be carried forth from it, whereas the
sounds subordinate to them as signs can be uttered pub-
licly.’’2
Two iconoclastic ideas are contained in germ in this
passage: first, the Augustinian conceit that concepts form a
mental language in parallel to spoken and written language;
secondly, the consequential insight that this language
cannot be signified by spoken and written language since it
is itself a language and so open to interpretation. Rather,
Ockham described spoken language, and written language
in turn, as subordinated to mental language, deriving its
signification from the signification of that language of
thought. Mental language too, as a language, needs to
obtain its interpretation and signification in some way. But
how? By being common to all men, as Aristotle said (De
Interpretatione 16a7)—but contrary to his observation that
all signs signify by convention (16a26)—mental terms
signify naturally, not by convention as do spoken and
written terms in different languages. But what do they
signify?
Here the London school of Ockham and his sympathizer
Wodeham, opposed by the realist Chatton, takes inspiration
from Avicenna’s commentary on Aristotle’s Metaphysics.
Everything which is one and not many is a singular and
individual thing. Nothing is common to other things except
by signification. The only universals are names. Avicenna
expresses this nominalist credo in a passage cited by
Ockham: ‘‘One form in the mind is related to many and in
this respect is a universal, since it is a concept in the mind
… This form, although universal in its relation to indi-
viduals, is individual in its relation to the particular mind in
1 See Ockham (1974) for the full critical edition of the Latin text.
Parts I and II, and a small part of Part III (which itself comprises more
than half the work), have been translated into English. For details, see
Spade (1999), 8.
S. Read (&)
Department of Philosophy, University of St Andrews, St
Andrews, Fife, Scotland, UK
e-mail: [email protected]
2 Ockham (1974), I 1: 7. All references to the Summa Logicae will be
to Ockham (1974), citing Part, chapter and page number.
123
Topoi (2007) 26:271–277
DOI 10.1007/s11245-007-9024-x
which it is imprinted.’’ (I 14: 48) The idea is this: uni-
versals are words, whether spoken, written or mental.
Spoken and written words derive their signification from
being subordinated to mental words. Mental words are acts
of the mind, acts of cognition of, in general, extra-mental
things, all of which are individual. Some of these acts,
however, embrace many things—they are universal to
them, and unite them in a single mental act. These acts are
thereby universal.
Ockham did not always hold this view. He was per-
suaded of it by his Franciscan colleague Walter Chatton.
His earlier thought was this: everything is individual, but
we can think of universals. Hence universals must be
without real existence, but existing only as an object of
thought (tantum obiective—existing only ‘‘objectively’’).3
This is his notorious fictum theory: universals are fictive
entities existing only in thought. Chatton criticized the
theory presented in Ockham’s lectures on the Sentences in
his own lectures: either each fictum depends essentially on
the corresponding act of thought for its existence—in
which case we multiply ficta unacceptably for each and
every act—or it does not, in which case we could have a
fictum existing ‘‘objectively’’ (i.e., as the object of an act of
thought) without any act of thought—which is a plain
contradiction. The argument is invalid,4 but was so per-
suasive with Ockham that he repeated it verbatim in his
Quodlibetal Disputations presented shortly before com-
posing the Summa Logicae, and revised shortly afterwards,
possibly in Avignon.
What, then, is the object of an act of thought concerning
universals, for example, that Socrates is a man? It needs no
object other than men; indeed, that is what makes the act a
universal, its being common, by natural signification, to all
men. Ockham had already eliminated the intermediary
species (or form) in so-called ‘‘intuitive’’ cognition of
individuals—in thinking of Socrates I think of him, not of
or by means of any representative image; now in abstrac-
tive cognition, in abstracting the universal from a range of
individuals, what is formed is not the object of an
abstractive act, but the act itself which embraces, directly,
those individuals.
This reductive philosophy has dramatic, possibly
heretical, implications. For it occasions Ockham to rethink
entirely Aristotle’s project in his Categories. The bulk of
Part I of Summa Logicae is taken up with consideration of
the meaning of terms, which Ockham claims was Aris-
totle’s real project. But if nothing is universal except by
signification, then what fall into the categories are words,
not things. It is a classification of types of expression. But
names are of essentially two types, not ten. Either they
describe something absolutely and simply, like ‘man’ and
‘animal’; or they describe something indirectly, by con-
noting some accident of it, like ‘white’ or ‘cause’: ‘‘[con-
notative names] have what is, in the strict sense, called a
nominal definition. In the nominal definition of a conno-
tative term it is frequently necessary to put one expression
in the nominative case and another in one of the oblique
cases. The term ‘white’ provides an example … if someone
should ask for the nominal definition of ‘white’ the answer
would be … ‘something having a whiteness’.’’5
Ockham proceeds to show that all the divisions of
Aristotle’s non-substance categories are misleading and
unnecessary. Take privations, for example, like blindness.
This isn’t any real quality existing in the blind person, but
its lack or absence. It’s no more than a function of the way
words signify. Ockham cites Anselm in support of his
view. Language can mislead: ‘‘‘to fear’ is grammatically in
the active voice; in actual fact it is something passive.
Similarly, according to the form of speech blindness is said
to be something; in actual fact it is not anything at all.’’ (I
36: 119) Passions don’t inhere in subjects, but are only in
the mind (or loosely, in speech or in writing), for passions
are predicated of things, and only elements of propositions,
that is, words, are predicated. Indeed, substance is only a
word: first substance is a proper name, and second sub-
stance a common name: for example, ‘‘when Aristotle says
that if first substance was destroyed it would be impossible
for any of the other things to remain [2b4-6], he is not
talking of real distinction and real existence. He means,
rather, destructive by way of a negative proposition. Thus,
he is saying that when ‘to be’ is not predicated of anything
contained under a common term, it is only denied of the
common term itself as well as of the properties and acci-
dents proper to that common term.’’ (I 42: 134)
The most radical application of Ockham’s reduction of
the categories is elaborated in chs. 44–52 of Part I of the
Summa Logicae, where he denies the distinct reality of
quantity and relation. For the central doctrine of the Aris-
totelian categories is not only that they are exhaustive and
exclusive (distinct things belong to distinct categories) but
they are essential in that what is, for example, an animal (a
substance) is essentially an animal, and cannot cease to be
an animal without ceasing to be; a weight of five kilos (a
quantity) is essentially five kilos, distinct from a quantity of
six kilos; similarity (a relation) between two things is
essentially similarity, and cannot become a different rela-
tion; and so on. Ockham rejects this orthodox interpreta-
tion: the only essences are substance and quality. This
3 On the origin of the notions of objective and subjective existence,
and the almost total switch in their usage during the eighteenth cen-
tury, see Hamilton (1846), §I, especially the footnote to Proposition 6,
pp. 806–808.4 See, e.g., Adams (1987), 105 and Read (1977), 28. 5 Ockham (1974), I 10: 36.
272 S. Read
123
claim is heretical,6 and Ockham realises it, so he attributes
the view to Aristotle, saying he will ‘‘outline the account
without committing myself to it.’’ (I 44: 145) Take quan-
tity, for example. The quantity of air in a container can
change, when it condenses or is rarefied. If quantity were a
real accident, this would be impossible unless the original
quantity were destroyed and replaced by an entirely new
quantity. Since condensation and rarefaction are continu-
ous, this would entail an actual infinity of quantities, which
all Aristotelians believe is impossible. The correct expla-
nation is that quantity is a connotative term, naming some
quantity of something. Quantity is not distinct from that
substance of which it is some quantity.
Ockham likewise denies the reality of points, lines and
surfaces distinct from the lines, surfaces and solids which
they delimit. For example, if lines were real parts of a
surface, there would be an actual infinity of them, which is
impossible. Rather, a surface is indefinitely divisible, and
each division creates a line, but only as the limit and so as
an attribute of the surface of the body. Again, time and
place are not real things; rather something has a quality at
some time at some place, so time and place connote attri-
butes of something real, but are not real separable entities
themselves.
In ch. 49, Ockham proceeds to argue that (for Aristotle,
at least) relations are not really distinct from their relata.
‘Relation’ is, he says, a term of second intention, that is,
relations are terms, not things, for they are, Aristotle says,
qualified by some expression in an oblique case (genitive,
dative or ablative): a father is father of someone, a cause is
a cause of something, something similar is similar to
something, a slave is someone’s slave. Relations are con-
notative names, naming one relatum and connoting the
other(s). So this is not to deny the division of the ten cat-
egories. There are indeed ten different types of terms, and
types of question one can ask. But underlying these lin-
guistic categories there are only two types of thing, sub-
stance and quality.
Why does Ockham maintain this dualism? He writes:
‘‘to determine when a quality should be posited as a thing
distinct from substance and when not, one can employ the
following test: predicables which, while incapable of being
truly applied to one thing at the same time, can succes-
sively hold true of an object merely as a result of a local
motion [motum localem], need not be construed as signi-
fying distinct things.’’ (I 55: 180) For example, something
straight becomes curved simply by the movement of its
parts, so curvature (curvitas) and straightness (rectitudo)
are not real qualities distinct from the curved and straight
substances; but this is not true of, for example, whiteness
and blackness or heat and cold, so these are real qualities.
This might seem to be an application of Ockham’s
Razor, but a closer look shows matters are more subtle. It’s
well known that the famous phrase, ‘‘Entia non sunt mul-
tiplicanda praeter necessitatem’’, occurs in many other
medieval authors besides Ockham. In fact, it is not found in
Ockham at all. The ontological principle which does guide
Ockham is cited by Adams (1987), 269: ‘‘It is impossible
for contraries to be successively true about the same thing
unless because of the locomotion of something or because
of the passage of time, or because of the production or
destruction of something.’’7 The closest Ockham comes to
the Razor, she says, is: ‘‘No plurality should be assumed
unless it can be proved by reason, or experience, or by
some infallible authority.’’8 This hardly says that entities
must not be multiplied beyond necessity, if necessity
means reason or experience: it defers to revelation—the
Bible and the sayings of the saints.9
Despite these qualifications, however, Ockham’s ap-
proach is reductive, at least as far as the denial of real
universals outside the mind is concerned. This comes out
strikingly in his theory of truth, detailed in Part II of the
Summa Logicae. In a notorious passage in ch. 2, he says
that a singular proposition like ‘Socrates is a man’ is not
true because Socrates has humanity, or because humanity is
in Socrates, or man is in Socrates, or that man is part of the
quidditative concept of Socrates. Rather, it is true simply
because ‘Socrates’ and ‘man’ are both names of Socrates,
the first a proper name, the second a common name. He
generalizes this to all atomic propositions using the tech-
nical notion of supposition. As he explains in I 63, strictly
speaking supposition is the relation of the subject-term to
what it stands for, whereas appellation is the corresponding
relation for predicates. But given that universals are no
more than names, predicates do not differ enough seman-
tically from subjects to justify two concepts, so broadly, he
says, both subject and predicate have supposition. Taken
significatively (that is, in the jargon, ‘‘personally’’), what
terms in a proposition supposit for depends on the tense
and mood of the copula. With a present-tense copula, a
term ‘/’ supposits for just those things which it signifies,
that is, of which it can be truly predicated in a singular
6 On the question whether Ockham’s ontological doctrines were in-
deed heretical, see e.g., Adams (1987), 979 ff.
7 Cited from Ockham (1979), 369. See also Adams (1987), 155, 176,
251 and 279.8 Adams (1987), 1008, citing his Treatise on Quantity, which is
probably a surviving fragment of the Reportatio of Book I of his
Sentences corresponding to the revised Ordinatio at Ockham (1979),
290.9 Ockham did not believe the Pope or the Church were included
among the infallible, as dramatically demonstrated by the fact that, on
examining the question of apostolic poverty, Ockham accused Pope
John XXII himself of heresy.
William of Ockham’s The Sum of Logic 273
123
proposition, ‘This is / ’. Now take an indefinite or par-
ticular proposition of the form ‘Some / is w’. This is true
just when ‘/’ and ‘w’ supposit for the same, that is, are
truly predicable of the same thing. Its contradictory, the
universal negative, ‘No / is w’, is true if ‘/’ and ‘w’ do not
supposit for anything in common. Its contrary in turn,
‘Every / is w’, is true, following standard medieval prac-
tice in preserving the square of opposition, if ‘/’ supposits
for something and ‘w’ supposits for everything for which
‘/’ supposits. Finally, the contradictory of the universal
affirmative, namely, the particular negative, ‘Some / is not
w’, or perhaps better, ‘Not every / is w’, is true if ‘/’ does
not supposit for something for which ‘w’ supposits—so in
particular, it is true if ‘/’ supposits for nothing.
Geach (1972) deplored Ockham’s introduction of this
‘‘two-name theory’’ (as Geach called it) as compounding
by a further ‘‘corruption of logic’’ Aristotle’s initial fall
from grace in introducing the ‘‘two-term theory’’ inherent
in the theory of the syllogism. To read Geach, one would
think Ockham had jettisoned the linguistic dualism of
subject and predicate to proclaim a monism of substance
and name. But that is not the doctrine. Terms name indi-
viduals either by signifying their essential natures (sub-
stance) or connoting their accidents (quality). Without the
dualism of substance and quality, Ockham would find
himself drawn into a Leibnizian necessity where each
predication was essential. Connotation of accidents main-
tains the contingency of accidental predication. What he
avoids in all this is any regress of instantiation, as we saw
in the passage from Summa Logicae II 2: ‘‘for all propo-
sitions such as these are false: ‘Man is of the quiddity of
Socrates’, ‘Man is of the essence of Socrates’, ‘Humanity
is in Socrates’, ‘Socrates has humanity’, ‘Socrates is a man
in virtue of humanity’,’’ and so on. All that is required is
that there be Socrates, the individual, and his individual
qualities, whiteness, snub-nosedness and so on, what are
nowadays called ‘‘tropes’’.10 The world is a collocation of
substance and quality.
This sounds very like Humean supervenience. To be
sure, as stated by David Lewis, that doctrine incorporates
physicalism; he writes: ‘‘Humean supervenience … is the
doctrine that all there is to the world is a vast mosaic of
local matters of particular fact … maybe point-sized bits of
matter … [a]nd at those points, we have local qualities.’’11
But Lewis concedes that materialism is included in the
doctrine only to endorse ‘‘our best physics’’. Indeed,
Ockham goes further: not only does everything supervene
on local matters of fact; it is reducible to them. At least,
that is his project.
At the heart of the theory is the singular predication,
‘This is /’. It is also used to define the modes of common
personal supposition needed to frame the non-syllogistic
modes of inference. Take determinate supposition, for
example, which some 70 years earlier, Lambert of Lagny
(1988, 111) had described vaguely as ‘‘what a common
term has when it can be taken equally well for one or for
more than one, as when one says ‘A man is running’.’’
Ockham makes this idea precise by the doctrine of ascent
and descent, whereby he can relate the modes of supposi-
tion of common terms to that of discrete terms like ‘this’.
‘‘Determinate supposition occurs when it is possible to
descend to singulars by way of a disjunctive proposition.
Thus, the following is a good inference: a man runs,
therefore this man runs or that man and so on for singu-
lars.’’ (I 70: 210) Ockham is not the first to exploit descent
and ascent in the definition of the modes of common per-
sonal supposition. Walter Burley did so 20 years earlier, at
least if we correct the reading in Brown’s edition of Bur-
ley’s early treatise De Suppositionibus (which otherwise is
nonsense): ‘‘Determinate supposition occurs when a com-
mon term supposits disjunctively [reading disiunctive for
Brown’s distributive] for supposita as here ‘Some man
runs’. Whence by determinate supposition and disjunctive
[reading disiunctive with MS C] supposition I understand
the same.’’12 Burley goes on to characterize merely con-
fused supposition (e.g., in the predicate of A-propositions)
when one can ascend from any singular (‘Every / is this
w’) but cannot descend conjunctively or disjunctively;
confused and distributive supposition (e.g., the subject of
A-propositions) when one can descend conjunctively.
Ockham follows him in this, adding that in the case of
merely confused supposition, one can descend by way of a
disjunct predicate: from ‘Every / is w’ infer ‘Every / is
this w or that w and so on’. Though not original to Ockham,
the doctrine of ascent and descent suits his reductive pur-
poses perfectly, in taking every case back to the singular
predication, ‘This is / ’. For example, from ‘Every / is w’
we can first infer ‘Every / is this w or that w and so on’,
then infer ‘This / is this w or that w … and that / is this wor that w … and …’, and finally infer a conjunction of
disjunctions of the form ‘This / is that w’, true just when
subject and predicate co-supposit.
Thus the truth-conditions of non-modal present-tense
propositions can be reduced to that of singulars. What,
however, of past-tense, future-tense, modal and intensional
propositions? Here Ockham is radical and original, but
alone. Other authors deal with such cases by invoking the
doctrine of ampliation. Ampliation is that property of terms
which extends (‘‘ampliates’’) the supposition of terms to
past, future and possible (or even impossible) supposita.10 See, e.g., Campbell (1990).11 Lewis (1986), ix–x. 12 Brown (1972), 38.
274 S. Read
123
However, the way ampliation works on them is different.
Moreover, there is a significant difference between the
treatment in Britain and in Paris. In Paris, past- and future-
tense propositions are given a disjunctive interpretation.
For example, ‘Some / was w’ is said to be true if and only
if something which either is or was / (at some time) was w(at some time—not necessarily the same time). Burley and
Ockham, however, treat it as ambiguous, either as saying
that what is / was w or as saying that what was / was w.
Even if something that is / was w, the proposition is
accordingly false on one reading, whereas on the Parisian
account it will come out unequivocally true. For modal
propositions, both groups treat them as ambiguous, but
differently from tensed propositions. ‘Some / must be w’,
for example, has both a compounded sense, that ‘Some / is
w’ is necessarily true, and a divided sense, saying of
something which is / that it must be w. It’s easy to miss
this dissimilarity between tensed and modal propositions,
and indeed, Ockham’s remarks in Part III-4 encourage it,
where he sets out the analysis of tensed propositions side
by side in a way that at first glance looks analogous. But in
fact it is not. He writes: a modal ‘‘proposition should be
distinguished because the subject-term can stand for those
that are or for those that can be or for those that can be and
can not be.’’ (III-4 4: 763). It’s that final ‘‘can be and can
not be’’ (contingit esse) which shows up the difference. In
the composite sense, ‘Some / must be w’ is true if ‘Some
/ is w’ is necessarily true, i.e., true for all time and in all
possibilities, and in those possibilities, ‘This is / and w’
can be true where ‘this’ refers to contingent existents which
do not actually exist. Nonetheless, the truth-condition is
radically different in structure from that of ‘Some / were
w’.
Although there is no unequivocal statement of his po-
sition, it seems clear that Ockham is both a presentist and
an actualist. What exists is what actually exists now. A
presentist thinks belief to the contrary arises only from
sloppy use of tensed expressions. Neither the past nor the
future exists,13 but are what did or will exist. Similarly, no
mere possibilia exist—rather, they might or might have
existed. Thus the truth-condition of tensed and modal
propositions is repeatedly given in terms of the past, future
or possible truth of present-tense propositions. Take modal
propositions in the divided sense, for example. Ockham
reduces their truth to that of ‘‘a non-modal proposition in
which the very same predicate is predicated of a pronoun
indicating that for which the subject supposits’’ (II 10:
276), effecting a recursive reduction of the truth-conditions
of all propositions to that of singulars.
Much of Ockham’s account of consequence in Part III is
framed in terms of the syllogism, non-modal and modal. To
a modern logician, the treatment is frustratingly particular
and unsystematic, treating every possible combination of
premise-pair and conclusion in the three figures separately.
Once modal syllogisms are introduced, with mixed pre-
mises where the mode of either can be ‘necessary’, ‘pos-
sible’, ‘contingent’ or ‘impossible’, or one can be non-
modal, or from another mode such as ‘known’ or ‘be-
lieved’, the sheer variety is overwhelming. After 68
chapters of Part III-1, and a further 41 on the demonstrative
syllogism in III-2, treatise III-3 appears to promise some
relief: a general account of consequence. But what we find
in fact is an addendum to the theory of two-premise
inference in the syllogism, namely, one-premise inference,
again treated piecemeal with little systematic generaliza-
tion.
This is unfortunate, because there is an underlying
systematization available. Aristotle himself showed this for
the non-modal syllogism: the dictum de omni et nullo
grounds first-figure syllogisms, and simple and per acci-
dens conversion and reduction per impossibile reduce
validity in the second and third figures to the first. But such
systematization was not the medievals’ forte, and it has its
costs, for it encourages concentration on cases that fit the
chosen Procrustean bed, overlooking others (e.g., first-or-
der predicate logic is very powerful, but it does not prop-
erly represent arguments containing demonstratives,
common nouns, mass terms and many others). The medi-
evals revelled in diversity, and it is part of Ockham’s
contribution to the theory of the modal syllogism that he
extends the treatment to cases Aristotle had overlooked,
resolving the so-called problem of the ‘‘two Barbaras’’.14
Aristotle accepts modal Barbara where major premise and
conclusion have the mode of necessity (and the minor is
non-modal) but not when the minor is a necessity propo-
sition and the major is non-modal. This suggests that he
reads ‘w necessarily applies to all /’ de re (or in the di-
vided sense). But so read, it does not convert per accidens,
as Aristotle says it should (25a29), and as it would if read
de dicto.15
Ockham diagnoses the ambiguity and works out the
detail of what follows for each combination of premises
(III-1 31). In fact, there is a double ambiguity, for not only
may the modal premise be taken in a compounded or a
divided sense, but the non-modal premise may be true
absolutely (simpliciter) or only as-of-now (ut nunc, at
13 See, e.g., Ockham (1978) ch. 10, p. 211: ‘‘Moreover, no part of
time exists because neither the past nor the future do; so time is not
something really existing totally distinct from other things.’’
14 See, e.g., Thom (2003), 27–30.15 Of course, the compounded/divided distinction is broader than, but
includes the de dicto/de re distinction. For example, any proposition
of the form ‘You believe p and not-p’ has compounded and divided
senses, but is not ambiguous de dicto/de re.
William of Ockham’s The Sum of Logic 275
123
present but not always). Given that all propositions true
absolutely are necessarily true, then whether the modal
minor is taken in the divided or compounded senses, the
syllogism is valid provided the non-modal major premise is
true absolutely. But if the major is only true at present, and
not necessarily or absolutely, the syllogism is invalid.
Karger (1976, 185–90) infers that Ockham adopts the
Diodorean account of necessity and equates necessary truth
with truth at all times, by reference to Summa Logicae II 9:
275. But this passage merely claims that a necessarily true
proposition is only true when it exists. In fact, Ockham
nowhere defines what it is for a proposition to be true
‘‘simpliciter’’ or ‘‘ut nunc’’ as such. However, if we turn to
Part III-3 ch. 1, where he defines inference ut nunc et
simpliciter, we find him conclude in ch. 2: ‘‘for when a
predication of a superior of an inferior is necessary, then
the inference is absolute; but when the predication of a
superior of an inferior is contingent, then the inference is
only ut nunc.’’ (III-3 2: 591) All becomes clear when we
turn to the definitions in ch. 1: ‘‘Inference ut nunc is when
the premise can be true at some time without the conclu-
sion but not at this time … Absolute inference is when at
no time could the premise be true without the conclusion.’’
(III-3 1: 587–8) So rather than equate necessary truth with
truth at all times, Ockham equates absolute truth with
necessary truth. Absolute truth is already a modal notion.
Ockham’s treatment of intensional propositions other
than modals, e.g., ‘I promise you a horse’ or ‘I know the
one approaching’, is again reductionist. These proposi-
tions open the door to sophistical reasoning: consider, for
example, the crooked horse-dealer who points to each
horse in turn, asking rhetorically: ‘Did I promise you this
horse?’. He claims there is no (particular) horse he
promised you, and so no particular horse he need give
you. There’s obviously a fallacy here, and in Part III-4
Ockham proceeds to discuss and illustrate Aristotle’s 13
types of misleading constructions. He diagnoses this
example as falling under the third type of equivocation,
diversity of supposition (III-4 4): ‘horse’ doesn’t exhibit
a lexical ambiguity (the first type), where a word has
different meanings; nor is there any extended or meta-
phorical meaning (the second type) to ‘horse’ in this
example. De Rijk argued persuasively in the 1960s that
the spur to the development of the medieval theory of
supposition was a desire to create a technical tool for
diagnosing fallacies like this, and Ockham applies it here
in what seems a novel way. Burley argued that ‘horse’ in
this example had simple supposition, for the universal
horse.16 The promise is fulfilled by giving the universal
in the only way possible, in a particular horse. Ockham
has to reject this: if universals are just acts of mind,
then what was promised was certainly not an act of
mind. Rather, what was promised was a horse. So how
does ‘horse’ supposit in ‘I promise you a horse’? It can
supposit either determinately, or merely confusedly.
Taken the first way, the proposition is false—there was
no particular horse he promised you; taken the second
way, it is true, for ‘horse’ is equivalent to ‘this horse
or that horse and so on’, provided the disjunction
ranges over horses which may be given you, namely,
present and future horses (again, Ockham does not
speak of ampliation). So ‘I promise you a horse’ is
equivalent to ‘I promise you this horse or that horse
and so on’, but not to ‘I promise you this horse or I
promise you that horse and so on’, so ‘horse’ supposits
merely confusedly and not determinately. (See I 72:
219) Accordingly, the rule forbidding the move from
merely confused to determinate supposition explains
the fallacy.
The puzzle of the hooded man cannot be solved in this
way. If I know Coriscus and Coriscus is the one
approaching, then it seems I must know the one
approaching. Ockham agrees—that argument is valid. The
puzzle arises, he says, because we confuse this argument
with a different one, for example, Coriscus is the man and
Coriscus is the one approaching, so the one approaching is
the man—a valid expository syllogism. However, if we
know the major premise, it does not follow that we know
the conclusion. It is a fallacy of accident, for it does not
always follow that ‘‘when some things are conjoined in
predication with a third, they are mutually conjoined in a
valid conclusion.’’ (III-4 11: 819) To know the one
approaching I would have to know that Coriscus was the
one approaching, that is, know both premises and not just
one of them.
To conclude: how does Ockham’s Summa Logicae
fare as a classic? Can it still provide inspiration for
contemporary scholars, as a source of fresh ideas and
insights? The opening words of Adams (1987) are crucial
to this evaluation; she writes: ‘‘Ockham’s philosophical
focus, whether he is doing logic, natural science, or
theology, is on the branch of metaphysics commonly
called ‘ontology’.’’ (p. 3) The Summa Logicae is a classic
of philosophy, more narrowly of metaphysics, not of
logic. Ockham uses the context of a work on logic, in the
broader sense of the philosophy of logic and language, to
defend his central reductive ontological theme. As a work
of logic, it is embedded in its own cultural milieu; as a
work of reductionist metaphysics, it is timely and time-
less. The Summa Logicae is a model of analytical
metaphysics whose reductive metaphysics is as arresting
now as it was in 1324.16 Burley (2000), 96.
276 S. Read
123
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