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INTRODUCTION TO JEAN BURIDAN’S LOGIC
particular man is not ϕ. Even if other men are ϕ, the sentence will be false,
for they are not being referred to. Modern logicians are accustomed to read
‘some’ attributively, and so to take the ϕ-ness of other men to suffice for
the truth of the sentence. Yet nothing forces us to accept the attributive
reading; the referential reading is certainly a possible interpretation, and
in fact seems to accord with ordinary language and linguistic intuitions far
better than the attributive reading.
It might be objected that on the referential reading there is no differ-
ence between discrete and determinate supposition. But this is an artifact
of our examples; we have taken ‘some’ to stand for a single individual. In
such a case there is no difference. But ‘some’ may also stand for a determi-
nate number of individuals: I may assert “Some men are bald,” referring to
six friends of mine whom I know or believe to be bald. Taken referentially,
if any is bald, the sentence is true; if not, not. The semantic understanding
of determinate supposition should now be evident. A term has determinate
supposition if it is taken referentially for at least one determinate individ-
ual it signifies. Thus what Geach took to be the great sin of mediæval logic
turns out to be its great virtue. There is nothing incoherent in the notion
that a term may stand only for some of its significates on a particular occa-
sion of its use in a sentence: Geach’s worries stem from not taking seriously
the pragmatic dimension of semantics, and the contribution of the logical
grammar of a given sentence to determining the reference of a term.
A final point. The same term may appear in different sentences,
and in each case have determinate supposition. The theory of supposition
has nothing to say about when such occurrences are coreferential.
Nor
should it; supposition theory specifies the reference of a term in a given
sentential context. Coreferentiality involves more than a single sentence;
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additional semantic principles are needed for the wider context of several
sentences. Clearly such principles are vital for the theory of inference: they
are provided in the general theory of the syllogism. In particular, the dictum
de omni et nullo, discussed in Section 8.2, fixes coreferentiality.
A common term has confused supposition in a sentences if it is not
sufficient for the truth of that sentence that it be true for a singular term
falling under the common term (TS 3.5.1). This is equivalent to saying that
conditions (1)–(2) for determinate supposition are not met (TS 3.5.7).
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Strictly speaking, this is not true; the same term may appear several times with
a sentence. Coreferentiality in such cases is established (or not) anaphorically, by
relative supposition.
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.
INTRODUCTION TO JEAN BURIDAN’S LOGIC
45
6.7 Distributive and Non-Distributive Supposition
There are two forms of confused supposition; Buridan gives a condi-
tion for each, and then a series of syntactical rules. A term in distributive
confused supposition is used to talk about any or all of the things it signifies;
a term in non-distributive confused supposition (sometimes called “merely
confused supposition”) is used to talk about several of the things it signifies
indifferently.
A common term has distributive confused supposition in a sentence
when any of the singulars falling under the common term can be inferred in-
dividually, or all inferred conjunctively in a conjunctive sentence (TS 3.6.1).
Hence the term ‘man’ in “Every man is running” has distributive confused
supposition, because (i ) “Every man is running; therefore, Socrates is run-
ning” is an acceptable consequence; (ii ) “Every man is running; therefore,
Socrates is running and Plato is running and Aristotle is running et sic de
singulis” is an acceptable consequence. Distributive confused supposition,
then, is similar to universal quantification. The semantic relations involved
in distributive confused supposition are clear: reference is made to every-
thing (presently existing) which the term signifies; it is “distributed” over
each individual.
Buridan gives five rules for when a common term in a sentence has
distributive confused supposition; they syntactically indicate, by means of
scope conventions governing negation and quantification (and comparison),
when a common term has distributive confused supposition. First, a uni-
versal affirmative sign distributes the common term it governs (Rule DC-1
in TS 3.7.1); Buridan has a long analysis of what counts as such a uni-
versal affirmative sign (TS 3.7.2–3.7.33). Second, negations affect distri-
bution: an infinitizing negation distributes terms in its scope (Rule DC-
3 in TS 3.7.42), while a negating negation distributes every term in its
scope which would otherwise not be distributed (Rule DC-2 in TS 3.7.34)–
and terms which imply negative syncategoremata have similar effects (Rule
NDC-5 in TS 3.7.50). Third, comparative contexts produce distribution,
that is, the use of a comparison, and adjective of degree or a superlative
(Rule DC-4 in TS 3.7.45).
On the other hand, a common term in a sentence has non-distributive
confused supposition when neither 9i) any of the singulars individually fol-
low, nor (ii ) do the singulars follow disjunctively in a disjunctive sentence,
although sometimes a sentence with a disjunctive extreme follows (TS 3.6.1).
the term ‘animal’ in “Every man is an animal” is in non-distributive con-
fused supposition, because (i ) “Every man is this animal” does not follow;
(ii ) “Every man is this animal or every man is that animal or. . . ” does not
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.