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INTRODUCTION TO JEAN BURIDAN’S LOGIC
follow—although in this case, “Every man is this animal or that animal
or. . . ” does follow.
Semantically, a term has non-distributive confused supposition when
it is used attributively of its extension. This explains why a sentence con-
taining such a term does not entail any of the singulars individually or in
a disjunctive sentence—this characterizes referential uses—but why a sen-
tence with a disjunctive extreme does follow. The attributive use of a term
will apply to a definite number of individuals in its extension (depending
on the facts of the matter), but it does so indifferently, applying to each for
exactly the same reasons. Such sentences presuppose their truth to deter-
mine the (actual) reference of the term, i. e. the subclass of the signification
which actually have the property in question. In this sense, non-distributive
confused supposition is close to our use of existential quantification.
Thus distributive confused supposition will correspond to universal
quantification, determinate supposition to existential quantification used
attributively, and discrete supposition to naming or denotation. It is clear
that this scheme is complete: there is no room left for other sorts of ref-
erence. Mediæval semantic theory, therefore, codifies reference-relations by
their use and by their extension.
The syntactic specification of non-distributive confused supposition
is more motley than distributive confused supposition; two rules deal with
the effect of quantification, and two with special terms. First, a universal
affirmative sign causes non-distributive confused supposition in a term not
in its scope which is construed with a term in its scope (Rule NDC-1 in
TS 3.8.1 and 3.8.4), and a common term has non-distributive confused sup-
position where it is in the scope of two universal signs, either of which would
distribute the rest were the other not present (Rule NDC-2 in TS 3.8.13).
third, temporal and locative locutions “often” produce non-distributive con-
fusion (Rule NDC-3 in TS 3.8.19), as do terms involving knowing, owing,
and desiring (Rule NDC-4 in TS 3.8.24), where the latter have certain spe-
cial characteristics.
Buridan’s syntactic rules accomplish more than merely telling us
which kind of confused supposition a term has; they permit the extension of
supposition-theory beyond the narrow realm of simple categorical sentences,
to deal with complex cases of multiple quantification such as “Every woman
gives some food to every cat.”
Nevertheless, if we restrict ourselves to
sentences in which the subject and predicate are logically simple, then we
can briefly summarize the kinds of supposition possessed by the subject-
term and the predicate-term in the Square of Opposition:
(1) In universal affirmatives such as “All S is P ” [A-form], S has dis-
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.
INTRODUCTION TO JEAN BURIDAN’S LOGIC
47
tributive confused supposition and P has non-distributive confused
supposition.
(2) In universal negatives such as “No S is P ” [E-form], S and P each
have distributive confused supposition.
(3) In particular affirmatives such as “Some S is P ” [I-form], S and p
each have determinate supposition.
(4) In particular negatives such as “Some S is not P ” [O-form], S has
determinate supposition and P has distributive confused supposi-
tion.
If we augment the Square of Opposition by adding sentences with singular
subject-terms, then in singular affirmatives and negatives the predicate ahs
the same supposition as the corresponding particular form, and the subject
has discrete supposition. Do not overlook the fact that Buridan’s theory is
much more general than (1)–(4) suggest.
Once the supposition of a term has been determined, the sentence
may be inferentially related to other sentences. The most interesting such
sentences are those in which terms which do not have discrete supposition
are replaced by terms which do have discrete supposition; depending on the
inferential direction, the relations are relations of ascent or descent.
72
For
example, the I-form sentence “Some dog is healthy” entails “Some dog is
this healthy thing or that healthy thing or. . . ” where ‘some dog’ can be
replaced by the reference-class in question, since it has a referential use.
Modern mediæval scholarship finds a fatal flaw in the theory of sup-
position at this point, known as the “Problem of the O-form.” The difficulty
is as follows. Suppose that only Socrates and Plato exist, each of whom is
Greek, and consider the (false) O-form sentence “Some man is not Greek.”
If we descend under the subject-term, then (assuming that the reference is
to Socrates and Plato) we get “Socrates is not Greek or Plato is not Greek.”
Each of the disjuncts is false, and so the sentence is false. However, if we
descend under the predicate-term, we get “some man is not this Greek and
some man is not that Greek.” If ‘this Greek’ and ‘that Greek’ refer to
Socrates and Plato respectively, then the first conjunction is true, taking
‘some man’ to be Plato, and the second conjunct is true, taking ‘some man’
to be Socrates; both conjuncts are true, and so the conjunction is true,
though the original sentence is false.
The interpretation of supposition-theory offered above suggests a
72
Buridan uses these terms only rarely, as in TS 2.6.75–76 and 3.8.22–23, but does
frequently talk about ‘descending’ from a general sentence to a string of less general
sentences. Despite the fact that it was a standard part of supposition-theory, though,
Buridan does not give any systematic or theoretical account of the doctrine.
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.