24
INTRODUCTION TO JEAN BURIDAN’S LOGIC
generally, nouns and oblique terms Rule Sup-8); (v ) certain combinations
of categorematic and syncategorematic terms (Rules Sup-9 and Sup-10).
Conversely, taken per se the following cannot serve as subject or predicate:
(i ) pure syncategoremata (Rule Sup-2); (ii ) oblique terms not combined
with a substantive (Rule Sup-3); (iii ) finite verbs (Rules Sup-4 and Sup-7);
(iv ) sentences (Rule Sup-6).
Categorical sentences may be distinguished with respect to quantity,
quality, or mode.
Regarding quantity, first, signs of quantity are prop-
erly not parts of the subject or predicate, but are “conditions of the whole
sentence” (TS 2.2.15), the same way a negating negation (though not an
infinitizing negation) is a condition of the copula. Second, the quantity
of a sentence is determined by the syncategorematic terms present in the
sentence. Distributive and particular signs of quantity are the usual syn-
categorematic terms which specify the quantity of a sentence, but other
syncategoremata may also affect the quantity—negations, exceptives, and
the like (see Section 4.1). Finally, the quantity of a sentence is, in general,
given by the semantic generality of the subject of the sentence, and not by
the items actually denoted; “All unicorns have horns” is distributive, and
so has more quantity than “Some men are sexists,” despite the fact that
‘unicorn’ is an empty term and ‘man’ is not.
Modern logicians recognized differences of quantity and of mode:
sentences are universal or particular, assertoric or modal. Differences of
quality—whether a sentences is affirmative or negative—are not usually
taken into account. Yet Buridan takes two forms of the copula, ‘is’ and
‘is not,’ as primitive; hence there are two fundamental types of sentences,
affirmative and negative. Is this defensible? The answer turns on the signif-
icance attached to the distinction between predicate negation and sentence
negation, which cannot be clearly drawn in modern logic: there is no differ-
ence between belonging to the extension of the complement of a predicate
and not belonging to the extension of the predicate. Buridan, however,
insists on the difference: the truth of “Socrates is non-blue” suggests that
Socrates has a property, being non-blue, or at least presupposes that he
exists.
41
Thus for Buridan the truth-conditions for sentences differing in
quality may be quite different. Fore example, since negatives are denials
which do not presuppose the existence of their subjects, negatives with
empty subject-terms are automatically true: of course unicorns fail to have
a given property; they fail to have every property, since they do not exist.
41
This may be the key intuition behind the mediæval view that quantity is irrelevant
to ontological commitment, but quality is not. See Section 6.9 below.
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.
INTRODUCTION TO JEAN BURIDAN’S LOGIC
25
Conversely, affirmative sentences with empty subject-terms must be false,
even if the predicate is infinite.
Categorical sentences may also be distinguished with respect to their
mode: they are either assertoric or modal (TC 2.1.3). Buridan distinguishes
them in the following way: although every sentence is either possible, nec-
essary, or contingent, only those sentences explicitly including a “mode”
are counted as modal; the terms ‘possible,’ ‘necessary,’ ‘contingent,’ ‘true,’
‘false,’ ‘known,’ and so forth are modes. Buridan thus treats ‘modal logic’
as much wider than the logic of possibility and as “that whole found in the
sentence aside from the mode and the copula and the negations and the
quantifiers, or other determinations the mode or the copula” (TC 2.3.3).
42
Examples are “That a man runs is composite, the latter divided : a modal
sentence is composite when the mode is put as the subject and the dictum
is predicated, or conversely (TC 2.2.2); a modal sentence is divided when
part of the dictum is put as the subject and the other part as the predicate,
and the mode is taken as a determination of the copula (TC 2.2.5).
Divided modal sentences ampliate their subjects and can be treated
easily as a case of sentences with a special ampliative copula (see Section
6.8). Composite modal sentences, on the other hand, are a peculiar type of
assertoric categorical: we may understand
It is possible that p
as equivalent to
A possible [sentence] is that-p
where the analyzed sentence has an ordinary copula and the predicate is
‘that-p’ (TC 2.7.1-5). Such sentences are indefinite and may thus be quan-
tified:
Some possible [sentence] is that-p
Every possible [sentence] is that-p
To understand this we need to know what it means to call something a
‘possible’ or a ‘possible [sentence].’ Buridan implicitly endorses the following
analysis:
“Some possible [sentence] is that-p” is true if and only if for a sen-
tence p
∗
equiform to p, how p
∗
(if formed) signifies to be can be the
case.
There are two points to note. First, the clause ‘a sentence p
∗
equiform to p’
must be included because the predicate of the original sentence is ‘that-p,’
42
Strictly speaking this definition is too loose, for the dictum of “It is possible that
a man is running is “that a man is running,” and so includes an occurrence of the
copula occurrences of logical particles. It is less clear how to explain ‘non-primary’ in a
non-trivial fashion; this is precisely Frege’s distinction between ‘force’ and ‘assertion.’
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.