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INTRODUCTION TO JEAN BURIDAN’S LOGIC
4 (TS 6.2.1) he suggests that a term may supposit for things which never
exist, the “merely possible.”
What are the ontological commitments or temporal and modal dis-
course? Contemporary philosophers, following Quine, take the idiom of
ontological commitment to be determined by quantity alone: existentially-
quantifed sentences are the bearers of ontological commitment. Buridan,
however, takes the idiom of ontological commitment to be determined by
time, quality, and mode: present-time affirmative assertoric sentences are
the bearers of ontological commitment. This alternative view has several
important consequences.
First, quantity is irrelevant; universal as well
as existential present-time affirmative assertoric sentences carry ontologi-
cal commitment—the so-called “existential import” of universal sentences.
Thus “All unicorns have horns” commits one to the existence of unicorns
as surely as “Some unicorns have horns” does. Second, negative sentences
do not carry any ontological commitment; their truth-value is determined
by the truth-value of their contradictory affirmative. Thus “Some unicorns
do not have horns” does not carry any commitment to the existence of uni-
corns.
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Third, Buridan insists that time and mode are relevant to ontologi-
cal commitment. Time is not normally taken into account by contemporary
logicians; Quine, for example, takes “eternal sentences” to be the logical
form of sentences in his canonical language. Buridan, though, allows tensed
sentences in Mental, and so his insistence that time is relevant to ontological
commitment is a substantive disagreement with the modern tradition. Thus
“Some man will be born in exactly ten years” does not carry any ontologi-
cal commitment for Buridan. Equally, mode is relevant; “Some man can be
standing in the doorway” does not carry any ontological commitment for
Buridan.
Let us explore this difference further. Modal logicians today usually
reduce de re to de dicto modality, and cash the latter out in terms of what
actually happens in peculiar conditions: modal sentences are reduced to
ordinary assertoric sentences with the ontology expanded to include pos-
sible worlds. Thus “Socrates can be bald” is canonically represented as
“There is a possible world in which Socrates is bald.”
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Mediæval logicians,
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Quality is not completely irrelevant for contemporary philosophers; there is no on-
tological commitment if a negation precedes the existentially-quantified sentence on
the modern view. But “Some unicorns do not have horns” would be represented as
(∃x)(U x ∧ ¬Hx), which does commit one to the existence of unicorns.
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It makes no difference whether the reference to possible worlds is included in the
sentence (e. g. as an operator) or is part of the semantic apparatus, included in the
interpretation function assigning truth-values to sentences; the net result is the same—
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.
INTRODUCTION TO JEAN BURIDAN’S LOGIC
53
on the other hand, reduce de dicto to de re modals, or countenance both
sorts. In particular, Buridan refuses to reduce modal discourse to any other
form: rather than being a disguised form of assertoric discourse under pe-
culiar conditions, modal discourse is a primitive form of discourse in normal
conditions. Similarly, tensed discourse is not reducible to present-time or
tenseless discourse with an expanded ontology including past and future
existents; it is a primitive form of discourse in normal conditions. We might
capture the difference by saying that mediæval logicians sever quantifica-
tion (and hence supposition or reference from ontological commitment. The
truth of modal or tensed sentences does not require us to expand our ontol-
ogy. Buridan is a nominalist: he does not admit any abstract entities. But
it is not at all clear that he must likewise refuse to quantify across past or fu-
ture items, or possible items, so long as they are not abstract. Indeed, since
supposition is a theory of reference, it seems clear that can can talk about
such items; what is important is that we not take them to exist. And that
is the moral of Buridan’s alternative conception of ontological commitment.
6.9 Truth-Conditions
Armed with the theory of supposition, we can return to the truth-
conditions of categorical sentences. First, Buridan takes the proposed defi-
nition of truth “howsoever a sentence signifies to be, so it is, in the thing(s)
signified”—to apply directly to a present-time affirmative assertoric sen-
tence. But there are other kinds of sentence. Past-time sentences are true
if howsoever the sentence signifies to have been, so it was, in the thing(s)
signified; future-time sentences are true if howsoever the sentence signifies
to be going to be, so it will be, in the thing(s) signified; and modal sentences
are true if e. g. howsoever the sentence signifies to be able to be, so can be,
in the thing(s) signified (TC 1.1.7–11, QM 6.8). As remarked at the end of
Section 5.5, the application of this definition requires the theory of suppo-
sition, explaining what is meant by the clause “in the thing(s) signified.”
If we confine ourselves to the simple sentences of the traditional Square of
Opposition, then we may state their correspondence truth-conditions
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as
follows:
(1) If an A-form sentence such as “Every S is P ” is true, then everything
the subject supposits for the predicate supposits for.
(2) If an I-form sentence such as “Some S is P ” is true, then something
the subject supposits for the predicate supposits for.
an assertoric sentence true in an expanded ontology.
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I borrow this name from Hughes [1982] 22.
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.