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INTRODUCTION TO JEAN BURIDAN’S LOGIC
5. Sentences
5.1 Sentences as Assertions
Sentences express assertions: an inscription or utterance is a sen-
tence only through subordination to a Mental sentence, which is an act of
thinking. Inscription which are not being read, utterances which are not
heard (as a tape recorder playing in the wilderness), are sentences in only a
derivative fashion. To construe sentences assertions, as Buridan does, has
three important consequences. First, only a Mental sentence is true or false;
inscriptions and utterances have truth-value only derivatively, as we call a
furry winter coat ‘warm’ (TS 1.3.3-11). Strictly, only the act of thinking
which is the Mental sentence is the act of assertion. Second, no part of
an assertion may itself be an assertion, as Frege also maintained; hence
no part of a sentence is itself a sentence (Rule Sup-6 in TS 2.6.1, Hughes
[1982] 13.4.1.1.1). However, a sentence may have constituent parts which are
equiform to or supposit for sentences.
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Third, the reason for the existen-
tial import of universal affirmatives is clear: a sentence like “All swans are
white” is not to be understood as the disguised conditional (∀x)(Sx → W x),
from which (∃x)(Sx ∧ W x) does not follow, but rather as something like
“Consider the swans: Each is white” or “About the swans: They are all
white,” where ‘Consider the swans’ or ‘About the swans’ captures the as-
sertive force of a sentence. The existential claim “Some swans are white” is
then “Consider the swans: some are white” which in fact does seem to fol-
low from the universal sentence.
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This is why Buridan takes quantification
to be a condition of the whole sentence, as discussed in Section 4.1.
Buridan says that every sentence is either categorical or hypothetical
(TC 1.3.2), which is an exclusive and exhaustive division.
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These should
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Buridan will speak loosely about the ‘sentences’ which make up a consequence, but this
is a permissible looseness, not a deviation from his doctrine. It is therefore incorrect,
strictly speaking, to represent Buridan’s logic by means of the propositional calculus;
it is equally incorrect to metalinguistically quote sentential letters. But as Buridan
often speaks loosely, relying on his general rule that terms have the same semantic
role in equiform sentences (TC 3.7.41), I shall occasionally use such quasi-technical
devices in my exposition.
38
This method for interpreting universal and existential sentences so that existential
import is validated I take from Belnap [1973]; it works because ‘each’ presupposes the
existential import of the subject-term—see TS 3.7.19 and the discussion of anaphoric
reference in Section 6.4.
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Buridan admits a class of sentences which he first calls “quasi-hypothetical,” but
immediately says that such sentences are in fact hypothetical, and they are so-called
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.
INTRODUCTION TO JEAN BURIDAN’S LOGIC
23
be regarded as sentence-frames;
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the expressions which may be substituted
in each frame may be logically complex. The categorical sentence-frame
functionally defines its constituents as subject and predicate (TS 1.3.8); its
general form is therefore:
(subject)-[copula]-(predicate)
There seem to be three types of hypothetical sentences: conjunctive sen-
tences, disjunctive sentences, and consequences The last functionally defines
its constituents as antecedent and consequent; its general form is therefore:
(antecedent)-[illation]-(consequent)
where the illation is usually signaled by ‘therefore’ or its equivalent, or
by ‘if’ preposed to the antecedent or its equivalent; Buridan favors the
former method. Disjunctive or conjunctive sentences are sentences which
are disjunctions or conjunctions or parts equiform to sentences; Buridan
does not investigate their general form; neither shall we, since their behavior
is familiar.
5.2 Categorical Sentences
The general form of the categorical sentence discussed above, namely
subject-copula-predicate, is the actual form of the Mental sentence; in Spo-
ken or Written not all of these components will be apparent (TC 1.8.72).
For example, existential statements have misleading surface grammar; the
Spoken or Written expression “S is” is represented in Mental as “S is a be-
ing” or “S are beings” (TS 1.3.8 and TC 1.8.84). Equally, subjects paired
with intransitive verbs are resolved into the copula with a participle, so “S
runs” becomes “S is running”; and the like. Buridan tentatively suggests
that the copula in Mental is timeless (TS 3.4.8), but does not explore the
implications. We have remarked above the complexive nature of the copula.
Strictly speaking there are two forms of the copula: ‘is’ and ‘is not,’ which
correspond to distinct functions in Mental (TS 2.3.12).
It is hard to describe the nature of the subject and the predicate,
which Buridan discusses in TS II-2 and II-6. A complex series of rules
specify some restrictions on which expressions can serve as subject or pred-
icate. In general, any noun phrase can be subject or predicate; this in-
cludes (i ) any substantive nominative term, whether discrete or common,
and any adjective taken substantively (Rules Sup-1 and Sup-5); (ii ) all
referring expressions (Rule Sup-2); (iii ) infinitive verbs (Rules Sup-4 and
Sup-7); (iv ) grammatical combinations of nouns and adjectives, or, more
only because they are very similar to certain categorical sentences (TC 3.7.20)
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Buridan actually suggest such frames in several places: TC 1.8.62, 2.6.34, 3.4.59, for
example.
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.