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INTRODUCTION TO JEAN BURIDAN’S LOGIC
Though difficult to state precisely, Theorem I-8 is extremely important:
sentences will be shown to be equipollent by having the same causes of
their truth, and so by (b) mutually follow from each other. This result
Buridan deemed sufficiently important to repeat it in a separate theorem,
theorem I-9. Equally, one sentence will be shown to be the conversion of
another by having the same or more causes of its truth than the original
sentence, that is, by Theorem I-8(a) or (b). These two theorems are the
basis of not only assertoric equipollences and conversions, but also of modal
equipollences and conversions (TC 1.8.50), though these are explored later.
These theorems are perfectly general; Buridan points out (TC 1.8.51 that
the sentences “Of-any-man no ass is running” and “Of-no-man an ass is
running” are equipollent. Hence his theory is applicable far beyond the
simple sentences which appear in the Square of Opposition.
Buridan gives only some examples of equipollences in TC 1.8.51;
they are the equivalences of signs of quantity and negations, so that e. g.
‘Every . . . is not —’ is equipollent to ‘No . . . is —’. The equipollences are
standard, but note that Buridan does not take them as definatory of the
signs of quantity, as modern logicians define one quantifier by another; their
equipollence must be established, which is a corollary of Buridan’s semantic
approach to quantification.
Conversions are treated at greater length, in Theorems I-10 through
I-17. Buridan begins in Theorem I-10 with consequences by subalterna-
tion and conversions of universals into particulars; the theorem is stated
for terms with distributive confused supposition, and generalized to terms
with non-distributive confused supposition in Theorem I-II. The next pair
of theorems, Theorem I-12 and Theorem I-13, deal with conversions of sen-
tences containing ampliation or non-ampliating restrictions (such as the
“what is. . . ” locution).
Theorem I-14 is a turning-point in Buridan’s discussion, specifying
rules of simple and accidental conversion:
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[Theorem I-14 ] (a) From any universal or particular affirmative as-
sertoric sentence there follows a particular affirmative by conversion
of the terms; (b) from any universal negative there follows a uni-
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Conversions are simple when the subject-term and predicate-term are reversed and
the result is equipollent. E-form and I-form sentences convert simply, e. g. “No S is P ”
and “No P is S ” are equipollent. Conversions are accidental when the subject-term
and the predicate-term are reversed and the quantity is changed; the result is not
equipollent. Thus an A-form is converted accidentally to an I-form, such as “Every S
is P ” to “Some P is S,” and an E-form is converted accidentally to an O-form, such
as “No S is P ” to “Some P is not S.”
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.
INTRODUCTION TO JEAN BURIDAN’S LOGIC
61
versal and a particular negative; and (c) no sentence follows from a
particular negative by its form alone.
Buridan discusses this theorem in TC 1.8.70–95. The extended analysis is
required by cause of the generality of Theorem 1-14: it applies to sentences
in which the logical constituents (subject-copula-predicate) may be implicit
rather than explicit, such as the one-word sentence “Ambulo”; the copula
of such sentences, whether explicit or implicit, may be present-time, past-
time, or future-time; the predicate term r the subject-term, or both, may
be ampliative; the ‘what is. . . ’ locution may be used; the sentence may be
existential, and so (apparently) lack a predicate-term; the rules of gram-
mar may be violated in reversing the subject-term and predicate-term; the
subject-term or the predicate-term may be logically complex, containing
syncategoremata; they may contain or consist in terms in oblique cases;
certain syncategoremata may require special analysis. Buridan takes each
of these possibilities into account, and his discussion is a marvel of complex
precision.
A singular sentence follows from another singular sentence by con-
version of the terms, as Buridan notes in Theorem I-15, paying attention to
ampliation and the form of the singular term.
In the next pair of theorems Buridan considers the results when the
subject-term or predicate-term is changed “according to finite and infinite,”
i. e. the effects of term-negation (infinitizing negation) on conversions. This
may be called ‘conversion’ in a broad sense, even though the terms them-
selves are altered (TC 1.8.101). Theorem I-16 and Theorem I-17 set forth
such relations of conversion; it is often necessary to suppose that the varied
term is non-empty, the assumption of the constantia terminorum.
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It is a travesty to present mediæval logic as though only sentences
appearing on the Square of Opposition were investigated. Buridan’s dis-
cussion of assertoric consequences is perfectly general, and adequate for his
philosophy of logic and language.
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The technical names for these conversions are as follows. First, if the subject-term
and predicate-term are not reversed, then (i ) if the predicate-term is changed ac-
cording to finite and infinite the result is called obversion; (ii ) if the subject-term is
changed according to finite and infinite the result is called partial inversion; (ii ) if
both subject-term and predicate-term are changed according to finite and infinite the
result is called full inversion. Second, if the subject-term and the predicate-term are
reversed, (i ) the obversion of the resulting sentence is called obverted conversion; (ii )
the partial inversion of the resulting sentence is called partial contraposition; (iii ) the
full inversion of the resulting sentence is called full contraposition. (Do not confuse
the latter case with ‘contraposition’ as applied to consequences themselves.)
c Peter King, from Jean Buridan’s Logic (Dordrecht: D. Reidel 1985) 3–82.