Handbook of the History of Logic: - Fordham University Faculty

Port Royal: The Stirrings of Modernity 679
between universal and particular propositions on the basis of whether a common
term is taken in its entire extension or whether it is taken as an indeterminate
part (115). Singular propositions are then classified with universal, even though
their subject is not a common term, because they are always taken through their
entire extensions (115). Despite the fact that the quantifier expressions are seen
grammatically as attaching to the subject terms, there is a sense in which propositions
are to be understood as universal or particular and not simply their subject
terms. The real interest in the Port-Royal Logic is in whether a term in a proposition
is taken throughout its entire extension or not. This way of phrasing things
replaces the account of “distributed terms” familiar to students of what is now
taught as syllogistic logic. As we shall see, the Port-Royal analysis of propositions
and inferences relies very heavily on this concept.
Jean-Claude Pariente has suggested that the Port-Royal Logic is best understood
as holding an identity theory of the copula. E. A. Moody [Moody, 1953, 36]
characterized two understandings of the copula from mediaeval semantics. The
identity theory holds that in some sense the copula in an affirmative proposition
asserts some kind of identity. Clearly with such cases as “All men are mortal” the
view has to be understood not as identifying the subject term with the predicate
term, but as saying that the proposition asserts an identity of the extension of the
subject term with part of the extension of the predicate. Ockham has been associated
with the identity theory, 20 but he made it clear that he does not require that
the subject and predicate be identical, but rather, “that the subject and predicate
supposit for the same thing”. 21 The other theory, the inherence theory, did not
take the copula as a sign of identity, but as a sign of the inherence of the property
signified by the predicate term into those objects which were supposited by
the subject term. The identity theory was very much motivated by nominalism,
since the earlier theory took the predicate term to refer to a universal or common
nature. Pariente takes some remarks from the Port-Royal Logic concerning conversion,
and a further remark from Arnauld’s La perpétuité delafoias evidence
that the copula is taken as a symbol of identity. 22
It seems on the face of it that the nominalism of Port Royal would not have them
adopt the inherence theory, and the language as Pariente points out, does suggest
the identity theory. However, the situation is a bit more complex, as the discussion
of the function of the copula in affirmative propositions takes into consideration
both the comprehensions and extensions of the ideas. This discussion is most
explicit in the account of conversion of propositions. There Arnauld and Nicole
give four “indubitable axioms” concerning affirmative propositions:
d’autres selon l’usage des langues. (114)
20 See [Moody, 1953, 36–37].
21 Ockham, Summa Logicae, II, Ch. 2. See [Freddoso and Shuurman, 1980, 86].
22 [Pariente, 1985, 263]. The remark from The Perpetuation of the Faith was “the nature of
all affirmative propositions is to indicate that the subject is the same thing as the attribute
[predicate]” [Arnauld, 1775-1783, III, 167]. In the chapter introducing conversion in the Logic,
Arnauld and Nicole say “. . . it is clear that the nature of affirmation is to unite and to identify
. . . the subject with the attribute, since this is what is signified by the word is.” (168)