Handbook of the History of Logic: - Fordham University Faculty

680 Russell Wahl
1. The attribute is put in the subject by an affirmative proposition according
to the entire extension the subject has in the proposition.
2. The attribute of an affirmative proposition is affirmed according to its entire
comprehension.
3. The attribute of an affirmative proposition is not affirmed according to its
entire extension if it is in itself greater than that of the subject.
4. The extension of the attribute is restricted by that of the subject, such that
it does not signify more than the part of its extension which applies to the
subject. (170) 23
Thus in the proposition “All F are G”, by (1) and (2) the comprehension of G
is affirmed of all of the extension of F , and by (3) and (4) the extension of G
is not affirmed according to its entire extension, but is restricted to the part of
its extension which is common to F . It is somewhat difficult to interpret the
last two axioms, but it seems that in some sense the claim is that in affirmative
universal propositions, the whole of the extension of the subject is signified, but
not the whole of the extension of the predicate. These claims replace the doctrine
of distribution, where the term is distributed when it signifies its entire extension,
and is undistributed when it doesn’t. Pariente takes the second two axioms to
indicate that in the case of an affirmative proposition “All F are G” what is being
asserted is an identity between the extension of F and a part of the extension
of G (namely those G’s that are F , given Axiom 4). The proposition “Some
F are G” then would assert an identity between an indeterminate part of the
extension of F and an indeterminate part of the extension of G. Now Pariente,
though, also claimed that in the case of “All F are G”, the Port Royal view is
that the comprehension of G is included as a subset of the comprehension of F
[Parient, 1985, 266]. As Jill Buroker has pointed out, this claim does not appear to
follow from these axioms, nor is it plausible in the case of non-necessary universal
affirmatives and even less plausible in the case of particular affirmatives. When I
affirm “All swans are white”, I am claiming that the extension of swan is a subset
of the extension of white. Am I also claiming that the comprehension of white
is contained in the comprehension of swan? This would only be plausible if we
thought of the comprehension of an idea as including all the ideas which apply to
the entire extension. Given the view that the comprehension was essential to the
idea and the extension was not, this position is implausible. Again it seems very
implausible, to use Buroker’s example, that when we say “some bears are white”
we are including the comprehension of white in the comprehension of bear, orin
the comprehension of the idea of some particular bear [Buroker, 1994, 10–11].
While there are places where Arnauld and Nicole seem to hold a theory of
the copula as asserting an identity between the extension of the subject and the
23 An important feature of axiom 1 is that the subject of a universal proposition has the entire
extension of the idea, while that of a particular has only an indeterminate part of that extension.