Handbook of the History of Logic: - Fordham University Faculty

Port Royal: The Stirrings of Modernity 681
extension of the predicate and this seems most supported by the third and fourth
axioms above, the easiest reading of the first two axioms simply is a predicative
view of the copula, where the entire comprehension of the predicate is predicated
of the extension of the subject term — either the entire extension of the idea
in the case of the universal proposition, or an indeterminate part in the case of
the particular. As Buroker has pointed out, these first two axioms suggest an
asymmetry between subject and predicate which doesn’t fit well with the identity
theory. However, some remarks at the end of the fourth axiom (“. . . when we say
that humans are animals, the word ‘animal’ no longer signifies all animals, but
only those animals which are human.” (170)) suggest something like the identity
theory and the unfortunate view that the significance of the word ‘animal’ when
in predicate position is different in different universal affirmative statements.
These four axioms were given as a prelude to the account of conversion, the
only immediate inference discussed in the Port-Royal Logic. The rejection of the
conversion of the A proposition is taken as a consequence of these axioms, for in
a proposition such as “all men are animals”, all ideas contained in the comprehension
of “animals” are asserted of the entire extension of “men,” but by the
third axiom, nothing is claimed about the entire extension of “animals”. Thus
the proposition, “all animals are men” is not contained in “all men are animals”.
Following this analysis, Arnauld and Nicole give two rules for the conversion of
affirmative propositions, the first that universal affirmative propositions can be
converted by adding a mark of particularity to the attribute which becomes the
subject, and the second that particular affirmative propositions can be converted
without any change. Given that in “all men are mortal” the extension of the
term “mortal” that is in question is only a part of the total extension of the idea,
from the fourth axiom, that part of the extension is said to be identical with the
extension of the term “men”, so “some mortals are men” will be true.
As Jean-Claude Pariente has pointed out, the Port-Royal Logic gives a separate
account of negation. The negation of a categorical proposition is not defined in
terms of the truth values of propositions negated, but separately. It then will
follow from this account that the E proposition will take the opposite truth value
of the I and the O will take the opposite truth value of the A. Again with the
account of negative propositions, there is a part of an identity theory, as the
account opens by saying that the nature of a negative proposition is “to conceive
that one thing is not another” (173). Three further axioms are given specifically
concerning negative propositions:
1. A negative proposition does not separate all the parts contained in the comprehension
of the attribute from the subject: but it separates only the total
and complete idea composed of these attributes together.
2. The attribute of a negative proposition is always taken generally [i.e. throughout
the entire extension].
3. Every attribute denied of a subject is denied of everything contained in the
extension of the subject in the proposition [i.e. the entire extension of the