Handbook of the History of Logic: - Fordham University Faculty

674 Russell Wahl
Royal Logic, although it is fairly clear that singular terms do have a comprehension
as well as an extension, and this is certainly true of definite descriptions. It is clear
that the Port-Royal Logic holds the principle that if the comprehension of an idea
A includes the comprehension of an idea B then the extension of B includes the
extension of A, but there isn’t any reason to think Arnauld and Nicole hold the
converse, that if the extension of the idea A is included in the extension of B,
then the comprehension of B is included in the comprehension of A. Such a
principle would make explications simply a making explicit the comprehension
already contained in an idea. Unfortunately there is one spot where Arnauld and
Nicole come close to expressing this view. In Part III, chapter 10 they discuss a
general method of testing arguments and seeking premises, and are in particular
discussing a syllogism in Disamis,
Some saint is poor.
All saints are friends of God.
Therefore some friend of God is poor.
The general method holds that the conclusion is contained in the major premise
and that the minor premise makes this explicit. They say that for the major
premise to contain the conclusion, “it is necessary and sufficient that the term
some saint contain the term some friend of God.” For this to be the case, they
continue, “it is necessary that friend of God be contained in the comprehension
of the idea saint” (213). What is at issue here is the truth of the minor premise.
Certainly if friend of God is contained within the comprehension of saint, we could
know this, but I don’t think we need to read into this remark the claim that this
must be true for any such A proposition to be true.
Complex terms, and the distinction between explicative and determinative additions
play an important role in the analysis of propositions, particularly the
discussion of incidental (or subordinate) propositions. This discussion will be important
to the discussion of inference. One tension which arises immediately is
the relation of complex ideas to such incidental propositions. Arnauld and Nicole
follow tradition by holding that ideas are prior to propositions, yet they hold that
“it is the same thing to say ‘a transparent body’ or a ‘body that is transparent”’
(66). Yet the first appears to be a complex idea while the second contains, they
hold in Part II, an implicit assertion. As we shall see, the line they wish to draw
between conception, which is of ideas, and judgment, which is of propositions is
not as easy to make as it seems. But to explore this further, as well as other issues
involving terms, it will be useful to look at their account of propositions.
4 PROPOSITIONS
The Logic has a traditional view of propositions as containing two terms and a
copula. One term is the subject term, the other, the predicate; the subject is that
of which one affirms or denies something, and what is affirmed is the predicate