Handbook of the History of Logic: - Fordham University Faculty

Port Royal: The Stirrings of Modernity 685
The exponibles were thought of as implicit compounds because while they appear
to be categorical propositions, on analysis they are seen to contain at least
two separate assertions. I will just mention two of them, the exclusives and the
exceptives. Exclusive propositions (propositions such as “Only F and G”) tend
to be treated by modern logic books as a variant on the categorical proposition
“All G are F ”. The Port-Royal Logic treats exclusives as a conjunction of two
propositions, but it discusses only such propositions which have a singular subject,
such as “Virtue alone is admirable”, or “Only God is worthy of being loved for
his own sake” (138). These propositions are seen as a conjunction of two propositions,
e.g. “Virtue is admirable” and “Nothing else is admirable”. This restriction
to singular subjects is also found in their treatment of exceptives. The example
they give, “No ancient philosophers, except the Platonists, recognized God’s
incorporeality” is treated as the compound of “the Platonists recognized God’s
incorporeality”, and “No other ancient philosophers did”. A similar treatment is
given to the proposition, “Except for the sage, all people are truly mad (fous)”
(141). We are not given an explicit treatment of exclusives which do not have a
singular subject, although the suggestion is that these too would be considered as
having compound subjects. “Only the brave deserve the fair”, would presumably
be seen by Arnauld and Nicole as asserting that the brave deserve the fair and no
others do. With respect to the exceptives, the rule given is that in these propositions
we “affirm a thing of an entire subject with the exception of some of the
inferiors of this subject, which we show by an exceptive particle that this thing
does not apply to them ...” (140). This account includes propositions such as
“None but the brave deserve the fair,” which would be treated as asserting the
same two claims as above.
6 CATEGORICAL SYLLOGISMS
The Port-Royal discussion of syllogisms is a mixed bag. On the one hand, Arnauld
and Nicole maintain their skepticism toward formal logic and the importance of
the study of reasoning or inference, saying that “there is reason to doubt whether
it is as useful as is imagined”, and “it happens rarely that we let ourselves be
misled by arguments that are false merely because the conclusion is badly drawn”
(177-178). Yet despite this dismissive attitude, the treatment of syllogisms is fairly
careful and quite clear.
The need for reasoning, they hold, is a consequence of our limited minds. The
suggestion seems to be that a mind which had sufficiently clear and distinct ideas
would not need any reasoning at all. Reasoning only comes in when we cannot
decide on whether a proposition is true or false by considering the ideas which it
contains. To help determine whether a proposition is true we bring in a third idea,
the middle term, which helps us see the relation between the subject and predicate
of the proposition in question. An important feature of this way of viewing things
is that the inquirer always starts with the conclusion. The premises are sought
as an aid in determining the truth of the conclusion, but arguments do not have