Handbook of the History of Logic: - Fordham University Faculty

Port Royal: The Stirrings of Modernity 683
discussion in the section on incidental propositions and compound subjects where
the Logic suggests one can affirm an A proposition without asserting the existence
of anything which falls under its subject term.
In any case, the section on the square of opposition is brief, and the section on
modal propositions (130) is also extremely brief. There is no discussion of modal
syllogisms.
5 COMPOUND PROPOSITIONS AND INCIDENTAL OR SUBORDINATE
PROPOSITIONS
The Port-Royal Logic includes a discussion of a variety of propositions which do not
fit easily into the pattern of simple categorical propositions. Arnauld and Nicole
characterize compound propositions as those that have either complex subjects or
complex predicates. In fact, most of their examples are propositions in which just
one or the other terms is complex, such as propositions of the form “either a or
b is F ”, or “b is F and G.” However, they allow both terms to be complex as
well, and in their discussion of conditionals include such conditionals as “If the
earth is immovable, the sun revolves”. As they see all conditionals as statements
of inference, these conditionals containing different terms and predicates in their
subordinate propositions are said to be statements of “mediate inference”. All
the other cases of compound propositions they discuss involve complex subjects
or predicates, although it is possible to extend their account generally.
Compound propositions are divided into two classes, those in which the composition
is explicit, and those in which it is not, these latter being called “exponibles”.
The explicit ones include copulatives (“P and Q”), disjunctives (“Either P or
Q”), conditionals (“If P then Q”), causals (“P because of Q”), relatives (other
than causal, e.g. “As a person lives, so he dies”) and discretives (“P but Q”).
The original (first edition) list of exponibles included exclusives (“Only F is G”),
exceptives (“All F , except G, areH”), comparatives (“A is more F than B”),
inceptives (“Beginning at t, P ”), desitives (“P ended at t”), and reduplicatives
(“A, insofar as it is B, isC”). In the later editions, the inceptives and desitives
were treated together, and the reduplicatives simply mentioned under the causals.
These propositions were for the most part not treated as truth-functions, with
the exception of basic conjunctions, or copulatives. With respect to these, Arnauld
and Nicole say “the truth of these propositions depends on the truth of both
parts” (132). 26 However, under each of these classifications there is a discussion
26It is interesting to note that for the example of a copulative with both a complex subject
and a complex predicate Arnauld and Nicole take a negative proposition which in English is
naturally seen as a negation of a disjunction, but which in Latin and French are easily seen as a
conjunction of negations. The line is from Horace:
Non domus & fundus, non aeris acervus et auri, Aegroto Domini deduxit corpore
febres, non animo curas.
Which they translate as Ni les maisons, ni les terres, ni les plus grandes amas d’or & d’argent ne