in Jean-Yves Beziau & Gilman Payette,
eds., The Square of Opposition, A General Framework for Cognition
(Bern: Peter Lang, 2012), pp. 61-97.
Abstract
This paper investigates the truth-conditions put
forth in the Port Royal Logic for categorical propositions in terms of
“extension”. The new Cartesian semantics
was motivated by the rejection of medieval logic’s causal theory of reference
because of its commitment to the transmission of formal properties from
material objects to the mind. Arnauld
and Nicole formulate a new referential theory of signification that retains
large parts of the medieval semantics of mental language but adopts a dualist
metaphysics committed to causal occasionalism.
The new account is founded on the use of objective being, a concept
developed in medieval philosophy but rejected as problematic by major medieval
logicians committed to Aristotelian semantics.
Considered as a term in mental language, the objective being of a
subject – the idea’s comprehension – contains modes that describe the subject
and these determine the possible objects outside the mind that the idea
signifies. Signification, a relation
between mental terms and external things, in turn is used to define extension,
which in the Cartesian context is a relation among ideas: the extension of a
term, which is understood to be a mental “species”, consists of its inferiors, namely those
species-ideas that signify entities that instantiate the modes in the higher
species’ comprehension.
Truth-conditions are then defined in terms of extension. Objective being of a subject, as the object of
consciousness, also correlates with the propositional knowledge that predicates
its content modes of a subject. This
correlation is used to unpack the medieval notion of false idea – one with a
descriptive content false of every actual being. It is explained how the truth-conditions of
the categorical propositions, which are stated in terms of extension, and the analysis of false idea entail (contra
the interpretation of Jean-Claude Pariente) that the terms of a true affirmative categorical
carry existential import.