Distributive Terms, Truth and The Port Royal Logic
History
and Philosophy of Logic
Jan. 17, 2013, pp. 133-154.
Abstract
The paper shows that in the Art of Thinking (The Port-Royal
Logic) Arnauld and Nicole introduce a new way to state the truth-conditions
for categorical propositions. The
definition uses two new ideas: the notion of distributive or, as they call it, universal term, which they abstract from distributive supposition in medieval logic,
and their own version of what is now called a conservative quantifier in general quantification theory. Contrary to the interpretation of Jean-Claude
Parienté and others, the truth-conditions do not
require the introduction of a new concept of ‘indefinite’ term restriction
because the notion of conservative quantifier is formulated in terms of the
standard notion of term intersection. The discussion shows the following. Distributive supposition could not be used in
an analysis of truth because it is explained in terms of entailment, and
entailment in terms of truth. By
abstracting from semantic identities that underlie distribution, the new
concept of distributive term is definitionally prior
to truth and can, therefore, be used in a non-circular way to state truth-conditions. Using only standard restriction, the Logic’s truth-conditions for the
categorical propositions are stated solely in terms of (1) universal (distributive) term, (2) conservative quantifier, and (3) affirmative and negative
proposition. It is explained why the Cartesian notion of extension as a set
of ideas is in this context equivalent to medieval and modern notions of
extension. (See also a supplement: “A
Note on ‘Distributive Terms, Truth, and The Port Royal Logic,’ History and
Philosophy of Logic, 18 Feb., 2016, pp. 1-2. http://dx.doi.org/10.1080/01445340.2015.1138045)