Implicit Quantification of the Predicate and Port-Royal Logic

Abstract

The author questions the claim advanced by historians of logic Jill Vance Buroker, Sylvain Auroux and Jean- Claude Pariente that Antoine Arnauld and Pierre Nicole were adherents of the thesis of implicit quantification of the predicate (IQP thesis). Author’s argumentation is as the following: he starts with the explication of the IQP thesis, then explores the reasons for the attribution of this thesis to Arnauld and Nicole as well as a relation of IQP thesis to Port-Royal logic, and then suggests the answer to the question who was the first adherent of thesis. The conclusions of this investigation are following: first, it is possible to attribute to Arnauld and Nicole negation of the IQP thesis and the thesis of analogous structure – thesis of implicit quantification of the subject; second, chapters of Port-Royal logic discussing conversion provide the evidence not for attribution of IQP thesis, but only for the attribution of a weaker proposition and, third, William Hamilton should be held to be the first adherent of IQP thesis.