The Structure of Ideas in The Port Royal Logic,

The Journal of Applied Logic, 19 (2016), pp. 1-19.

Abstract

This paper addresses the degree to which The Port Royal Logic anticipates Boolean Algebra. According to Marc Dominicy the best reconstruction is a Boolean Algebra of Carnapian properties, functions from possible worlds to extensions. Sylvain Auroux’s reconstruction approximates a non-complemented bounded lattice. This paper argues that it is anachronistic to read lattice algebra into the Port Royal Logic. It is true that the Logic treats extensions like sets, orders ideas under a containment relation, and posits mental operations of abstraction and restriction. It also orders species in a version of the tree of Porphyry, and allows that genera may be divided into species by privative negation. There is, however, no maximal or minimal idea. Abstraction is not binary. Neither abstraction nor restriction is closed. Ideas under containment, therefore, do not form a lattice. Nor are the relevant formal properties of lattices discussed. Term negation is privative, not a complementation operation. The technical ideas relevant to the discussion are defined. The Logic’s purpose in describing the structure was not to develop algebra in the modern sense but rather to provide a new basis for the semantics of mental language consistent with Cartesian metaphysics. The account was not algebraic, but metaphysical and psychological, based on the concept of comprehension, a Cartesian version of medieval objective being.