The Modal Equivalence Rules of the Port-Royal Logic

Abstract

The Port-Royal Logic includes a brief discussion of modal propositions, containing several mnemonic devices for rules of equivalence governing the possibility, necessity, impossibility, and contingency of propositions. When the mnemonics are decoded, it can be seen that these rules treat possibility and contingency as formally equivalent modes. The aim of this paper is twofold: to show that this identification of possibility and contingency follows from the Logic’s formal treatment of those modes; and to show that such a treatment of these modes conflicts with claims the authors make in other contexts. In particular, the equivalence of possibility and contingency conflicts with the Cartesian principle that whatever is clearly and distinctly conceivable is possible—a principle that Arnauld and Nicole explicitly endorse elsewhere in the Logic. Why, then, would the authors adopt such equivalence rules? The paper concludes with a discussion of the historical precedents for these rules: they were a standard feature of Scholastic logic textbooks in seventeenth century France. It is likely that Arnauld and Nicole simply reproduced the rules for this reason, without recognizing that they were a poor fit for a Cartesian logic textbook like the Port-Royal Logic.