The
Cartesian Semantics of the Port Royal
Logic
This book sets out for the first time in English and in the terms of modern logic the semantics of the Port Royal Logic (La Logique ou l’Art de penser, 1662–1685) of Antoine Arnauld and Pierre Nicole, perhaps the most influential logic book in the 17th and 18th centuries. Its goal is to explain how the Logic reworks the foundation of pre-Cartesian logic so as to make it compatible with Descartes’ metaphysics. The Logic’s authors forged a new theory of reference based on the medieval notion of objective being, which is essentially the modern notion of intentional content. Indeed, the book’s central aim is to detail how the Logic reoriented semantics so that it centered on the notion of intentional content. This content, which the Logic calls comprehension, consists of an idea’s defining modes. Mechanisms are defined in terms of comprehension that rework earlier explanations of central notions like conceptual inclusion, signification, abstraction, idea restriction, sensation, and most importantly within the Logic’s metatheory, the concept of idea-extension, which is a new technical concept coined by the Logic. Although Descartes is famous for rejecting “Aristotelianism,” he says virtually nothing about logic. His followers fill the gap. By putting to use the doctrine of objective being, which had been a relatively minor part of medieval logic, they preserve more central semantic doctrines, especially a correspondence theory of truth. A recurring theme of the book is the degree to which the Logic hews to medieval theory. This interpretation is at odds with what has become a standard reading among French scholars according to which this 17th-century work should be understood as rejecting earlier logic along with Aristotelian metaphysics, and as putting in its place structures more like those of 19th-century class theory.
The major interpretive claims of special interest in the book’s chapters are these:
Chapter 1 argues that the Logic fashions a notion of intentional content from the medieval concept of objective being that is consistent with Descartes’ substance-mode ontology and avoids assigning to objective being a special ontological status.
Chapter 2 argues that although the Logic’s notion of extension, in terms of which the truth-conditions for categorical propositions are defined, is a set of inferior ideas, containment and exclusion relations among extensions nevertheless track containment and exclusion relations outside the mind, with the result that the Logic espouses a genuine correspondence theory of truth.
Chapter 3 argues that although ideas and extensions possess the properties of parallel partially ordered structures, ideas are not dual to extensions and it is anachronistic to read into the Logic an early form of Boolean algebra. Its account of structure has more in common with the medieval theory of mental language and its associated tree of Porphyry.
Chapter 4 argues that the Logic’s truth-conditions for categorical propositions in terms of “universal term” is a non-circular abstraction from the medieval theory of distributive supposition, that its six general rules for the syllogistic provide a decision procedure for the valid moods, and that the valid moods are successfully characterized by the Logic’s so-called containment principle, which is much like the rule dici de omni.
Chapter 5 argues that the Logic’s account of analysis and synthesis draws from a long tradition of earlier syllogistic paradigms, and that although the formal logic it assumes is limited to the syllogistic, its analysis of the concept of “logical inference” is rule-governed and formal, similar to that of modern logic.
Chapter 6 argues that the Logic accepts sensation as a source of knowledge and with it a distinction between essential and contingent truth, in which the truth-conditions for essential affirmations do not carry existential import but those for contingent affirmations do.