# The Cartesian Semantics of the Port Royal Logic

The Cartesian Semantics of the Port-Royal Logic is a scholarly work by John N. Martin, first published in 2019 by Routledge. This book provides a comprehensive analysis of the semantics of the Port-Royal Logic (La Logique ou l’Art de penser), a key 17th-century text written by Antoine Arnauld and Pierre Nicole, which significantly influenced the development of logic and philosophy in the 17th and 18th centuries.

## Summary

The book provides an in-depth analysis of the semantics of the Port-Royal Logic (La Logique ou l’Art de penser), a seminal work by Antoine Arnauld and Pierre Nicole from the 17th century. The book is significant as it presents, for the first time in English, a modern logical interpretation of this influential text, which played a crucial role in shaping logic and philosophy during the 17th and 18th centuries.
Martin's work explores how the Port-Royal Logic reinterprets pre-Cartesian logic, aligning it with René Descartes' metaphysical framework. Central to this reinterpretation is the concept of "intentional content," which is rooted in the medieval notion of objective being. This intentional content, referred to in the Logic as comprehension, consists of the defining modes of ideas and forms the foundation of the Logic's theory of reference.
Throughout the book, Martin challenges the prevailing interpretation among French scholars that the Port-Royal Logic rejects Aristotelian metaphysics entirely. Instead, he argues that while it integrates Cartesian elements, it retains significant aspects of medieval semantic theory, particularly in its adherence to a correspondence theory of truth.

## Contents

The book delves into several key themes:
* Intentional Content and Comprehension: Martin begins by exploring how the Port-Royal Logic navigates the challenges posed by Cartesian dualism, particularly its impact on traditional logic rooted in Aristotelian substance-mode ontology. The book demonstrates how the Logic reformulates the medieval concept of "objective being" into a new theory of intentional content to reconcile these issues.
* Signification and Extension: The book then delves into the Logic's strong adherence to the correspondence theory of truth. Martin argues that the Logic defines truth by aligning ideas with the actual state of affairs, emphasizing that false ideas result from the improper combination of incompatible modes within a single intentional content.
* Structure of Ideas: Martin critically assesses the tendency to retrospectively interpret the Logic through the lens of Boolean algebra. He instead situates the Logic's theory of ideas within the continuity of medieval traditions, rejecting anachronistic readings and providing a more contextually accurate reconstruction.
* Propositions, Truth, and Consequences: Syllogistic theory and medieval supposition theory are key to understanding the Logic's approach to propositions. Martin offers a detailed, technical exploration of how the Logic establishes non-circular truth-conditions, highlighting the text's reliance on traditional logical frameworks.
* Discourse and Method: Martin addresses the logical methods employed in the Logic, discussing the tension between rationalism and empiricism. Despite the authors' rationalist inclinations, they incorporate empirical knowledge grounded in sensation, which Martin connects to broader historical and philosophical contexts.
* Existential Import: In the final chapters, the book examines how the Logic handles contingent truths, particularly through its treatment of existential import. Martin ties this discussion to Cartesian metaphysical concerns, concluding that the Logic secures contingent knowledge by ensuring the veridicality of sensation under divine guarantee.

## Critical reception

In his review Eyjólfur Kjalar Emilsson from the University of Oslo focused on the exploration of the concept of "privative negation" as discussed in the Port-Royal Logic. Emilsson noted that Martin connects this concept to Aristotle and the Neoplatonists, particularly Proclus, showing its development and application through history. The reviewer praised Martin for his originality in approaching Neoplatonic thought through the lens of logic, offering formalizations that are new to the field. Emilsson appreciated Martin's argument that the Port-Royal Logic should not be critiqued for failing to align with Boolean logic, as it operates under different philosophical influences.
Minhea Dobre stressed the book's comprehensive approach to bridging medieval and modern logic through the study of the Port-Royal Logic. He highlighted Martin's meticulous method, which involved staying "close to the text" to avoid "ungrounded reconstruction," making the book particularly valuable for historians of logic and philosophy. However, Dobre also acknowledged a potential drawback, noting that this detailed approach might be seen as tedious, potentially overwhelming or less engaging for some readers. Despite this observation, Dobre concluded that Martin's work set the Logic "in a broader historical framework," making it a significant contribution to the field.
In his review, Benjamin Hill praised Martin for his comprehensive analysis of the Port Royal Logic (PRL) and its connections to Scholastic philosophy, noting that Martin's work is a significant contribution to the field. Hill highlighted Martin's success in demonstrating how the PRL's truth conditions for categorical propositions are rooted in Scholastic traditions rather than being purely modern, a point Hill found more impactful than Martin's claims about the relevance of PRL to contemporary logicians. However, Hill did express some skepticism, particularly regarding Martin's assertion that intentional contents are second-order modes of the mind, describing this claim as “more dubious” compared to other aspects of Martin's analysis. Despite these reservations, Hill recommended the book for its clarity and valuable historical insights, especially for those interested in the history of logic and philosophy.
Elodie Cassan provided a thoughtful analysis of the book emphasizing its exploration of how Cartesian metaphysics integrates with traditional Aristotelian logic. She noted that Martin convincingly argued that Arnauld and Nicole's work represented “an effort to explain the semantic foundations of language and logic in a manner consistent with Descartes’ dualism.” Cassan also appreciated Martin's caution against anachronistic interpretations, highlighting the importance of understanding the text within its historical context rather than through the lens of modern formal logic.
Eric Stencil highlighted Martin's focus on how the Logic reconciles Cartesianism with traditional logic, noting that it "should be of interest to modern logicians." While praising Martin's detailed analysis, Stencil pointed out that the book is demanding and occasionally assumes significant background knowledge, but said it remains a valuable resource for those interested in the history of logic.