History and Philosophy of Logic 38 (3):210-221 (2017)

Authors
John R. T. Grey
Michigan State University
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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1080/01445340.2017.1318256
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 53,586
Through your library

References found in this work BETA

Articulating Medieval Logic.Terence Parsons - 2014 - Oxford University Press.
Aristotle's Categories and De Interpretatione.[author unknown] - 1965 - Les Etudes Philosophiques 20 (3):334-334.
Descartes and the First Cartesians.Roger Ariew - 2014 - Oxford University Press.

View all 9 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Derivation Rules as Anti-Axioms in Modal Logic.Yde Venema - 1993 - Journal of Symbolic Logic 58 (3):1003-1034.
Expressive Logics for Coalgebras Via Terminal Sequence Induction.Dirk Pattinson - 2004 - Notre Dame Journal of Formal Logic 45 (1):19-33.
Unification and Passive Inference Rules for Modal Logics.V. V. Rybakov, M. Terziler & C. Gencer - 2000 - Journal of Applied Non-Classical Logics 10 (3-4):369-377.
Predicate Logics on Display.Heinrich Wansing - 1999 - Studia Logica 62 (1):49-75.
Implementing a Relational Theorem Prover for Modal Logic K.Angel Mora, Emilio Munoz Velasco & Joanna Golińska-Pilarek - 2011 - International Journal of Computer Mathematics 88 (9):1869-1884.

Analytics

Added to PP index
2017-05-19

Total views
13 ( #691,431 of 2,348,644 )

Recent downloads (6 months)
1 ( #512,546 of 2,348,644 )

How can I increase my downloads?

Downloads

My notes