Distributive Terms, Truth, and the Port Royal Logic

History and Philosophy of Logic 34 (2):133-154 (2013)

Abstract
The paper shows that in the Art of Thinking Arnauld and Nicole introduce a new way to state the truth-conditions for categorical propositions. The definition uses two new ideas: the notion of distributive or, as they call it, universal term, which they abstract from distributive supposition in medieval logic, and their own version of what is now called a conservative quantifier in general quantification theory. Contrary to the interpretation of Jean-Claude Parienté and others, the truth-conditions do not require the introduction of a new concept of ‘indefinite’ term restriction because the notion of conservative quantifier is formulated in terms of the standard notion of term intersection. The discussion shows the following. Distributive supposition could not be used in an analysis of truth because it is explained in terms of entailment, and entailment in terms of truth. By abstracting from semantic identities that underlie distribution, the new concept of distributive term is definitionally prior to truth and can, therefore, be used in a non-circular way to state truth-conditions. Using only standard restriction, the Logic’s truth-conditions for the categorical propositions are stated solely in terms of universal term, conservative quantifier, and affirmative and negative proposition. It is explained why the Cartesian notion of extension as a set of ideas is in this context equivalent to medieval and modern notions of extension.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1080/01445340.2012.748331
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 41,583
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Meaning and Necessity.Rudolf Carnap - 1947 - University of Chicago Press.
The Development of Logic.W. C. Kneale - 1962 - Oxford University Press.
The Development of Logic.A. R. Lacey, W. Kneale & M. Kneale - 1964 - Journal of Hellenic Studies 84:194-195.

View all 19 references / Add more references

Citations of this work BETA

Fred Sommers’ Contributions to Formal Logic.George Englebretsen - 2016 - History and Philosophy of Logic 37 (3):269-291.

Add more citations

Similar books and articles

The Doctrine of Distribution.Terence Parsons - 2006 - History and Philosophy of Logic 27 (1):59-74.
Truth and Collective Truth.Gilbert Plumer - 1996 - Dialectica 50 (1):3-24.
Existential Import in Cartesian Semantics.John N. Martin - 2011 - History and Philosophy of Logic 32 (3):211-239.
Rigid General Terms and Essential Predicates.Ilhan Inan - 2008 - Philosophical Studies 140 (2):213 - 228.
The Transparency of Truth.ME Kalderon - 1997 - Mind 106 (423):475-497.
The Fourth Account of Conditionals in Sextus Empiricus.Michael J. White - 1986 - History and Philosophy of Logic 7 (1):1-14.
Entailment and Bivalence.Fred Seymour Michael - 2002 - Journal of Philosophical Logic 31 (4):289-300.

Analytics

Added to PP index
2013-01-18

Total views
22 ( #376,889 of 2,249,178 )

Recent downloads (6 months)
3 ( #605,616 of 2,249,178 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature