Journal of Symbolic Logic 52:886-887 (1987)

Authors
John Corcoran
State University of New York, Buffalo
Abstract
This self-contained one page paper produces one valid two-premise premise-conclusion argument that is a counterexample to the entire three traditional rules of distribution. These three rules were previously thought to be generally applicable criteria for invalidity of premise-conclusion arguments. No longer can a three-term argument be dismissed as invalid simply on the ground that its middle is undistributed, for example. The following question seems never to have been raised: how does having an undistributed middle show that an argument's conclusion does not follow from its premises? This result does nothing to vitiate the theories of distribution developed over the period beginning in medieval times. What it does vitiate is many if not all attempts to use distribution in tests of invalidity outside of the standard two-premise categorical arguments—where they were verified on a case-by-case basis without further theoretical grounding. In addition it shows that there was no theoretical basis for many if not all claims of fundamental status of rules of distribution. These results are further support for approaching historical texts using mathematical archeology.
Keywords LOGIC  CRITICAL THINKING  FALLACIES  DISTRIBUTED MIDDLE  UNDISTRIBUTED MIDDLE  SCHOLASTIC LOGIC  HISTORY OF LOGIC  PHILOSOPHY OF LOGIC  ARGUMENTATION  PREMISE-CONCLUSION ARGUMENT
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
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

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Conceptual Structure of Classical Logic.John Corcoran - 1972 - Philosophy and Phenomenological Research 33 (1):25-47.
Complete Enumerative Inductions.John Corcoran - 2006 - Bulletin of Symbolic Logic 12:465-6.
Contra-Argumento/Contraejemplo.John Corcoran - 2011 - In Luis Vega and Paula Olmos (ed.), Compendio de Lógica, Argumentación y Retórica. Editorial Trotta. pp. 137--141.
The Doctrine of Distribution.Terence Parsons - 2006 - History and Philosophy of Logic 27 (1):59-74.
A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
Aristotle's Many-Sorted Logic.J. Corcoran - 2008 - Bulletin of Symbolic Logic 14 (1):155-156.
Abstract Argumentation.Robert A. Kowalski & Francesca Toni - 1996 - Artificial Intelligence and Law 4 (3-4):275-296.
On the Rules of Intermediate Logics.Rosalie Iemhoff - 2006 - Archive for Mathematical Logic 45 (5):581-599.

Analytics

Added to PP index
2015-05-23

Total views
119 ( #81,425 of 2,403,714 )

Recent downloads (6 months)
13 ( #53,376 of 2,403,714 )

How can I increase my downloads?

Downloads

My notes