Three rules of distribution: one counterexample.

Journal of Symbolic Logic 52:886-887 (1987)
Download Edit this record How to cite View on PhilPapers
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.
PhilPapers/Archive ID
CORTRO-20
Revision history
Archival date: 2015-05-23
View upload history
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index
2015-05-23

Total views
62 ( #27,733 of 38,900 )

Recent downloads (6 months)
5 ( #35,949 of 38,900 )

How can I increase my downloads?

Monthly downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.