Establishing Connections between Aristotle's Natural Deduction and First-Order Logic

History and Philosophy of Logic 29 (4):309-325 (2008)
Abstract
This article studies the mathematical properties of two systems that model Aristotle's original syllogistic and the relationship obtaining between them. These systems are Corcoran's natural deduction syllogistic and ?ukasiewicz's axiomatization of the syllogistic. We show that by translating the former into a first-order theory, which we call T RD, we can establish a precise relationship between the two systems. We prove within the framework of first-order logic a number of logical properties about T RD that bear upon the same properties of the natural deduction counterpart ? that is, Corcoran's system. Moreover, the first-order logic framework that we work with allows us to understand how complicated the semantics of the syllogistic is in providing us with examples of bizarre, unexpected interpretations of the syllogistic rules. Finally, we provide a first attempt at finding the structure of that semantics, reducing the search to the characterization of the class of models of T RD
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1080/01445340801976516
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,224
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
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Elementary Logic.Benson Mates - 1965 - New York: Oxford University Press.
Completeness of an Ancient Logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Added to PP index
2010-08-10

Total downloads
124 ( #40,347 of 2,191,991 )

Recent downloads (6 months)
2 ( #144,931 of 2,191,991 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature