Validity, the Squeezing Argument and Alternative Semantic Systems: the Case of Aristotelian Syllogistic
 Edgar AndradeLotero,
 Catarina Dutilh Novaes
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Abstract
We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran’s deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the goal is to offer a general discussion of the relations between informal notions—in this case, an informal notion of deductive validity—and logical apparatuses such as deductive systems and (modeltheoretic or other) semantic systems that aim at offering technical, formal accounts of informal notions. Specifically, we will be interested in Kreisel’s famous ‘squeezing argument’; we shall ask ourselves what a plurality of semantic systems (understood as classes of mathematical structures) may entail for the cogency of specific applications of the squeezing argument. More generally, the analysis brings to the fore the need for criteria of adequacy for semantic systems based on mathematical structures. Without such criteria, the idea that the gap between informal and technical accounts of validity can be bridged is put under pressure.
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 Title
 Validity, the Squeezing Argument and Alternative Semantic Systems: the Case of Aristotelian Syllogistic
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Journal of Philosophical Logic
Volume 41, Issue 2 , pp 387418
 Cover Date
 20120401
 DOI
 10.1007/s109920109166y
 Print ISSN
 00223611
 Online ISSN
 15730433
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Syllogistic
 Semantic systems for syllogistic
 Proofs of completeness
 Validity
 Squeezing argument
 Authors

 Edgar AndradeLotero ^{(1)}
 Catarina Dutilh Novaes ^{(2)}
 Author Affiliations

 1. Faculty of Natural Sciences and Mathematics, Universidad del Rosario, Bogotá, D.C., Colombia
 2. ILLC/Department of Philosphy, Universiteit van Amsterdam, Oude Turfmarkt 141147, Amsterdam, 1012 GC, Netherlands