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ISOMORPHISM INVARIANCE AND OVERGENERATION

Published online by Cambridge University Press:  30 December 2016

OWEN GRIFFITHS  and
A.C. PASEAU
OWEN GRIFFITHS
Affiliation:
ST JOHN’S COLLEGE UNIVERSITY OF CAMBRIDGE CAMBRIDGE CB2 1TP, UKE-mail: oeg21@cam.ac.uk
A.C. PASEAU
Affiliation:
WADHAM COLLEGE UNIVERSITY OF OXFORD OXFORD OX1 3PN, UKE-mail: alexander.paseau@philosophy.ox.ac.uk
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Abstract

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The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thought that logic is distinctively general or topic neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of ‘logical constant’ which respects the intuitively clear cases. Despite its attractions, the criterion has recently come under attack. Critics such as Feferman, MacFarlane and Bonnay argue that the criterion overgenerates by incorrectly judging mathematical notions as logical. We consider five possible precisifications of the overgeneration argument and find them all unconvincing.

Keywords

03A0503B1003B1503C98isomorphism invariancelogical constantssecond-order logiclogical consequencemodel theoryovergeneration argument
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 22 , Issue 4 , December 2016 , pp. 482 - 503
Copyright
Copyright © The Association for Symbolic Logic 2016 

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