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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, UK E-mail: [email protected]
A.C. PASEAU
Affiliation:
WADHAM COLLEGE UNIVERSITY OF OXFORD OXFORD OX1 3PN, UK E-mail: [email protected]
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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 

References

REFERENCES

[1] Bonnay, D., Logicality and invariance, this Bulletin, vol. 14 (2008), pp. 29–68.Google Scholar
Bonnay, D., Logical constants, or how to use invariance in order to complete the explication of logical consequence . Philosophy Compass, vol. 9 (2014), pp. 54–65.Google Scholar
Boolos, G., Nominalist platonism . Philosophical Review, vol. 94 (1985), pp. 327–344.Google Scholar
Burgess, J. P., Which modal logic is the right one? Notre Dame Journal of Formal Logic, vol. 40 (1999), pp. 81–93.Google Scholar
Casanovas, E., Logical operations and invariance . Journal of Philosophical Logic, vol. 36 (2007), pp. 33–60.Google Scholar
Dutilh Novaes, C., The undergeneration of permutation invariance as a criterion for logicality . Erkenntnis, vol. 79 (2014), pp. 81–97.Google Scholar
Etchemendy, J., The Concept of Logical Consequence, Harvard University Press, Cambridge, MA, 1990.Google Scholar
Feferman, S., Logic, logics and logicism . Notre Dame Journal of Formal Logic, vol. 40 (1999), pp. 31–54.CrossRefGoogle Scholar
Feferman, S., Set-theoretical invariance criteria for logicality . Notre Dame Journal of Formal Logic, vol. 51 (2010), pp. 3–20.Google Scholar
[10] Feferman, S., Is the Continuum Hypothesis a definite mathematical problem? unpublished manuscript, 2011.Google Scholar
Feferman, S., Which quantifiers are logical? A combined semantical and inferential criterion , Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics and Language (Torza, A., editor), Springer, 2015, pp. 19–30.Google Scholar
Hamkins, J. D., The set-theoretic multiverse . Review of Symbolic Logic, vol. 5 (2012), pp. 416–449.CrossRefGoogle Scholar
[13] MacFarlane, J., What does it mean to say that logic is formal? Ph.D. dissertation, University of Pittsburgh, 2000.Google Scholar
MacFarlane, J., Logical constants , The Stanford Encyclopedia of Philosophy (Fall 2015 edition) (Zalta, E., editor), 2015.Google Scholar
McCarthy, T., The idea of a logical constant . Journal of Philosophy, vol. 78 (1981), pp. 499–523.CrossRefGoogle Scholar
McGee, V., Logical operations . Journal of Philosophical Logic, vol. 25 (1996), pp. 567–580.Google Scholar
Milne, P., Existence, freedom, identity, and the logic of abstractionist realism . Mind, vol. 116 (2007), pp. 23–53.Google Scholar
Oliver, A., The matter of form: Logic’s beginnings , The Force of Argument: Essays in Honor of Timothy Smiley (Oliver, A. and Lear, J., editors), Routledge, London, 2010, pp. 165–185.Google Scholar
Paseau, A. C., The overgeneration argument(s): A succinct refutation . Analysis, vol. 74 (2014), pp. 40–47.Google Scholar
Peacocke, C., What is a logical constant? Journal of Philosophy, vol. 73 (1976), pp. 221–240.Google Scholar
Read, S., Identity and harmony . Analysis, vol. 64 (2004), pp. 113–119.Google Scholar
Sagi, G., The modal and epistemic arguments against the invariance criterion for logical terms . Journal of Philosophy, vol. 112 (2015), pp. 159–167.Google Scholar
Shapiro, S., Foundations without Foundationalism, Oxford University Press, Oxford, 1991.Google Scholar
Shapiro, S., Logical consequence: Models and modality , The Philosophy of Mathematics Today (Schirn, M., editor), Oxford University Press, New York, 1998, pp. 131–156.Google Scholar
Sher, G., The Bounds of Logic, MIT Press, Cambridge, MA, 1991.Google Scholar
[26] Sher, G., The foundational problem of logic, this Bulletin, vol. 19 (2013), pp. 145–198.Google Scholar
Sher, G., Epistemic Friction, Oxford University Press, Oxford, 2016.Google Scholar
Tarski, A., O pojciu wynikania logicznego. Przegląd Filozoficzny, vol. 39 (1963), pp. 58–68, transl. by J. Woodger as ‘On the concept of logical consequence’ and repr. in Tarski’s Logic, Semantics, Metamathematics, second ed. (J. Woodger, editor), Hackett, Indianapolis, pp. 409–420.Google Scholar
Tarski, A., Introduction to Logic and the Methodology of the Deductive Sciences, Dover, New York, 1937. Refs to 1995 reprint.Google Scholar
Tarski, A., What are logical notions? History and Philosophy of Logic, vol. 7 (1966), pp. 143–154. Refs to 1986 reprint.Google Scholar
Tharp, L. H., Which logic is the right logic? Synthese, vol. 31 (1975), pp. 1–21.Google Scholar
Woods, J., Logical indefinites . Logique et Analyse , vol. 57 (2014), pp. 277–307.Google Scholar