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INVARIANCE CRITERIA AS META-CONSTRAINTS

Part of: Model theory Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  02 December 2021

GIL SAGI
GIL SAGI*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HAIFA 199 ABA KHOUSHY AVE MT. CARMEL, HAIFA 3498838, ISRAEL E-mail: [email protected]
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Abstract

Invariance criteria are widely accepted as a means to demarcate the logical vocabulary of a language. In previous work, I proposed a framework of “semantic constraints” for model-theoretic consequence which does not rely on a strict distinction between logical and nonlogical terms, but rather on a range of constraints on models restricting the interpretations of terms in the language in different ways. In this paper I show how invariance criteria can be generalized so as to apply to semantic constraints on models. Some obviously unpalatable semantic constraints turn out to be invariant under isomorphisms. I shall connect the discussion to known counter-examples to invariance criteria for logical terms, and so the generalization will also shed light on the current existing debate on logicality. I analyse the failure of invariance to fulfil its role as a criterion for logicality, and argue that invariance conditions should best be thought of as merely methodological meta-constraints restricting the ways the model-theoretic apparatus should be used.

Keywords

logical consequencelogical constantsinvariance criteriasemantic constraints

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 03C99: None of the above, but in this section
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 28 , Issue 1 , March 2022 , pp. 104 - 132
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

Asher, N., Lexical Meaning in Context: A Web of Words , Cambridge University Press, Cambridge, 2011.Google Scholar
Barwise, J. and Feferman, S., editors, Model-Theoretic Logics , Springer, New York, 1985.Google Scholar
van Benthem, J., Logical constants across varying types . Notre Dame Journal of Formal Logic , vol. 30 (1989), no. 3, pp. 315–342.CrossRefGoogle Scholar
Bonnay, D., Logicality and invariance, this Journal, vol. 14 (2008), no. 1, 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), no. 1, pp. 54–65.CrossRefGoogle Scholar
Bonnay, D. and Westerståhl, D., Compositionality solves Carnap’s problem . Erkenntnis , vol. 81 (2016), pp. 721–739.CrossRefGoogle Scholar
Burgess, A. and Sherman, B., Metasemantics: New Essays on the Foundations of Meaning , Oxford University Press, Oxford, 2014.CrossRefGoogle Scholar
Carnap, R., Meaning and Necessity , The University of Chicago Press, Chicago, 1947.Google Scholar
Carnap, R., Meaning postulates . Philosophical Studies , vol. 3 (1952), no. 5, pp. 65–73.CrossRefGoogle Scholar
Casanovas, E., Logical operations and invariance . Journal of Philosophical Logic , vol. 36 (2007), no. 1, pp. 33–60.CrossRefGoogle Scholar
Došen, K., Logical constants as punctuation marks . Notre Dame Journal of Formal Logic , vol. 30 (1989), no. 3, pp. 362–381.CrossRefGoogle Scholar
Feferman, S., Logic, logics and logicism . Notre Dame Journal of Formal Logic , vol. 40 (1999), no. 1, pp. 31–55.CrossRefGoogle Scholar
Frege, G., Sense and reference . The Philosophical Review , vol. 57 (1948), no. 3, pp. 209–230.CrossRefGoogle Scholar
Gómez-Torrente, M., The problem of logical constants, this Journal, vol. 8 (2002), no. 1, pp. 1–37.Google Scholar
Groenendijk, J. and Stokhof, M., Why compositionality? , Reference and Quantification: The Partee Effect (G. Carlson and J. Pelletier, editors), CSLI Press, Stanford, 2005, pp. 83–106.Google Scholar
Haze, T. G., The accident of logical constants . Thought: A Journal of Philosophy , vol. 9 (2020), no. 1, pp. 34–42.CrossRefGoogle Scholar
Janssen, T. M. and Partee, B. H., Compositionality , Handbook of Logic and Language (J. van Benthem and A. T. Meulen, editors), Elsevier, Amsterdam, 1997, pp. 417–473.CrossRefGoogle Scholar
MacFarlane, J., Logical constants , The Stanford Encyclopedia of Philosophy (Fall 2009 edition) (E. N. Zalta, editor), 2009. Available at http://plato.stanford.edu/archives/fall2009/entries/logical-constants/.Google Scholar
Mautner, F., An extension of Klein’s Erlanger program: Logic as invariant-theory . American Journal of Mathematics , vol. 68 (1946), no. 3, pp. 345–384.CrossRefGoogle Scholar
McGee, V., Logical operations . Journal of Philosophical Logic , vol. 25 (1996), pp. 567–580.CrossRefGoogle Scholar
Montague, R., The proper treatment of quantification in ordinary English , Formal Philosophy (R. Thomason, editor), Yale University Press, New Haven, 1974, pp. 247–270.Google Scholar
Mostowski, A., On a generalization of quantifiers . Fundamenta Mathematicae , vol. 44 (1957), no. 1, pp. 12–36.CrossRefGoogle Scholar
Pagin, P. and Westerståhl, D., Compositionality I: Definitions and variants . Philosophy Compass , vol. 5 (2010a), no. 3, pp. 250–264.CrossRefGoogle Scholar
Pagin, P. and Westerståhl, D., Compositionality II: Arguments and problems . Philosophy Compass , vol. 5 (2010b), no. 3, pp. 265–282.CrossRefGoogle Scholar
Putnam, H., Reason, Truth and History , vol. 3 , Cambridge University Press, Cambridge, 1981.CrossRefGoogle Scholar
Sagi, G., Formality in logic: From logical terms to semantic constraints . Logique et Analyse , vol. 57 (2014), no. 227, pp. 259–276.Google Scholar
Sagi, G., Logicality and meaning . The Review of Symbolic Logic , vol. 11 (2018), no. 1, pp. 133–159.CrossRefGoogle Scholar
Sagi, G., Logic in natural language: Commitments and constraints . Disputatio , vol. 12 (2020), no. 58, pp. 377–408.CrossRefGoogle Scholar
Sagi, G., Extensionality and logicality . Synthese , vol. 198 (2021), pp. 1095–1119.CrossRefGoogle Scholar
Shapiro, S., Logical consequence: Models and modality , The Philosophy of Mathematics Today (M. Schirn, editor), Oxford University Press, Oxford, 1998, pp. 131–156.Google Scholar
Sher, G., The Bounds of Logic: A Generalized Viewpoint , MIT Press, Cambridge, 1991.Google Scholar
Sher, G., Did Tarski commit “Tarski’s fallacy”? The Journal of Symbolic Logic , vol. 61 (1996), no. 2, pp. 653–686.CrossRefGoogle Scholar
Sher, G., The logical roots of indeterminacy , Between Logic and Intuition: Essays in Honor of Charles Parsons (G. Sher and R. Tieszen, editors), Cambridge University Press, Cambridge, 2000, pp. 100–123.CrossRefGoogle Scholar
Sher, G., Epistemic Friction , Oxford University Press, New York, 2016.CrossRefGoogle Scholar
Stalnaker, R. C., Reference and necessity , A Companion to the Philosophy of Language (C. Wright and B. Hale, editors), Blackwell, Malden, 1997.Google Scholar
Tarski, A., On the concept of logical consequence , Logic, Semantics, Metamathematics (J. Corcoran, editor), Hackett, Indianapolis, 1983, pp. 409–420.Google Scholar
Tarski, A., What are logical notions? History and Philosophy of Logic , vol. 7 (1986), no. 2, pp. 143–154.CrossRefGoogle Scholar
Zimmermann, T. E., Model-theoretic semantics , Semantics: An International Handbook of Natural Language Meaning (C. Maienborn, K. von Heusinger, and P. Portner, editors). Walter de Gruyter, Berlin, 2011.Google Scholar
Zinke, A., The Metaphysics of Logical Consequence , Klostermann, Frankfurt, 2018.CrossRefGoogle Scholar
Zinke, A., Reinterpreting logic , The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning (G. Sagi and J. Woods, editors), Cambridge University Press, Cambridge, 2021.Google Scholar