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LOGICALITY AND MEANING

Published online by Cambridge University Press:  16 January 2018

GIL SAGI
GIL SAGI*
Affiliation:
Department of Philosophy, University of Haifa
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HAIFA HAIFA, ISRAEL E-mail: [email protected]
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Abstract

In standard model-theoretic semantics, the meaning of logical terms is said to be fixed in the system while that of nonlogical terms remains variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing their meaning precisely amounts to. My proposal is that when a term is considered logical in model theory, what gets fixed is its intension rather than its extension. I provide a rigorous way of spelling out this idea, and show that it leads to a graded account of logicality: the less structure a term requires in order for its intension to be fixed, the more logical it is. Finally, I focus on the class of terms that are invariant under isomorphisms, as they render themselves more easily to mathematical treatment. I propose a mathematical measure for the logicality of such terms based on their associated Löwenheim numbers.

Keywords

03A05logical constantsLöwenheim numbersinvariance criteriamodel theorymeaning
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 1 , March 2018 , pp. 133 - 159
Copyright
Copyright © Association for Symbolic Logic 2018 

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References

BIBLIOGRAPHY

Barwise, J. (1985). Model-theoretic logics: Background and aims. In Barwise, J. and Feferman, S., editors. Model-Theoretic Logics. New York: Springer, pp. 3–24.Google Scholar
Bolzano, B. (1929). Wissenschaftslehre. Leipzig: Felix Meiner.Google Scholar
Bonnay, D. (2008). Logicality and invariance. The Bulletin of Symbolic Logic, 14(1), 29–68.CrossRefGoogle Scholar
Carnap, R. (1962). Logical Foundations of Probability. Chicago: University of Chicago Press.Google Scholar
Casanovas, E. (2007). Logical operations and invariance. Journal of Philosophical Logic, 36(1), 33–60.CrossRefGoogle Scholar
Dutilh Novaes, C. (2012). Reassessing logical hylomorphism and the demarcation of logical constants. Synthese, 185(3), 387–410.CrossRefGoogle Scholar
Ebbinghaus, H. (1985). Chapter II: Extended logics: The general framework. In Barwise, J. and Feferman, S., editors. Model-Theoretic Logics. New York: Springer, pp. 25–76.Google Scholar
Etchemendy, J. (1990). The Concept of Logical Consequence. Cambridge, MA: Harvard University Press.Google Scholar
Etchemendy, J. (2006). Reflections on consequence. In Patterson, D., editor. New Essays on Tarski and Philosophy. Oxford: Oxford University Press, pp. 263–299.Google Scholar
Feferman, S. (1999). Logic, logics and logicism. Notre Dame Journal of Formal Logic, 40(1), 31–55.CrossRefGoogle Scholar
Gómez-Torrente, M. (1996). Tarski on logical consequence. Notre Dame Journal of Formal Logic, 37(1), 125–151.CrossRefGoogle Scholar
Gómez-Torrente, M. (2002). The problem of logical constants. The Bulletin of Symbolic Logic, 8(1), 1–37.CrossRefGoogle Scholar
Hanson, W. H. (1997). The concept of logical consequence. The Philosophical Review, 106(3), 365–409.CrossRefGoogle Scholar
Jeřábek, E. (2016). Lowenheim numbers for ordinary language quantifiers. MathOverflow. Available at: http://mathoverflow.net/q/249284 (version: 2016-09-07).Google Scholar
Kuhn, S. (1981). Logical expressions, constants, and operator logic. The Journal of Philosophy, 78(9), 487–499.CrossRefGoogle Scholar
Magidor, M. & Väänänen, J. (2011). On Löwenheim–Skolem–Tarski numbers for extensions of first order logic. Journal of Mathematical Logic, 11(01), 87–113.CrossRefGoogle Scholar
McCarthy, T. (1981). The idea of a logical constant. The Journal of Philosophy, 78(9), 499–523.CrossRefGoogle Scholar
McGee, V. (1996). Logical operations. Journal of Philosophical Logic, 25, 567–580.CrossRefGoogle Scholar
Menzel, C. (1990). Actualism, ontological committment, and possible worlds semantics. Synthese, 85(3), 355–389.CrossRefGoogle Scholar
Mostowski, A. (1957). On a generalization of quantifiers. Funamenta Mathematicae, 44(1), 12–36.CrossRefGoogle Scholar
Peacocke, C. (1976). What is a logical constant? The Journal of Philosophy, 73(9), 221–240.CrossRefGoogle Scholar
Read, S. (1994). Formal and material consequence. Journal of Philosophical Logic, 23(3), 247–265.CrossRefGoogle Scholar
Sagi, G. (2014). Models and logical consequence. Journal of Philosophical Logic, 43(5), 943–964.CrossRefGoogle Scholar
Shapiro, S. (1998). Logical consequence: Models and modality. In Schirn, M., editor. The Philosophy of Mathematics Today. Oxford: Oxford Univerity Press, pp. 131–156.CrossRefGoogle Scholar
Sher, G. (1991). The Bounds of Logic: A Generalized Viewpoint. Cambridge, MA: MIT Press.Google Scholar
Sher, G. (1996). Did Tarski commit ‘Tarski’s fallacy’? The Journal of Symbolic Logic, 61(2), 653–686.CrossRefGoogle Scholar
Sher, G. (2013). The foundational problem of logic. Bulletin of Symbolic Logic, 19(2), 145–198.CrossRefGoogle Scholar
Tarski, A. (1936). On the concept of logical consequence. In Corcoran, J., editor. Logic, Semantics, Metamathematics. Indianapolis: Hackett (1983), pp. 409–420.Google Scholar
Tarski, A. (1986). What are logical notions? History and Philosophy of Logic, 7, 143–154.CrossRefGoogle Scholar
Väänänen, J. (1985). Chapter XVII: Set-theoretic definability of logics. In Barwise, J. and Feferman, S., editors. Model-Theoretic Logics. New York: Springer, pp. 599–643.Google Scholar
van Benthem, J. (1989). Logical constants across varying types. Notre Dame Journal of Formal Logic, 30(3), 315–342.CrossRefGoogle Scholar
Warmbrōd, K. (1999). Logical constants. Mind, 108(431), 503–538.CrossRefGoogle Scholar
Westerståhl, D. (1989). Quantifiers in formal and natural languages. In Gabbay, D., and Guenthner, F., editors. Handbook of philosophical logic, Vol. IV. Dordrecht: D. Reidel, pp. 1–131.Google Scholar
Woods, J. (2014). Logical indefinites. Logique et Analyse, 227, 277–307.Google Scholar
Zimmermann, T. E. (1999). Meaning postulates and the model-theoretic approach to natural language semantics. Linguistics and Philosophy, 22(5), 529–561.CrossRefGoogle Scholar
Zimmermann, T. E. (2011). Model-theoretic semantics. In Maienborn, C., von Heusinger, K., and Portner, P., editors. Semantics: An International Handbook of Natural Language Meaning, Vol. 33. Berlin: Walter de Gruyter.Google Scholar