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LOGICALITY AND MEANING

  • GIL SAGI (a1)
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.

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*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HAIFA HAIFA, ISRAEL E-mail: gsagi@univ.haifa.ac.il
References
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Barwise, J. (1985). Model-theoretic logics: Background and aims. In Barwise, J. and Feferman, S., editors. Model-Theoretic Logics. New York: Springer, pp. 324.
Bolzano, B. (1929). Wissenschaftslehre. Leipzig: Felix Meiner.
Bonnay, D. (2008). Logicality and invariance. The Bulletin of Symbolic Logic, 14(1), 2968.
Carnap, R. (1962). Logical Foundations of Probability. Chicago: University of Chicago Press.
Casanovas, E. (2007). Logical operations and invariance. Journal of Philosophical Logic, 36(1), 3360.
Dutilh Novaes, C. (2012). Reassessing logical hylomorphism and the demarcation of logical constants. Synthese, 185(3), 387410.
Ebbinghaus, H. (1985). Chapter II: Extended logics: The general framework. In Barwise, J. and Feferman, S., editors. Model-Theoretic Logics. New York: Springer, pp. 2576.
Etchemendy, J. (1990). The Concept of Logical Consequence. Cambridge, MA: Harvard University Press.
Etchemendy, J. (2006). Reflections on consequence. In Patterson, D., editor. New Essays on Tarski and Philosophy. Oxford: Oxford University Press, pp. 263299.
Feferman, S. (1999). Logic, logics and logicism. Notre Dame Journal of Formal Logic, 40(1), 3155.
Gómez-Torrente, M. (1996). Tarski on logical consequence. Notre Dame Journal of Formal Logic, 37(1), 125151.
Gómez-Torrente, M. (2002). The problem of logical constants. The Bulletin of Symbolic Logic, 8(1), 137.
Hanson, W. H. (1997). The concept of logical consequence. The Philosophical Review, 106(3), 365409.
Jeřábek, E. (2016). Lowenheim numbers for ordinary language quantifiers. MathOverflow. Available at: http://mathoverflow.net/q/249284 (version: 2016-09-07).
Kuhn, S. (1981). Logical expressions, constants, and operator logic. The Journal of Philosophy, 78(9), 487499.
Magidor, M. & Väänänen, J. (2011). On Löwenheim–Skolem–Tarski numbers for extensions of first order logic. Journal of Mathematical Logic, 11(01), 87113.
McCarthy, T. (1981). The idea of a logical constant. The Journal of Philosophy, 78(9), 499523.
McGee, V. (1996). Logical operations. Journal of Philosophical Logic, 25, 567580.
Menzel, C. (1990). Actualism, ontological committment, and possible worlds semantics. Synthese, 85(3), 355389.
Mostowski, A. (1957). On a generalization of quantifiers. Funamenta Mathematicae, 44(1), 1236.
Peacocke, C. (1976). What is a logical constant? The Journal of Philosophy, 73(9), 221240.
Read, S. (1994). Formal and material consequence. Journal of Philosophical Logic, 23(3), 247265.
Sagi, G. (2014). Models and logical consequence. Journal of Philosophical Logic, 43(5), 943964.
Shapiro, S. (1998). Logical consequence: Models and modality. In Schirn, M., editor. The Philosophy of Mathematics Today. Oxford: Oxford Univerity Press, pp. 131156.
Sher, G. (1991). The Bounds of Logic: A Generalized Viewpoint. Cambridge, MA: MIT Press.
Sher, G. (1996). Did Tarski commit ‘Tarski’s fallacy’? The Journal of Symbolic Logic, 61(2), 653686.
Sher, G. (2013). The foundational problem of logic. Bulletin of Symbolic Logic, 19(2), 145198.
Tarski, A. (1936). On the concept of logical consequence. In Corcoran, J., editor. Logic, Semantics, Metamathematics. Indianapolis: Hackett (1983), pp. 409420.
Tarski, A. (1986). What are logical notions? History and Philosophy of Logic, 7, 143154.
Väänänen, J. (1985). Chapter XVII: Set-theoretic definability of logics. In Barwise, J. and Feferman, S., editors. Model-Theoretic Logics. New York: Springer, pp. 599643.
van Benthem, J. (1989). Logical constants across varying types. Notre Dame Journal of Formal Logic, 30(3), 315342.
Warmbrōd, K. (1999). Logical constants. Mind, 108(431), 503538.
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. 1131.
Woods, J. (2014). Logical indefinites. Logique et Analyse, 227, 277307.
Zimmermann, T. E. (1999). Meaning postulates and the model-theoretic approach to natural language semantics. Linguistics and Philosophy, 22(5), 529561.
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.
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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