Logic, Logics, and Logicism

Notre Dame Journal of Formal Logic 40 (1):31-54 (1999)
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Abstract

The paper starts with an examination and critique of Tarski’s wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which is invariant with respect to arbitrary permutations of the domain. The class of such operations has been characterized by McGee as exactly those definable in the language L∞,∞. Also characterized similarly is a natural generalization of Tarski’s thesis, due to Sher, in terms of bijections between domains. My main objections are that on the one hand, the Tarski-Sher thesis thus assimilates logic to mathematics, and on the other hand fails to explain the notion of same logical operation across domains of different sizes. A new notion of homomorphism invariant operation over functional type structures (with domains M0 of individuals and {T, F} at their base) is introduced to accomplish the latter. The main result is that an operation is definable from..

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Citations of this work

Logicality and Invariance.Denis Bonnay - 2006 - Bulletin of Symbolic Logic 14 (1):29-68.
Invariance as a Basis for Necessity and Laws.Gila Sher - 2021 - Philosophical Studies 178 (12):3945-3974.
Alfred Tarski: Philosophy of Language and Logic.Douglas Patterson - 2012 - Basingstoke and London, UK: Palgrave-Macmillan.

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References found in this work

The Development of Logic.William Kneale & Martha Kneale - 1962 - Oxford, England: Clarendon Press.
Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.

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