A conception of Tarskian logic

Pacific Philosophical Quarterly 70 (4):341-368 (1989)
In this paper I develop a new conception of Tarskian logic based on Tarski’s intuitive characterization of logical consequence as formal and necessary in his 1936 paper. Special emphasis is placed on the role of logic in our system of knowledge, the origins of semantics, the semantic definition of logical consequence, and the role of logical and non-logical terms in a logical system. The paper offers a new definition of logical terms based on the question: what division of terms into logical and extra-logical would yield a logical system that satisfies Tarski’s intuitive characterization of logical consequence in complete generality? I discuss the consequences of the new conception for revision in logic, the logicist thesis, and the relation between logic and mathematics. I offer a proof-theoretic perspective on the semantic conception delineated in this paper. And I conclude with a postscript on Tarski’s lecture, “What are Logical Notions?”, which was published shortly after the present conception of logic was developed.
Keywords Logic  Tarski  Tarskian logic  Semantics  Logical consequence  Logical terms  Task of logic  Definition of logical terms  Logicism
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Gila Sher (1990). Ways of Branching Quantifers. Linguistics and Philosophy 13 (4):393 - 422.

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