Are There Model-Theoretic Logical Truths that Are not Logically True?

In Douglas Patterson (ed.), New essays on Tarski and philosophy. New York: Oxford University Press. pp. 340-368 (2008)
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Abstract

Tarski implicitly postulated that a certain pre-theoretical concept of logical consequence and his technical concept of logical consequence are co-extensional. This chapter makes explicit a few theses about logical consequence or logical truth that sound Tarskian somehow, including one that most deserves the name ‘Tarski's Thesis’. Some of these theses are probably true or close to true but weaker than Tarski's. Some are false but stronger than Tarski's. Tarski's Thesis plausibly postulated that a sentence of a classical language possibly extended with non-traditional extensional logical constants is logically true, if it is true in all classical interpretations of all its non-logical constants. But it is noted that this thesis turns out to be false on most conceptions of logical truth, for some sentences of a classical language extended with extensional logical constants are true in all classical interpretations of all its non-logical constants, but are not necessary.

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Mario Gomez-Torrente
National Autonomous University of Mexico

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