Mario Gomez-Torrente

Logic is formal in the sense that all arguments of the same form as logically valid arguments are also logically valid and hence truth-preserving. However, it is not known whether all arguments that are valid in the usual model-theoretic sense are truthpreserving. Tarski claimed that it could be proved that all arguments that are valid (in the sense of validity he contemplated in his 1936 paper on logical consequence) are truthpreserving. But he did not offer the proof. The question arises whether the usual modeltheoretic sense of validity and Tarski's 1936 sense are the same. I argue in this paper that they probably are not, and that the proof Tarski had in mind, although unusable to prove that model-theoretically valid arguments are truth-preserving, can be used to prove that arguments valid in Tarski's 1936 sense are truth-preserving

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.

The purpose of this paper is to examine some passages of Tarski‘s paper ’On the concept of logical consequence’ and to show that some recent readings of those passages are wrong. John Etchemendy has claimed that in those passages Tarski gave an argument purporting to show that the notion of logical consequence defined by him (as opposed to some pretheoretic notion of logical consequence) possesses certain modal properties. Etchemendy further claims that the argument he attributes to Tarski is fallacious. Some of Etchemendy’s critics have granted him that Tarski did give an argument purporting to show that the defined notion possesses certain modal properties ; but they have claimed that Tarski’s argument was not a fallacious one. I will show that both Etchemendy and his critics are wrong; in the relevant passages, Tarski did not offer (nor did he intend to offer) an argument that the defined notion of logical consequence possesses any modal properties