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Etchemendy on logical truth. (English) Zbl 0901.03007

The paper discusses three aspects of the critique of Tarski’s 1936 definition of validity given by J. Etchemendy [The concept of logical consequence (1990; Zbl 0743.03002)]. (1) The first is Etchemendy’s central claim that the Tarskian definition is prone to both overgenerate (render intuitively invalid inferences valid) and undergenerate (render intuitively valid inferences valid). A central example of this concerns sentences containing only quantifiers and identity. The paper argues that the problem posed by this example may be avoided by modifying Tarski’s definition in such a way as to make the possibility of domain-variation explicitly. (The same effect may be obtained by preserving the original definition and modifying the syntax of quantification. Etchemendy also has other examples of the same phenomenon that this paper does not discuss. On both of these matters, see G. Priest, “Etchemendy and logical consequence” [Can. J. Philos. 25, 283-292 (1995)]. (2) The second aspect is a modal fallacy Etchemendy claims to find in an argument Tarski uses for the correctness of his definition. The paper gives a different exegesis of Tarski. According to this, Tarski has a position that does not commit a modal fallacy. The argument of the correctness of this position does, however, depend on the notion of possible worlds, which, in the reviewer’s opinion, is unlikely to have been acceptable to Tarski, one of whose aims was to replace appeal to modal notions. (3) The third aspect of the critique concerns the remarks of Etchemendy on the significance of the Completeness Theorem for first-order logic, but its heart is another of Etchemendy’s examples of overgeneration/undergeneration: the \(\omega\)-rule. The paper refuses Etchemendy’s criticisms by insisting that this rule, at least as expressed in first-order logic, is intuitively invalid.

MSC:

03A05 Philosophical and critical aspects of logic and foundations

Citations:

Zbl 0743.03002
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