Alfred Tarski - Logical Consequence

Logical Consequence

In 1936, Tarski published Polish and German versions of a lecture he had given the preceding year at the International Congress of Scientific Philosophy in Paris. A new English translation of this paper, Tarski (2002), highlights the many differences between the German and Polish versions of the paper, and corrects a number of mistranslations in Tarski (1983).

This publication set out the modern model-theoretic definition of (semantic) logical consequence, or at least the basis for it. Whether Tarski's notion was entirely the modern one turns on whether he intended to admit models with varying domains (and in particular, models with domains of different cardinalities). This question is a matter of some debate in the current philosophical literature. John Etchemendy stimulated much of the recent discussion about Tarski's treatment of varying domains.

Tarski ends by pointing out that his definition of logical consequence depends upon a division of terms into the logical and the extra-logical and he expresses some skepticism that any such objective division will be forthcoming. "What are Logical Notions?" can thus be viewed as continuing "On the Concept of Logical Consequence".