| The model-theoretic definition of logical consequence, credited to Alfred Tarski, 1936, has proven to be extremely valuable. It has spawned the entire discipline of mathematical logic whose theorems are highly applicable within contemporary philosophy. Recently, however, John Etchemendy has argued that it fails as an analysis of the intuitive notion of logical consequence for several reasons. One is that it cannot adequately treat the quantifiers. Another is that it does not guarantee that its logical truths are necessary truths. Furthermore, he argues, it relies upon non-logical truths in order to get the right extension. Since it only generates the right answers if we accept infinite set theory, he claims that it cannot represent an adequate conceptual analysis of a logical notion. He lastly faults Tarski's definition for relying upon a spurious distinction between the logical and non-logical terms. He aims to prove that the distinction cannot be adequately drawn even for simple languages.; I reply to each of Etchemendy's objections. The quantifiers can be adequately handled by parsing the original sentences so as to bring out their more complete logical forms. I go on to prove that Tarskian logical truths (and consequences) are in fact logically necessary. I then defeat half of Etchemendy's non-logical objection by advocating simple domain-relativization. I defend against the second half by demonstrating that it is no shame for a conceptual analysis to rely upon non-logical truths for its adequate extension. Indeed any informative analysis must do so. Next, I claim that the distinction between the logical and non-logical terms can be adequately drawn, and note some promising such definitions (including Tarski's own). I then go on to show that Tarskian logical truths are true in virtue of their forms—completing the intuition that logical truths are both necessary and formal.; Finally, I find fault in three other competing definitions of logical truth and consequence. The proof-theoretical, substitutional, and representational definitions are shown to be full of flaws. I conclude that Tarski's model-theoretic approach stands firm as an adequate and superior analysis of an important logical notion. |
