Truth

Abstract

Tarski’s interest in the early 1930s is in the expression of metamathematical concepts within mathematical deductive theories. Having expressed the concept of logical consequence as he understood it at the time, Tarski moved on to semantic concepts, motivated by the clash between philosophical scruples and mathematical practice with which we opened the previous chapter. Since Intuitionistic Formalism requires that an expression that expresses a semantic concept be bound up in theorems that constrain it to express that concept, the exercise requires a conception of what these theorems are. This requirement appears in an inchoate way in early 1930 as the requirement that these eliminative definitions be “intuitively” or “materially” adequate, but in late 1929 or early 1930 Tarski lacks any particularly clear idea of what this amounts to in the case of semantic concepts, though he shows some signs of groping toward the right idea in his treatment of the “completely mechanical method” of translating arithmetic formulae into set-theoretic ones—a clear precursor of CTFL’s appeal to translation.