Alfred Tarski: Philosophy of Language and Logic (History of by Douglas Patterson

By Douglas Patterson

This learn seems to the paintings of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders the entire significant matters in Tarski scholarship in gentle of the perception of Intuitionistic Formalism built: semantics, fact, paradox, logical outcome.

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Those of propositions, should depend, in a correctly constructed precise language, upon the functions or the order of particular words—on the bases of certain pattens determined by general normative conventions the knowledge of which permits the correct symbolization of an object in a given language or the decoding of a symbol for a given language [Le´sniewski, 1992c, 56]. Note the use, here and elsewhere, of “decode” (odcyfrowanie [Le´sniewski, 1913, 324]) for what the reader does in understanding a symbol in accord with conventional-normative schemata.

Turning to Hilbert himself, we find remarks like this one, from the programmatic “Mathematical Problems” of 1900, to the effect that the meaning of an expression is somehow determined by the axioms in which it figures:1 When we are engaged in investigating the foundations of a science, we must set up a system of axioms which contains an exact and complete description of the relations subsisting between the elementary ideas of that science. The axioms so set up are at the same time the definitions of those elementary ideas; and no statement within the realm of the science whose foundations we are testing is held to be correct unless it can be derived from those axioms by means of a finite number of logical steps.

It is this content which is the “meaning” of a name. [note] We designate in every case as the meaning of an expression that mental content which it is the real task, the goal, of the name to arouse in the listener. [Twardowski, 1977, 8–9]. As for Kotarbinski, ´ thoughts are about objects and names refer to them. 21 One mark of this is that Le´sniewski and Kotarbinski ´ find no puzzle about the linguistic significance of empty names: they have connotations, and this is what is required for being meaningful.

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