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 mild of the notion of Intuitionistic Formalism constructed: semantics, fact, paradox, logical outcome.

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1 Le´sniewski’s early work When we turn to Le´sniewski’s early (1911–1914) papers, we find some much more articulate comments on a view which is in agreement with the remarks in the passage Tarski cites. An appeal to the early works is problematic, however, since Le´sniewski later repudiated them [Le´sniewski, 1992h, 197–8]. 3 After looking at the evidence from the early work I will confirm this view, and bolster my attribution of it to Tarski, in two ways: first by chasing down its traces in Le´sniewski’s later papers, and second by finding exactly the same view in the main work of Tarski’s other mentor, Tadeusz Kotarbinski, ´ published in 1929—the year in which Le´sniewski published the passage Tarski cites, and in which Tarski did the bulk of the work on his strategy for defining truth [Hodges, 2008, 120–5].

Indeed, all reasoning concerning a concept is restricted to that which is provided for by its introducing axioms [Detlefsen, 2008, 294–5]. 3 Formalism Up to now, in constructing a language, the procedure has usually been, first to assign a meaning to the fundamental mathematicological symbols, and then to consider what sentences and inferences are seen to be logically correct in accordance with this meaning. Since the assignment of the meaning is expressed in words, and is, in consequence, inexact, no conclusion arrived at in this way can very well be otherwise than inexact and ambiguous.

By applying a formal procedure in proving theorems of a given discipline we may thereby also prove theorems of some other discipline, if the objects investigated by the latter so correspond to the objects investigated by the former that sentences of the same form, according to the interpretation of the constants they include, state theorems either of the former or of the latter discipline [Kotarbinski, ´ 1966, 256]. This contrasts with Hilbert in a way broadly in tune with Padoa: unlike Hilbert, the primitive terms of an axiom system are associated with ideas not determined by the axioms, and it is simply an intriguing sort of generality that it can turn out that the same axiom system can receive different intuitive interpretations.

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