By Douglas Patterson
This research appears to the paintings of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all the significant concerns in Tarski scholarship in gentle of the belief of Intuitionistic Formalism constructed: semantics, fact, paradox, logical end result.
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As Le´sniewski mentions elsewhere, such conventions can amount to definitions or not [Le´sniewski, 1992c, 75–6]: either way they are rules that determine the intuitive meanings of symbols. A passage from the transitional “Foundations of the General Theory of Sets” of 1916 already states the Intuitionistic Formalist view well: On the question concerning the way of using expressions, I mention that of the mathematical terms which I use, the expression ‘part’ is the only one I do not deﬁne, supposing that this term will not cause misunderstandings—considering that its intuitive character acquires considerable clarity in the light of Axioms I and II [Le´sniewski, 1992d, 131].
However, turning to Kotarbinski ´ [Kotarbinski, ´ 1966], we ﬁnd the same view as we have discerned in Le´sniewski’s early work. Tarski notes at the outset in CTFL that “in writing the present article I have repeatedly consulted this book and in many points adhered to the terminology there suggested” [Tarski, 1983a, 153]. 14 Kotarbinski’s ´ basic conception of meaning includes elements of intention and convention: That sentence S is a (direct) statement of John’s thought as to content, means: John thought that p (“p” stands for the whole sentence) and uttered S so that the listener might recognize that John thought that p.
In the troublesome theoretical situations in which I found myself due to this state of affairs, I shared the misfortune of all who are forced by circumstances to convey in ‘their own words’ the sense of the various primitive terms of deductive theories which they were constructing [Le´sniewski, 1992h, 374–5]. The remark is then followed by a discussion of various “colloquial” formulations that might help someone to cotton on to Le´sniewski’s sense. Notice again the contrast here with Hilbert and especially with Carnap, whom we have seen in Logical Syntax taking this very problem to be the reason that one ought to ignore anything that isn’t determined by the structure of a deductive theory.
Alfred Tarski: Philosophy of Language and Logic by Douglas Patterson