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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Additional resources for Alfred Tarski: Philosophy of Language and Logic (History of Analytic Philosophy)
G. 6 The main point for us is that the adequacy of conventions here is a matter of properly answering to a speaker’s “referential intentions”. The point of language is to express thoughts, but natural language does this poorly and the purpose of deductive sciences is to do it well. A system of language needs to be rigorously compositional in the sense that the content expressed by a non-lexical expression must always be uniquely determined by the contents associated with its parts and by the way they are assembled.
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. The system bears an intended interpretation not settled by its structure, though generality can be achieved by varying the interpretation imposed upon it. Tarski’s own remarks on formalism have a similar ﬂair.
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. The connection will only become clear when approached from the opposite direction: let any postulates and any rules of inference be chosen arbitrarily; then this choice, whatever it may be, will determine what meaning is to be assigned to the fundamental logical symbols [Carnap, 2002, xv]. This is quite the opposite of Le´sniewski’s view; rather than the intuitive content that lies outside of the deductive system being the important thing, the difﬁculty of determining it rigorously is for Carnap in the passage precisely a reason to get rid of it.
Alfred Tarski: Philosophy of Language and Logic (History of Analytic Philosophy) by Douglas Patterson