By Douglas Patterson
This research seems to the paintings of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all the significant matters in Tarski scholarship in mild of the perception of Intuitionistic Formalism constructed: semantics, fact, paradox, logical outcome.
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Extra info for Alfred Tarski: Philosophy of Language and Logic
It isn’t an object of study in its own right, and it must Intuitionistic Formalism 43 thereby be crafted to respect the logical relationships among thoughts intuitively judged. 3 Five doctrines We have now seen ﬁve main aspects of Intuitionistic Formalism in Le´sniewski and in the related philosophy of language of Kotarbinski: ´ 1. The understanding of language as a medium for the expression of thought via a speaker’s intentions. 2. The conception of conventions of language as determining which thoughts are expressed by the use of a given sentence when a language is used correctly.
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.
28 Alfred Tarski: Philosophy of Language and Logic One aspect of Le´sniewski’s vision here is that axioms and deﬁnitions mattered less to the intuitive interpretation thereby forced upon his primitives than did certain theorems. That is, Le´sniewski, in order to capture intuitive meaning, wanted certain theses to be theorems of his system so as to guarantee its expression of intuitive content, but he was more open about the formulation of axioms and deﬁnitions. Here is how he comments on the formalization of his “Ontology”: I wished to take one step further and, using the ‘singular’ propositions of the type ‘Aεb’, to base all my deliberations on some clearly formulated axiomatization which would harmonize with my theoretical practice in this domain at the time.