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Paula Quinon, "Is the Church-Turing Thesis a Carnapian Explication?"

January 16, 2014
All Day
347 University Hall

Abstract: In 1950 Carnap denied that semi-formal axiomatic systems constituted explications. He exemplified his argument with Peano arithmetic, which sometimes is taken to be an explication of such arithmetical concepts as "one, "two or "plus. But according to Carnap the lack of an explicit interpretation of primitive axiomatic terms used in axioms formulation prevents the Peano axioms from ful lling this demand. In this talk I disagree with Carnap. I claim that some semi-formal axiomatic systems actually do explicate. As my example I consider the concept of recursive functions used to formalise the Church-Turing thesis concerning computable function.