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Language, Truth and Logic in Mathematics (Jaakko Hintikka Selected Papers) | |||||
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Rok: 1997 AnotaceSome of the most fundamental concepts of mathematics and logic are shown to need re-examination and re-definition. They include the received logic of quantification, the idea of the completeness of a mathematical system as well as the notions of a model in higher-order logic, of formalism, of computability and of parallel processing. Even the notion of a model in first-order logic admits of interesting variation. These analyses have important repercussions concerning such matters as the notion of proofs, Church's Thesis, the foundational projects of Frege, Russell, Hilbert and Carnap, and the philosophical significance of the impossibility results of Godel and Tarski, which turns out to be much smaller than has been generally assumed. Thus this book opens a radically new perspective on the entire foundations of mathematics. Dostupné zdroje
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