Abstract
The theorems of Kurt Gödel and Alan Turing are likely to be remembered as the two most important achievements in mathematics of the twentieth century. Their far-reaching consequences are valid for any formal system and in particular for arithmetic and any advanced mathematical theory. Their formulation in the thirties has changed completely the objectives of the research for the foundations of mathematical theories. The task Hilbert had indicated, namely the reduction of mathematics to logic through the process of axiomatisation and the formulation of a method to answer mechanically any mathematical question, has been proved to be unfeasible.
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© 1997 Springer Science+Business Media Dordrecht
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Cacace, F. (1997). Meaning, Reality and Algorithms: Implications of the Turing Theorem. In: Driessen, A., Suarez, A. (eds) Mathematical Undecidability, Quantum Nonlocality and the Question of the Existence of God. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5428-4_3
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DOI: https://doi.org/10.1007/978-94-011-5428-4_3
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