Economics Dictionary of ArgumentsHome
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| Church-Turing Thesis: The Church-Turing thesis is the thesis according to which there are no principally calculable functions that cannot be calculated by a Turing machine. The thesis is not proved since the set of principally (or intuitively) calculable functions cannot be definitively determined. It follows from the Church-Turing thesis that a computer can execute any algorithm if its storage capacity is sufficient. See also Turing machine, predictability._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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Hennig Genz on Church-Turing Thesis - Dictionary of Arguments
II 329 Church-Turing-Thesis/Church/Genz: (Church 1936): thesis: everything that is calculable at all can be calculated by a Turing machine. Genz: whether this is true, is a physical question. It cannot be determined by logical evidence. For example, if nature allowed a Turing machine that would take infinite logical steps in finite time, the Church-Turing thesis would be wrong. It would also be wrong, e. g. if there could be countless physical states in a physical system. Analogous calculations would then be possible, and this exceeded the machine's repertoire. Quantum mechanics: rescues the thesis from refutation by classic computers by prohibiting to build some that could do this. On the other hand, quantum mechanics could allow to build computers that falsify the Church Turing thesis! Cf. >Quantum mechanics. Vs: But according to experts, this is not the case. II 330 Question: could one not add the "secret calculations" of nature to our repertoire and thus refute the Church-Turing thesis? Vs: without understanding the corresponding laws of nature we cannot know what nature calculates. >Laws of nature, >Laws, >Rules, >Knowledge, >Understanding, >Rule following. II 332 Church-Turing-Thesis/Genz: if it were wrong, it is an empirical question whether it can be valid in a weakened form ((s) after all, it has not yet been refuted). II 333 Weaker/variant: thesis: nature provides us with the mathematical and logical means by which its laws can be recognized. VsChurch-Turing-Thesis/Genz: the antithesis would be that at least the action of the human mind requires unpredictable functions to describe it. Then they are random, seen from the Turing machine (representative/group: Penrose). >Mind, >Dependence. 1. Alonzo Church (1936). A note on the entscheidungsproblem. Journal of Symbolic Logic 1 (1):40-41 (1936)_____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Gz I H. Genz Gedankenexperimente Weinheim 1999 Gz II Henning Genz Wie die Naturgesetze Wirklichkeit schaffen. Über Physik und Realität München 2002 |
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