Philosophy 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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Paul Lorenzen on Church-Turing Thesis - Dictionary of Arguments
Berka I 266 Church thesis/Lorenzen: the thesis is an equation of "constructive" with "recursive". >Constructivism, >Recursion, >Recursivity. LorenzenVsChurch: this is a too narrow view: thus it no longer permits the free use of the quantification over the natural numbers. >Quantification, >Numbers, >Infinity. I 267 Decision-making problem/ChurchVsLorenzen: (according to Lorenzen): Advantage: greater clarity: when limiting to recursive statements, there can never be a dispute as to whether one of the admitted statements is true or false. The definition of recursiveness guarantees precisely the decision-definition, that is, the existence of a decision-making process. >Decidability, >decision problem.(1) 1. P. Lorenzen, Ein dialogisches Konstruktivitätskriterium, in: Infinitistic Methods, (1961), 193-200_____________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. |
Lorn I P. Lorenzen Constructive Philosophy Cambridge 1987 Berka I Karel Berka Lothar Kreiser Logik Texte Berlin 1983 |
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> Counter arguments against Lorenzen
> Counter arguments in relation to Church-Turing Thesis
Ed. Martin Schulz, access date 2024-04-28