|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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|P. Lorenzen Ein dialogisches Konstruktivitätskriterium (1959) in Karel Berka/L. Kreiser Logik Texte Berlin, 1983
Berka I 266
Church thesis/Lorenzen: the thesis is an equation of "constructive" with "recursive".
LorenzenVsChurch: too narrow view: thus it no longer permits the free use of the quantification over the natural numbers.
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. > Decisibility, decision-making problem._____________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.
Constructive Philosophy Cambridge 1987
K. Berka/L. Kreiser
Logik Texte Berlin 1983