|Recursion, theory of science, philosophy: recursion is a certain form in which rules are formulated, and which makes it possible to produce infinitely many possible cases from the application of a finite system of rules. See also inserting, embedding, infinity, systems, models, theories._____________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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Recursion / recursive method / Tarski: starting from simple propositional calculus specifying the operations with which we construct composite functions
Recursion / Tarski: problem: composite statements are constructed from simpler prop. calc., but not always from simpler statements - hence no general recursion is possible. Recursive definition of satisfaction is only possible in a much richer metalanguage (i.e. in m.l. we have variables of a higher logical type than the in the object language._____________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.
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983