|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.|
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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.
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983