## Philosophy Lexicon of Arguments | |||

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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Books on Amazon |
IX 58 Recursive definition/recursion/sum/product/potency/arithmetic/Quine: recursion scheme: x + 0 = x - x + S°y = S°(x + y); - x times 0 = 0; - x times (S°y) = x + x times y (s) difference to the successor for x u y equal)>; - x0 = S°0 (=1) ; - x S°y = x times x y. - "Plus"/plus sign/Quine: so we can eliminate "+" completely from "x + 3": c - but not from "x + y" (Because we do not know how often we need the successor of x) - multiplication: we can eliminate the "times" from "x 3 times": "x + (x + (x + 0))" but not from "x times y" - recursions are real definitions if we regard the characters as scheme letters for numbers, not as bound variables. --- IX 126 Transfinite recursion/sum/product/potency/Quine: c transformed into a real or direct definition: a " 0 = k, a " (S "z) = b "(a "z) - a " y = b Iy " k - from the last element: a = U{w: w e Seq u e w u w I S ^w < b}. - Advanced, liberal recursion: not only from the last previous element - instead totality of the previous elements - a = U{w: w e Seq u "y(y e ^w " " J > |
Q I W.V.O. Quine Wort und Gegenstand Stuttgart 1980 Q II W.V.O. Quine Theorien und Dinge Frankfurt 1985 Q III W.V.O. Quine Grundzüge der Logik Frankfurt 1978 Q IX W.V.O. Quine Mengenlehre und ihre Logik Wiesbaden 1967 Q V W.V.O. Quine Die Wurzeln der Referenz Frankfurt 1989 Q VI W.V.O. Quine Unterwegs zur Wahrheit Paderborn 1995 Q VII W.V.O. Quine From a logical point of view Cambridge, Mass. 1953 Q VIII W.V.O. Quine Bezeichnung und Referenz InZur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982 Q X W.V.O. Quine Philosophie der Logik Bamberg 2005 Q XII W.V.O. Quine Ontologische Relativität Frankfurt 2003 |

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Ed. Martin Schulz, access date 2017-05-25