Philosophy Dictionary of ArgumentsHome
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| Implication: Implication in logic is a relationship between two statements, where the second statement follows from the first statement. It is symbolized by the arrow symbol (→). See also Konditional, Inference, Conclusion, Logic._____________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 on Implication - Dictionary of Arguments
Berka I 267f Implication/dialogical logic/Lorenzen: here it is different than in the case of "and", "or", where only the proponent is affected by instructions. In "if, then", there are also obligations for the opponent. If P asserts a > b, the dialogical meaning of > is that P is obliged to assert also b if O on its part asserts a and defends it against P successfully. Cf. Brandom: >commitment, >Scorekeeping model. Lorenzen: from this determination it follows already that P can always win an assertion of the form (A v B) u C > (A u C) v (B u C) (With statement variables A, B, ...). Spelling/(s): Lorenzen writes the main operator with a point above it: E.g. A v B u' C > A u C v' B u C. Could also be written like this, e.g. A v B u C > A u C v B u C. Winning strategy/dialogical logic/Lorenzen: one can write it as follows: O P (A v B) u C > (A u C) v (B u C) (A v B) u C ? A v B, C ? A I B (A u C) v (B u C) ? I ? A u C I B u C ? I ? A, C I B, C This corresponds precisely to the semantic tableaux of Beth. Implication/winning strategy: because the Gs of P are such that it can only assert those primacy statement which have already been asserted by O, P can obtain any statement of this form. If, on the other hand, P may be forced by O to assert a primacy statement in any other assertion which O has not yet asserted, then P will not be able to obtain every statement of the asserted form. He may not be able to prove precisely the primacy statement that has to be asserted.(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 Implication
Ed. Martin Schulz, access date 2024-04-16