Philosophy Lexicon of Arguments

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Lorenzen, Paul
 
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Implication P. Lorenzen Ein dialogisches Konstruktivitätskriterium (1959) in Karel Berka/L. Kreiser Logik Texte Berlin, 1983

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. (> Brandom: determination!)
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.

Lorn I
P. Lorenzen
Constructive Philosophy Cambridge 1987

Brk I
K. Berka/L. Kreiser
Logik Texte Berlin 1983


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Ed. Martin Schulz, access date 2017-04-27