Philosophy Lexicon of Arguments

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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:

(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.

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.

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 2018-03-22