Lexicon of Arguments

 

Berka I 268
Negation/Dialogical Logic/Lorenzen: If i a is asserted by P, it has lost when O asserts the assertion a and successfully defends it.
N.B.: precisely in this way the intuitionist logic arises.
Intuitionist Logic/Lorenzen: there is no winning strategy for A v i A: E.g.

O P

A v i A
? A I i A
? I A

I 269
Here, for the variable A, we put a statement such that O knows a proof of it, but P does not.
Winning strategy/negation/dialogical logic/Lorenzen: for the explanation I show additionally that there is a winning strategy for:
i i (A v i A)

O P
i i (A v i A)

i (A v i A) A v i A
? i A
A A v i A
? A ⁽¹⁾


1. P. Lorenzen, Ein dialogisches Konstruktivitätskriterium, in: Infinitistic Methods, (1961), 193-200