Philosophy Lexicon of Arguments

Negation, philosophy, logic: negation of a sentence. In logic, this is done by prefixing the negation symbol. Colloquially expressed by the word "not", which can be at different positions in the sentence. If the negation refers only to one sentence part, this must be made clear by the position, e.g. a predicate can be denied without negating the whole sentence. In logic, therefore, inner and outer negation is distinguished by the use of different symbols.

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

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

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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 2017-10-22