Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
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Berka I 270
Truth/Dialogical Logic/Lorenzen: with the infinite inductive definitions, one can transform, e.g. the semantic concept of truth into a dialogically definite concept.
>Dialogical Logic, >Semantic Truth.
There are two sets, the
set T of the true formulas and the
set F of the wrong formulas.
Cf. >Truth/Kripke.
I 271
If the formulas with the logical particles are constructed from decision-definite prime formulas, then T (true) and F (false) are defined infinitely inductively as follows:

A e T u B e T > A u B e T

A e F > A u B e F

B e F > A u B e F

(correcpondingly for v)

A e F > i A e T

A e T > i A e F

(n)A(n) e T > (x)A(x) e T

A(n) e F > (x)A(x) e F

(correspondingly for (Ex)).
Foundation/Lorenzen: for this definition one does not need ordinal numbers as step numbers, because the definition scheme is "sound". That is, one gets after a finite number of steps to a prime formula.(1)
>Foundation, >Step number.

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

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