|Logic: logic is the doctrine of the admissibility or inadmissibility of relations between statements and thus the validity of the compositions of these statements. In particular, the question is whether conclusions can be obtained from certain presuppositions such as premises or antecedents. Logical formulas are not interpreted at first. Only the interpretation, i. e. the insertion of values, e.g. objects instead of the free variables, makes the question of their truth meaningful.|
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Operational logic/dialogical/Lorenzen/Berka: Variant of the constructivist interpretation of intuitionism.
Functors and quantifiers are constructively defined with regard to a dialogue game.
Truth-functions: can then be proved as sentences about the dialogic use of the functions. (See, VIII 3).
N.B.: the successful defense of a formula in dialogue is not sufficient to prove the effective logical truth (logical validity) of this formula. For this proof it must be shown that the formula can be successfully defended against any possible strategy of the opponent.
Thiel I 103
Logic/Lorenzen: It was only in the sixties that a construction of logic was developed, which can also be described as a justification in scientific theory and in a philosophical sense.
It provides a possibility, not yet seen, for the justification of both the classical and the constructive concept of the "validity" of logical propositions.
(Lorenzens' "dialogical logic" with proponent and opponent, also "argumentation-theoretical structure of logic").
It is supposed to show that the axiomatic derivation does not constitute the whole meaning of the proof, but that a proof should provide reasons for the truth or validity of the proved proposition. .. + .. I 105.
Constructive Philosophy Cambridge 1987
Philosophie und Mathematik Darmstadt 1995