# Philosophy Lexicon of Arguments

Dialogical logic: dialogical logic is an approach that takes the reverse approach to classical logic and breaks down composite statements into their elementary components. The statement is first presented by a proponent and is challenged bit by bit by an opponent and subsequently defended. True statements are those that can always be won. The dialogical logic was developed by P. Lorenzen (P. Lorenzen, Einführung in die operative Logik und Mathematik, 1955).

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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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Wessel I 260
Dialogical Logic/Paul Lorenzen/Wessel: PO: Proponent, O: Opponent.
1. The dialogue begins with the setting of a formula by the proponent.
2. The proponent may attack only one of the opponent's formulas claimed by the the latter, or the proponent may defend itself against the opponent's last attack.
3. The opponent may only attack the formula set in the preceding proponent's move, or defend itself against the attack in the previous move.
Operational rules:

Assertion attack defense
~A A? not possible!
A u B ?L A
A u B ?R B
A v B ? A
A v B ? B
A > B A? B
AiA ?(j) A{i/j}
EiA ? A{i/j}
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I 261
Rule of winning: the proponent has won if he has to defend a statement variable or predicate formula c that has already been asserted by the opponent.
Definition Dialogical Tautology: a dialogical tautology is present, precisely when it wins against any opponent's strategy. A dialogue always leads from complicated to simpler formulas and finally to statement variables or predicate formulas.
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Berka I 206
Dialogical Logic/Lorenzen/Berka:
Dialogical logic suppresses in the recent discussion the conception of a symmetry of rule and general formula in favor of the rule-logical representation.
If the logic is realized in sensible speech actions, a process schema constructed as a set of rules is the adequate description of the logical as the regulation of the generation of actions from given actions.
(> Operationalism, pragmatism). This is a context of actions which is itself a kind of action. (> Identity/Fichte).
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Thiel I 103
Logic/Dialogical Logic/Lorenzen: It was only in the sixties that a construction of logic was developed, which can also be described as a justification in the scientific theory and philosophical sense.
It provides a possibility, not yet seen, for the foundation of both the classical and the constructive concept of the "validity" of logical propositions. (Lorenzens' "dialogical logic" with proponent and opponent, also "argumentation-theoretic structure of logic").
Dialogical logic should 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.

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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

We I
H. Wessel
Logik Berlin 1999

Brk I
K. Berka/L. Kreiser
Logik Texte Berlin 1983

T I
Chr. Thiel
Philosophie und Mathematik Darmstadt 1995

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Ed. Martin Schulz, access date 2018-04-22