March 7, 2017

A modern formal logic primer: sentence logic by Paul Teller

By Paul Teller

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In order to facilitate the discussion of some further original objectives of dialogic logic it is advisable to state one precise version of structural rules, in fact the one which defines intuitionistic truth and falsehood: S1 Dialogues about propositions consist of finitely many moves which are put forth alternately by an opponent O and a proponent P. The moves obey certain special rules that belong to the game such that each play ends up with win or loss for either player. S2 With exception of the improper initial move by P, each move either attacks prior ones of the other player or defends those of one’s own upon such an attack, but does not act simultaneously in both ways: The proper moves split into attacks and defenses.

12 Beyond finding different structural rules with a common core of particle rules such that the set of formally true propositions matches certain logics already under discussion, it was part of the original objective of dialogic logic to exhibit and to evaluate the relations of intuitionistic dialogue games with other dialogue games as well as with other approaches to logical reasoning. Yet, apart from this, the concept of dialogue-definiteness will always have to belong to the rock bottom of dialogic logic.

17–95. Lorenz, Kuno, 1982: Die irreführende Gleichsetzung von Begründungen und Argumentationen, in: Logik und Pragmatik. Zum Rechtfertigungsproblem logischer Sprachregeln, ed. by Carl Friedrich Gethmann, Frankfurt am Main: Suhrkamp, pp. 78–91. Lorenz, Kuno, 1996: Dialogspiele und Syntax, in: Sprachphilosophie/Philosophy of Language/La philosophie du langage. Ein internationales Handbuch zeitgenössischer Forschung/An International Handbook of Contemporary Research/ Manuel international des recherches contemporaines, ed.

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