Antilogic

Abstract

This paper is an interim report of joint work begun in Castelnérac & Marion (2009) on dialectic from Parmenides to Aristotle. In the first part we present rules for dialectical games, understood as a specific form of antilogikê developed by philosophers, and explain some of the key concepts of these dialectical games in terms of ideas from game semantics. In the games we describe, for a thesis A asserted by the answerer, a questioner must elicit the answerer's assent to further assertions B 1 , B 2 ,.. . , B n , which form a scoreboard from which the questioner seeks to infer an impossibility (adunaton); we explain why the questioner must not insert any of his own assertions in the scoreboard, as well as the crucial role the Law of Non Contradiction, and why the games end with the inference to an impossibility, as opposed to the assertion of ¬A. In the second part we introduce some specific characteristics of Eleatic Antilogic as a method of enquiry. When Antilogic is used as a method of inquiry, then one must play not only the game beginning with a given thesis A, but also the game for ¬A as well as for A & ¬A, while using a peculiar set of opposite predicates to generate the arguments. In our discussion we hark back to Parmenides' Poem, and illustrate our points Antilogic 2 with Zeno's arguments about divisibility, Gorgias' ontological argument from his treatise On Not-Being, and the second part of Plato's Parmenides. We also identify numerous links to Aristotle, and conclude with some speculative comments on the origin of logic.

Dialogical Argumentation and Textual Entailment

“…We now progressively present dialogical logic. Although the study of dialecticsthe art of correct debate -and logic -the science of valid reasoning -have been intrinsically linked since their beginnings [8,35,7], modern mathematical logic had to wait until the 50s of the last century to ensure that the logical concept of validity was expressed through the use of dialogical concepts and techniques. Inspired by the Philosophical Investigations of Wittgenstein [40], the German mathematician and philosopher Lorenzen [28] proposed to analyze the concept of validity of a formula F through the concept of winning strategy in a particular type of two-player game.…”

Two Types of Refutation in Philosophical Argumentation

“… 4 There are a number of detailed reconstructions of the basic features of this practice in the literature (Castelnérac and Marion 2009 , 2013 ; Fink 2012 ). Scholars disagree on how best to understand the concept of dialectic, even in the restricted context of ancient Greek thought (Duncombe and Dutilh Novaes 2016 ).…”