Logica Universalis

, Volume 10, Issue 2–3, pp 377–392

The Klein Group, Squares of Opposition and the Explanation of Fallacies in Reasoning


DOI: 10.1007/s11787-016-0150-3

Cite this article as:
Robert, S. & Brisson, J. Log. Univers. (2016) 10: 377. doi:10.1007/s11787-016-0150-3


During the last decades, the psychology of reasoning has identified experimentally many fallacies committed by spontaneous reasoners. Given these experimental results, some theories have been developed about this phenomenon, mainly algorithmic theories. This paper develops instead a computational modelling of these current fallacies which appear as simplifications in the treatment of information that do not respect the formal rules of classical propositional logic. These fallacies are explained as crushes in the Klein group structure and so, in squares of opposition. These crushes are an effect of not to take into account the dual of the binary operator at work in the major premise of the inference. This analysis allows predictions on fallacies not identified before, which are fallacies produced when reasoning with incompatibilities. The paper concludes with consequences of the analysis on pedagogical strategies for the teaching of logic.


Human reasoning fallacies Klein group mental models computational modelling group crush predictions on fallacies reasoning with incompatibilities squares of opposition teaching of logic 

Mathematics Subject Classification

Primary 06E05 Secondary 03A05 03B05 

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of PhilosophyUniversité du Québec à MontréalDowntown, MontrealCanada

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