Vol. 42 No. 2 (2022)
Articles

A Geometric Fallacy

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  • José Seoane
José Seoane
Universidad de la República, Montevideo, Uruguay / Sistema Nacional de Investigadores
DOI: https://doi.org/10.36446/af.2022.436

Published 2022-11-11

Keywords

  • Expressive Heterogeneity,
  • Inferential Heterogeneity,
  • Diagrams,
  • Fallacies,
  • Euclid
  • Heterogeneidad expresiva,
  • Heterogeneidad inferencial,
  • Diagramas,
  • Falacias,
  • Euclides
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Abstract

The sentence “all triangles are isosceles” is obviously false; however, a supposed “demonstration” of such an assertion has become very popular. Apparently, the authorship of this argument is due to Rouse Ball (Rouse Ball, 1905, pp. 38-39). Various authors have described it as a “fallacy” or “sophistry”. For example, Rouse Ball (1905, p. 38), E. A. Maxwell (1963, p. 13), Ya. S. Dubnov (2006, p. 2), Jesse Norman (2006, p. 2), Marvin J. Greenberg (2008, p. 25), K. Manders (2008, p. 94). Hamblin teaches that a fallacy, from the point of view of a long tradition dating back to Aristotle, is an argument that is not valid, but it seems so (Hamblin 1970, p. 12). So, if you want to claim that a given argument is a fallacy, two questions are essential: why is the argument wrong? Why does it look like it is correct? The objective is, answering both questions, to enrich the understanding of this case and, in general, some aspects of heterogeneous geometric proof.

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