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Is Modern Logic Non-Aristotelian?

Chapter
Part of the Synthese Library book series (SYLI, volume 387)

Abstract

In this paper we examine up to which point Modern logic can be qualified as non-Aristotelian. After clarifying the difference between logic as reasoning and logic as a theory of reasoning, we compare syllogistic with propositional and first-order logic. We touch the question of formal validity, variable and mathematization and we point out that Gentzen’s cut-elimination theorem can be seen as the rejection of the central mechanism of syllogistic – the cut-rule having been first conceived as a modus Barbara by Hertz. We then examine the non-Aristotelian aspect of some non-classical logics, in particular paraconsistent logic. We argue that a paraconsistent negation can be seen as neo-Aristotelian since it corresponds to the notion of subcontrary in Boethius’ square of opposition. We end by examining if the comparison promoted by Vasiliev between non-Aristotelian logic and non-Euclidian geometry makes sense.

Notes

Acknowledgements

I would like to thanks my colleagues of Moscow State University and Russian Academy of Science in Moscow, in particular Dmitry Zaitsev, Vladimir Markin and Vladimir Vasyukov as well as Valentin Bazhanov, Ioannis Vandoulakis, Jean Paul van Bendegem, Jean-Lous Hudry and José Veríssimo for help in providing me useful information.

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Authors and Affiliations

  1. 1.University of BrazilRio de JaneiroBrazil
  2. 2.Brazilian Research CouncilBrasíliaBrazil
  3. 3.Brazilian Academy of PhilosophyRio de JaneiroBrazil

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