Logica Universalis

, Volume 12, Issue 1–2, pp 55–81 | Cite as

Is the Principle of Contradiction a Consequence of \(x^{2}=x\)?

  • Jean-Yves Beziau


According to Boole it is possible to deduce the principle of contradiction from what he calls the fundamental law of thought and expresses as \(x^{2}=x\). We examine in which framework this makes sense and up to which point it depends on notation. This leads us to make various comments on the history and philosophy of modern logic.


Boole Principle of contradiction Laws of thought Symbolic logic Subtraction Universal logic Boolean algebra Square of opposition 

Mathematics Subject Classification

Primary 03A05 Secondary 00A30 01A55 03B53 03B22 03B05 03B10 03G05 


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Brazilian Research CouncilUniversity of BrazilRio de JaneiroBrazil
  2. 2.Ecole Normale SupérieureParisFrance

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