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Paradoxes in a Semantic Perspective

  • Bengt Hansson
Part of the Synthese Library book series (SYLI, volume 122)

Abstract

Let us take Russell’s set of all sets that do not contain themselves as a paradigm of paradox. We assume that there is such a set, and if so, it has to be either a member of itself or not. But, as we know, either way leads to a contradiction. However, this is not the paradox. So far, the argument is just like a reductio ad absurdum proof, and the conclusion to draw is that our assumption was wrong, i.e. there is no such set. The paradox enters when we nevertheless insist that there has to be one — our intuitions about the existence of sets are so strong that we are not prepared to give them up even if they lead to a contradiction. And we cannot deny that they do — the logic of that part is impeccable.

Keywords

Logical Structure Preceding Sentence Material Implication False Proposition Daylight Saving 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1979

Authors and Affiliations

  • Bengt Hansson
    • 1
    • 2
  1. 1.Department of PhilosophyUniversity of LundSweden
  2. 2.International Institute for Applied Systems AnalysisSchloss LaxenburgAustria

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