Nonsets

Abstract : Our topics are set theory and the problem of the definition of a set. With the existence of non-collectivizing relations and inconsistent multiplicities, the usual definition meets some limits. But, what is a nonset? Making a difference between sets and collections could appear as a subtle concern. In fact, this does not work very well. Indeed, philosophers show a lot of examples when naive sets and collectivizing relations fail, and modern mathematicians, from Cantor and Dedekind to Aczel suspect themselves that rising objections to the uncritical use of collectivizing relations is not unreasonable. A solution of the problem may be found in a rational model.
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https://hal-univ-lyon3.archives-ouvertes.fr/hal-01783906
Contributor : Daniel Parrochia <>
Submitted on : Wednesday, May 2, 2018 - 5:35:45 PM
Last modification on : Wednesday, November 20, 2019 - 7:46:24 AM

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Daniel Parrochia. Nonsets. Birkhaüser. The Road to Universal Logic , 1, Birkhaüser, pp. 409-421, 2015, The Road to Universal Logic, 978-3-319-10192-7. ⟨10.1007/978-3-319-10193-4_19⟩. ⟨hal-01783906⟩

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