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The Paradoxes of Reflexivity Revisited

Author:

Leon, Antonio

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

December 23, 2023

File:

/Research Papers-Mathematics and Applied Mathematics/Download/8218

Downloads:

313

Keywords:

Dedekind’s definition of the infinite sets, paradoxes of reflexivity, Galileo’s paradox, exhaustive and non-exhaustive injections, inconsistencies in the foundation of set theories, actual infinity, potential infinity.

Abstract:

This chapter discusses the paradoxes of reflexivity from a new perspective according to which such paradoxes could be inconsistencies derived from the hypothesis of the actual infinity that legitimizes Dedekind’s definition of the infinite sets.