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Paradoxes and Theorems

Author:

Leon, Antonio

Category:

Research Papers

Sub-Category:

Philosophy

Language:

English

Date Published:

September 20, 2023

File:

/Research Papers-Philosophy/Download/9630

Downloads:

Keywords:

Gödel first incompleteness theorem, Liar paradox, Richard paradox, Russell paradox, Undecidable sentences, self-reference, logic

Abstract:

This book is a critique of self-reference in ordinary language and mathematics. From this critical point of view, the most well-known semantic paradoxes are analyzed, such as the liar's paradox, Russel's barber's paradox, the paradox of the set of all sets that do not belong to themselves, Richard's paradox, Berry's paradox, etc. It also includes a critical analysis of the interpretation in natural language of Gödel's sentence that is the protagonist of his famous incompleteness theorem, because this sentence has the same formal structure as the paradoxes analyzed in the book.