Models & Optimisation and Mathematical Analysis Journal
Volume 5, Numéro 1, Pages 11-26
2017-12-21
Can Logical Techniques Developed During Last Centuries Allow Us Today Complete Axiomatization Of Any Theory Based On Stable, Self-consistent Systems Of Principles I.e. Of Any Mathematical Theory???
Authors : Belarbi Mostefa .
Abstract
“How far can we proceed with the axiomatization of some theory? Complete elimination of intuition, i.e. full reduction to a list of axioms and rules of inference, is this possible?” The work by Bertrand Russell showed how this could be achieved even with the most complicated mathematical theories. All theories can be reduced to axioms and rules of inference without any admixture of intuition. The work of Bertrand Russel inspires Kurt Gödel to prove the opposite!! In this context I suggest to re-read Gödel's first incompleteness theorem published in 1931.
Keywords
Gödel's first incompleteness theorem ; Theory; Axioms
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