Journal Title
Title of Journal: Synthese
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Publisher
Springer Netherlands
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Authors: Solomon Marcus
Publish Date: 2013/09/26
Volume: 192, Issue: 7, Pages: 2139-2149
Abstract
Our aim is to propose several itineraries which follow the scenario having as a first step Euclid’s Fifth Postulate as a second step the Bolyai–Lobachevsky’s nonEuclidean geometries and as a third step Einstein’s relativity theory The role of Euclid’s fifth postulate is successively assumed by Archimedes’ axiom Zermelo’s choice axiom Cantor’s continuum hypothesis von Neumann’s foundation axiom for set theory Church–Turing thesis and Turing’s computability the validity of classical logic under the form of the principles of identity noncontradiction and excluded middle the macroscopic universe assumed as form of existence including the fact that humans are macroscopic beings human language and semiosis assumed as the unique way to approach understanding and communication the old Greek ideal of order symmetry and harmony adopted for representation of the world in Art and Poetry The common denominator of these starting steps is the fact that they all correspond to the sensorialempirical perception of the world We point out the strong interaction among the steps corresponding in these different itineraries to Einstein’s relativity theory We infer in this way the need of a transdisciplinary approach
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