Starting from the scenario Euclid-Bolyai-Einstein.
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 non-Euclidean geometries and as a third step Einstein's relativity theory. The role of Euclid's fifth postulate is successively assumed by Ar...
| Published in: | Synthese Vol. 192; no. 7; pp. 2139 - 2150 |
|---|---|
| Main Author: | |
| Format: | Article |
| Published: |
Springer Nature
Jul2015
|
| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=109574773&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 109574773 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: Jul2015 vid: 192 iid: 7 pid: 237 pub: Springer Nature artinfo: ui: 109574773 10.1007/s11229-013-0346-5 ppf: 2139 ppct: 11 formats: fmt: @attributes: type: P size: 356KB tig: atl: Starting from the scenario Euclid-Bolyai-Einstein. aug: au: Marcus, Solomon su: Relativity (Physics) Axioms Metric geometry Affine geometry Computable functions Euclidean algorithm sug: subj: Relativity (Physics) Axioms Metric geometry Affine geometry Computable functions Euclidean algorithm keyword: Archimedes' axiom Bolyai-Lobachevsky's non-Euclidean geometries Einstein's relativity theory Euclid's fifth postulate Turing's computability ab: 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 non-Euclidean 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, non-contradiction 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 sensorial-empirical 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2015. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2015 holdings: @attributes: islocal: N |
|---|