Sets and Functions in Theoretical Physics.
It is easy to show that in many natural axiomatic formulations of physical and even mathematical theories, there are many superfluous concepts usually assumed as primitive. This happens mainly when these theories are formulated in the language of standard set theories, such as Zermelo-Fraenkel's. In...
| Publicado en: | Erkenntnis Vol. 79; no. 2; pp. 257 - 282 |
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| Autores principales: | , |
| Formato: | Artículo |
| Publicado: |
Springer Nature
Apr2014
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=95515106&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 95515106 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 01650106 5KZ jtl: Erkenntnis issn: 01650106 maglogo: N pubinfo: dt: Apr2014 vid: 79 iid: 2 pid: 237 pub: Springer Nature artinfo: ui: 95515106 10.1007/s10670-013-9491-y ppf: 257 ppct: 25 formats: fmt: @attributes: type: P size: 399KB tig: atl: Sets and Functions in Theoretical Physics. aug: au: Sant'Anna, Adonai Bueno, Otávio affil: Department of Mathematics, Federal University of Paraná, Curitiba 81531-990 Brazil Department of Philosophy, University of Miami, Coral Gables 33124-4670 USA su: Physics Set theory Mathematical functions Von Neumann, John, 1903-1957 Group theory Mathematics sug: subj: Physics Set theory Mathematical functions Von Neumann, John, 1903-1957 Group theory Mathematics ab: It is easy to show that in many natural axiomatic formulations of physical and even mathematical theories, there are many superfluous concepts usually assumed as primitive. This happens mainly when these theories are formulated in the language of standard set theories, such as Zermelo-Fraenkel's. In 1925, John von Neumann created a set theory where sets are definable by means of functions. We provide a reformulation of von Neumann's set theory and show that it can be used to formulate physical and mathematical theories with a lower number of primitive concepts very naturally. Our basic proposal is to offer a new kind of set-theoretic language that offers advantages with respect to the standard approaches, since it doesn't introduce dispensable primitive concepts. We show how the proposal works by considering significant physical theories, such as non-relativistic classical particle mechanics and classical field theories, as well as a well-known mathematical theory, namely, group theory. This is a first step of a research program we intend to pursue. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Erkenntnis is a copyright of Springer, 2014. All Rights Reserved. item: Erkenntnis holder: Springer Nature dt: @attributes: year: 2014 holdings: @attributes: islocal: N |
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