Mathematics, Philosophical and Semantic Considerations on Infinity (II): Dialectical Vision

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Title: Mathematics, Philosophical and Semantic Considerations on Infinity (II): Dialectical Vision
Authors: Usó i Domènech, Josep Lluís | Nescolarde-Selva, Josué Antonio | Belmonte-Requena, Mónica | Segura, Lorena
Research Group/s: Sistémica, Cibernética y Optimización (SCO) | Acústica Aplicada
Center, Department or Service: Universidad de Alicante. Departamento de Matemática Aplicada | Universidad de Alicante. Departamento de Matemáticas
Keywords: Actual infinite | Antinomy | Bipolarity | Limit | Paradoxes | Quality | Quantity | Succession | Potential infinite | Transfinite
Knowledge Area: Matemática Aplicada | Análisis Matemático
Issue Date: Sep-2017
Publisher: Springer Science+Business Media Dordrecht
Citation: Foundations of Science. 2017, 22(3): 655-674. doi:10.1007/s10699-016-9488-5
Abstract: Human language has the characteristic of being open and in some cases polysemic. The word “infinite” is used often in common speech and more frequently in literary language, but rarely with its precise meaning. In this way the concepts can be used in a vague way but an argument can still be structured so that the central idea is understood and is shared with to the partners. At the same time no precise definition is given to the concepts used and each partner makes his own reading of the text based on previous experience and cultural background. In a language dictionary the first meaning of “infinite” agrees with the etymology: what has no end. We apply the word infinite most often and incorrectly as a synonym for “very large” or something that we do not perceive its completion. In this context, the infinite mentioned in dictionaries refers to the idea or notion of the “immeasurably large” although this is open to what the individual’s means by “immeasurably great.” Based on this linguistic imprecision, the authors present a non Cantorian theory of the potential and actual infinite. For this we have introduced a new concept: the homogon that is the whole set that does not fall within the definition of sets established by Cantor.
Sponsor: The fourth author’s research was partially supported by Generalitat Valenciana under project GV/2015/035.
URI: http://hdl.handle.net/10045/69491
ISSN: 1233-1821 (Print) | 1572-8471 (Online)
DOI: 10.1007/s10699-016-9488-5
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Springer Science+Business Media Dordrecht 2016
Peer Review: si
Publisher version: http://dx.doi.org/10.1007/s10699-016-9488-5
Appears in Collections:INV - SCO - Artículos de Revistas

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