Mathematical, Philosophical and Semantic Considerations on Infinity (I): General Concepts

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Title: Mathematical, Philosophical and Semantic Considerations on Infinity (I): General Concepts
Authors: Usó i Domènech, Josep Lluís | Nescolarde-Selva, Josué Antonio | Belmonte-Requena, Mónica
Research Group/s: Sistémica, Cibernética y Optimización (SCO) | Acústica Aplicada
Center, Department or Service: Universidad de Alicante. Departamento de Matemática Aplicada
Keywords: Actual infinity | Coincidentia oppositorum | Limit | Paradoxes | Succession | Potential infinity | Transfinite
Knowledge Area: Matemática Aplicada
Issue Date: Nov-2016
Publisher: Springer Science+Business Media Dordrecht
Citation: Foundations of Science. 2016, 21(4): 615-630. doi:10.1007/s10699-015-9428-9
Abstract: In the Reality we know, we cannot say if something is infinite whether we are doing Physics, Biology, Sociology or Economics. This means we have to be careful using this concept. Infinite structures do not exist in the physical world as far as we know. So what do mathematicians mean when they assert the existence of ω (the mathematical symbol for the set of all integers)? There is no universally accepted philosophy of mathematics but the most common belief is that mathematics touches on another worldly absolute truth. Many mathematicians believe that mathematics involves a special perception of an idealized world of absolute truth. This comes in part from the recognition that our knowledge of the physical world is imperfect and falls short of what we can apprehend with mathematical thinking. The objective of this paper is to present an epistemological rather than an historical vision of the mathematical concept of infinity that examines the dialectic between the actual and potential infinity.
URI: http://hdl.handle.net/10045/60134
ISSN: 1233-1821 (Print) | 1572-8471 (Online)
DOI: 10.1007/s10699-015-9428-9
Language: eng
Type: info:eu-repo/semantics/article
Rights: © Springer Science+Business Media Dordrecht 2015
Peer Review: si
Publisher version: http://dx.doi.org/10.1007/s10699-015-9428-9
Appears in Collections:INV - SCO - Artículos de Revistas
INV - Acústica Aplicada - Artículos de Revistas

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