Mathematical, Philosophical and Semantic Considerations on Infinity (I): General Concepts
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http://hdl.handle.net/10045/60134
Title: | Mathematical, Philosophical and Semantic Considerations on Infinity (I): General Concepts |
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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 - SYC - Artículos de Revistas INV - Acústica Aplicada - Artículos de Revistas |
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2016_Uso_etal_FoundSci_final.pdf | Versión final (acceso restringido) | 302,04 kB | Adobe PDF | Open Request a copy |
2016_Uso_etal_FoundSci_rev.pdf | Versión revisada (acceso abierto) | 774,29 kB | Adobe PDF | Open Preview |
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