1887

n Acta Academica - Philosophical reflections on continuity

Volume 34, Issue 3
  • ISSN : 0587-2405

Abstract

Against the background of concept formation, limits of definition and the unavoidability of indefinable primitive terms, this study investigates the uniqueness of continuity. Considerations from the history of philosophy and mathematics are taken into account and treated within the context of the "coherence of irreducibles". The meaning of continuity is shown to be intimately connected with that of infinity. This connection requires a reconsideration of both the notion of infinity and the interconnections between number and space. This background provides the basis for an alternative appreciation of the relationship between Aristotle on the one hand and the Cantor-Dedekind (set-theoretical) approach to continuity on the other. In conclusion, the abuse of the notion of continuity in the supposed arithmetisation of mathematics is challenged, mainly in terms of a new analysis of the meaning of the actual infinite, preferably designated as the at once infinite (as distinct from the potential infinite or the successive infinite).

Teen die agtergrond van bestaande insigte in begripsvorming, in die grense van begrip en definisie en in die onvermydelikheid van primitiewe terme, word ondersoek ingestel na die uniekheid van kontinuïteit. Oorwegings uit die geskiedenis van die filosofie en van die wiskunde word behandel binne die konteks van die samehang van dit wat uniek is. Dit blyk dat die menslike sin van kontinuïteit ten nouste verbonde is aan sy belewing van die aard van oneindigheid. Hierdie verband benodig 'n heroorweging van beide die aard van oneindigheid en die samehang tussen getal en ruimte. Hierdie agtergrond vorm vervolgens die basis van 'n alternatiewe waardering van die verhouding tussen, enersyds, Aristoteles en, andersyds, Cantor-Dedekind se (versamelingsteoretiese) benadering tot kontinuïteit. Ten slotte word die misbruik van die kontinuïteitsnosie in die vermeende aritmetisering van die wiskunde bevraagteken, hoofsaaklik in terme van 'n nuwe analise van die sin van die aktueel-oneindige, wat verkieslik aangedui word as die opeens-oneindige (onderskeie van die potensieeloneindige of die suksessief-oneindige).

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/content/academ/34/3/EJC15250
2002-12-01
2019-11-15

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