n Acta Academica - Defining mathematics

Volume 43, Issue 4
  • ISSN : 0587-2405


Any definition of mathematics falls outside its field of investigation. When mathematics is set theory, the history of mathematics prior to the investing of set theory is eliminated. Arguing that the aspects of number and space delimit mathematics makes it possible to avoid both Platonism and constructivism in mathematics. Every philosophy of mathematics should be able to account for the nature and status of the infinite. That set theory is a spatially deepened theory of numbers cannot be accounted for by what Lakoff and Núñez call the Basic Metaphor of Infinity. Gödel's 1931 results point to an immediate, evident, intuitive insight.

Enige definisie van wiskunde beweeg buite die veld van ondersoek daarvan. As wiskunde versamelingsleer is, word the geskiedenis van die wiskunde voor die koms van versamelingsleer geëlimineer. Die argument dat die aspekte van getal en ruimte die wiskunde begrens, omseil beide die Platonisme en konstruktivisme. Elke filosofie van die wiskunde moet in staat wees om 'n verantwoording te gee van die aard en status van die oneindige. Dat die versamelingsteorie 'n ruimtelik-verdiepte teorie van getalle is, kan nie verantwoord word met behulp van wat Lakoff en Núñez aandui as "the Basic Metaphor of Infinity" nie. Gödel se 1931 resulate verwys na 'n onmiddellik-evidente insig.

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