Systematic perspectives on diverging mathematical orientations

D.F.M. Strauss
2005 Koers : Bulletin for Christian Scholarship  
It is recommendable to consider the distinction between the 'arithmetical' and 'geometrical' intuition not according to the moments of the spatial and temporal, but with a view to the difference between what is discrete and what is continuous. 2 Abstract Systematic perspectives on diverging mathematical orientations The popular view that mathematics is "objective" and "neutral" in the sense that it does not know different standpoints is contradicted by the factual state of modern mathematics.
more » ... dern mathematics. In the light of the dominant one-sided trends in the history of mathematics, fluctuating between arithmeticism and a geometrisation of this discipline, this article explores some provisional startingpoints for a different view. This third option is explored by investigating some features of an acknowledgement of the 1 I want to thank two mathematicians -Proff. B. de la Rosa and H. Bargendafor many valuable suggestions made during thorough-going discussions of the text of an earlier version of this article. 2 "Es empfiehlt sich, die Unterscheidung von 'arithmetischer' und 'geometrischer' Anschauung nicht nach den Momenten des Räumlichen und Zeitlichen, sondern im Hinblick auf den Unterschied des Diskreten und Kontinuierlichen vorzunehmen" (Bernays, 1976:81) . 632 Koers 70(4) 2005:631-659 Koers 70(4) 2005:631-659
doi:10.4102/koers.v70i4.286 fatcat:bqa7mgzltvf53pkowsvq2x4kmi