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International Studies in Phenomenology and Philosophy

Journal | Volume | Article

173818

The significance of a non-reductionist ontology for the discipline of mathematics

a historical and systematic analysis

D. F. M. Strauss

pp. 19-52

Abstract

A Christian approach to scholarship, directed by the central biblical motive of creation, fall and redemption and guided by the theoretical idea that God subjected all of creation to His Law-Word, delimiting and determining the cohering diversity we experience within reality, in principle safe-guards those in the grip of this ultimate commitment and theoretical orientation from absolutizing or deifying anything within creation. In this article my over-all approach is focused on the one-sided legacy of mathematics, starting with Pythagorean arithmeticism ("everything is number"), continuing with the geometrization of mathematics after the discovery of irrational numbers and once again, during the nineteenth century returning to an arithmeticistic position. The third option, never explored during the history of mathematics, guides our analysis: instead of reducing space to number or number to space it is argued that both the uniqueness of these two aspects and their mutual coherence ought to direct mathematics. The presence of different schools of thought is highlighted and then the argument proceeds by distinguishing numerical and spatial facts, while accounting for the strict correlation of operations on the law side of the numerical aspect and their correlated numerical subjects (numbers). Discussing the examples of 2 + 2 = 4 and the definition of a straight line as the shortest distance between two points provide the background for a brief sketch of the third alternative proposed (inter alia against the background of an assessment of infinity and continuity and the vicious circles present in contemporary mathematical arithmeticistic claims).

Publication details

Published in:

Clouser Roy (2010) Philosophy and science in the thought of Herman Dooyeweerd. Axiomathes 20 (1).

Pages: 19-52

Full citation:

Strauss D F M (2010) „The significance of a non-reductionist ontology for the discipline of mathematics: a historical and systematic analysis“. Axiomathes 20 (1), 19–52.