Arthur Holmes (1977)
Abstract
This paper raises the issue of whether in fact mathematics is not presuppositionless. It discusses three common theories of universals – realism, nominalism, and conceptualism and illustrates them with the perspectives of several thinkers. It also identifies three stakes Christians have in this matter. 1) Much recent nominalism rejects ontological questions as meaningless – Christians cannot do this. 2) Is the creation order due to universal archetypes in the mind of God or is it a sovereign choice by the creator? 3) Physicalist interpretations of things (such as locating mathematics in the structure of the human brain) seem a form of materialism that Christians necessarily reject. It suggests that Christian responses to these issues are not clear-cut.
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Wanted: Christian Perspectives in the Philosophy of Mathematics