Overview

This Element looks at the problem of inter-translation between mathematical realism and anti-realism and argues that so far as realism is inter-translatable with anti-realism, there is a burden on the realist to show how her posited reality differs from that of the anti-realist. It also argues that an effective defence of just such a difference needs a commitment to the independence of mathematical reality, which in turn involves a commitment to the ontological access problem – the problem of how knowable mathematical truths are identifiable with a reality independent of us as knowers. Specifically, if the only access problem acknowledged is the epistemological problem – i.e. the problem of how we come to know mathematical truths – then nothing is gained by the realist notion of an independent reality and in effect, nothing distinguishes realism from anti-realism in mathematics.

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9781108716932

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'Ontology and the Foundations of Mathematics is extremely thought-provoking and will surely spur additional reading of the Element series. … Rush's tenacity in pressing [ontological access problem] questions about the relevance of objecthood and independence is unique, unsettling, unrelenting, and effective.' Nicholas Danne, Metascience

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