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.

The philosophical positions of realism and anti-realism are difficult to distinguish, nowhere more so than in the philosophy of mathematics.
Reviews
'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



Book Information
ISBN 9781108716932
Author Penelope Rush
Format Paperback
Page Count 75
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 90g
Dimensions(mm) 229mm * 150mm * 4mm