Ontology and the Foundations of Mathematics : Talking Past Each Other
Book Details
Format
Paperback / Softback
Book Series
Elements in the Philosophy of Mathematics
ISBN-10
1108716938
ISBN-13
9781108716932
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Feb 10th, 2022
Print length
75 Pages
Weight
92 grams
Dimensions
15.10 x 22.80 x 0.80 cms
Product Classification:
Philosophy of mathematicsPhilosophy of science
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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.
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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