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Ontology and the Foundations of Mathematics: Talking Past Each Other (Elements in the Philosophy of Mathematics) (in English)
Penelope Rush
(Author)
·
Cambridge University Press
· Paperback
Ontology and the Foundations of Mathematics: Talking Past Each Other (Elements in the Philosophy of Mathematics) (in English) - Rush, Penelope
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Synopsis "Ontology and the Foundations of Mathematics: Talking Past Each Other (Elements in the Philosophy of Mathematics) (in English)"
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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The book is written in English.
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