Ontology and the Foundations of Mathematics

Released on by Penelope Rush
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  • Ontology and the Foundations of Mathematics Book Detail

  • Author : Penelope Rush
  • Release Date : 2022-02-10
  • Publisher : Cambridge University Press
  • Genre : Science
  • Pages : 93
  • ISBN 13 : 1108626564
  • File Size : 48,48 MB
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Ontology and the Foundations of Mathematics by Penelope Rush PDF Summary

Book Description: 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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