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Ontology and the Foundations of Mathematics

Penelope Rush
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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. 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.
      Format: CONTRIBUTORS: Penelope Rush EAN: 9781108716932 COUNTRY: United Kingdom PAGES: WEIGHT: 90 g HEIGHT: 229 cm
      PUBLISHED BY: Cambridge University Press DATE PUBLISHED: 2022-02-10 CITY: GENRE: SCIENCE / Philosophy & Social Aspects WIDTH: 150 cm SPINE:

      Book Themes:

      Philosophy of mathematics, Philosophy 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. 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.
      Format: CONTRIBUTORS: Penelope Rush EAN: 9781108716932 COUNTRY: United Kingdom PAGES: WEIGHT: 90 g HEIGHT: 229 cm
      PUBLISHED BY: Cambridge University Press DATE PUBLISHED: 2022-02-10 CITY: GENRE: SCIENCE / Philosophy & Social Aspects WIDTH: 150 cm SPINE:

      Book Themes:

      Philosophy of mathematics, Philosophy of science

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