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Ontology and the Foundations of Mathematics: Talking Past Each Other: Elements in the Philosophy of Mathematics

Autor Penelope Rush
en Limba Engleză Paperback – 9 feb 2022
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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Specificații

ISBN-13: 9781108716932
ISBN-10: 1108716938
Pagini: 75
Dimensiuni: 150 x 229 x 4 mm
Greutate: 0.09 kg
Ediția:Nouă
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Elements in the Philosophy of Mathematics

Locul publicării:Cambridge, United Kingdom

Cuprins

1. What are we Talking about?; 2. Inter-translatability; 3. Two Access Problems; 4. Independence; 5. Justification.

Descriere

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