Ontology and the Foundations of Mathematics
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Ontology and the Foundations of Mathematics by Penelope Rush
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.
'Ontology and the Foundations of Mathematics is extremely thought-provoking and will surely spur additional reading of the Element series… Rush's tenacity in pressing [ontological access problem] questions about the relevance of objecthood and independence is unique, unsettling, unrelenting, and effective.' Nicholas Danne, Metascience
Rush, Penelope: - Penelope Rush is Honorary Associate with the School of Philosophy and Online Lecturer for Student Learning at the University of Tasmania. She has published articles in journals including Logic and Logical Philosophy, Review of Symbolic Logic, South African Journal of Philosophy, Studia Philosophica Estonica, and Logique et Analyse. She is also the author of The Paradoxes of Mathematical, Logical, and Scientific Realism (forthcoming).
| SKU | Unavailable |
| ISBN 13 | 9781108716932 |
| ISBN 10 | 1108716938 |
| Title | Ontology and the Foundations of Mathematics |
| Author | Penelope Rush |
| Series | Elements In The Philosophy Of Mathematics |
| Condition | Unavailable |
| Binding type | Paperback |
| Publisher | Cambridge University Press |
| Year published | 2022-02-10 |
| Number of pages | 75 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |