London and New York: Palgrave MacMillan (2014)
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Abstract |
An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge.
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Keywords | Philosophy of Mathematics Aristotelian realism Quantities |
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ISBN(s) | 9781137400734 1137400730 |
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Citations of this work BETA
Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
The Mereology of Structural Universals.Peter Forrest - 2016 - Logic and Logical Philosophy 25 (3):259-283.
Uninstantiated Properties and Semi-Platonist Aristotelianism.James Franklin - 2015 - Review of Metaphysics 69 (1):25-45.
Discrete and Continuous: A Fundamental Dichotomy in Mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
Geometrical Objects as Properties of Sensibles: Aristotle’s Philosophy of Geometry.Emily Katz - 2019 - Phronesis 64 (4):465-513.
View all 25 citations / Add more citations
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