Palgrave MacMillan (2014)

James Franklin
University of New South Wales
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.
Keywords Philosophy of Mathematics  Aristotelian realism  Quantities
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ISBN(s) 9781137400734   1137400730
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References found in this work BETA

What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Real Patterns.Daniel C. Dennett - 1991 - Journal of Philosophy 88 (1):27-51.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Realism in Mathematics.Penelope MADDY - 1990 - Oxford University Prress.

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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.
The Epistemic Indispensability Argument.Cristian Soto - 2019 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 50 (1):145-161.

View all 20 citations / Add more citations

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