Semi-Platonist Aristotelianism: Review of James Franklin, An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure [Book Review]

Australasian Journal of Philosophy 93 (4):837-837 (2015)
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Abstract

This rich book differs from much contemporary philosophy of mathematics in the author’s witty, down to earth style, and his extensive experience as a working mathematician. It accords with the field in focusing on whether mathematical entities are real. Franklin holds that recent discussion of this has oscillated between various forms of Platonism, and various forms of nominalism. He denies nominalism by holding that universals exist and denies Platonism by holding that they are concrete, not abstract - looking to Aristotle for inspiration.

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Philosophy, mathematics and structure.James Franklin - 1995 - Philosopher: revue pour tous 1 (2):31-38.
Aristotelianism in the Philosophy of Mathematics.James Franklin - 2011 - Studia Neoaristotelica 8 (1):3-15.
Proof in Mathematics: An Introduction.James Franklin - 1996 - Sydney, Australia: Quakers Hill Press.
Discrete and continuous: a fundamental dichotomy in mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
Philosophy of Mathematics.Christopher Pincock - 2011 - In J. Saatsi & S. French (eds.), Companion to the Philosophy of Science. Continuum. pp. 314-333.
Philosophy of Mathematics.Stewart Shapiro - 2003 - In Peter Clark & Katherine Hawley (eds.), Philosophy of Science Today. Oxford University Press UK.

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Cathy Legg
Deakin University

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