An Aristotelian realist philosophy of mathematics: Mathematics as the science of quantity and stucture

Palgrave MacMillan (2014)

Authors
James Franklin
University of New South Wales
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.
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

Real Patterns.Daniel C. Dennett - 1991 - Journal of Philosophy 88 (1):27-51.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford University Press.
Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - New York ;Oxford University Press.

View all 54 references / Add more references

Citations of this work BETA

Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
Animal Cognition, Species Invariantism, and Mathematical Realism.Helen De Cruz - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. London: Bloomsbury Academic. pp. 39-61.
Discrete and Continuous: A Fundamental Dichotomy in Mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
Aristoteles’in Matematik Felsefesi ve Matematik Soyut­lama.Murat Kelikli - 2017 - Beytulhikme An International Journal of Philosophy 7 (2):33-49.

View all 20 citations / Add more citations

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Reflections on Mathematics.Edward N. Zalta - 2007 - In V. F. Hendricks & Hannes Leitgeb (eds.), Philosophy of Mathematics: Five Questions. Automatic Press/VIP.
Mathematics. A Science of Patterns?Gianluigi Oliveri - 1997 - Synthese 112 (3):379-402.
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Realism in Mathematics.Penelope MADDY - 1990 - Oxford University Prress.
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