THE SYDNEY SCHOOL: MATHEMATICS, THE SCIENCE OF STRUCTURE
| AN ARISTOTELIAN REALIST PHILOSOPHY OF MATHEMATICS
We are a school of philosophers of mathematics centred in Sydney, Australia. Our line is realist (about structure and quantity), but Aristotelian rather than Platonist: we hold that mathematics studies real properties of things such as symmetry and continuity . . .
intro . . .
our manifesto . . .
a tutorial on Aristotelian realism. . .
review of other schools in philosophy of maths. . .
The Australian's Higher Ed Supplement article. . .
introductory talk on infinity ...
Philosopher's Zone interview 2010 ... 2014 ...
| || Explanation of diagram|
|James Franklin's book, An Aristotelian Realist Philosophy of Mathematics, appeared from Palgrave Macmillan in 2014.|
(Philosophia Mathematica's review: extract ... (full text) ... New Criterion's review)
J Franklin, Discrete and continuous: a fundamental dichotomy of mathematics, Journal of Humanistic Mathematics 7 (2017), 355-378.
J Franklin, Early modern mathematical principles and symmetry arguments, in The Idea of Principles in Early Modern Thought, ed. P. Anstey, Routledge, 2017, ch. 1.
C Legg and J Franklin, Perceiving necessity, Pacific Philosophical Quarterly 98 (2017), 320-343.
J Franklin, Logical probability and the strength of mathematical conjectures, Mathematical Intelligencer 38 (3) (Sept 2016), 14-19, ... full text.
J Franklin, Global and local, Mathematical Intelligencer 36 (4) (Dec 2014), 4-9 ... full text.
J Franklin, Quantity and number, in Neo-Aristotelian Perspectives in Metaphysics, ed. D.D. Novotny and L. Novak (Routledge, New York and London, 2014), 221-44.
James Franklin, The mathematical world, Aeon 7 Apr 2014.
- J Franklin, Non-deductive logic in mathematics: the probability of conjectures, in A. Aberdein and I. Dove, eds, The Argument of Mathematics (Springer, Dordrecht, 2013), 11-29.
- A Newstead and J Franklin, Indispensability without Platonism, in Properties, Powers and Structures, ed. A. Bird, B. Ellis and H. Sankey (Routledge, New York, 2012), 81-97.
- J Franklin, Aristotelianism in the philosophy of mathematics, Studia Neoaristotelica 8 (2011), 3-15.
(short but comprehensive statement of our view)
- A Newstead & J Franklin, The epistemology of geometry I: the problem of exactness, ASCS09: Proceedings of the 9th Conference of the Australasian Society for Cognitive Science, 2010, pp. 254-260.
- J Franklin, Aristotelian realism, chapter in The Philosophy of Mathematics, ed. A. Irvine (Handbook of the Philosophy of Science series, North-Holland Elsevier, 2009), 101-153.
(fullest statement of our view before the book listed above)
- P Forrest and D M Armstrong, The nature of number, Philosophical Studies 16 (1987), 165-186.
(classic paper explaining counting numbers as relations between universals and heaps)
- J Franklin, Mathematical Necessity and Reality, Australasian Journal of Philosophy, 67 (1989), 286-294
(argues that mathematical statements can be both necessary and about reality)
- J Franklin, The formal sciences discover the philosophers' stone, Studies in History and Philosophy of Science, 25 (1994), 513-33
(argues that the mathematical sciences like operations research and computer science have achieved the goal of necessary truths about real objects)
- A Newstead and J Franklin,
On the reality of the continuum Philosophy 83 (2008), 117-27.
(defends the reality of the continuum understood as an actual infinity)
- A Newstead
Review of Oppy's Philosophical Perspectives on Infinity Australasian J. of Philosophy 85 (2007), 679-82.
- A Irvine, Introduction to A. Irvine, ed, Physicalism in Mathematics (1990)
(survey of nominalism, realism and physicalism in mathematics)
- A Heathcote, Unbounded operators and the incompleteness of quantum mechanics, Philosophy of Science, (1990), 523-34
(a form of incompleteness in QM follows from the use of unbounded operators)
- A Heathcote, Quantum heterodoxy: realism at the Planck length, Science and Education, 12 (2003), 513-29
(it is possible to be realist about QM without adopting a hidden-variables interpretation)
- A G J Newstead, Aristotle and modern mathematical theories of the continuum, in Aristotle and Contemporary Science, ed. D. Sfendoni-Mentzou, Lang, New York, 2001, vol. 2
- C Cheyne & C R Pigden, Pythagorean powers Australasian Journal of Philosophy, 74 (1996), 639-45
(the indispensability argument for the existence of mathematical objects
requires them to have causal powers)
- L Lehrer Dive,
An Epistemic Structuralist Account of Mathematical Knowledge, PhD Thesis, University of Sydney, 2003.
- J Franklin, Non-deductive logic in mathematics, British J. for the Philosophy of Science 38 (1987), 1-18
(on the logical status of evidence for unproved conjectures in mathematics)
- An interview: Philosophy, mathematics and structure Philosopher 1 (2) (Winter, 1995), 31-38
- J Franklin, On the parallel between mathematics and morals, Philosophy 79 (2004), 97-119.
(defends the absolute objectivity of both mathematical and ethical truths; winner of the 2005 Eureka Prize for Research in Ethics)
- J Franklin, Last bastion of reason, New Criterion 18 (9) (May 2000), 74-8
(polemical review on Lakatos's philosophy of mathematics)
- A Heathcote, a forthcoming review/essay on complex numbers
- P Forrest, Sets as mereological tropes, Metaphysica 2 (2002), 5-10
- J Franklin & A Daoud, Proof in Mathematics: An Introduction
(textbook on proof from an Aristotelian perspective)
- J Franklin, Two caricatures II: Leibniz's best world, International Journal for Philosophy of Religion 52 (2002), 45-56
(defence of Leibniz's solution to the problem of evil in terms of mathematical restrictions on local and global structure)
- J Franklin, Chapter on 'Artifice and the natural world: Mathematics, logic, technology' in
Cambridge History of Eighteenth Century Philosophy
(full account of eighteenth century philosophy of mathematics and logic)
- J Franklin, Achievements and fallacies in Hume's account of infinite divisibility,
20 (1994), 85-101.
(Hume was right to say we can't prove space is infinitely divisible, but wrong
to claim it isn't)
- J Franklin, Corrupting the Youth: a history of philosophy in Australia
(contains a chapter on Australian philosophy of science and mathematics)
- J Franklin, Resurrecting logical probability, Erkenntnis 55 (2001), 277-305
(philosophy of probability considered as logic)
Philosophy of mathematics resources we recommend
- David Armstrong, Truth and Truthmakers
(a defence of Aristotelian realism in general, including applications to numbers and sets)
- John Bigelow, The Reality of Numbers
(an Australian book defending an Aristotelian realism about numbers)
John Baez's pages
(a must for anyone interested in the role of mathematics in physics)
- David Corfield's site
"The n-Category Cafe"
- Stanford Encyclopedia of Philosophy article on
indispensability arguments in mathematics
- Doron Zeilberger's
defence of finitism; Norman Wildberger's attack on infinities.
(all mathematics is finite: crazy but interesting)
- Philosophia Mathematica
(the journal of philosophy of mathematics)
- R W Hamming, The unreasonable effectiveness of mathematics
(a leading applied mathematician reflects on the applicability of mathematics)
- Dale Jacquette, Toward a Neoaristotelian inherence philosophy of mathematical entities, Studia Neoaristotelica 11 (2) (2014)
(another Aristotelian approach to the philosophy of mathematics)
- Donald Gillies, An Aristotelian approach to mathematical ontology, in Mathematics, Substance and Surmise, 2015.
- Bob Knapp, Mathematics is About the World (2014)
(book based on Ayn Rand's version of Aristotelianism)
- Vladislav Shaposhnikov, The applicability problem and a naturalistic perspective on mathematics (2014)
(article reflecting on prospects for an Aristotelian applied-mathematics-centred philosophy of mathematics)
- Wikipedia's list of philosophers of mathematics
- Institute for the Study of Nature, devoted to Aristotelian philosophy of science
- Macquarie University's Centre for Research in Mathematics and Science Education has a project on Pattern & structure in early mathematics learning
|For further information, contact
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