Abstract
Much of the unpleasantness in traditional philosophy of mathematics – its neglect of applied mathematics, its fixation on sets, numbers and logic rather than complex structures, its concern with infinities before small finite structures, its epistemological impasse over how to know about ‘abstract’ objects – comes from its oscillation between Platonism and nominalism, as if those were the only alternatives. So it is desirable to begin with a brief introduction to the Aristotelian option in metaphysics. The chapter is conceived as a ‘tutorial’ introduction, which outlines Aristotelian realism about properties and an overview of the main reasons for believing it. While Aristotelian realism has been a neglected option in the philosophy of mathematics,1 it is well known in general metaphysics, so the ground can be covered in summary, leaving the extensive debates for and against Aristotelianism, Platonism and nominalism to the references in the notes.
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Notes and Bibliography
D.M. Armstrong, A World of States of Affairs (Cambridge University Press, Cambridge, 1997).
D.M. Armstrong, Universals: An Opinionated Introduction (Westview Press, Boulder, CO, 1989).
D.M. Armstrong, Universals and Scientific Realism (Cambridge University Press, Cambridge, 1978), 66–68.
J.R. Brown, Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures (2nd edn, Routledge, New York, 2008).
J.R. Weinberg, Abstraction, Relation, Induction (University of Wisconsin Press, Madison, 1965).
B. Russell, Mysticism and Logic (Allen & Unwin, London, 1917), 75.
B. Russell, Introduction to Mathematical Philosophy (Allen & Unwin, London, 1919).
J. Bigelow and R. Pargetter, Science and Necessity (Cambridge University Press, Cambridge, 1990), 82–92.
D. Lewis, Parts of Classes (Blackwell, Oxford, 1991).
D.M. Armstrong, What is a Law of Nature? (Cambridge, Cambridge University Press, 1983).
N. Goodman, Fact, Fiction and Forecast (4th edn Harvard University Press, Cambridge, Mass., 1983), 40–41.
Details in D.M. Armstrong, Belief, Truth and Knowledge (Cambridge University Press, Cambridge, 1973).
J.Y. Lettvin, H.R. Maturana, W.S. McCulloch and W.H. Pitts, What the frog’s eye tells the frog’s brain, Proceedings of the Institute of Radio Engineers 47 (1959), 1950–1961.
M.A. Schmuckler, Visual-proprioceptive intermodal perception in infancy, Infant Behavior and Development 19 (1996), 221–232.
J.J. Gibson, The Senses Considered as Perceptual Systems (Houghton Mifflin, Boston, 1966).
R.L. Gregory, The Intelligent Eye (Weidenfeld & Nicolson, London, 1970).
P. Geach, Mental Acts: Their Content and Their Objects (Routledge & Kegan Paul, London, 1957), 18–44.
Introductory survey in P.C. Quinn and J. Oates, Early category representation and concepts, in J. Oates and A. Grayson, eds, Cognitive and Language Development in Children (Blackwell, Malden, MA, 2004), 21–60.
R.D. McKirahan, Principles and Proofs: Aristotle’s Theory of Demonstrative Knowledge (Princeton University Press, Princeton, NJ, 1992).
J. Maritain, Distinguish to Unite: Or, The Degrees of Knowledge (G. Bles, London, 1959).
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© 2014 James Franklin
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Franklin, J. (2014). The Aristotelian Realist Point of View. In: An Aristotelian Realist Philosophy of Mathematics. Palgrave Macmillan, London. https://doi.org/10.1057/9781137400734_2
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DOI: https://doi.org/10.1057/9781137400734_2
Publisher Name: Palgrave Macmillan, London
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