Abstract
If Aristotelian realists are to establish that mathematics is the science of some properties of the world, they must explain which properties. That is particularly necessary since it is much less obvious what the answer is for mathematics than it is for sciences like physics, biology or sociology. It is clear enough what properties of things physics studies – properties such as mass and attraction (even if it is hard to say what they have in common that makes them physical). Likewise it is clear that biology studies the properties unique to living things. But when the properties of things studied by those special sciences have been listed, what properties are there left over for mathematics to be about? The answer is less than obvious.
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Notes and Bibliography
S. Shapiro, Thinking About Mathematics: The Philosophy of Mathematics (Oxford University Press, New York, 2000), 257–264.
S. Shapiro, Philosophy of Mathematics: Structure and Ontology (Oxford University Press, New York, 1997).
D. Dennett, Real patterns, Journal of Philosophy 88 (1991), 27–51.
H. Field, Science Without Numbers: A Defence of Nominalism (Princeton University Press, Princeton, NJ, 1980).
J. Bacon, K. Campbell and L. Reinhardt, eds, Ontology, Causality and Mind: Essays in Honour of D.M. Armstrong (Cambridge University Press, Cambridge, 1993).
M.R. Cohen and E. Nagel, An Introduction to Logic and Scientific Method, abridged edn, Routledge, London, 1939, 183–187.
D.M. Armstrong, Sketch for a Systematic Metaphysics (Oxford University Press, Oxford, 2010).
From P.M. Simons, Against the aggregate theory of number, Journal of Philosophy 79 (1982), 163–167.
J.P. Mayberry, The Foundations of Mathematics in the Theory of Sets (Cambridge University Press, Cambridge, 2000), 18.
P. Maddy, Naturalism in Mathematics (Oxford University Press, Oxford, 1997).
J. Franklin, The Science of Conjecture: Evidence and Probability before Pascal (Johns Hopkins University Press, Baltimore, MD, 2001).
D.M. Armstrong, Classes are states of affairs, Mind 100 (1991), 189–200.
P. Forrest, Sets as mereological tropes, Metaphysica 3 (1) (2002), 5–9.
P. Simons, Negatives, numbers and necessity: some worries about Armstrong’s version of truthmaking, Australasian Journal of Philosophy 83 (2005), 253–261.
B.C. Smith, On the Origin of Objects (MIT Press, Cambridge, Mass., 1996).
Maddy, Realism in Mathematics (Oxford University Press, Oxford, 1990), 88–96.
N. Goodman and W.V. Quine, Steps towards a constructive nominalism, in N. Goodman, Problems and Projects (Bobbs-Merrill, Indianapolis, 1972), 173–198.
C. Chihara, Constructibility and Mathematical Existence (Oxford University Press, Oxford, 1990), 201–202.
C.B. Crowley, Universal Mathematics in Aristotelian-Thomistic Philosophy (University Press of America, Washington, DC, 1980).
J. Franklin, Quantity and number, in D. Novotný, ed., Neo-Aristotelian Perspectives in Metaphysics (Routledge, London, 2014).
J. Franklin, Achievements and fallacies in Hume’s account of infinite divisibility, Hume Studies 20 (1994), 85–101.
B.S. Massey, Units, Dimensional Analysis and Physical Similarity (Van Nostrand Reinhold, London, 1971), 2.
B. Ellis, Basic Concepts of Measurement (Cambridge University Press, Cambridge, 1968).
B.A Davey and H.A. Priestley, Introduction to Lattices and Order (2nd edn, Cambridge University Press, Cambridge, 2002).
N. Cliff and J.A. Keats, Ordinal Measurement in the Behavioral Sciences (Erlbaum, Mahwah, NJ, 2003).
J. Forge, Quantities in quantum mechanics, International Studies in the Philosophy of Science, 14 (2000), 43–56.
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© 2014 James Franklin
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Franklin, J. (2014). Elementary Mathematics: The Science of Quantity. In: An Aristotelian Realist Philosophy of Mathematics. Palgrave Macmillan, London. https://doi.org/10.1057/9781137400734_4
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DOI: https://doi.org/10.1057/9781137400734_4
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