Abstract
The last three centuries have seen mathematics move well beyond its original subject-matter of quantity. It has discovered an entirely different subject-matter, structure or pattern. We survey the historical development with an eye to philosophically significant examples, then address the crucial philosophical question of characterizing precisely what ‘structure’ is.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes and Bibliography
M. Ascher, Ethnomathematics: A Multicultural View of Mathematical Ideas (Brooks/Cole, Pacific Grove, CA, 1991).
N. Biggs, E. Lloyd and R. Wilson ed., Graph Theory 1736–1936 (Oxford University Press, Oxford, 1976), 3–8.
H. Weyl, Symmetry (Princeton University Press, Princeton, NJ, 1952).
P. Benacerraf, What numbers could not be, Philosophical Review 74 (1965), 495–512.
S. Shapiro, Philosophy of Mathematics: Structure and Ontology (Oxford University Press, New York, 1997).
M.D. Resnik, Mathematics as a Science of Patterns (Oxford University Press, Oxford, 1997).
D. Dennett, Real patterns, Journal of Philosophy 88 (1991), 27–51.
H. Poincaré, Science and Hypothesis (Walter Scott, London, 1905), 20.
N. Bourbaki, The architecture of mathematics, American Mathematical Monthly 57 (1950), 221–232.
S. Mac Lane, Mathematics: Form and Function (Springer, New York, 1986).
G.H. Hardy, A Mathematician’s Apology (Cambridge University Press, Cambridge, 1940), 59–60.
M. Giaquinto, Visual Thinking in Mathematics (Oxford University Press, Oxford, 2007), 207–208.
D.M. Armstrong, A Theory of Universals: Universals and Scientific Reasoning, vol. II (Cambridge University Press, Cambridge, 1978), 69.
S. Haack, Deviant Logic, Fuzzy Logic: Beyond the formalism (University of Chicago Press, Chicago, 1996).
D. Lewis, Parts of Classes (Blackwell, Oxford, 1991).
G. Hellman, Mathematics Without Numbers: Towards a Modal-Structural Interpretation (Oxford University Press, Oxford, 1989), 48–49.
S. Willard, General Topology (Addison-Wesley, Reading, Mass, 1970), 23.
C.S. Peirce, On the logic of number, American Journal of Mathematics 4 (1881), 85–95.
A. Newstead and J. Franklin, On the reality of the continuum, Philosophy 83 (2008), 117–127.
S. Hegarty, Aristotle’s notion of quantity and modern mathematics, Philosophical Studies (Ireland) 18 (1969), 25–35.
Author information
Authors and Affiliations
Copyright information
© 2014 James Franklin
About this chapter
Cite this chapter
Franklin, J. (2014). Higher Mathematics: Science of the Purely Structural. In: An Aristotelian Realist Philosophy of Mathematics. Palgrave Macmillan, London. https://doi.org/10.1057/9781137400734_5
Download citation
DOI: https://doi.org/10.1057/9781137400734_5
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-48618-2
Online ISBN: 978-1-137-40073-4
eBook Packages: Palgrave Religion & Philosophy CollectionPhilosophy and Religion (R0)