Abstract
What we are proposing in the following pages is an analysis of the structure of mathematics such as we have represented it in diagram (D). An essential organizational factor of the diagram is the opposition Discrete (on the left) — Continuous (on the right), which constitutes the horizontal axis X’X. The descendant vertical axis Y’Y describes, on the contrary, the nature of the generativity which is active in all of the mentioned theories. The form of a structure — i.e. an ensemble of operations capable of acting in a given space — is by definition tied to the algebraic properties of the structure. What essentially intervenes is the nature of the generativity of the operations, that is to say, the structure’s capacity to extend itself through the use of permitted operations, and in particular, through concatenation, alias the composition g o f of the two operations f and g (f being followed by g), when these are permitted.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Cherniss, H. F. [1949] Aristotle’s Criticism of Plato and the Academy, Baltimore: Johns Hopkins University Press.
Graham, D. W. [1987] Aristotle’s two Systems, Oxford: Clarendon Press Oxford, pp. 226–227.
Gromov, M. [1992] Asymptotic Invariants of Infinite Groups; reprint I.H.E.S., February, 1992.
Thom, R. S. [1988] Esquisse d’une Sémiophysique, Paris: Interéditions, 1988, [English translation: Addison Wesley, 1991].
Wigner, E. P. [1970] The unreasonable effectiveness of mathematics in the natural sciences, Symmetries and Reflections, Scientific Essays, Cambridge, MA: M.I.T. Press, chap. 4, 17, p. 222.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Thom, R. (1997). The Hylemorphic Schema in Mathematics. In: Agazzi, E., Darvas, G. (eds) Philosophy of Mathematics Today. Episteme, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5690-5_6
Download citation
DOI: https://doi.org/10.1007/978-94-011-5690-5_6
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6400-2
Online ISBN: 978-94-011-5690-5
eBook Packages: Springer Book Archive