Abstract
In his recent book, the noted mathematician Roger Penrose defends mathematical realism as an explanation for the growth of mathematics:
How ‘real’ are the objects of the mathematician’s world? From one point of view it seems that there can be nothing real about them at all. Mathematical objects are just concepts; they are the mental idealizations that mathematicians make, often stimulated by the appearance and seeming order of aspects of the world about us, but mental idealizations nevertheless. Can they be other than mere arbitrary constructions of the human mind? At the same time there often does appear to be some profound reality about these mathematical concepts, going quite beyond the mental deliberations of any particular mathematician. It is as though human thought is, instead, being guided towards some eternal external truth — a truth which has a reality of its own, and which is revealed only partially to us.
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References
Dyson, F. J. (1969). “Mathematics In The Physical Sciences.” The Mathematical Sciences. Ed. Committee on Support of Research in the Mathematical Sciences (COSRIMS) of the National Research Council. Cambridge: Massachusetts Institute of Technology Press. 97–115.
Feynman, Richard. (1967). The Character Of Physical Law. Cambridge: Massachusetts Institute of Technology Press.
Parsons, Charles. (1990). “The Structuralist View Of Mathematical Objects.” Synthèse. Volume 84: 303–46.
Resnik, Michael D. (1981). “Mathematics As A Science Of Patterns: Ontology And Reference.” Noûs. Volume 15: 529–50.
Steiner, Mark. (1990). “Mathematical Autonomy.” lyyun. Volume 39: 101–14.
Ulam, S. M. (1976). Adventures Of A Mathematician. New York: Charles Scribner’s Sons.
Waismann, Friedrich. (1982). Lectures On The Philosophy Of Mathematics. Wolfgang Grass. (Ed.). Amsterdam: Rodopi.
Wittgenstein, Ludwig. (1976). Wittgenstein’s Lectures On The Foundation Of Mathematics. Cora Diamond. (Ed.). Ithaca: Cornell University Press.
Wittgenstein, Ludwig. (1978). Remarks On The Foundations Of Mathematics. G. H. Von Wright, R. Rhees, and G. E. M. Anscombe. (Eds.). Cambridge: Massachusetts Institute of Technology Press.
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Steiner, M. (2000). Penrose and Platonism. In: Grosholz, E., Breger, H. (eds) The Growth of Mathematical Knowledge. Synthese Library, vol 289. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9558-2_10
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DOI: https://doi.org/10.1007/978-94-015-9558-2_10
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