David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
Philosophy of Science 50 (4):523-548 (1983)
The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Roman Frigg (2010). Models and Fiction. Synthese 172 (2):251-268.
Peter Godfrey-Smith (2009). Models and Fictions in Science. Philosophical Studies 143 (1):101 - 116.
Roman Frigg & Ioannis Votsis (2011). Everything You Always Wanted to Know About Structural Realism but Were Afraid to Ask. European Journal for Philosophy of Science 1 (2):227-276.
Chris Swoyer (1991). Structural Representation and Surrogative Reasoning. Synthese 87 (3):449 - 508.
Mark Balaguer (1996). A Fictionalist Account of the Indispensable Applications of Mathematics. Philosophical Studies 83 (3):291 - 314.
Similar books and articles
Stewart Shapiro (2004). Foundations of Mathematics: Metaphysics, Epistemology, Structure. Philosophical Quarterly 54 (214):16 - 37.
James Franklin (1989). Mathematical Necessity and Reality. Australasian Journal of Philosophy 67 (3):286 – 294.
Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics. Palgrave Macmillan
Carlo Cellucci (1996). Mathematical Logic: What has It Done for the Philosophy of Mathematics? In Piergiorgio Odifreddi (ed.), Kreiseliana. About and Around Georg Kreisel, pp. 365-388. A K Peters
O. Linnebo (2003). Stewart Shapiro. Philosophy of Mathematics: Structure and Ontology. Philosophia Mathematica 11 (1):92-103.
Christopher Pincock (2011). Philosophy of Mathematics. In J. Saatsi & S. French (eds.), Companion to the Philosophy of Science. Continuum 314-333.
John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. Oxford University Press.
Roman Murawski (2010). Philosophy of Mathematics in the Warsaw Mathematical School. Axiomathes 20 (2-3):279-293.
Michael D. Resnik (1997). Mathematics as a Science of Patterns. New York ;Oxford University Press.
Christian Hennig (2010). Mathematical Models and Reality: A Constructivist Perspective. [REVIEW] Foundations of Science 15 (1):29-48.
Added to index2009-01-28
Total downloads292 ( #8,299 of 1,935,135 )
Recent downloads (6 months)36 ( #15,133 of 1,935,135 )
How can I increase my downloads?