David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Australasian Journal of Philosophy 87 (4):589-608 (2009)
I discuss a puzzle that shows there is a need to develop a new metaphysical interpretation of mathematical theories, because all well-known interpretations conflict with important aspects of mathematical activities. The new interpretation, I argue, must authenticate the ontological commitments of mathematical theories without curtailing mathematicians' freedom and authority to creatively introduce mathematical ontology during mathematical problem-solving. Further, I argue that these two constraints are best met by a metaphysical interpretation of mathematics that takes mathematical entities to be constitutively constructed by human activity in a manner similar to the constitutive construction of the US Supreme Court by certain legal and political activities. Finally, I outline some of the philosophical merits of metaphysical interpretations of mathematical theories of this type
|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
Stephen Yablo (2005). The Myth of Seven. In Mark Eli Kalderon (ed.), Fictionalism in Metaphysics. Clarendon Press 88--115.
Stewart Shapiro (1997). Philosophy of Mathematics: Structure and Ontology. Oxford University Press.
Hartry Field (1989). Realism, Mathematics & Modality. Basil Blackwell.
Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
Citations of this work BETA
Julian C. Cole (2010). Mathematical Structuralism Today. Philosophy Compass 5 (8):689-699.
Shay Allen Logan (2015). The Semantics of Social Constructivism. Synthese 192 (8):2577-2598.
Similar books and articles
Stewart Shapiro (2004). Foundations of Mathematics: Metaphysics, Epistemology, Structure. Philosophical Quarterly 54 (214):16 - 37.
Davide Rizza (2010). Mathematical Nominalism and Measurement. Philosophia Mathematica 18 (1):53-73.
Chris Pincock (2007). A Role for Mathematics in the Physical Sciences. Noûs 41 (2):253-275.
Mary Leng (2010). Mathematics and Reality. OUP Oxford.
Davide Rizza (2011). Magicicada, Mathematical Explanation and Mathematical Realism. Erkenntnis 74 (1):101-114.
Christian Hennig (2010). Mathematical Models and Reality: A Constructivist Perspective. [REVIEW] Foundations of Science 15 (1):29-48.
Susan Vineberg (1996). Confirmation and the Indispensability of Mathematics to Science. Philosophy of Science 63 (3):263.
Otavio Bueno (2005). Dirac and the Dispensability of Mathematics. Studies in History and Philosophy of Science Part B 36 (3):465-490.
Jean-Pierre Marquis (1999). Mathematical Engineering and Mathematical Change. International Studies in the Philosophy of Science 13 (3):245 – 259.
Added to index2010-08-10
Total downloads24 ( #160,403 of 1,907,383 )
Recent downloads (6 months)2 ( #343,301 of 1,907,383 )
How can I increase my downloads?