Creativity, Freedom, and Authority: A New Perspective On the Metaphysics of Mathematics

Australasian Journal of Philosophy 87 (4):589-608 (2009)
Abstract
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)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,493
External links
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
John P. Burgess (2004). Mathematics and Bleak House. Philosophia Mathematica 12 (1):18-36.
Julian C. Cole (2008). Mathematical Domains: Social Constructs? In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematics Association of America. 109--128.

View all 12 references

Citations of this work BETA
Similar books and articles
Analytics

Monthly downloads

Added to index

2010-08-10

Total downloads

16 ( #104,831 of 1,102,514 )

Recent downloads (6 months)

2 ( #184,259 of 1,102,514 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.