Strict Constructivism and the Philosophy of Mathematics

Dissertation, Princeton University (2000)

The dissertation studies the mathematical strength of strict constructivism, a finitistic fragment of Bishop's constructivism, and explores its implications in the philosophy of mathematics. ;It consists of two chapters and four appendixes. Chapter 1 presents strict constructivism, shows that it is within the spirit of finitism, and explains how to represent sets, functions and elementary calculus in strict constructivism. Appendix A proves that the essentials of Bishop and Bridges' book Constructive Analysis can be developed within strict constructivism. Appendix B further develops, within strict constructivism, the essentials of the functional analysis applied in quantum mechanics, including the spectral theorem, Stone's theorem, and the self-adjointness of some common quantum mechanical operators. Some comparisons with other related work, in particular, a comparison with S. Simpson's partial realization of Hilbert's program, and a discussion of the relevance of M. B. Pour-El and J. I. Richards' negative results in recursive analysis are given in Appendix C. ;Chapter 2 explores the possible philosophical implications of these technical results. It first suggests a fictionalistic account for the ontology of pure mathematics. This leaves a puzzle about how truths about fictional mathematical entities are applicable to science. The chapter then explains that for those applications of mathematics that can be reduced to applications of strict constructivism, fictional entities can be eliminated in the applications and the puzzle of applicability can be resolved. Therefore, if strict constructivism were essentially sufficient for all scientific applications, the applicability of mathematics of mathematics in science would be accountable. The chapter then argues that the reduction of mathematics to strict constructivism also reduces the epistemological question about mathematics to that about elementary arithmetic. The dissertation ends with a suggestion that a proper epistemological basis for arithmetic is perhaps a mixture of Mill's empiricism and the Kantian views
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,928
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

No references found.

Add more references

Citations of this work BETA

On Naturalizing the Epistemology of Mathematics.Jeffrey W. Roland - 2009 - Pacific Philosophical Quarterly 90 (1):63-97.
Indispensability Argument and Anti-Realism in Philosophy of Mathematics.Feng Ye - 2007 - Frontiers of Philosophy in China 2 (4):614-628.
Indispensability Argument and Anti-Realism in Philosophy of Mathematics.Y. E. Feng - 2007 - Frontiers of Philosophy in China 2 (4):614-628.

Add more citations

Similar books and articles

A Defense of Strict Finitism.J. P. Bendegem - 2012 - Constructivist Foundations 7 (2):141-149.
Social Constructivism as a Philosophy of Mathematics.Paul Ernest - 1997 - State University of New York Press.
A Defense of Strict Finitism.J. P. Van Bendegem - 2012 - Constructivist Foundations 7 (2):141-149.
Philosophy of Mathematics Education.Andrew Davis - 1992 - Journal of Philosophy of Education 26 (1):121–126.
The Many Faces of Mathematical Constructivism.B. Van Kerkhove & J. P. Van Bendegem - 2012 - Constructivist Foundations 7 (2):97-103.
The Many Faces of Mathematical Constructivism.B. Kerkhove & J. P. Bendegem - 2012 - Constructivist Foundations 7 (2):97-103.
Strict Finitism and the Happy Sorites.Ofra Magidor - 2012 - Journal of Philosophical Logic 41 (2):471-491.
Varieties of Constructive Mathematics.D. S. Bridges - 1987 - Cambridge University Press.
Did Bishop Have a Philosophy of Mathematics?Helen Billinge - 2003 - Philosophia Mathematica 11 (2):176-194.
Mathematical Domains: Social Constructs?Julian C. Cole - 2008 - In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematics Association of America. pp. 109--128.


Added to PP index

Total views

Recent downloads (6 months)

How can I increase my downloads?

Monthly downloads

Sorry, there are not enough data points to plot this chart.

My notes

Sign in to use this feature