Ye, Feng (Author)

Princeton University

Benacerraf, Paul

Burgess, John P.

Publication date: 2000

Language: English

Publication Date: 2000

Edition Details: Advisor: Burgess, John P.; Benacerraf, Paul

Physical Details: 422 pp.

Edition Details: Advisor: Burgess, John P.; Benacerraf, Paul

Physical Details: 422 pp.

Outside Links

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.

...MoreDescription Cited in *Diss. Abstr. Int. A* 61 (2000): 223. UMI order no. 9957375.

Citation URI

This citation is part of the Isis database.

Article
Shabel, Lisa;
(2003)

Reflections on Kant's Concept (and Intuition) of Space
(/p/isis/citation/CBB000340870/)

Article
Pourciau, Bruce;
(2000)

Intuitionism as a (failed) Kuhnian revolution in mathematics
(/p/isis/citation/CBB000110940/)

Book
Atten, Mark Sebastiaan Paul Rogier van;
(2004)

On Brouwer
(/p/isis/citation/CBB000301970/)

Book
James Woodward;
(2021)

Causation with a Human Face: Normative Theory and Descriptive Psychology
(/p/isis/citation/CBB906408144/)

Book
Peter T. Struck;
(2018)

Divination and Human Nature: A Cognitive History of Intuition in Classical Antiquity
(/p/isis/citation/CBB366861486/)

Article
Liesbet De Kock;
(2016)

Helmholtz's Kant Revisited (once More). the All-Pervasive Nature of Helmholtz's Struggle with Kant's Anschauung
(/p/isis/citation/CBB062912986/)

Book
James R. Beebe;
Jennifer Nado;
(2016)

Advances in Experimental Philosophy and Philosophical Methodology
(/p/isis/citation/CBB212881271/)

Article
Hagop Sarkissian;
(2018)

Neo-Confucianism, Experimental Philosophy and the Trouble with Intuitive Methods
(/p/isis/citation/CBB499524958/)

Article
MacDougall, Margaret;
(2010)

Poincaréan Intuition Revisited: What Can We Learn from Kant and Parsons?
(/p/isis/citation/CBB001021665/)

Article
Mumford, David;
(2011)

Intuition and Rigor and Enriques's Quest
(/p/isis/citation/CBB001211748/)

Article
Tieszen, Richard;
(2002)

Gödel and the Intuition of Concepts
(/p/isis/citation/CBB000300364/)

Article
Gockel, Bettina;
(2008)

Paul Klee's Picture-Making and Persona: Tools for Making Invisible Realities Visible
(/p/isis/citation/CBB000931149/)

Article
Marga Vicedo;
(2023)

Epistemological discipline in animal behavior studies: Konrad Lorenz and Daniel Lehrman on intuition and empathy
(/p/isis/citation/CBB596910880/)

Article
Axel Gelfert;
(2014)

Observation, Inference, and Imagination: Elements of Edgar Allan Poe’s Philosophy of Science
(/p/isis/citation/CBB191773633/)

Article
Dion, Sonia Maria;
(2013)

Pierre Duhem and the Inconsistency between Instrumentalism and Natural Classification
(/p/isis/citation/CBB001211300/)

Article
Charles Braverman;
(2016)

Pourquoi classer les facultés de l’esprit ? André-Marie Ampère : de la science à la philosophie et vice versa
(/p/isis/citation/CBB035751076/)

Article
Kira Lussier;
(March 2018)

From the Intuitive Human to the Intuitive Computer
(/p/isis/citation/CBB266223107/)

Article
Harman, Oren Solomon;
(2007)

Powerful Intuitions: Re-reading Nature versus Nurture with Charles Darwin and Clifford Geertz
(/p/isis/citation/CBB000740748/)

Article
Bowler, Peter J.;
(2000)

Philosophy, Instinct, Intuition: What Motivates the Scientist in Search of a Theory?
(/p/isis/citation/CBB000110752/)

Article
Cassou-Noguès, Pierre;
(2006)

Signs, Figures and Time: Cavaillès on “Intuition” in Mathematics
(/p/isis/citation/CBB000933621/)

Be the first to comment!