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Houchens, Jesse accepted thesis 04-11-13 Sp 13.pdf (580.01 KB)
ETD Abstract Container
Abstract Header
Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis
Author Info
Houchens, Jesse P.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1365705311
Abstract Details
Year and Degree
2013, Master of Arts (MA), Ohio University, Philosophy (Arts and Sciences).
Abstract
We attempt to clarify and evaluate what shall be called Mac Lane’s thesis—the thesis that nonstandard analysis (NSA) and smooth infinitesimal analysis (SIA) are alternatives to the standard approach to the calculus. In doing so, we outline the historical approaches to the calculus, the standard approach to the calculus, and two nonstandard approaches, namely NSA and SIA; we also attempt to clarify and evaluate a set of comparisons of NSA and SIA, namely John L. Bell’s 5 mathematico-philosophical contentions and Bell’s historical contention.
Committee
Philip Ehrlich, PhD (Advisor)
Stewart Shapiro, PhD (Committee Member)
Todd Eisworth, PhD (Committee Member)
Pages
84 p.
Subject Headings
Mathematics
;
Philosophy
;
Philosophy of Science
Keywords
Alternatives to the calculus
;
alternatives
;
calculus
;
nonstandard analysis
;
NSA
;
John L. Bell
;
J.H. Keisler
;
smooth infinitesimal analysis
;
synthetic differential geometry
;
philosophy of mathematics
;
mathematical philosophy
;
analysis
;
intuitionistic
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Citations
Houchens, J. P. (2013).
Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis
[Master's thesis, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1365705311
APA Style (7th edition)
Houchens, Jesse.
Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis.
2013. Ohio University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1365705311.
MLA Style (8th edition)
Houchens, Jesse. "Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis." Master's thesis, Ohio University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1365705311
Chicago Manual of Style (17th edition)
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Document number:
ohiou1365705311
Download Count:
3,471
Copyright Info
© 2013, all rights reserved.
This open access ETD is published by Ohio University and OhioLINK.