Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis

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.

Name thesis:degree_name

Master of Arts (MA)

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Philosophy (Arts and Sciences)

Grantor dc:publisher

Ohio University

Year dc:date

2013

Author dc:creator

• Houchens, Jesse P.

Contributors dc:contributor

• Ehrlich, Philip

• Philosophy
• Philosophy of Science
• Mathematics
• 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

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1365705311

OAI identifier oai:identifier

oai:etd.ohiolink.edu:ohiou1365705311