{"id":{"repo_id":"ohiolink","oai_identifier":"oai:etd.ohiolink.edu:ohiou1365705311"},"canonical_url":"https://search.dev.ndltd.org/etd/ohiolink/oai:etd.ohiolink.edu:ohiou1365705311","repository":{"repo_id":"ohiolink","name":"OhioLINK","base_url":"https://etd.ohiolink.edu/acprod/odb_etd/ws/oai/oai"},"display":{"title":"Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Houchens, Jesse P."],"institution":"Ohio University","degree_name":"Master of Arts (MA)","degree_level":"masters","degree_discipline":"Philosophy (Arts and Sciences)","degree_department":null,"school":null,"contributors":["Ehrlich, Philip"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-06-13","date_published":"2013-06-13","updated_at":"2026-07-24T03:37:31Z","subjects":["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"],"languages":["English"],"rights":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. 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Bell’s 5 mathematico-philosophical contentions and Bell’s historical contention."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf","p.84","580. KB"]},{"key":"dc:title","label":"Title","values":["Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis"]}]}],"canonical_facts":{"dc:contributor":["Ehrlich, Philip"],"dc:creator":["Houchens, Jesse P."],"dc:date":["2013-06-13"],"dc:description":["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. 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Keisler","smooth infinitesimal analysis","synthetic differential geometry","philosophy of mathematics","mathematical philosophy","analysis","intuitionistic"],"dc:title":["Alternatives to the Calculus: Nonstandard Analysis and Smooth Infinitesimal Analysis"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Philosophy (Arts and Sciences)"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Arts (MA)"],"thesis:institution_name":["Ohio University"]},"updated_at":"2026-07-24T03:37:31Z"}