The Continuum: History, Mathematics, and Philosophy

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dc.contributor.advisorZach, Richard
dc.contributor.authorHayashi, Teppei
dc.contributor.committeememberBauer, Kristine
dc.contributor.committeememberLinsky, Bernard
dc.contributor.committeememberMacIntosh, Jack
dc.contributor.committeememberMigotti, Mark
dc.date2018-02
dc.date.accessioned2018-01-19T00:58:17Z
dc.date.available2018-01-19T00:58:17Z
dc.date.issued2017-12-21
dc.description.abstractThe main aim of this dissertation is to depict a wide variety of the conceptions of the continuum by tracing the history of the continuum from the ancient Greece to the modern times, and in so doing, to find a new way to look at the continuum. In the first part, I trace the history of the continuum with a special emphasis on unorthodox views at each period. Basically, the history of the continuum is the history of the rivalry between two views, namely, between the punctiform and the non-punctiform views of the continuum. According to the punctiform view, the continuum is composed of indivisibles; on the other hand, according to the non-punctiform view, the continuum cannot be composed of indivisibles. In the second part, I present Richard Dedekind’s and Georg Cantor’s standard mathematical theories of the continuum as the modern representative of the punctiform view of the continuum, and then examine Charles Saunders Peirce’s non-punctiform view of the continuum. In the last chapter, I give some mathematical interpretations to Aristotle’s and Peirce’s theories of the continuum according to both of which the continuum cannot be composed of points. In interpreting Aristotle’s view, I use modern topology and show that Aristotle’s view can be nicely captured by topology. On the other hand, in interpreting Peirce’s view, I appeal to the theory of category and show that in the category-theoretic framework the continuum appears quite differently from the standard one conceived in the Dedekindian and Cantorian ways. In conclusion, I try to defend a sort of pluralistic view concerning the conceptions of the continuum.en_US
dc.identifier.citationHayashi, T. (2017) The Continuum: History, Mathematics, and Philosophy (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/5364
dc.identifier.urihttp://hdl.handle.net/1880/106283
dc.language.isoenen_US
dc.publisher.facultyArtsen_US
dc.publisher.institutionUniversity of Calgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en_US
dc.subjectphilosophyen_US
dc.subjectphilosophy of mathematicsen_US
dc.subjecthistory of mathematicsen_US
dc.subjectcontinuumen_US
dc.subjectcategory theoryen_US
dc.subject.classificationEducation--Mathematicsen_US
dc.subject.classificationPhilosophyen_US
dc.subject.classificationEconomics--Historyen_US
dc.titleThe Continuum: History, Mathematics, and Philosophyen_US
dc.typedoctoral thesisen_US
thesis.degree.disciplinePhilosophyen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameDoctor of Philosophy (PhD)en_US
ucalgary.item.requestcopytrue
ucalgary.thesis.checklistI confirm that I have submitted all of the required forms to Faculty of Graduate Studies.en_US
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