Thesis ID: CBB001560636

Unthinkable: Mathematics and the Rise of the West (2011)

unapi

Welsh, Whitney Elizabeth (Author)


Duke University


Publication Date: 2011
Physical Details: 124 pp.
Language: English

This dissertation explores the ideational underpinnings of the rise of the west through a comparison of ancient Greek geometry, medieval Arabic algebra, and early modern European calculus. Blending insights from Thomas Kuhn, Michel Foucault, and William H. Sewell, I assert that there is an underlying logic, however clouded, to the unfolding of a given civilization, governed by a cultural episteme that delineates the boundaries of rational thought and the accepted domain of human endeavor. Amid a certain conceptual configuration, the rise of the west happens; under other circumstances, it does not. Mathematics, as an explicit exhibition of logic premised on culturally determined axioms, presents an outward manifestation of the lens through which a civilization surveys the world, and as such offers a window on the fundamental assumptions from which a civilization's trajectory proceeds. To identify the epistemological conditions favorable to the rise of the west, I focus specifically on three mathematical divergences that were integral to the development of calculus, namely analytic geometry, trigonometry, and the fundamental theorem of calculus. Through a comparative/historical analysis of original source documents in mathematics, I demonstrate that the logic in the earlier cases is fundamentally different from that of calculus, and furthermore, incompatible with the key developments that constitute the rise of the west. I then examine the conceptual similarities between calculus and several features of the rise of the west to articulate a description of the early modern episteme.

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Description “Explores the ideational underpinnings of the rise of the west through a comparison of ancient Greek geometry, medieval Arabic algebra, and early modern European calculus.” (from the abstract) Cited in ProQuest Diss. & Thes. : doc. no. 3453310.


Citation URI
https://data.isiscb.org/isis/citation/CBB001560636/

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Authors & Contributors
Zellini, Paolo
Massimi, Marina
De Risi, Vincenzo
Halák, Jan
Tournès, Dominique
Shnider, Steven
Concepts
Mathematics
Geometry
Western world, civilization and culture
Philosophy of mathematics
Philosophy
Science, general histories
Time Periods
Medieval
Ancient
Early modern
Modern
Renaissance
17th century
Places
Europe
China
Brazil
Greece
Mesopotamia
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