Article ID: CBB066890396

An Okapi Hypothesis: Non-Euclidean Geometry and the Professional Expert in American Mathematics (2022)

unapi

Open Court began publishing The Monist in 1890 as a journal “devoted to the philosophy of science” that regularly included mathematics. The audience was understood to be “cultured people who have not a technical mathematical training” but nevertheless “have a mathematical penchant.” With these constraints, the mathematical content varied from recreations to logical foundations, but everyone had something to say about non-Euclidean geometry, in debates that ranged from psychology to semantics. The focus in this essay is on the contested value of mathematical expertise in legitimating what should be considered as mathematics. While some mathematicians urged The Monist to uphold disciplinary standards of geometrical reasoning, authors opposed to non-Euclidean geometry aligned their reasoning with practical applications, universal know-how, and nonhierarchical democracy. As one contributor inquired, “How is the professional expert better fitted to see more lucidly in dealing with the elements of geometry than any other person of good geometric faculty?”

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Authors & Contributors
De Ceglia, Francesco Paolo
Colyvan, Mark
Gray, Jeremy
Shoji, Kota
Voelke, Jean-Daniel
Bachimont, Bruno
Journals
Studies in History and Philosophy of Science
Historia Scientiarum: International Journal of the History of Science Society of Japan
Transactions of the Charles S. Peirce Society
Synthese
Historia Mathematica
Foundations of Science
Publishers
Edizioni Giuseppe Laterza
Cambridge University Press
The MIT Press
Lang
Walter de Gruyter
Guaraldi
Concepts
Mathematics
Philosophy of mathematics
Controversies and disputes
Non-euclidean geometry
Geometry
Reasoning in science
People
Bolyai, Janos (Johann) von
Gauss, Carl Friedrich
Poincaré, Jules Henri
Quine, Willard Van Orman
Putnam, Hilary
Killing, Wilhelm Karl Joseph
Time Periods
19th century
17th century
20th century
20th century, early
18th century
Medieval
Places
Italy
Tuscany (Italy)
Europe
United States
France
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