The Relationship between Hypotheses and Images in the Mathematical Subsection of the Divided Line of Plato's Republic

Bibliographic Data

ID9687258
AuthorsMoon-Heum Yang (0000-0003-4848-2304, Dongguk University, corresponding author)
Year2005
Volume44
Issue2
Pages285-312
Publication date2005-01-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueDialogue (JOURNAL)
Journal identifiersISSN: 0012-2173 • E-ISSN: 1759-0949
PublisherCambridge University Press (CUP) (PUBLISHER)
DOI10.1017/s0012217300006211
OpenAlexW2120208016
LanguageEN
Citations received3
References cited23

In explaining the relationship between hypotheses and images in the Line of Plato's Republic VI, I first focus on Plato's elucidation of the nature of mathematics as the mathematician himself understands it. I go on to criticize traditional interpretations of the relationship above based on the doubtful assumption that mathematics concerns Platonic Forms. To formulate my view of that relationship I exploit the notion of “structure.” I show how “hypotheses” as principles of proof can determine the structures of “images” by which the corresponding intelligible ones of mathematical objects become known

Epistemology · Exploit · Focus (optics) · Geometry · Line (geometry) · Physics · Reflexive pronoun · The Republic · Classical Philosophy and Thought · Computer Science · Historical Philosophy and Science · Mathematics · Philosophy · Philosophy, Science, and History

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