Ex hypothéseōs: the method of the geometer in Plato’s Republic
O MÉTODO DOS GEÔMETRAS NA REPÚBLICA DE PLATÃO
DOI:
https://doi.org/10.13102/ideac.v1i51.11549Abstract
There has been speculation since Antiquity whether Plato had made some original contribution to geometry or whether the reports of Eudemus (via Proclus), Diogenes Laertius, Philodemus and Simplicius were exaggerated. Given what is known today about Greek geometry in the IVth century b.C., it would be a mistake to see in Plato anything more than someone well educated by the standards of the time. Despite this, this article seeks to show how Plato may have been decisive in the analysis and dissemination of geometric knowledge. Plato refers to the method of the geometers in the Meno (86d), the Phaedo (100a), and the Republic (510). The passage in the Republic will be considered the most important due to the comparison between the methods of geometry and dialectics.Concerning the hypothetical method mentioned in the Republic, contrary to what a first reading might suggest, there is no guarantee that Plato was thinking about first principles in the style of Euclid, even less that his hypotheses were propositions. Greek mathematical practice shows that it was most common to include only definitions. It is also discussed whether dialectics could be thought of as a type of foundation for mathematics or even an anticipation of the axiomatic method.
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