The intermediate character of mathematics and the ontological structure of its elements by Plato and Aristotle
n 19 (January, 2017) • Archai: As Origens do Pensamento Ocidental
Autor: Gilfranco Lucena dos Santos
Abstract:
This article examines the ontological structure of mathematical “objects”, focusing on the opposing views of books VI-VII of Plato’s Republic and books XIII-XIV of Aristotle’s Metaphysics. Plato understands Mathematics as a means or a path (method) of obtaining a philosophical education, and considers the “subject” of Mathematics as ????????, rather than ?????? (separate entities). In agreement with Plato, Aristotle seeks to describe the ontological structure of mathematical “objects” not as ??????, but as quantity, quality or relation; which is to say, as the separable elemental properties (?????????) of entities. I will argue that while neither Plato nor Aristotle understood the objects of Mathematics as separated entities, Aristotle’s description is more effective by virtue of its consideration of an “object’s” separable elemental properties as the “subject” of mathematics.
DOI: https://doi.org/10.14195/1984-249X_19_5
Texto Completo: http://periodicos.unb.br/index.php/archai/article/view/5765/5219
Palavras-Chave: Plato,Aristotle,Mathematics
Archai: As Origens do Pensamento Ocidental
Archai: Journal on the origins of Ancient Thought is published three times a year by Archai UNESCO Chair (University of Brasilia, Brazil).
It is published in Brazil (University of Brasília/Annablume) and in Portugal (Coimbra University Press, IUC), both printed and electronic free online access.
All manuscripts will undergo blind-review by peers.
Archai Journal is committed to a speedy and author-friendly review process; Authors can expect to receive notification the editorial decision within four months.
It is indexed by Web of Science - ESCI (Emerging Sources Citation Index), SciELO, European Reference Index for the Humanities and Social Sciences (ERIH Plus), L’Année Philologique, Philosopher‘s Index, DOAJ, Phil Brasil, Latindex, Cengage Learning, Google Schoolar, BASE, Diadorim, PKP Index and Portal de Periódicos da CAPES. It has Impact Factor 5.171 in the Scientific Journal Impact Factor and it got the second best grade (A2) of its field (Philosophy) in the latest Qualis CAPES evaluation.