Plato's mathematical “platonism”
DOI:
https://doi.org/10.31977/grirfi.v23i3.3411Keywords:
Mathematics Entities; Platonism; Intermediates; Divided line.Abstract
Several contemporary philosophers and mathematicians admit the existence of a branch of mathematical philosophy called “Platonism”, according to which mathematical entities - numbers, points, lines, planes, etc. - are things that exist in the world independently of us. In the specialized literature, it is common to understand that this philosophical thesis has its origins in Plato's theory of Forms. However, the statement that mathematical entities exist in themselves is not found in the philosophy of this Athenian philosopher, as observed in passage 509d and the following sections of his dialogue "The Republic." In reality, according to Plato's mathematical thinking, mathematical entities have an intermediate value, as we demonstrate in the following sections by "reconstructing" his reasoning of the “divided line”, based on excerpts from “The Republic”: (1) Book V: 477a-b, 477e, 478b, 478c, 478d; (2) Book VI: 509d-e, 510a, 510b, 510c-d, 510e, 511a, 511a-b, 511d, 511e; (3) Book VII: 533b-c, 534a.
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