AS ‘‘MATEMÁTICAS’’ ENQUANTO CIÊNCIA NO PENSAMENTO PLATÔNICO
DOI:
https://doi.org/10.13102/ideac.v1i53.12228Keywords:
Epistemologia. Filosofia da Matemática. Filosofia da Ciência. Demonstração. Metafísica.Abstract
We intend to explain how mathematics can be considered science in Platonic thought
based on the Athenian philosopher's intermediate dialogues (Meno, Phaedo, and Republic), where
the hypothetical method of mathematics takes a preeminent place in the Platonic discussion of what
is intended for philosophy as a rigorous science. Plato's reflection on the relationship between
mathematics and philosophy around the concept of science, which we find in its most complete
version in the Republic, leads us to the conclusion that mathematics is a logical-methodological
model for philosophy and the basis for what Plato understands as dialectic—a method that confers
scientificity on philosophy. Our conclusion may make it clear that, in addition to reflecting on
mathematics from the point of view of philosophy as a science, Plato talks about mathematics,
proposing that the mathematical method could be a rigorous science if its method were improved,
from which we will show that Plato's epistemic ideal for mathematics has an axiomatic character,
just as Euclid later did when he formalized Greek mathematics into a deductive system
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