Abstract

UGAGLIA, Monica. Is Aristotle’s cosmos hyperbolic?. Educação e Filosofia [online]. 2016, vol.30, n.60, pp.547-573. ISSN 1982-596x.  https://doi.org/10.14393/REVEDFIL.issn.0102-6801.v30n60a2016-p547a573.

Aristotle’s refusal of the actual infinite, in any form, leads him to conceive a universe finite in magnitude, containing a finite multiplicity of things. His strict “immanentism” implies that not only physics but mathematics too must be done in this real universe, without concessions to imagination: in Aristotle’s mathematics there are no sets of actually infinite elements, nor lines of actually infinite length. Even worse, there are not even lines of finite length potentially infinitely extendible, no curves going to the infinite. This notwithstanding, Aristotle explicitly says that his restricted way of understanding the infinite is not a problem for mathematicians. Fortunately, he goes further than the mere statement explaining why mathematicians can do without infinite sets, infinite lines and infinitely extensible ones.

Keywords : Aristotle; Infinite; Philosophy of Mathematics.

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