There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and (...) continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous. (shrink)

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Plato’s nephew Speusippus has been widely accepted as the historical person behind the mask of the anti-hedonists in Phlb. 42b–44c. This hypothesis is supported by, inter alia, the link between Socrates’ char- acterization of them as δυσχερεῖς and the frequent references of δυσχέρεια as ἀπορία to Speusippus in Aristotle’s Metaphysics MN. This study argues against assigning any privileged status to Speusippus in the assimilation of δυσχέρεια with ἀπορία. Instead, based on a comprehensive survey of how δυσχερ- words were used in (...) classical antiquity, the semantic shift of δυσχέρεια can be explained in an alternative way. (shrink)

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The Eleventh Aporia results from the breakup of the entire Greek philosophy previous to Aristotle in two manners of conceiving and proposing the first principles (archai), specially the One (to hen): (i) the manner by which Physiologoi conceived the One as a principle, namely, assuming an underlying nature, different from the One in itself, not adequately characterized by the simple fact of being one and which is denoted by the concept of One, and (ii) the manner inaugurated by the Pythagoreans (...) and later endorsed by Plato, marked by the abandonment of the appeal to an underlying nature and by conceiving the One in itself (auto to hen) as a principle, depriving it of any connection with some reality not strictly characterized by being one. Aristotle faces this aporia in Metaphysics Iota 2 and, according to the interpretation I propose: (a) refuses the Pythagorean-Platonic manner of conceiving and proposing principles, (b) endorses the course of action of the Physiologoi, and, in doing so, (c) steps back and retakes the “project” of the Physiologoi at the point where it was interrupted, namely, during the search for a principle of motion. From this scenario, I will try to show that the final outcome of the Eleventh Aporia can be the introduction of the Prime Mover as the properly Aristotelian (and cosmological) candidate to the title of One between the principles. (shrink)

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In the following pages, the reader will find a detailed study of what Aristotle considered the most difficult aporia formulated in Metaphysics III (Beta), which is answered in chapter 2 of Book X (Iota): the Eleventh Aporia. In such aporia, Aristotle rivals: (i) the conception assumed by the ancient Physiologoi, which takes the One to be an underlying nature whose being is not exhausted by being One, and (ii) the Platonic-Pythagorean view, which prefers to conceive the One in itself, according (...) to its own determinations and apart from any connection with some reality outside it. (shrink)

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