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| Program > Proof, Prediction and Mathematics in Ancient and Islamic Science |
| Programme > Preuve, prédiction et mathématiques dans les sciences antiques et islamiques |
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Alan C. Bowen
(IRCPS) The Exact Sciences in Fourth-Century Greece and their Interpretation in Aristotle's Posterior Analytics 1.13 |
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Usually one should segregate questions about the meaning of what ancient philosophers say regarding the exact sciences from historical questions about the truth of their claims. But this rule fails when the philosophical remarks are insufficient to allow a sure grasp of what was meant. Here, we must turn to what is known of the contemporary sciences to delimit possible interpretations. This is the case with Aristotle’s comments about mathematics and the sciences that use mathematics in Posterior Analytics 1.13. To understand him, we must determine what the exact sciences were like in his time, and then proceed tentatively on the charitable assumption that what he says is true. Accordingly, I will first argue that there are but three surviving sources of the exact sciences in Aristotle’s time: Aristoxenus’ Elements of Harmonia, his Elements of Rhythm, and Hipparchus’ quotations of Eudoxus’ Phaenomena. This will entail demonstrating that the common practice of including Euclid’s works among the scientific documents of the fourth century is based on a faulty appreciation of the evidence for his dates and of the signs in his treatises of later developments. Next, in light of these sources, I will propose that, when Aristotle says, for example, that optics is subordinate to geometry because it concerns the fact that something is the case and geometry gives the reason why, he means not that optics is applied geometry, but that optics often (but not always) draws on geometry to make its inferences, whereas geometry never draws on optics.
IRCPS
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