Aristotle on Geometrical Potentialities

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This paper examines Aristotle’s discussion of the priority of actuality to potentiality in geometry at Metaphysics Θ9, 1051a21–33. Many scholars have assumed what I call the ‘geometrical construction’ interpretation, according to which his point here concerns the relation between an inquirer’s thinking and a geometrical figure. In contrast, I will defend what I call the ‘geometrical analysis’ interpretation, according to which it concerns the asymmetrical relation between geometrical propositions in which one is proved by means of the other. His argument as so construed is ultimately based on the asymmetrical relation between the corresponding geometrical facts. Then I explore this ontological priority in geometry by drawing attention to the parallel passage Posterior Analytics II.11, 94a24–35, where Aristotle explains the relation between the same geometrical propositions in connection to material causation.
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