Orthodoxy has it that, for Aristotle, change is absolutely banned from geometry: eternal and necessary truths must be about eternal and unchangeable objects; Aristotle himself claims that geometrical objects result from abstracting from motion and matter.
In this talk, I will argue that orthodoxy cannot account for some essential features of Greek geometry. Looking at the actual practice of ancient geometry, it seems impossible to deny that it does appeal to change and motion, to some degree. I will discuss three levels of ‘dynamical involvement’ in geometry: they regard the drawing of diagrams, the definition of geometrical objects, and geometrical proofs.
Since change and motion do play a role in Greek geometry, every viable reconstruction of Aristotle’s theory should be able to account for this fact. This means that we have to revise the received view. Moreover, it follows that we can individuate a number of constraints or desiderata that any viable interpretation of Aristotle’s philosophy of geometry must meet; this can be used to adjudicate between rival models.
The first aim of this paper, therefore, is to spell out these constraints. The second aim is to suggest how we can interpret Aristotle’s claims that geometrical objects derive from abstraction from motion, and that they are separable in thought from motion in a way that makes them compatible with the three kinds of dynamical involvement of Greek geometry. I conclude by suggesting that these considerations support a fictionalist interpretation of Aristotle’s philosophy of geometry.
If you would like to join the speaker for dinner after the seminar, please email the chair by Tuesday before the workshop.
Workshop in Ancient Philosophy Convenors: Ursula Coope, Simon Shogry and Luca Castagnoli