This paper re-constructs Plato's ‘philosophy of geometry’ by arguing that he uses a geometrical method of hypothesis in his account of the cosmos’ generation in the Timaeus. Commentators on Plato's philosophy of mathematics often start from Aristotle's report in the Metaphysics that Plato admitted the existence of mathematical objects in-between ( metaxu) Forms and sensible particulars ( Meta. 1.6, 987b14–18). I argue, however, that Plato's interest in mathematics was centred on its methodological usefulness for philosophical inquiry, rather than on questions (...) of mathematical ontology. My key passage of interest is Timaeus’ account of the generation of the primary bodies in the cosmos, i.e. fire, air, water and earth ( Tim. 48b–c, 53b–56c). Timaeus explains the primary bodies’ origin by hypothesising two right-angled triangles as their starting-point ( arkhê) and describing their individual geometrical constitution. This hypothetical operation recalls the hypothetical method which Socrates introduces in the Meno (86e–87b), as well as the use of hypotheses by mathematicians which is described in the Republic (510b–c). Throughout the passage, Timaeus is focussed on explicating the bodies in terms of their formal structure, without however considering the ontological status of the triangles in relation to the physical world. (shrink)

In a 1985 article entitled “The Art of Glaukos,” Diskin Clay suggested that the enigmatic passage at the beginning of the geological myth in Phaedoreferred toRepublic10, where the soul is likened to the sea-creature Glaucus whose true nature, like the soul’s, is obscured by the distortions imposed by underwater life. Starting with a defense of Clay’s ingenious suggestion, my purpose is to compare Phaedoto Glaucus, with its true nature obscured by traditional assumptions about the order in which Plato composed his (...) dialogues, and thus how they should be read. At least part of the reason that Clay’s thesis has not been embraced is because it clashes with the dogma that Phaedocannot refer back to Republic; I want to challenge that dogma. Borrowing from Catherine Zuckert the notion that, since Phaedocomes at the end of Socrates’ story, it can usefully be read as the culmination of the Platonic dialogues, I will show how a “late” Phaedo—i.e., a reading of the dialogue that is open to the possibility that it refers to more than one dialogue generally considered to be later than it with respect to composition—recovers its true nature, presently encrusted with the oysters and seaweed of an outdated developmentalism that has obscured this culminating masterpiece of Plato’s dramatic and philosophical art. (shrink)

: Metaphysics B considers two sets of views that hypostatize mathematicals. Aristotle discusses the first in his B.2 treatment of aporia 5, and the second in his B.5 treatment of aporia 12. The former has attracted considerable attention; the latter has not. I show that aporia 12 is more significant than the literature suggests, and specifically that it is directly addressed in M.2 – an indication of its importance. There is an immediate problem: Aristotle spends most of M.2 refuting the (...) view that mathematicals are separate; but the B.5 mathematicals are inherent. I argue that the B.5 inherence is compatible with the M.2 separateness, and further, that aporia 12 is more than just a puzzle about the hypostatization of mathematicals. It is also a puzzle about the ontological status of mathematicals relative to sensibles. (shrink)