Many people frown in disbelief when they hear that Plato assigns ten years of mathematical study to future philosopher kings of the ideal city (kallipolis) in the Republic. For Plato, this type of study is necessary to prepare souls for dialectic whose ultimate goal is to grasp the Form of the Good. How exactly the study of mathematics helps to accomplish this task is less clear. Burnyeat has argued against Annas that the purpose of mathematical study cannot be only instrumental in the grasping of the Form of the Good but must be constitutive. This makes good sense if we acknowledge that mathematics is valued for both its consequences as well as for its own sake. Burnyeat’s argument, however, hinges on the claim that the Form of the Good can be identified with unity as a mathematical concept. The weakness of this argument is that it picks out a mathematical sense of unity when there are others available that may be better a fit for the Form of the Good. Moreover, it shifts the discussion to the Form of Good away from features of mathematics. Considering that mathematics on its own cannot reach the Form of the Good, or any Form (at most images of Forms), but only prepares for dialectic which enables souls to grasp the Form of the Good, it is not clear that the Form of the Good must be mathematical. The explicitly mentioned feature that makes mathematics an ideal propaedeutic study for the Form of the Good is that it “makes the soul look upwards”. Studies that make the soul look upwards are (1) about what is and (2) what cannot be perceived by the senses. To illustrate this Plato introduces what is now often called summoners (Republic VII 523-527): Perception sometimes presents us with apparently opposing characteristics of an object. For us to make sense of this perception and its opposites the soul must summon intellect where perception cannot help. Plato starts with non-mathematical examples (big and small, smooth and hard) and then proceeds to claim that mathematical concepts likewise summon the intellect. I will discuss philosophical problems that occur in these arguments and investigate whether the summoner passage on its own can show whether mathematics is specifically well suited, or at all, to make the soul look upwards.
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The Seminar will take place in the Ryle Room. Colleagues and students who are unable to attend in person are welcome to join remotely, via Microsoft Teams, by clicking this link. You will be redirected to a page in which you will be prompted to sign in with your Oxford SSO.
Workshop in Ancient Philosophy Convenors: Ursula Coope, Simon Shogry and Luca Castagnoli