HPhil Seminar: February 22, 2024

The talk is about Aristotle’s use of representations of magnitudes, motions and times. I am going to argue first that in those cases where Aristotle presents representations in order to show some interconnection or dependence between some features of different types of entities, this interconnection is not an explicit part of the representation. For instance, in order to establish that magnitude, change (or motion) and time are infinitely divisible Aristotle introduces representations of these entities. Then there are instructions to direct the reader to see the correspondence between their divisibility (or indivisibility). But this latter step does not introduce some specific way of representing the interconnection within the diagram itself. These representations only provide a frame within which such a correspondence can be pointed out as the argument unfolds.

After this I turn to the discussion of an immediately following passage in Physics VI.4, introducing two different kinds of divisibility of motions: the one according to time, and the other according to the parts of the moving entity. The claim about these two kinds of parts of motion is that just as all the temporal parts of a motion constitute the motion itself, in a similar manner, the parts of the motion according to the parts of the moving body constitute the overall motion of which they are parts. The argument for this latter claim is set out in terms of a lettered diagram, where moving body and its motion are represented by lines, allowing for the representation of their parts by the segments of the two lines. In this part of the talk I will concentrate on Alexander of Aphrodisias’ exposition of this argument (as reported on by Simplicius, in his Commentary on the Physics, 974, 25 – 29), that the division of motion according to the parts of the moving body should happen as it were according to breadth (platos), unlike the temporal division, which has to happen according to length (mêkos). I will argue that this means that for this case Alexander suggests a representation of motions in a two-dimensional chart. After this I will discuss whether and how the two different divisions of motion – the one according to time and the other according to the moving entity – can be integrated into a single frame of representation.

In closing I will contrast the representations discussed above to some different alternative types. These are (1) presenting items in grids of a map, (2) presenting correspondences in the form of charting functions in systems of coordinates of different types of entities, like time and distance covered, or time and velocity, and as a third option, (3) the representations of intensions of qualities and of motions, as in late medieval philosophy.

István Bodnár teaches ancient philosophy at the Department of Ancient and Medieval Philosophy of the  Eötvös University, Budapest, and the Department of Philosophy of the Central European University, Vienna. Educated in Budapest (PhD in 1992), he held various post-doctoral fellowships in the U.S. and Germany, and was a fellow at the Center for Advanced Study in the Behavioral Sciences (Stanford). He is editor-in-chief of Rhizomata: A journal for ancient philosophy and science (published by De Gruyter).