Aristotle and his commentators often refer to representations of stretches of time, bodies, and their motion in their discussions about the divisibility or indivisibility of these magnitudes. These representations can focus on some issues – or otherwise put: raising different issues may require different means of representation. This talk presents a case study and is also an overview of the history of the interpretation of a somewhat curious passage in Aristotle.
The starting point Is a brief discussion of the key medium of these representations, lettered and unlettered diagrams, then we can turn to how Aristotle deploys his rather elementary lettered diagrams. The key considerations about these will be to stress that Aristotle’s argumentation requires that we detect correspondences across the different magnitudes that are represented in these diagrams. Nevertheless, these representations can only provide an external prop to the arguments, the key steps of the argument themselves do not receive a representation within these diagrams.
After presenting these constraints, I turn to the discussion of a baffling passage, where two of Aristotle’s foremost interpreters in antiquity – his student, Eudemus, and his most authoritative ancient commentator, Alexander of Aphrodisias – took alternative paths of interpretation. Eudemus for his part queried whether Aristotle’s claim can be made across the board about all possible types of changes. Accordingly, he does not link his proposal to the representation Aristotle uses in the passage. Contrary to this, Alexander tries to uphold the generality of Aristotle’s claim, suggesting that the labels in Aristotle’s diagram should refer to two-dimensional representations of motion. Such two-dimensional representations in principle do allow for a direct representation between these two dimensions themselves. In closing I will have to discuss to what extent Alexander’s diagrams can be compared to our representations of motions in a system of coordinates.