﻿ Plato's Sophist 81
81

§15 [117-119]

He arrived at this understanding of the continuum in connection with the theory of relativity in contemporary physics, for which, in opposition to the astronomical geometry that resulted from the impetus Newton gave to modem physics, the notion of field is normative. Physical Being is determined by the field. This course of development lets us hope that physicists might perhaps in time, with the help of philosophy, come to understand what Aristotle understood by motion, abandon the old prejudices, and no longer maintain that the Aristotelian concept of motion is primitive and that motion is to be defined simply by velocity, which is of course one characteristic of motion. Perhaps in time the Aristotelian concept of motion will be appreciated even more radically. I make this reference in order to indicate how much Aristotle, free of all precipitous theory, arrived at facts natural scientific geometry is striving for today, though from the opposite direction.

Aristotle displays, in his Categories, keen insight into the consequences of the conception of the continuum for the determination of number. The genuineness of this work has been controversial in the history of philosophy. I consider it to be authentic; no disciple could write like that. In chapter 6, Aristotle provides the fundamental differentiation of ποσόν.11

γγ) Consequences for the connecting of the manifold in geometry and arithmetic (Cat., 6).

Τοῦ δὲ ποσοῦ τὸ μέν ἐστι διωρισμένον, τὸ δὲ συνεχές· καὶ τὸ μὲν ἐκ θέσιν ἐχόντων πρὸς ἄλληλα τῶν ἐν αὐτοῖς μορίων συνέστηκε, τὸ δὲ οὐκ ἐξ ἐχόντων θέσιν. (4b20ff.). Quantity is different in the συνεχές, that which coheres in itself, and in the διωρισμένον, that which is in itself delimited against other things in such a way that each moment of the plurality is delimited against the others. The parts of the συνεχές relate to each other insofar as they are θέσιν ἔχοντα; what is posited in this θέσις is nothing else than the continuum itself. This basic phenomenon is the ontological condition for the possibility of something like extension, μέγεθος: site and orientation are such that from one point there can be a continuous progression to the others; only in this way is motion understandable. In the other way of possessing ποσόν, the διωρισμένον, the parts relate to one another such that they are οὐκ ἐξ ἐχόντων θέσιν μορίων (b22); ἔστι δὲ διωρισμένον μὲν οἷον ἀριθμὸς καὶ λόγος, συνεχὲς δὲ γραμμή, ἐπιφάνεια, σῶμα, ἔτι δὲ παρὰ ταῦτα χρόνος καὶ τόπος (ibid. ff.).

11. Heidegger's manuscript only contains references to the passages without any remarks on their interpretation. The editor offers the following interpretation (up to page 83) on the basis of the transcriptions of H. Jonas, F. Schalk, and H. Weiß.