Plato's Sophist [101-102]

Aristotle analyzes these things in Physics II, 2. The mathematical objects, e.g., στερεόν and γραμμή, can to be sure also be considered as φυσικά; the natural man sees a surface as πέρας, as the limit of a body. Versus this, the mathematician considers the mathematical objects purely in themselves, ἀλλ' οὐχ ᾗ φυσικοῦ σώματος πέρας ἕκαστον (193b32), i.e., "not insofar as these (e.g., a line or a surface) are the πέρας, limit (termination), of a natural body. " Aristotle's negative delineation of the mathematical here—namely, that it is not the πέρας of a φυσικόν σῶμα—means nothing other than that the mathematical is not being considered as a "location. " Insofar as the φυσικὰ ὄντα are κινούμενα, i.e., insofar as motility is a basic determination of their Being, the mathematical can be considered initially as appertaining to beings that move. The mathematical as such is removed from things characterized by motion. χωριστά γὰρ τῇ νοήσει κινήσεώς ἐστι (b34), the mathematical, e.g., a point, is "extracted from beings insofar as they move," i.e., insofar as they change, turn around, increase and decrease. And specifically the mathematical is χωριστά τῇ νοήσει, "discerned," extracted simply in a particular mode of consideration. Κίνησις itself, however, is initially and for the most part κίνησις κατὰ τόπον, change of location. τῆς κινήσεως ἡ κοινὴ μάλιστα καὶ κυριωτάτη κατὰ τόπον ἐστίν, ἣν καλοῦμεν φοράν (Phys. IV, 1, 208a31f.). The most general motion is local motion, which presents itself in the revolution of the heavens. The mathematician extracts something from the φυσικόν σῶμα, but οὐδὲν διαφέρει (Phys. II, 3, 193b34f.), "this makes no difference"; this extracting changes nothing of the objective content of that which remains as the theme of the mathematician. It does not turn into something else; the "what" of the πέρας is simply taken for itself, as it appears. It is simply taken as it presents itself in its content as limit. οὐδὲ γίγνεται ψεῦδος χωριζόντων (b35). "In extracting, the mathematician cannot be subject to any mistake," i.e., he does not take something which is actually not given to be what is showing itself. If the mathematician simply adheres to his special theme, he is never in danger that that will present itself to him as something other than it is. It is indeed here nothing other than what has been extracted. Beings are not distorted for the mathematician through χωρίζειν; on the contrary, he moves in a field in which something determinate may be disclosed. Thus with this χωρισμός everything is in order.

λανθάνουσι δὲ τοῦτο ποιοῦντες καὶ οἱ τὰς ἰδέας λέγοντες (b35ff.). Those who discuss the Ideas, and disclose them in λόγος, proceed this way as well: χωρίζοντες, "they extract." It is just that they themselves λανθάνουσι, "are covered over, " as regards what they are doing and how they are doing it; they are not transparent to themselves in their procedure, neither as to its limits nor its distinctions. Λανθάνουσι, "they remain concealed while they do this," concealed precisely to themselves. (This is a characteristic usage of the term λανθάνειν. Conversely, there is then also an ἀλήθεια pertaining to Dasein itself.)