§16 [120-121]

Thus a line has another mode of unity: ἡ δὲ γραμμὴ συνεχές ἐστιν· ἔστι γὰρ λαβεῖν κοινὸν ὅρον πρὸς ὃν τὰ μόρια αὐτῆς συνάπτει, στιγμήν· καὶ τῆς ἐπιφανείας γραμμήν (5a1ff.). The line, as continuous, has another mode of unity. That is, one can extract from the line, from the continuous, something with regard to which each part of the line can be called a part in the same sense, namely the point. But it must be noted that these extracted points do not together constitute the line. No point is distinct from any other. What is remarkable for the possibility of this κοινὸς ὅρος resides in the fact that the line is more than a multiplicity of points, that it, namely, has a θέσις. On the other hand, in the case of the manifold of the series of numbers, there is no θέσις, so that this series is determined only by the ἐφεξῆς. Now, insofar as the co-positing of a θέσις is not required for the grasping of mere succession as the mode of connection of numbers, then, viewed in terms of the grasping as such, in terms of νοεῖν, number is ontologically prior. That is, number characterizes a being which is still free from an orientation toward beings which have the character of the continuum and ultimately are in each case an αἰσθητόν. Therefore number enters into an original connection, if one interrogates the structure of beings as the structure of something in general. And this is the reason the radical ontological reflection of Plato begins with number. Number is more original; therefore every determination of beings carried out with number, in the broadest sense, as the guiding line is closer to the ultimate ἀρχαί of ὄν.

When Aristotle brings up the distinction between geometry and arithmetic in Metaphysics I, chapter 2,12 his concern is simply to show that within the ἐπιστῆμαι there are gradations of rigor. But he does not claim that arithmetic would be the most original science of beings in their Being. On the contrary, Aristotle shows precisely that the genuine ἀρχή of number, the unit or oneness, is no longer a number, and with that a still more original discipline is predelineated, a discipline which studies the basic constitution of beings: σοφία.

§16. Continuation: σοφία (Met. I, 2, part 1). The fourth essential moment of σοφία: the autonomy of its ἀληθεύειν (ἑαυτῆς ἕνεκεν. μὴ πρὸς χρῆσιν).

The fourth and last moment of σοφία is its autonomy in itself. Aristotle demonstrates it in a twofold way: first, on the basis of what is thematic in σοφία; second, on the basis of the comportment of Dasein itself.

12. 982a28.