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[992b] [1]

Further, one might regard the substance which they make the material substrate as too mathematical, and as being a predicate and differentia of substance or matter rather than as matter itself, I mean the "Great and Small," which is like the "Rare and Dense" of which the physicists speak,1 holding that they are the primary differentiae of the substrate; because these qualities are a species of excess and defect.Also with regard to motion, if the "Great and Small" is to constitute motion, obviously the Forms will be moved; if not, whence did it come? On this view the whole study of physics is abolished. And what is supposed to be easy, to prove that everything is One, does not follow; because from their exposition2 it does not follow, even if you grant them all their assumptions that everything is One, but only that there is an absolute One—and not even this, unless you grant that the universal is a class; which is impossible in some cases.3 Nor is there any explanation of the lines, planes and solids which "come after" the Numbers4: neither as to how they exist or can exist, nor as to what their importance is. They cannot be Forms (since they are not numbers) or Intermediates (which are the objects of mathematics) or perishables; clearly they form yet another fourth class.

In general, to investigate the elements of existing things without distinguishing the various senses in which things are said to exist is a hopeless task; [20] especially when one inquires along these lines into the nature of the elements of which things are composed. For (a) we cannot surely conceive of the elements of activity or passivity or straightness; this is possible, if at all, only in the case of substances. Hence to look for, or to suppose that one has found, the elements of everything that exists, is a mistake.(b) How can one apprehend the elements of everything ? Obviously one could not have any previous knowledge of anything; because just as a man who is beginning to learn geometry can have previous knowledge of other facts, but no previous knowledge of the principles of that science or of the things about which he is to learn, so it is in the case of all other branches of knowledge.Hence if there is a science which embraces everything5(as some say), the student of it can have no previous knowledge at all. But all learning proceeds, wholly or in part, from what is already known; whether it is through demonstration or through definition—since the parts of the definition must be already known and familiar. The same is true of induction.

1 Cf. iv. 10.

2 The word ἔκθεσις has various technical meanings. The process referred to here apparently consisted in taking, e.g., particular men, and reducing them with reference to their common nature to a single unit or universal, "man"; then taking "man," "horse," "dog," etc. and treating them in the same way, until a unit is reached which embraces everything (Alexander).

3 Probably those of relative or negative terms. Cf. Aristot. Met. 1.3.

4 See note on Aristot. Met. 1.23.

5 e.g. Plato's Dialectic.

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