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[996a] [1] Further, (8.) we must ask whether the first principles are limited in number or in kind1—both those in the definitions and those in the substrate—and (ix.) whether the principles of perishable and of imperishable things are the same or different; and whether all are imperishable, or those of perishable things are perishable.2Further, there is the hardest and most perplexing question of all: (x.) whether Unity and Being (as the Pythagoreans and Plato maintained) are not distinct, but are the substance of things; or whether this is not so, and the substrate is something distinct3(as Empedocles holds of Love,4 another thinker5 of fire, and another6 of water or air7);and (xi.) whether the first principles are universal or like individual things8; and (12.) whether they exist potentially or actually; and further whether their potentiality or actuality depends upon anything other than motion9; for these questions may involve considerable difficulty.Moreover we must ask (13.) whether numbers and lines and figures and points are substances in any sense, or not; and if they are, whether they are separate from sensible things or inherent in them.10 With regard to these problems not only is it difficult to attain to the truth, but it is not even easy to state all the difficulties adequately.11

(1.) Firstly, then, with respect to the first point raised: whether it is the province of one science or of more than one to study all the kinds of causes. [20] How can one science comprehend the first principles unless they are contraries? Again, in many things they are not all present.How can a principle of motion be in immovable things? or the "nature of the Good"? for everything which is good in itself and of its own nature is an end and thus a cause, because for its sake other things come to be and exist; and the end and purpose is the end of some action, and all actions involve motion; thus it would be impossible either for this principle to exist in motionless things or for there to be any absolute Good.Hence in mathematics too nothing is proved by means of this cause, nor is there any demonstration of the kind "because it is better or worse"; indeed no one takes any such consideration into account.And so for this reason some of the sophists, e.g. Aristippus,12 spurned mathematics, on the ground that in the other arts, even the mechanical ones such as carpentry and cobbling, all explanation is of the kind "because it is better or worse," while mathematics takes no account of good and bad.13

1 Discussed Aristot. Met. 3.4.8-10; answered Aristot. Met. 12.4-5, Aristot. Met. 13.10.

2 Discussed Aristot. Met. 3.4.11-23; for Aristotle's general views on the subject see Aristot. Met. 7.7-10, Aristot. Met. 12.1-7.

3 Discussed Aristot. Met. 3.4.24-34; answered Aristot. Met. 7.16.3-4, Aristot. Met. 10.2.

4 Actually Love was no more the universal substrate than was any other of Empedocles' elements; Aristotle appears to select it on account of its unifying function.

5 Heraclitus.

6 Thales.

7 Anaximenes.

8 Discussed Aristot. Met. 3.6.7-9; for the answer see Aristot. Met. 7.13-15, Aristot. Met. 13.10.

9 Discussed Aristot. Met. 3.6.5-6; for the relation of potentiality to actuality see Aristot. Met. 9.1-9; for actuality and motion see Aristot. Met. 12.6-7.

10 Discussed Aristot. Met. 3.5; answered Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6.

11 For another statement of the problems sketched in this chapter see Aristot. Met. 9.1, 2.

12 Founder of the Cyrenaic school in the early fourth century.

13 For a defense of mathematics see Aristot. Met. 13.3.10-12.

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