Anaximander's Apeiron1

H. B. GOTTSCHALK

years ago W. Kraus began an article on the Abeiyon by that "It is now that Anaximander's ifteenF saying generally agreed Infinite is not material in any real sense".2 Since then a consider- able number of studies have been published and several divergent views of the Apeiron have been maintained.3 The problem arises from the apparent inconsistencies in the evidence of Aristotle and Theo- phrastus. Their statements fall into three groups:

1. At Metabh. 1069b22 and Phys. 207a21ff and b35ff4 Aristotle appears to identify the APeiron with his own completely potential prime matter. It is obvious that Anaximander cannot have thought of it in this way, but does Aristotle really claim that he did, as Cherniss asserts?5 In the Metaphysics passage his object is to illustrate his doctrine that all things come into being out of what is potentially, but not actually. As an example of this he refers to those physical systems in which the world is made to arise from a substance without any specific character of its own, i.e., those of Anaximander and Demo- critus, to whose first principles no sensible qualities could be assigned, and of Empedocles and Anaxagoras, who are treated, for the purpose of this argument, as if their first principles were respectively the cryoczpoqand the primeval mixture; looked at in this way they become

37 monists having an indeterminate substance as their first principle. If these substances are completely indeterminate, it follows that they are nothing in actuality but everything potentially, and so indistinguishable from Aristotle's prime matter.6 But Aristotle does not pretend that this accurately represents his predecessors' thought. On the contrary, the very tentative language in which he states his conclusion shows quite 7 clearly that he was drawing his own inference from their writings.' The Physics passage comes at the end of Aristotle's discussion of infinity. Since every complete thing is determined and therefore limited, Aristotle concludes that the infinite is essentially incomplete and can only become something complete by being limited; in itself it is only potentially anything, i.e., it behaves as matter rather than form. Moreover, he goes on, all earlier thinkers appear to treat the infinite as matter, therefore it is nonsense to speak of it as that which embraces all things rather than that which is embraced. The last clause almost certainly alludes to Anaximander's doctrine,9 but Aristotle does not attribute his own doctrine of matter to him. What he says is that Anaxiinander should have arrived at this concept, if he had thought out the implications of his own statements about the first principle.

2. More important are two passages in which Anaximander is grouped with the Pluralists. One of these is Phys. 187 a20 (= VS A 16), where the early philosophers are divided into two groups, those who take as their first principle a specific substance of which other substances are modifications, and those who derive the other substances from the by a process of 'separating-out' implying that these substances pre-existed in the in some way. The second group is made to include Anaximander, Empedocles and Anaxagoras; but Anaximander's principle is referred to as To while it is said of the others that they regard the one and the many as truly existing, and

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