The Presocratic Philosophers

cannot be neither nor nonfor every value of . Aristotle, it need hardly be said, was well aware of this (cf., e.g., GC 329a10). But if the ‘unlimited’ was not entirely characterless, what was its character? In several passages Aristotle talks of phusiologoi who took as their principle a stuff ‘between’ (metaxu) the other elements; and he probably had Anaximander in mind. According to some scholars, Theophrastus thought that Anaximander’s principle was a ‘mixture’ (migma) of all stuffs. These passages are all controversial, but one thing is fairly clear: if the Peripatetics did actually ascribe a metaxu or a migma theory to Anaximander, they were whistling in the dark. Anaximander’s text gave them no light; and I guess that they did not know what Anaximander thought, for the excellent reason that Anaximander himself did not know what to think. Argument (C) assumes, in (8), the spatial infinity of the universe. That proposition is the conclusion of argument (B). The argument is invalid, as Aristotle points out: In order that coming to be should not fail, it is not necessary that there should be a sensible body which is actually unlimited. The passing away of one thing may be the coming to be of another, the whole being limited’ (Phys 208a7–10). This objection is overcome by adding a further premiss to (B), viz: (18) The material supplied by the destruction of existing things cannot be used in the generation of new things. But it is implausible to ascribe (18) to Anaximander. Sentence [iv] of the fragment, whether or not it is Anaximandrian, is not, strictly speaking, incompatible with (18): [iv] does not imply that the dust produced by destroying a thing is equal in mass to the dust consumed in its generation; and it is not grossly implausible to imagine that the processes of generation and destruction involve a certain wastage of stuff. Sentence [v], however, suggests fairly strongly that Anaximander had some sort of equal balancing in mind; and the probability is that he would have rejected (18). Argument (B) can be repaired without the help of (18); instead of (18) we may add: (19) The mass of existing things is perpetually increasing. An adherent of (19) believes that the cosmos is expanding; and there is no direct evidence that any Presocratic held such a belief. But there is a sentence from Anaxagoras which apparently commits him to an expanding universe; and in some respects at least Anaxagoras was a scientific traditionalist. If Anaxagoras embraced (19), perhaps he took it from Anaximander. It is pertinent to quote here a fragment of Anaximander’s pupil, Anaximenes: Air is close to the incorporeal; and since we come into being by an effluxion of this, it is necessary for it to be both unlimited and rich, because it never gives out (18:13 B 3). The presocratic philosophers 26