The word translated 'oneness' (morns) at 105c6 may stand for the Form of One, as it clearly does at 101c6. But it may also be rendered 'a unit'. Hackforth translates it thus, and explains it (158, n.2) as 'the one left over in the middle when an odd number is divided into two equal parts'. This explanation conforms to two definitions of 'odd' criticized by Aristotle in the Topics: 'that which is greater by one (morns) than an even number' (142b8), and 'a number with a middle' (149a30—31). See also Euclid, Elements vii, Def. 7, ed. T. L. Heath, ii. 281, and H. F. Cherniss, ACiM. 25, n.19. Hackforth's interpretation gives a clear sense in which the 'odd' or unpaired unit makes a number odd, and is well suited to the root meaning of the Greek word for 'odd'. Cf. also O.E.D., s.v. 'odd'.
Thus understood, 'a unit' would be both a necessary and sufficient condition for three, five, etc. being odd. It would then be out of line with the cases of fire and fever, but in line with that of soul. Hackforth's interpretation, however, seems inconsistent with his further account (162), in which 'Unit' is treated as a Form, importing Oddness. For it is hard to see how 'a unit', as Hackforth explains it, could be thought of as a Form. If a Form is meant, it must be the Form of One, thought of as bringing oneness to any particular 'one' that it occupies, and thereby making it odd. In that case the translation 'oneness' will be required, and the example would be in line with the cases of fire and fever, giving a sufficient, but not a necessary condition for oddness. Cf. O'Brien, C.Q. 1967,
224-5.
Would 'a unit' itself be odd? W. D. Ross (ed. Aristotle, Physics, 604) says that according to the normal view of Greek mathematicians, two was the first number. On this view, 'a unit' would not, strictly, be a number, but that of which numbers consist, or in terms of which 'number' is defined. See also T. L. Heath, H.G.M. i. 69-71, and M. E. Hager, C.R. 1962, 1-2. The 'unit' (morns) was sometimes called 'even-odd', being thought of as a parent of all numbers. This, if relevant here, would create some difficulty for the principle that a 'reason' must exclude the opposite of that for which it is a reason. But, a different, perhaps more popular, conception of 'one' (to hen) is found at Hippias I, 302a3—5, where it is explicitly said to be odd. It must be so regarded here on any interpretation of the argument. It remains unclear, however, whether what is made odd is regarded as a pure number or as a single-membered set. This turns on the meaning of 'number' at 105c4. See on 104d5— e6 (p.206),
(3) As noted above, the present series of answers give sufficient, but not necessary conditions. They do not, therefore, satisfy the principle, implicit in the earlier discussion, that no opposite, F, can count as the reason for something, if its opposite, G, can give rise to the same thing (see on 100e5—101b8, p.186). Thus, the answer 'fever' is open to the very objection that Socrates raised against 'addition' at 97a7—b3: illness could be due to the opposite of fever, hypothermia. Evidently, therefore, the present 'reasons' are not meant as constitutive of what they explain. They do not aim at answering the conceptual question 'what (logically) makes things F?'
What, then, is their purpose? There are two different ways of interpreting them, according as they are or are not construed as Forms.
(A) If they are not taken as Forms, they will specify reasons that 'make' whatever they are in to be F, in a causal and not merely a logical sense of 'make'. On this account, the new answer does not supersede the old 'safe' one in terms of Forms, but supplements it, by showing how a particular object or number comes to be occupied by the Form in question. Thus, fire makes bodies participate in Hotness. Similarly, fever, regarded as a cause rather than as a symptom of illness, makes them participate in Illness. This account fits the numerical example less well, since the notion of causal 'making' is strictly inapplicable here. But an unpaired unit may be thought of, analogously, as imparting a Form, Oddness, to a number or set that participates in that Form. Soul will be thought of, similarly, as imparting the Form Life to the body that it occupies (105c9—dl2). It 'makes' the body to be alive, in no mere logical
sense of 'makes', but in the sense that it gives it life, or quickens it.
Alternatively, (B) The reasons here specified are Forms of Fire, Fever, and Oneness. Thus, with variations, Hackforth, 162, G. Vlastos, P.R. 1969 , 317-20, D. O'Brien, C.Q. 1967, 223-8, E. L. Burge, Phronesis 1971, 11—12. Understood thus, the new answers specify, not 'causes' of a thing's being F, but logically sufficient conditions from which its F-ness may be inferred.
Once again, no conclusions can be drawn from Plato's terminology. There is no explicit reference to Forms in the passage, unless it be held that at 105c6 'oneness' must be meant, in conformity with 101c6. But no decisive inference can be based upon the locutions for numbers (see on 104d5-e6, p.205—6).
If the 'reasons' given here are taken as Forms, the 'bodies' in which they are said to be present cannot, unless Plato's examples are hopelessly disparate, simply be //-instances of the Form in question, e.g. a particular fire, thought of as occupied by the Form of Fire. For such an interpretation would not fit the fever example. Socrates could not refer to the presence of the Form Fever in a particular fever as its presence in a 'body' (c3), for a particular fever, unlike a particular fire, is not itself a body. If, therefore, Forms are meant here, the 'bodies' they occupy cannot be fires, but must be things on fire, e.g. sticks. Nor can they be fevers; they must, rather, be things feverish, e.g. human bodies. Similarly, in the case of souclass="underline" Socrates could not be referring at 105c9-ll to the Form of Soul's presence in a particular soul. For the soul is not a body. In view of this, the Form interpretation of these lines can be made to fit the case of Soul and Life at 105c9-dl2 only with great difficulty. See next note.
(4) Some of the new answers of this passage, such as fire and fever, may seem no less 'mechanistic' than the ones earlier rejected (see C. C. W. Taylor, Mind 1969, 52-3). Indeed, by calling them 'subtler' (c2), Socrates links them with the answers that were unacceptable before (cf. 'subtleties' 101 c8, and 'those other wise reasons' lOOclO). Why, then, are such 'subtleties' now admitted as giving 'a different kind of safeness'? How could they be thought 'safe' from the dangers that had threatened such answers before?
As noted in (1) above, they do not enjoy the complete safeness of the old Form 'reasons', in that they are not necessary conditions for what they explain. But they do satisfy Socrates' other requirements for 'reasons'. In particular, and of paramount importance for the argument, they do not admit the opposite of the properties that they impart—e.g. fire cannot itself be cold. This what makes them 'safe' as well as 'subtle'. It is this principle that underlies the proof that soul is immortaclass="underline" since it is the 'reason' for life, soul cannot .itself admit death, and therefore cannot be dead (see also on 100e5—
101b8, p.186—7).
What can be said of this principle? It has some plausibility in such cases as fire and snow, which may be thought of as transmitting their own heat and cold to other bodies. Clearly, they could not do this, if those properties were 'neutralized' by the presence of their opposite. But the principle is less plausible in the other examples. Fever does not transmit illness from itself to the body in which it is present. It is an illness, but is not itself ill. Nor could the principle be held to apply to reasons more generally, (i) It would have no application to properties that are not members of a pair of opposites. (ii) Even where the properties to be explained are members of such a pair, it is untrue that a reason for one of them must exclude its opposite. A germ that is a 'reason' for illness in a body may itself be healthy. A saccharine pill that is a 'reason' for sweetness in coffee may itself be bitter. But fundamentally, (iii) in any given case it may be doubtful whether there is any 'reason' to be found that satisfies the principle under discussion. There seems nothing analogous, in this respect, to fire and snow that could be called a 'reason' for a thing's being large or small. In the case of life, 'soul' is, of course, taken to be a reason that meets the conditions stipulated. But this simply prejudges the question whether, in fact, life admits of explanation in terms of the kind of 'reason' that Socrates has displayed. Unless it does, his final proof of immortality cannot get off the ground. See next note.