104e7—105b4. This difficult passage divides into two parts: (1) At 104e7— 105a5 Socrates proposes a definition of the class of entities he had suggested defining at 104cll-12. (2) At 105a5-b3 he gives some further numerical examples.
(1) For the complex grammar of the 'definition' (a2—5) see note 74. It does not, unfortunately, read like a definition at all, but simply enunciates the general principle that whatever A items bring F to something cannot themselves admit G. This is a cardinal principle of the argument, which will be applied directly to the case of soul at 105dl0—11. See on 100e5-101b8 and next note. Its meaning, however, turns upon whether the designated A items are Forms, and this still remains unclear.
At 104e8—105al they are exemplified by 'threeness', 'twoness' and 'the fire'. The translation 'the fire' keeps the Greek definite article, but should not be read as a definite description, referring to an individual fire. It means either 'fire' in a generic sense, i.e. stuff called 'fire', or the Form of Fire. D. O'Brien (C.Q. 1967,220) argues from the numerical locutions 'threeness' and 'twoness' that Plato is probably 'now thinking of fire to some extent as form'. But the numerical language is quite inconclusive (see on 101b9-c9 and previous note). In the further examples (a6—7) of what is, presumably, the same point, Socrates switches to the ordinary terms for the cardinals 'five' and 'ten'. This confirms the view of J. Schiller (Phronesis 1967, 57) that Plato shows a 'studied indifference to the locutions by which he refers to numbers'. It cannot, therefore, be argued either, on the strength of 104e8—105al, that Forms are meant, or, on the strength of 105a6—7, that they are not. Hackforth's translation at 105a3—4 begs the question by importing Forms where there are none in the Greek.
At 104el0 and 105a3—4 Socrates speaks for the first time of the items in question 'bringing' an opposite to something. The same word is used later (105d3-4, d 10-11) of soul's 'bringing' life to body, and may be an extension of the military metaphor, referring to the 'bringing up' of reinforcements. However, the meaning of 'bring', and consequently the identity of the 'bringer' and the 'recipient' of an opposite Form, are disputed.
(A) 'Bringing' may be understood as 'causally imparting', and the 'bringer' may be taken not as the Form A, but as any x that participates in the Form A, and is therefore F, and by its presence imparts F to another individual, y. On this view, the principle being formulated here will be:
(xjO {(Ax.x causesy to be F) "D (~Gx)}. If this formula expresses Plato's meaning, its application will be as follows: 'A' will be replaced by 'participates in the Form Soul', and 'G' by 'participates in the Form Death', x's causing y to be F will represent an individual soul's 'bringing' life to any body that it enters, i.e. 'causing' it to be alive, and it will be from this that soul's refusal to admit death will be inferred. This fits Version A given at 104c7— d4 (p.204).
Alternatively, (B) 'bringing' may be taken to stand for the same relation as was illustrated at 104d by the Forms Three and Odd, i.e. a non-symmetrical relation between two Forms, A and F, such that whatever participates in Form A must also participate in Form F. Cf. G. Vlastos, P.R. 1969, 317. On this account, the 'bringer' will be a Form, such as Three, and the 'recipient' will be an individual that participates in that Form. Thus, where A is the 'bringing' Form, F the Form brought, and G the Form opposite to F, the principle being enunciated here would, on this view, be simply: (x) (Ax D ~Gx).
Note, however, that this formula would not fit Version B of the argument, and would not yield the premiss required for proving the soul's immortality. For Socrates will not argue that it refuses to admit Death merely on the ground that it participates in the Form Soul, i.e. that it is soul. He argues that it excludes death because it brings life to the body. If, therefore, the argument is to be construed in terms of entailment relations between Forms, the more complex pattern of argument given under (B) in the previous note (p.207) will be needed.
(2) The further numerical examples are well explained by D. O'Brien, op.cit. 221-3. See also F. M. Cornford, C.Q. 1909, 189—91. The words 'This, of course, is itself also the opposite of something else; nevertheless, it won't admit the form of the odd' (a8—bl) are difficult. They seem meant as an aside about 'the double' as such, and not about ten qua double. Hackforth (153, n.l) translates and interprets the second half of the sentence as if its subject were 'ten'. But it seems better to take the subject as 'the double' throughout. The point will then be that 'double', unlike the numbers two, three, five, and ten, that have been instanced as excluding odd or even, is itself an opposite of something else, namely 'half' (cf. Republic 438cl—2, 479b3); nevertheless—i.e. despite its infringing the norm by being an opposite—it still excludes the odd, since no number that is double can, in fact, be odd.
Two series of fractions are instanced (bl—3) as excluding the Form of Wholeness: 3, §, f, etc., and 3, %, etc. These examples are of no importance for the main argument.
105b5—c8. Socrates now puts forward a new kind of answer which he illustrates with a series of examples, 'fire', 'fever', and 'oneness' (or 'a unit'). The main problems here are: (1) What exactly is the grammar and sense of the lines indicating fire and fever as the reasons for a body's being hot or ailing (b8—c4)? (2) What is the meaning of the numerical example? (3) Flow is the new type of answer related to the old 'safe' answer in terms of Forms? (4) Why
does Socrates see in it 'a different kind of safeness'?
For the grammar and text at 105b8~c4 see note 75. Hackforth translates 105b8—9: 'what must be present in a thing's body to make it hot?' (with parallel renderings of the questions at 105c3—5). But this wrongly suggests that fire and fever are necessary conditions for heat and illness respectively; whereas fever, at least, is clearly not a necessary condition for illness but only a sufficient one (cf. Alcibiades II, 139e—140a). Fire, too, is probably not meant as a necessary condition for heat, since it is parallel in the argument to snow, and the latter could not be held a necessary condition for cold (note also 63d7—8). Hackforth (161) regards it as a weakness of the answers 'fire' and 'fever' that they give conditions that are merely sufficient and not also necessary. Of course, if the relevant phrases are translated as if they specified necessary conditions, they will appear to be making a false claim. But they clearly should not be so translated. It is only in the case of soul (105c9—d2) that the new answer gives a condition that is indisputably necessary as well as sufficient. In general, then, the new answers differ from the old ones in being merely sufficient, whereas the old ones were both sufficient and necessary.