B4. If a non-opposite Form A is such that, whatever body (x) it is present in, x will be F, then Form A brings F to x (supplied).
B5. The Form of Soul is a non- opposite Form, such that whatever body it is present in, that body will be living (105c9— d2).
[B4 + B5]:
B6. The Form of Soul brings Life to whatever body it occupies (105d3—5).
B7. The opposite of Life is Death (105d6-9).
[B3 + B6]:
B8. An TV-instance of the Form of Soul, i.e. an individual soul, will never admit the Form opposite to that which the Form of Soul brings (105dl0-12).
Version A
A11. What will not admit Death is im-mortal (105dl3—e3).
[A8 + A9 + A10]:
A12. Soul will not admit Death
(105e4—5).
[All + 12]:
A13. Soul is im-mortal (105e6— 7).
A14. What is im-mortal is imperishable (106c9-d9).
[A13 + A14]:
A15. Soul is imperishable (106- el—107al).
Version B
B9. What will not admit Death is im-mortal (105dl3—e3).
[B6 + B7 + B8]:
BIO. An individual soul will never admit Death (105e4—5).
[B9 + B10]:
Bll. An individual soul is immortal (105e6—7).
B12. What is im-mortal is imperishable (106c9-d9).
[Bll +B12]:
B13. An individual soul is imperishable (106el-107al).
104d5—e6. Socrates illustrates the suggestion made at 104dl—3 with the example of three. This passage contains the one and only unambiguous mention of a Form, other than Forms of opposites, in the entire argument. Those who believe that the items under discussion are Forms will naturally regard the Form of Three (d5—6) as an instance of the class that Socrates had proposed for definition at 104cll—12. The passage is important, in view of the deliberate parallel between the cases of three and soul, and the similarities of language with 105d3-5. But it does not settle the question whether the definienda are Forms. For, on the translation adopted at 104dl—3, they will be exemplified here not by the Form of Three, but rather by whatever it is supposed to occupy (see previous note). If so, the ,passage will be identifying the definienda not with Forms that import opposites, but with the items occupied by such Forms. Its argument will then be that those items will not admit the Form opposite to the one imported into them. This will not constitute a 'definition' of the items in question. Indeed, it is not until 105al—2 that Socrates says 'see if you define them thus'.
Here the problem of interpreting Plato's locutions for numbers again becomes acute. D. O'Brien has argued (C.Q. 1967, 216—19) that 'in the elaboration of the numerical example (i.e. from 104b6) there is a consistent distinction between form and particularisation. The form is described as "the Form of Three" or more simply as "threeness". The particularisation is described as "three".' But this alleged distinction is very hard to sustain. Both at 104c5 and 104e5, 'threeness' follows immediately upon occurrences of 'three', where the latter stands, in O'Brien's own view, for the number three. The point of switching from number to Form in these places is difficult to see. Moreover, as O'Brien recognizes (op.cit. 218), 'threeness' is used in parallel with 'two' at 104a4—b2, where 'threeness' and 'five- ness' exemplify the odd series of numbers, and 'two' and 'four' the even. O'Brien suggests that it is natural for Plato's language 'to become firmer with the elaboration of his example'. But Plato could quite well have registered this important distinction, had he wished to, from as early as 101c5—6, where the '-ness' terms were used for the Forms of One and Two. Again, if the distinction is supposed to be firmly established from 104b6 onwards, why does Socrates backslide at 105a6—7? See next note (p.208).
Hackforth (151, n.2, 152, n.l, 156) holds that 'three' and 'threeness' are used interchangeably to stand for the immanent Form Threeness, and that the meaning of 'three' at 104el—3 can be fixed from the use of 'threeness' at 104e5. In drawing no distinction between 'three' and 'threeness' he seems correct. But it does not follow that both are used to mean 'immanent Form'. It seems equally possible to hold that (i) neither 'three' nor 'threeness' means a Form of any kind, but that (ii) both alike refer to the number three; and that therefore (iii) the only reference to the Form of Three in the whole passage occurs in so many words at 104d5—6.
But even if 'three' and 'threeness' are taken as just suggested, the meaning of 104d5-7 and the point of the succeeding argument are still uncertain. For what is it that is supposed to be occupied by the Form of Three and compelled to be not only three but also odd? Is it the number three, or is it sets of three things? O'Brien (op.cit. 212, 217) argues that only the number three could be said to be odd 'by nature' (104a3, a7); a group of oxen, which might change in number, could not. But the claim that whatever the Form of Three occupies must ipso facto be odd seems as plausible for sets as for numbers. Cf. Hippias I, 302al—7. O'Brien also appeals to Socrates' later reference to a 'number's' being made to be odd (105c4). But this is not conclusive, since 'number' may mean a numbered set (cf. Phaedrus 247a2). It is therefore unclear whether Plato is thinking of the Form of Three as (A) occupying the number three or as (B) occupying a set of three things.
There are, accordingly, two ways of taking the argument of this section. (A) 'Whatever the form of three occupies' refers to the number three, and it is to this that 'a thing of that kind' refers back at 104d9. On this view, the argument runs as follows: (i) whatever the Form of Three occupies will be odd; (ii) the Form of Three occupies the number three; hence (iii) the number three will be odd, and hence (iv) uneven. This interpretation would suit Version A of the argument given in the previous note. Cf, J. Schiller, Phronesis 1967, 57-8.
Alternatively, (B) 'whatever the form of three occupies' may be taken as sets of three things, and the argument understood as follows: (i) whatever sets the Form of Three occupies must be odd (d5—8); hence (ii) the number three will have no part in the Form opposite to the Odd, i.e. the Form Even (d9—e4); hence, (iii) the number three will be uneven (e5—6). Here, as in Version A, 'a thing of that kind' (104d9) refers back to the number three. But the number is viewed as an iV-instance of the Form (see on 102d5—103a3, p. 196); and the argument runs from the effect exerted by the Form of Three upon its ^-instances, triadic sets, to the property of the number three: the number, or iV-instance, will have essentially that property which the Form compels the sets to have while it occupies them; it will therefore not admit that property's opposite.
The general principle implied on this interpretation would be that when a non-opposite Form A compels its T-instances to possess an opposite Form F, then aniV-instance of the Form A will never admit the Form G (see B3 in the summary of the previous note). This principle would be applied to the soul by treating it as an TV-instance of the Form of Soul (i.e. as 'the soul in us'), and the bodies it animates as ^-instances of that Form (i.e. as 'things besouled'). See B6 and B8.
On either of the above versions, the parallel between the number three and the soul is dubious. For it is hard to understand either the Form's occupancy of the number three (Version A), or the treatment of the number three as an TV-instance of the Form (Version B), if there is only one such number. The referent of 'the number three' is naturally taken, in English at least, to be unique, whereas that of 'the soul' need not be: 'the soul' may mean 'our souls' (just as 'the appendix' may mean 'our appendices'), whereas 'the number three' can hardly stand for a plurality. If Plato is taken to have believed in a plurality of threes, as in the doctrine of intermediates referred to on p.200, it would be possible to think of'a three' rather than of 'the number three'. But such expressions as 'a three' or 'threes' are more naturally used in English of sets than of pure numbers. The required parallel between 'three' and 'soul' is therefore peculiarly difficult to express.