74b7—c6. This passage is of the utmost importance for understanding the Theory of Forms, since it argues that the Form Equal, and by implication many other Forms (cf,75cl0—d5), must be non- identical with their sensible instances. It should therefore throw light upon the motives from which the Forms are 'separated' from sensible things in the fully-fledged version of the Theory adopted in this dialogue (see on 65d4—e5, p.94). Unfortunately, the argument itself is much vexed, and has become a notorious philosophical crux. See especially J. L. Ackrill, P.R. 1958, 106-8, and K. W. Mills, Phronesis 1957, 128-47,1958,40-58.
The non-identity of the Form Equal with its sensible instances is inferred from the fact that the latter do, but the former does not, possess a certain property. Thus, the argument is of the following form: sensible equals have the property P; but the Form Equal does not have that property; therefore sensible equals and the Form Equal are not the same thing. However, (1) what exactly is PI And (2) why does Socrates use the expression 'the equals themselves' (plural) at 74c 1, unparalleled elsewhere in the dialogue, instead of 'the equal itself, his usual expression for the Form, which reappears in the conclusion at 74c4—5?
(1) The property ascribed to equal stones and logs at 74b8—9 has been interpreted in four different ways. Socrates may be suggesting (a) that equal stones and logs, while remaining the same, seem equal to one observer but not to another; or (b) that they seem equal to one thing but not to another; or (c) that they seem equal in one respect (e.g. length) but not in another (e.g. weight); or (d) that sometimes, while remaining the same, they seem equal at one time, but not at another, (a), (b), and (c) are all based upon Burnet's text, (d) is based upon a variant reading with good MS. authority (see note 22).
Each interpretation has its supporters, and none can be conclusively disproved. It is, however, doubtful whether the Greek will bear sense (c), and it will not be further considered here, (d) is defended by Verdenius, who glosses the lines thus: 'under certain conditions, e.g. when you are walking around two equal stones, they in turn seem equal and unequal, whereas under other conditions, e.g. when you are sitting in front of them, they do not show such a variation in their mutual relation.' Verdenius argues that the temporal reference at 74c 1 ('did the equals themselves ever seem ...') requires a temporal contrast at 74b8—9. But just such a contrast is provided by the word 'sometimes', so the variant reading is not needed to obtain it. Nor does the fact that Socrates refers at 74cl to only a single observer ('to you') tell in favour of the variant reading, as Verdenius supposes. For if Burnet's text is not interpreted in sense (a), as referring to different observers, the fact that only a single observer is mentioned at 74c 1 would not tell against it at all. (d) is therefore a possible interpretation, but by no means necessary.
The present translation, 'sometimes seem equal to one, but not to another', is deliberately ambiguous between (a) and (b). With (a) the point will be that two different observers could disagree as to whether logs or stones were equal, whereas no such disagreement would be possible with respect to the Form Equal. With (b) the point will be that logs and stones can have contrasted predicates in different relations, whereas the Form Equal cannot.
Both interpretations are grammatically acceptable, but neither is without logical difficulty. For (a) see Mills, op.cit. 129—31. For(b) see N. R. Murphy, I.P.R. Ill, n.l, answered by Hackforth, C.R. 1952, 159. It is, indeed, a common enough Platonic reproach to sensible Fs, that they are only relatively F, and may, when viewed in a different relation, appear not to be F, or to be the opposite of it, G. Cf., e.g., Republic 479-80, 523c-524c. However, (i) since any given sensible equal is always unequal to something, it is somewhat odd to say that this seems to be the case only 'sometimes', (ii) It is very hard to suppose that the Form Equal is itself free from this defect, if this means attributing equality to it (see on 74d4—8, p.128).
And (iii) the names of the Forms mentioned at 75c 11—dl, to which the argument in general is supposed to apply, could not, on interpretation (b), be directly substituted for 'equal' at 74b8 without any further changes of wording, whereas on interpretation (a) they easily could. None of these objections to (b) is decisive, however, and the argument, if taken in this sense, can readily be adapted to the other relevant Forms—see G. E. L. Owen, S.P.M. 306. Either (a) or (b) therefore remains a defensible reading of Burnet's text.
Note that all the defects of sensible equals that feature in the above interpretations are implicitly ascribed to instances of the Form Beauty at Symposium 21 lal— 5. The doubt as to which particular defect is here in question should not be allowed to obscure the basic case for 'separating' Forms from sensibles to which they all contribute. The essential point, on any interpretation, is that no sensible F can be the true nominatum of *F\ can be 'that which F is', because all sensible Fs admit also of being called lG\ Yet 'F' and '(?' are names for two different and opposite things, so anything that admits of both names cannot be 'what F is'. The Form F must therefore be something 'other than', distinct from, its sensible instances. See Mills, op.cit. 145-7, and R. E. Allen, R.M. 1961, 328-9.
(2) Plato's use of the unusual plural, 'the equals themselves', has been variously interpreted. Burnet, Hackforth (69, n.2), Bluck (67, n.3), and W. D. Ross (Plato's Theory of Ideas, 23-5, 60) take it to refer to non-sensible mathematical objects, such as the angles at the base of an isosceles triangle. But equals of that sort would be irrelevant to the conclusion that sensible equals differ from the Form Equal, which is what the argument purports to prove. Moreover, as Ackrill has pointed out (op.cit. 108), the premiss would on this interpretation be false, since one might, if unfamiliar with the relevant Euclidean theorem, suppose that the angles at the base of an isosceles triangle were not equal, or not suppose that they were.
R. S. Bluck (Phronesis 1959, 5—11) proposes to read back into the present passage the distinction drawn later (102d6—103b5) between the Forms Large or Small and the Large or Small 'in us'. The Forms 'in us', which he calls 'Form-copies', may also, he thinks, be exemplified by 'the equals themselves' of 74c 1. But it seems unlikely that a distinction not drawn till much later, having no obvious relevance to the present context, should suddenly be introduced here without explanation. See J. M. Rist, Phronesis 1964, 28-9.
If the premiss at 74c 1—3 is to be both relevant to the argument and true, 'the equals themselves' is best understood as an alternative designation for the Form Equal, used, like 'equality' later in the same line, as a variant for 'the equal itself. Cf. Parmenides 128e— 129b, and see Rist, op.cit. 29-30. The plural designation is sometimes attributed to the fact that 'equal' implies at least two terms. It has been further suggested that this Form was conceived by Plato as a set of two (or more) Equals, a bipartite (or multipartite) entity, that could appropriately serve as a standard to which sensible equals approximate. See P. T. Geach, P.R. 1956, 76, Mills, op.cit. 49-50, and G. Vlastos, S.P.M. 287-91. But this explanation of the plural is neither free from difficulty nor necessary. 'Equal' has just been used (74b8) in the plural of logs and stones. As Owen has suggested (A.D. 114—15), the word is quite naturally picked up in its plural form when Socrates switches attention to the Form. In any case, whatever the explanation of the plural may be, there need be no shift of subject in the two halves of Socrates' question at 74cl—2. When he adds the second half, 'or (did) equality (ever seem to you to be) inequality?', he is asking a question about the same entity as in the first half, namely the Form of Equality.