From Vol. 1, No. 1, Winter 2016

By Elissa Foord, Trinity College, University of Cambridge 

P1) ἦ πάσχομέν τι τοιοῦτον περὶ τὰ ἐν τοῖς ξύλοις τε καὶ οἷς νυνδὴ ἐλέγομεν τοῖς ἴσοις; ἆρα φαίνεται ἡμῖν οὕτως ἴσα εἶναι ὥσπερ αὐτὸ τὸ ὃ ἔστιν, ἢ ἐνδεῖ τι ἐκείνου τῷ τοιοῦτον εἶναι οἷον τὸ ἴσον, ἢ οὐδέν;

καὶ πολύ γε, ἔφη, ἐνδεῖ.

P2) οὐκοῦν ὁμολογοῦμεν, ὅταν τίς τι ἰδὼν ἐννοήσῃ ὅτι βούλεται μὲν τοῦτο ὃ νῦν ἐγὼ ὁρῶ εἶναι οἷον ἄλλο τι τῶν ὄντων, ἐνδεῖ δὲ καὶ οὐ δύναται τοιοῦτον εἶναι ἴσον οἷον ἐκεῖνο, ἀλλ᾽ ἔστιν φαυλότερον, ἀναγκαῖόν που τὸν τοῦτο ἐννοοῦντα τυχεῖν προειδότα ἐκεῖνο ᾧ φησιν αὐτὸ προσεοικέναι μέν, ἐνδεεστέρως δὲ ἔχειν; 

ἀνάγκη.

τί οὖν; τὸ τοιοῦτον πεπόνθαμεν καὶ ἡμεῖς ἢ οὒ περί τε τὰ ἴσα καὶ αὐτὸ τὸ ἴσον; (Plato, Phaedo, 74d-e)

“Now then,” said he, “do the equal pieces of wood and the equal things of which we were speaking just now affect us in this way: Do they seem to us to be equal as equality itself is, or do they somehow fall short of being like equality itself?”

“They fall very far short of it,” said he.

“Do we agree, then, when anyone on seeing a thing thinks, 'This thing that I see aims at being like some other thing that exists, but falls short and is unable to be like that thing, and is inferior to it,’ that he who thinks thus must of necessity have previous knowledge of the thing which he says the other resembles but falls short of?”

“We must.”

“Well then, is this just what happened to us with regard to the equal things and equality itself?”[1]

A prolonged debate has not brought scholars into agreement over what Simmias here affirms unhesitatingly. Clear to all is that Socrates’ claims regarding the shortfall of equal sticks and stones are central to Plato’s ontological theory. Less clear is the substance of these claims. In this paper, I re-examine Socrates’ arguments with a view to unravelling Plato’s understanding of equal sticks and stones’ ‘falling short’, and its consequences for the Form-particular relationship.[2] I especially oppose the view that identifies their deficiency as approximation.[3] I will then offer some remarks as to the significance of this view of the relationship in the broader context of Plato’s ontological thought, particularly regarding the attention due to senses.

It will be useful to make some broad and preliminary introduction of the entities that Socrates’ claim relates, namely τὰ ἐν τοῖς ξύλοις τε καὶ οἷς νυνδὴ ἐλέγομεν τοῖς ἴσοις and αὐτὸ τὸ ὃ. Socrates earlier introduced these himself, asking Simmias,

φαμέν πού τι εἶναι ἴσον, οὐ ξύλον λέγω ξύλῳ οὐδὲ λίθον λίθῳ οὐδ᾽ ἄλλο τῶν τοιούτων οὐδέν, ἀλλὰ παρὰ ταῦτα πάντα ἕτερόν τι, αὐτὸ τὸ ἴσον: φῶμέν τι εἶναι ἢ μηδέν (74a);

We say there is such a thing as equality. I do not mean one piece of wood equal to another, or one stone to another, or anything of that sort, but something beyond that—equality itself. Shall we say there is such a thing, or not?

Plato here draws a contrast between equality, ξύλον…ξύλῳ and λίθον λίθῳ, and αὐτὸ τὸ ἴσον. He routinely employs sticks and stones to represent mundane physical objects in general (e.g. Gorg. 468a, Hipp. Ma. 292d, Parm. 129d, Tht. 156e).[4]  Although Socrates in the Phaedo makes repeated references to vision of these objects (ἰδόντες (74b), ἰδὼν (74d)), he situates them within the broader category of sensible objects; he refers to them as πάντα τὰ ἐν ταῖς αἰσθήσεσιν (75b), and remarks that their recollection-provoking experience is ἰδεῖν ἢ ἅψασθαι ἢ ἔκ τινος ἄλλης τῶν αἰσθήσεων: ταὐτὸν δὲ πάντα ταῦτα λέγω (75a). And although initially it is cases of equality that partake in the contrast, he quickly moves to contrasting the items themselves (e.g. 74b) with αὐτὸ τὸ ἴσον (74a).

The majority view is that the opposite element of the contrast, to which I have applied Plato’s term αὐτὸ τὸ ἴσον (74a), signifies, from the off, the Form of Equal, the intelligible entity of Equality itself, carrying all the metaphysical baggage that Plato’s theorising attaches to it, of which his reader would have been well aware.[5] As Sedley notes, ‘αὐτὸ τὸ F’ (where ‘F’ is an adjective of neuter, singular inflection), is Plato’s standard formula for ‘the Form of F,’[6] and Plato uses it to designate this ‘equality itself’ throughout his argument.. Socrates later remarks that this ‘equality itself’ falls into the class that we label ὃ ἔστι (75d), his preferred technical term for the Forms[7]. However, this opposite element is not introduced in such recognisable and well-established terminology. As quoted above, it is introduced as τι…ἴσον (74a); he offers some description, contrasting it with the equality between sticks and stones, and only then is it denominated as αὐτὸ τὸ ἴσον (74a). I do not doubt that Plato and his readers would have had the Form of Equal in mind from the off, but I do contest the view that Socrates here refers to the Form of Equal in all its development in Plato’s metaphysical and epistemological theories. Rather, I contend that by τι…ἴσον (74a), he intends to introduce some concept of equality, which we intuitively sense contrasts with cases of equality between sticks and stones (I refer to this as ‘the deflationary reading’). Plato does not mean the gloss αὐτὸ τὸ ἴσον (74a) to identify this concept with the Form of Equal, but simply to name the entity that he has introduced.

Sedley argues against placing such emphasis on the unusual terminology by which Plato introduces this ‘equality’, τι…ἴσον (74a),[8] For Socrates, he remarks, later makes uncontroversial references to recognisable Forms by using similar indefinite terminology, mentioning καλόν τέ τι καὶ ἀγαθὸν (76d). Yet I do not think that this terminology contradicts the view that Socrates’ introduction of the concept of equality does not carry the full theoretical force of the Forms. In the course of the argument, Plato attaches metaphysical baggage to this concept of equality, such that it emerges as what we would recognise as a Form. The terminology by which it was introduced and the terminology for a Form are, by page 76, therefore equivalent. But that does not mean that they start out as such.

Further, other than by comparison with this later usage, the terminology τι…ἴσον (74a) is unusual. As Sedley notes, we see it elsewhere with an “αὐτὸ” inserted. That insertion alone, I would suggest, is enough to establish that the terminology at 74a is notably eccentric; however, we might suggest tentatively that in each of Sedley’s examples, there is some implication that Socrates may not, at the very juncture at which he uses this terminology, yet be importing the full weight of his developed metaphysics. In Cratylus 439, Socrates uses such indefinite terminology to ask, in a way comparable to the Phaedo, whether or not they recognise ‘a beautiful itself and a good’ (439c), a question that has often occupied his dreams. The occurrence of this phrasing in the Republic comes before he makes his most substantial claims as to the nature of Forms of the work (Rep. 476c). In Parmenides 130b, Parmenides uses this terminology before Socrates has properly elaborated any theory of Forms. And in Timaeus 51b, again, this terminology arises as Timaeus asks whether we recognise abstract Forms, and offers an explanation of what he means by it; he does not, then, use it as a technical denomination of well-established meaning.

I would suggest that at none of these instances does Socrates bring out the theory of Forms with guns blazing; he is much more tentative. And, whether or not we accept this last point, this terminology, with the inserted αὐτὸ, as well as the formulae ‘αὐτὸ τὸ F’ and ὃ ἔστι, possesses a definite, specific tone (established by αὐτὸ, τὸ and ὃ respectively, and to differing degrees) that τι…ἴσον (74a) lacks. It is, I contend, sufficiently eccentric, then, to demand a reading that does not dismiss that eccentricity. I will return to this point below.[9]

    But why does Socrates relate these two terms, equal sticks and stones and the form of equal, as he does? Why does he introduce the ‘falling short’ of sticks and stones into his argument? Socrates’ project at this stage of the Phaedo is, in broad terms, to prove that the soul must have predated birth, since it can recall knowledge that it has previously had and lost: knowledge that it cannot have acquired at or after birth. He secures Simmias’ agreement to the premises that:

R1) εἴ τίς τι ἀναμνησθήσεται, δεῖν αὐτὸν τοῦτο πρότερόν ποτε ἐπίστασθαι (73c).

If anyone is to remember anything, he must know it at some previous time.

R2) ἐάν τίς τι ἕτερον ἢ ἰδὼν ἢ ἀκούσας ἤ τινα ἄλλην αἴσθησιν λαβὼν μὴ μόνον ἐκεῖνο γνῷ, ἀλλὰ καὶ ἕτερον ἐννοήσῃ οὗ μὴ ἡ αὐτὴ ἐπιστήμη ἀλλ᾽ ἄλλη (73c).

If a man, when he has heard or seen or in any other way perceived a thing, knows not only that thing, but also has a perception of some other thing, the knowledge of that thing is not the same, but different.

As has been frequently noted, R1 suggests a necessary condition for recollection, R2 a sufficient condition. [10]  Socrates seeks to show that our experience with regard to equal sensible items is a case of recollection so that he can apply the necessary condition contained in R1 to it; granted the premise of the necessary condition, then we have knowledge of the equality that we recall prior to our thinking of it. To establish this experience as a case of recollection, he endeavours to show that it fulfils the sufficient condition for recollection implied by R2.  He asks Simmias,

πόθεν λαβόντες αὐτοῦ τὴν ἐπιστήμην;…ἢ ξύλα ἢ λίθους ἢ ἄλλα ἄττα ἰδόντες ἴσα, ἐκ τούτων ἐκεῖνο ἐνενοήσαμεν, ἕτερον ὂν τούτων (74b);

Whence did we derive the knowledge of it?... Did we not, by seeing equal pieces of wood or stones or other things, derive from them a knowledge of abstract equality, which is another thing?

The sufficient condition falls into two tenets, each in correspondence with Socrates’ question. First, one must perceive one thing, and recall another. Second, the perceived object must be the object of knowledge different from what it leads us to recall. Socrates immediately goes on to argue for the application of the latter tenet, offering a syllogistic argument to establish the non-identity of equal sensible objects, and the form of equal. When he then turns to consider the line of thought of one confronted with sensible equal objects, and remarks on the awareness we will come to of the ‘falling short’ of sticks and stones (74d), he addresses the former tenet. The claim with which he has originally addressed this, that our knowledge of the form of equal is derived from sensible equal objects (74b), is not self-evident, and Socrates seems to offer this elucidation of the thought-process of one whom he claims to be recollecting in order to show how, and therefore that, perception of equal objects leads us to think of the form of equal.

I

   As most scholars agree, Socrates has offered an earlier precedent for the process of one experiencing recollection prompted by equal sticks and stones, as in P2. [11] Once he has defined the principles of recollection, he offers a portfolio of examples of its occurrence. He begins with cases of unlike recalling unlike (e.g. a lyre its owner (73d)), but ends with just one example of like recalling like: the scenario in which one sees a picture of Simmias and is reminded of Simmias himself. He then attaches an additional necessary condition to cases of like recalling like. He asks 

[P3] ὅταν γε ἀπὸ τῶν ὁμοίων ἀναμιμνῄσκηταί τίς τι, ἆρ᾽ οὐκ ἀναγκαῖον τόδε προσπάσχειν, ἐννοεῖν εἴτε τι ἐλλείπει τοῦτο κατὰ τὴν ὁμοιότητα εἴτε μὴ ἐκείνου οὗ ἀνεμνήσθη  (74a);

And whenever one recollects something from things like it, will he not also inevitably consider whether they bear a perfect resemblance to what is recalled, or fall short of it?[12]

The case for connecting this description of recollection to that in P2 is a strong one. Although Socrates and Simmias do not explicitly designate the example of recollection prompted by sticks and stones as an instance of like recalling like, it does appear to be such. For the distinction between the two breeds of recollection in Socrates’ list of examples is that like recalling like is a relation of similarity between the two entities that leads us to recollect. In the case of unlike recalling unlike, it is some other relation (e.g., ownership) that prompts recollection. Recollection of the form of equal prompted by equal things seems to be of the former character. Broadly, it is the immediately sensible equality, regardless of its possible shortcomings, of equal sticks and stones that leads us to think of the form of equal. This reading also explains Socrates’ addition of this necessary condition; it would be a surprising inclusion were he to make no further use of it. We might also note that the verbs ἐνδέω and ἐλλείπω share very close nuances. According to this reading, then, in P3 Socrates offers a model for the cognitive process at P2.

To begin to understand this model, we must consider what Plato regards as like things, or “ὁμοία” (74a). The Phaedo seems to suggest that anything that is like something else must bear some sensible resemblance to that thing.[13]  Yet Plato does not provide any great detail as to the nature of that resemblance. It is not clear in how many respects a likeness must imitate its original, nor how perfectly it must imitate it in each of these respects. 

We may find some helpful context in the Cratylus. There, Socrates remarks:

οὐδὲ τὸ παράπαν δέῃ πάντα ἀποδοῦναι οἷόν ἐστιν ᾧ εἰκάζει, εἰ μέλλει εἰκὼν εἶναι (Crat. 432b)

Certainly must not reproduce every feature of the nature of that which it imitates, if it is to be an image.

He also suggests that there would not be Κρατύλος…καὶ εἰκὼν Κρατύλου (‘Cratylus and his image’), but rather δύο Κρατύλοι (Crat. 432c) (two Cratyluses), if a god were to replicate not only Cratylus’ colour and form, as do painters, but also his insides, his mobility and warmth, his life, intellect and all other qualities (Crat. 432b-c). This implies that a likeness must have some features in some way in common with the original, but not every feature identical to its every feature. It would otherwise not be a likeness, but a duplicate.

I follow Harte in suggesting that a likeness must also stand in some dependent relation to that which it is like; this may be an intentional relation of representation (e.g. a life-painting), or an unintentional dependency, such as that between a reflection and the reflected object (Rep. 510a).[14] Here in the Phaedo, such a dependency emerges not only in the obvious case of the painting’s likeness to its object, Simmias, but in the case of equal sticks’ and stones’ likeness to the form of equal. It is suggested not only by the apparent analogy of the two cases, but by Socrates’ remarks that equal things “wish” (βούλεται (74d)) and “stretch”(ὀρέγεται (75a)) to be like the form of equal; this evokes a similar relationship of dependency as that of painting to original, ascribing to equal things the sentiments of the painter attempting to achieve a likeness.

With this in mind, I return to the model that Socrates sets up in P3; he suggests that it is “ἀναγκαῖον” (74a) whenever a person recollects something (‘y’) from the stimulus of something like it (‘x’), he considers whether or not x falls short of y. It has long been wondered why it should be “ἀναγκαῖον” (74a) that we make this assessment. It is no stretch to accept that this line of thought may be prompted by such recollection, but why must it be? This speaks to the heart of the cognitive process unfolding. I suggest that what Socrates shows us here is the process of distinguishing x from y, rather than that of qualitatively comparing them, and that to judge whether x ‘is lacking’ in comparison to y is simply to detect that it is different from y. By this reading, we can understand why this should be necessary in any case of recollection; were we to fail to detect the non-identity of x and y, the case would not be one of recollection, but of mistaking x for y.[15] And, in the cases of likenesses to originals, any basis for non-identity is not a neutral difference, but a falling short of the original on which it is dependent.

Let us consider the example of Simmias’ portrait. This might be like Simmias in form and colour, whether perfectly or approximately so. The shortcoming that we must detect need not lie in how well it fulfils its role as a likeness (e.g. in the accuracy of its colour), but simply in that it is a mere likeness; it is cold, it is two-dimensional, and it is therefore not identical to Simmias. Its colour may well be deficient, and that would assist us further in detecting its status as a likeness, but even it were a perfect visual representation, it would still be deficient of Simmias himself in that there is more to him than the visual, such as warmth and dimensionality. This interpretation finds support in the passage of the Cratylus cited above (Crat. 432); there, Socrates’ focus in demonstrating the deficiency of images was that they do not capture every feature of their originals, not that they capture those features imperfectly. And indeed he uses the same verb, ἐνδέω (Crat. 432d), to denote deficiency of this kind as Socrates uses in his later example of the same process in the case of sticks and stones.

Gallop objects to interpretations of this kind, claiming that according to this view, in differentiating between likenesses and originals, we articulate in our minds the nature of the differences between them.[16] I agree that it is possible (indeed, normal) to be entirely aware, upon looking at a life-painting, that it is a likeness of its original rather than mistaking it for the original itself, without explicitly acknowledging to ourselves how exactly it differs from the original.  But what Socrates here stresses is that we must somehow draw this distinction somewhere in the course of the cognitive process of recollecting, even if not explicitly, if we are not to mistake a likeness for its original; thinking or reflecting (ἐννοεῖν”(74a)) only requires that the idea be present somewhere in our minds, not that we consciously articulate the differences between likeness and original.

    Sedley raises a more serious objection.[17] He points out that in P3 Socrates takes the view that it is inevitable that either we consider whether x falls short of y, “εἴτε μὴ” (74a), “or we do not”. He argues that this “εἴτε μὴ” implies that there could be a case of recollection between like things in which the likeness in no way falls short of the original. On the interpretation of falling short, I have argued, a likeness will always fall short of its original, in so far as it is a likeness rather than a duplicate, to Plato’s mind. There would thus never be any possibility of a likeness not falling short, and so there would be no need to consider whether it falls short “εἴτε μὴ” (74a); in other words, the thought process implied by this “εἴτε μὴ” (74a) would be redundant. Sedley therefore prefers a reading in which we notice that likenesses fall short in the extent to which they fulfil their capacity as likenesses (i.e. in imperfectly representing the select aspects of the original that they imitate); many likenesses would fall short by this reading, but a perfectly true visual likeness would not. It would then make more sense to contemplate the possibility of a likeness not falling short.

However, as Sedley himself concedes, this reading does not make sense of the inevitability with which we undertake the process of contemplating whether x falls short of y.[18] Why could we not see a painting of Simmias, and immediately reflect on our desire to see him in person, rather than considering minor inaccuracies in the artist’s representation of the shape of his fingers? This reading does not entail the necessity that Plato seems to see for detecting shortfalls, which the kind of interpretation I have favoured does explain. And I do not believe that the “εἴτε μὴ” (74a) option does disqualify the reading I have taken, if understood as follows. At P3, Socrates considers the process of being reminded of y by x, not mistaking x for y. According to Socrates’ view, upon seeing something (‘a’) that resembles something else (‘b’), of which we have external knowledge, we, consciously or unconsciously, consider whether or not a is identical with b. If we decide that it is, then we mistake a for b, but if, and only if, we decide that it is not, then we think of b without believing a is b. In both cases, a evokes b, but only in the second case do we recollect; the first is a case of mistaken identity. Thus it is true to say that whenever one is reminded of b upon perceiving a, one considers whether or not a falls short of b in that a is non-identical with b (by the sense of ‘falling short’ that I have contended); in cases of recollection, we will always answer ourselves that it does fall short in this way. In other words, mistaking identity and recollecting share the first steps of their respective thought processes, the stage of questioning the identity of a and b; once we have answered ourselves, the experiences diverge.

I see no reason, therefore, to reject the reading I have favoured on the basis of these objections. Recollection in the case of Simmias and his portrait therefore proceeds as follows: one sees a picture of Simmias, which shares enough features with Simmias that Simmias himself surfaces in the mind; at this stage, we ask ourselves whether the picture falls short of Simmias himself or not. If we correctly notice that it does fall short, then we recollect; the picture has prompted us to recall Simmias, but we have not mistaken it for him. If we do not notice that it falls short, it still prompts us to recall Simmias, but we have mistaken it for him.

II

    What does this mean for the experience of Socrates’ recollector faced with equal sticks and stones at P2? This thought process is parallel to that which I have just described at P3. We might suggest that the knowledge that Socrates argues that we recover in this case, knowledge that has never surfaced in our embodied lifetime of the form of equal, seems to be more tenuous than what resurfaces when we look at a painting of Simmias, whom we recognise; the passage makes no stronger suggestion than that Simmias is simply not at the fore of our minds before we look at the painting. But from this we should merely conclude that Socrates conceives of our forgotten knowledge of the form of equal as latent just as our knowledge of Simmias is latent, such that perception of something with enough features in common with something else is called to mind; we must ask ourselves whether or not that something is identical with the form of equal. And that is what, according to this argument, occurs here: the recollector perceives equal, sensible items, they prompt the Form of Equal to resurface in his mind, and he distinguishes between the two entities, realising that they are not duplicates of the original, but fall short.

By this argument, any distinction that the recollector detects between equal things and the form of equal would be sufficient for him to distinguish between the two. But what does Socrates show us to be the difference in question? Here we should consider the subtle difference in phrasing between P1 and P2. P1 might, at first glance, appear to be restated in P2. P2 is, as we have discussed, states that in discerning original from copy, one must realise that they are not duplicates, that is, one must detect a ‘falling short’. However, P1 contains some detail as to the difference that we see: Socrates asks whether equal things seem to us to be equal as the Form of Equal is equal. This slight difference suggests that Socrates equates the process of detecting a ‘falling short’ and the process of detecting the difference in how each of the two entities are equal; in other words, the ‘falling short’ we detect is in the difference between their equalities.

    And, happily, Socrates has just provided an explanation as to the difference between their equalities in his syllogistic argument for the non-identity of equal things and the form of equal. As discussed, the formal function of this argument is to establish a non-identity such that the two entities will meet a criterion for recollection that he has set out, which demands that they be the objects of different knowledge. He seeks to show [S1], ∃P(Pm & P’n), which breaches his implicit condition for identity, [S2], ∀P(Pm ↔ Pn) (where P = a predicate, m = equal sticks and stones, n = the form of equal). He need only identify one predicate that satisfies S1 to do so, and it need not, in fact, be the difference by which the recollector distinguishes them; anything qualifying them as objects of different knowledge will do. However, the difference that he here highlights does indeed seem to be the precise difference that a recollector would detect: the difference in their equalities.

       The syllogism that Socrates sets up is riddled with interpretive difficulties. At the outset, we can roughly set out its form as follows (the translation of what I have left in Greek will be discussed below):

A1) Equal sticks and stones sometimes seem equal “τῷ μὲν” and not “τῷ δ᾽” (74b).

A2) To Simmias, the form of equal[19] never seems unequal, and equality never seems to be inequality[20] (74c).

A3) Therefore equal sticks and stones are not the same as the form of equal (74c).

Clearly, we must consider carefully whether the first two terms of this argument can be so construed as to yield its conclusion, and what the implications might be for our understanding of the relationship between equal items and the form of equal.

What Socrates means when he points out that equal sticks and stones “τῷ μὲν ἴσα φαίνεται, τῷ δ᾽ οὔ” (74b) has split the field of scholars. I follow Sedley in understanding “ἴσα” (74b) (‘equal things’) as ‘things that are equal to each other’; this is the far more natural interpretation of the Greek, and finds better support in Socrates’ earlier comments about equality (ξύλον ξύλῳ etc.)[21] than the alternative that he considers, that Socrates refers to a group of items which are each equal to some further item. Therefore, we can reject the interpretation rendering “τῷ μὲν…τῷ δ᾽” (74b) as equal ‘to one thing, but not to another’; it is the equality between them that is in question. 

We might next consider the possibility that Socrates here uses datives of reference to be taken alongside φαίνεται; equal things sometimes ‘appear equal to one person, but not to another’. This would allow us to modify the syllogism to:

B1) Equal sticks and stones sometimes seem equal to one man, and not to another man (74b).

B2) The form of equal never seems unequal, and equality never seems to be inequality, to Simmias (74c).

B3) Therefore equal sticks and stones are not the same as the form of equal (74c).

This interpretation, too, has its difficulties. Socrates seems, in B1, to predicate to equal sticks and stones the property of inconsistency of appearance to different people, but, in B2, to predicate to the form of equal the property of consistency of appearance to the same person, namely Simmias. He would not thereby have shown that the same predicate does not apply to his two entities. In my view, it is possible that Socrates here uses Simmias as a representative of all people, as Mills argues.[22] Alternatively, we may wish to translate “τῷ μὲν…τῷ δ᾽” as ‘to one spectator…to another,’,where Simmias would qualify as a different spectator when he a different position; Simmias in one position is one spectator, Simmias in another position is another. Thus, the “σοι” referring to Simmias would be a reference to different spectators (as it would refer to every different position or context of spectatorship that Simmias has ever taken up).

Socrates would then contrast equal things and the form of equal in that they respectively lack and possess a single property, that of consistency of appearance to different spectators, which would be the predicate involved in B1 and B2. That is to say, Socrates would be making a very broad point about the contextual dependence of the appearance of equal sticks and stones. I do not think these two interpretations are as obscure as Sedley believes, although they are not so obvious as to eliminate the need to consider further interpretative options.[23]

     Another possible interpretation is based on a respectable manuscript tradition replacing the problematic τῷ μὲν…τῷ δ᾽, which reads τότε μὲν ἴσα ϕαίνεται, τότε δ’ οὔ.[24] The syllogism would then stand as:

C1) Equal sticks and stones sometimes seem equal at one time and not at another (74b).

C2) The form of equal never seems unequal, and equality never seems to be inequality to Simmias (74c).

C3) Therefore equal sticks and stones are not the same as the form of equal (74c).

The predicate that Socrates suggests can be attributed to sticks and stones, but not to the form of equal, is that of appearing unequal over time, in contrast to the form, which never appears unequal. If we, reasonably, interpret “σοι” (74c) as referring to spectators in general, then this makes for a coherent syllogism. Sedley finds support for this reading in the Theaetetus, noting that this would render the argument very similar to that against the other-judging model of false belief (Theaet. 190b-d). It is, though, difficult to believe that Plato should write ἐνίοτε ταὐτὰ ὄντα τότε μὲν ἴσα φαίνεται, τότε δ᾽ οὔ, following ἐνίοτε with τότε in this way. Yet this does make sense; the ἐνίοτε is still required because this inconsistency cannot be assumed in every case (for example, if someone remains at the same angle to equal things, they may appear continuously equal, or continuously unequal). And, as Sedley notes,[25] this clumsiness may have been what motivated the scribal correction to the standard reading.[26] We therefore find here another plausible reading.

III

    This passage has often been taken to suggest the necessarily approximate nature of particulars to their Forms, with so-called equal sticks and stones never achieving exact equality, but always having the potential to approximate it more closely.[27]  My contention is that Plato’s argument involving sticks and stonescommits him to no such position, neither in his suggestion that equal sticks and stones fall short (“ἐνδεῖ” (74e)) of the form of equal, nor in the differences he highlights in the syllogism. [28] For, as I have argued, the sticks’ and stones’ falling short need only consist in that they do not capture every feature of the form (which, as physical items rather than an abstract concept, they clearly do not), not in that they imperfectly capture whatever features they do share with the form. On the argument so far, they might or might not capture perfectly those features that they have in common.

     Turning to the syllogism, whichever of the most plausible options we adopt (Mills’, or my version of the B reading, or the C reading), although the details of Socrates’ view might not be clear, his point is: the appearance of sticks and stones as equal is unstable and dependent on the context of their viewing.  But that is not to say that they are not by nature always objectively equal.[29] They are introduced as unequivocally, objectively equal (74b), as Sedley points out,[30] and there is no suggestion that their reality changes; it is the opposite, in fact, for Socrates notes that this change in their appearance takes place with them “ταὐτὰ ὄντα” (74b). And it would be very strange indeed for Socrates to imagine, without properly explaining, a situation in which the objective size relation between two sticks is changing, that is, in which at least one of them is growing or shrinking; we would have to possess a very good reason to assume such a peculiar reading. I cannot find any such reason. Sticks and stones differ from the form, in terms of equality, in that we assess their equality by means of the senses, and the senses provide necessarily unreliable evidence. Anything whose equality we assess by the senses will necessarily be of unstable appearance, and sometimes appear unequal. But the form of equal is not subject to such vulnerability, for we do not access or judge its equality through the senses. Contrary to the approximation view, Plato’s focus, then, is not on the actual size relation of e.g. sticks, but rather on their membership of a class (sensible, physical items) whose equality is judged by the senses, a necessarily unreliable authority.  

I find evidence that Plato was inclined towards this kind of thinking in the Symposium. There, he sets out that where the Form of Beautiful differs from beautiful particulars is that the Form is

οὐ τῇ μὲν καλόν, τῇ δ᾽ αἰσχρόν, οὐδὲ τοτὲ μέν, τοτὲ δὲ οὔ, οὐδὲ πρὸς μὲν τὸ καλόν, πρὸς δὲ τὸ αἰσχρόν, οὐδ᾽ ἔνθα μὲν καλόν, ἔνθα δὲ αἰσχρόν, ὡς τισὶ μὲν ὂν καλόν, τισὶ δὲ αἰσχρόν (Symp. 211a)

It is not in part beautiful, in part ugly, nor beautiful at one time and not at another, nor beautiful in one respect, but not in another, nor beautiful in one position, but not in another, such that it seems beautiful to some and not to others.

Again, Plato does not seem here to indict the objective nature of particulars as beautiful or not beautiful. For it would be extremely obscure to rely on the undefended view that particulars’ objective nature changes from time to time or place to place. A far more natural construal is that Plato here refers to different contexts of viewing (as especially suggested by the gloss “ὡς τισὶ μὲν ὂν καλόν, τισὶ δὲ αἰσχρόν” (Symp. 211a)). These particulars may well possess objective beauty; it is its appearance, how it is judged by the senses, which is unreliable.

Plato seems also to contrast objective reality with the unreliability of the senses as he discusses the appeal of art and poetry in the Republic; he remarks that the senses may easily be deceived as to differences of size, quantity and weight, but that in these cases measurement, counting and weighing will reveal the objective relations of the items, and set us aright (Rep. 602d). Furthermore, Plato does seem to conceive of perfect instantiations of the Forms, such as god, in Theaetetus 176b-c, and the ideal city Republic 427e.[31]  These particulars are also remarkable in that Plato seems to think that they could never be perceived by the senses;[32] the pairing of these eccentricities (perfect instantiation and non-sensibility) supports my view that it is belonging to the domain of the senses that explains the particulars’ shortfall.

And so, I hope that I have helped to wrest this passage of the Phaedo from those citing it in support of the approximation view of the Form-particular relationship. Equal sticks and stones fall short of the form of equal in that their size relation is necessarily approximate to objective equality; that is, they can never be more than inexactly equal, whereas the Form does exhibit perfect equality. Yet, as I have discussed, in remarking on the shortfall of sensible particulars, Plato here, as elsewhere, roots their deficiency in that, as sensible objects, we will necessarily judge their equality by means of the senses, which are unreliable.

He does not indict their objective nature, and indeed he does seem to suggest that these sticks and stones are objectively equal.  Nehamashas done a great deal of the work in refuting the approximation view more broadly. [33]  What I hope here to have contributed is some suggestion of how central Plato’s view of senses and sensibility must be to such refutation, and to any explanation of the Form-particular relationship seeking to supplant the approximation view.[34]

IV

     The importance of an accurate understanding of the Form-particular relationship to the general study of Plato needs no explanation here. But I think that a special significance of the interpretation of the shortfall of sticks and stones that I have urged in this passage emerges if we consider it in the light of the deflationary reading of “τι…ἴσον” (74a). This significance deserves some brief explanation, even if it cannot be fully explored within the confines of this paper.  

   If we accept the deflationary reading, then, this passage of the Phaedo may be construed as arguing for, rather than assuming, the Forms. By this reading, Socrates would start by suggesting that we entertain some general concept or standard of equality, which lies behind our understanding of individual cases of equality; this loosely-termed claim would seem uncontroversial to most interlocutors. His argument would then lead us to see that this concept of equality, as we entertain it, is something fundamentally different from individual cases of equality, and thus that it must be some separate entity, existing of itself and separate from these cases. The implication of this passage would thus be that our unexamined beliefs about equal things and equality yield the conclusion that there must be τι…ἴσον, existing of itself, beyond individual cases of equality, which he will denominate “αὐτὸ τὸ ἴσον” (74a). That is to say, Plato forces us to acknowledge that the concept of equality exists as some independent entity by pointing to its difference from equal things as we conceive of them.

This may well insinuate something further about how Plato himself reached his theory of Forms. I have argued that it is a difference of order that Plato highlights in this passage. A full exposition of how my account of this difference bears on the deflationary reading is for a work of greater scope. But what is immediately clear is that this difference may be not merely central, but formative, to the theory of Forms. An accurate understanding of it, then, takes on a corresponding significance.

Bibliography

Bluck, Richard, Plato’s Phaedo. A translation with Introduction, Notes, and Appendices. London: Routledge, 1959.

Bostock, David, Plato’s Phaedo. Oxford: OUP, 1986.

John Burnet, Plato’s Phaedo. Oxford: Clarendon, 1911.

Dancy, Russell, Plato's introduction of Forms. Cambridge: CUP, 2004.

Fine, Gail, Plato on Knowledge and Forms. Oxford: OUP, 2003.

Fowler, Harold North, Plato. Plato in Twelve Volumes. Vol. 1. Cambridge, Massachusetts: Harvard University Press, 1996.

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G. (ed.), New Essays on Plato. Wales: University of Wales Classical Press, 2006.

Mills, K. W. “Plato's "Phaedo", 74b7-c6”. Phronesis 2, no. 2 (1957): 128–47.

Nehamas, Alexander, “Plato on the imperfection of the sensible world.” In Fine, G. (ed.), Plato 1: Metaphysics and Epistemology. Oxford: Oxford University Press, 1999.

Sedley, David, “Form-particular resemblance in Plato’s Phaedo.” Proceedings of the Aristotelian Society 106 (2006): 311-27.

Sedley, David, “Equal Sticks and Stones.” In Scott, D. (ed.), Maieusis. Oxford: Oxford University Press, 2007.

Taylor, A.E., Plato. London: Methuen, 1922.

I am also grateful to Dr F.C.C. Sheffield for extremely helpful conversation on this topic, especially with regard to the arguments for the deflationary reading of “τι…ἴσον” (74a).