The ‘Forms’ that Plato famously postulated plainly have important links to how we conceive the world and its predicates. But just what, and how tight knit, are those links? Perhaps Forms are themselves conceptualized entities? Or if not, is prior acquaintance with them at any rate necessary to our own processes of conceptualization?
The present chapter will explore these and other possibilities with reference to a pertinent passage of the Parmenides (in Section 2) and another from the Phaedo (in Section 3). But I must start with a yet more fundamental question.
1 What are Forms?Footnote 1
In the early years of the fourth century bce, in the aftermath of Socrates’ execution and virtual martyrdom, Plato was one of a group of his followers who took up writing Socratic dialogues – fictional or semi-fictional transcripts which tried to keep alive the unique magic of the searching conversations Socrates had spent his life conducting on the streets of Athens. Plato’s first dialogues were thus, in this sense, about Socrates. But Plato became increasingly dissatisfied with the negative outcomes of the interrogations Socrates was portrayed as conducting, and increasingly ready to represent Socrates as venturing positive ideas which promised to break the deadlock those dialogues standardly reached. To what extent Plato as author would have avowed ownership of the theories that emerged is debated, but the theory of Forms was already credited to him by his contemporaries, and rightly so, since the Forms still play a key part in the Timaeus, a very late dialogue which, uniquely, seems to construct a Platonic system out of materials from preceding dialogues.
One of the ideas presented in the mouth of Socrates was the theory of Recollection.Footnote 2 When it comes to simple mathematical problems anybody, even with no prior expertise in the subject, can find the right answer out of their own inner resources, Plato suggested, simply by answering questions. Mathematical knowledge is, as we might want to say, a priori: when you think about an item of such knowledge, you realize that it could not be otherwise. Take Plato’s example,Footnote 3 our knowledge of equality. Something that you already know, whether or not you have ever thought about it before, is that equality is a transitive property: if two things are equal to a third thing, they are equal to each other. How do you know this? Not through your experience of the world, which often presents apparent counterexamples where two things look equal to a third thing but not to each other. Yet no amount of sensory counter-evidence could lead you to doubt the principle, because you already know it to be true: on reflection, that is, you see that it could not be otherwise. To Plato this can only mean that you were born already knowing such truths. And what applies in the case of simple mathematical and logical truths must also apply to the more difficult domain of philosophical discovery. In Plato’s view the reason why philosophers intuit that problems like the true nature of goodness can eventually be conclusively resolved by mere discussion is that the answers to these questions too are already present in our souls, waiting to be brought to the surface. Hence Plato’s famous doctrine of Recollection: all learning is recollection.
Plato’s deeply controversial further inference is that our souls must have acquired the knowledge before they entered our bodies, so as to be able to bring it with them in however buried a form. Take, then, your buried knowledge of equality. If before your birth your soul could, while detached from the body, know the true nature of equality, the nature of equality must be directly accessible to the soul without the mediation of the body’s sense organs. The same will apply to goodness, and to all the other items investigated in philosophical conversation. That, then, is Plato’s first presupposition, namely that the key entities and properties investigated by mathematicians and philosophers are intelligible, not sensible: they are accessible to the intellect directly, not via the senses.
The second presupposition is as follows: Our innate knowledge of entities like equality and goodness could not be objectively true, as it certainly is, if the objects of which it is true did not even exist. We will return to this later.
From these first two presuppositions it already seems to follow that entities like equality and goodness exist in their own right as objects of pure intellectual inquiry, unmediated by the senses.
A third assumption connects this finding in turn with Socrates’ own most prominent intellectual project, his constant search for definitions.Footnote 4 According to Socrates in Plato’s portrayal,Footnote 5 you cannot know something unless you are able to say what it is, that is, articulate a successful definition of it. It seems to follow that the objects of pure intellectual enquiry can be equated with objects of definition. Getting to know such items as equality and goodness is, in whole or in part, a matter of arriving at their definitions.
In the light of this we may now return to the objects of knowledge and definition, those entities, like equality and goodness, with which our souls are presumed to have become acquainted before birth. Are they changeable, or altogether unchanging? Given that knowledge of them is founded on their definitions, Plato seems justified in his assumption that they are in fact entirely unchanging. So far as knowledge as such is concerned, its objects might for all we know at this stage have been capable of change, in which case the knowledge of them would correspondingly become out of date: for example, my knowledge that today is Thursday will be out of date tomorrow, its object having changed at midnight. But since our knowledge of equality, goodness, and their like rests on our grasping their definitions, and given the further plausible assumption that those definitions are not such as to become out of date – for example what largeness actually is never changes even when new and larger things are created – Plato would seem to have confirmation that the proper objects of knowledge are themselves unchanging.
But even if what equality is never changes, doesn’t goodness, being a value, unavoidably vary according to local cultural norms and fashions, and hence also over time? Did Plato overlook this option? The answer is that he was familiar with such views but decidedly rejected them. The intellectual culture in which he grew up made widespread use of a distinction between objective or absolute facts, said to exist ‘by nature’ (phusis), and variable, culturally determined norms, said to depend on mere convention (nomos). Plato may seem to be recognizing this very distinction in his dialogue Euthyphro,Footnote 6 when he has Socrates point out that no one need quarrel about weights, measures, and the like, since there are agreed standards for settling such disputes, whereas it seems inevitable that there should be disagreements about such matters as good, beautiful, and just. But Plato would certainly not approve the diagnosis of this in terms of the nature-versus-convention distinction, or of what has subsequently come to be known as the fact–value distinction. In his view, what makes disagreements about values like goodness and beauty unavoidable is not that these are irreducibly subjective or relative, but that they are extremely difficult to define and understand. Basic mathematical thought is easy to master. In the Meno (82a–85b) Plato shows an uneducated slave, under interrogation, working out a simple geometrical theorem in just minutes; and he has Socrates readily formulate definitions of basic mathematical concepts like speed and shapeFootnote 7 in order to illustrate what a proper definition should look like. His point is, again and again, that mathematical disciplines are comparatively easy, and already successfully established. Ethics, by contrast, the science of the good, the beautiful and the just, is (a) incredibly difficult, and (b) still in its infancy. Indeed, it is Plato’s own self-appointed task, in the wake of Socrates, to create precisely such a science. In the RepublicFootnote 8 he will calculate, however fancifully, that the scientific study of goodness is so difficult as to require a preliminary ten years of mathematics, followed by a further five years of dialectical training.
In short, for Plato there is no fact–value distinction. Values are facts, just incredibly difficult ones to master. That is why simple mathematical properties like equality and demanding ethical properties like goodness can be treated under a single theory, and why mathematics, with its proven successes, can be seen as setting a model which a future science of ethics may be expected to follow.
We have now seen why it is that the objects of knowledge and definition, whether in mathematics or in ethics, must be unchanging entities, about which fixed and objective truths are available to discover. Given the widely agreed further assumption that all physical entities are subject to change, it follows for Plato that the objects of knowledge and definition are non-physical.
To sum up the results so far, the objects of knowledge must be eternal, changeless, non-physical entities, accessible directly to the intellect without reliance on the body and its sense organs.Footnote 9
We must now turn to a different consideration. According to Plato, special problems arise in connection with properties which have an opposite: largeness, equality, goodness, etc. For these are found in perceptible objects only in an impure and ambiguous form, mixed with, or alternating with, their own opposites – respectively smallness, inequality, and badness. That is, whatever perceptible object is large in one relation can also be seen in some other relation as small and so on for beautiful and ugly, equal and unequal, and all other pairs of opposite properties. To generalize: if ‘F’ and ‘un-F’ stand for any pair of opposites, then whatever sensible thing is in a way F is also un-F in some other respect, at some other time, for some other subject, or in some other relation. Pairs of opposite properties are thus no more than unstably present in the world around us. Any judgement about whether some given object is large or beautiful must be irreducibly provisional, context-dependent, and contingent: there is no single undeniably right answer.Footnote 10
This confirms that neither knowledge of largeness, a simple knowledge which we already have at our fingertips or can easily put there, nor knowledge of beauty, to which we at best may still aspire as a long-term goal, can possibly be empirical. It is a fundamental assumption of Plato’s that knowledge, once acquired, cannot be subject to revision: if it were, it would not have been knowledge in the first place. Yet if it had as its aim the identification of largeness or beauty as we experience these in the sensible world, it would inevitably be subject to revision, these being inherently unstable properties which constantly jostle with their own opposites to manifest themselves. The largeness and beauty of which we can have knowledge are not, then, the largeness and beauty physically present in the world around us.
One more background assumption still needs to be added. In the many dialogues devoted to definition, Plato’s Socrates insists that the object to be defined, regardless of the multiplicity and variety of its manifestations, must itself be one single thing. However disparate in other regards the set of things called beautiful may be, the beauty in which they share must be a unitary, unvarying property. Although this principle of the Unity of Definition, a vital underpinning of Plato’s theory of Forms, was already to be challenged by his own pupil Aristotle, its attractiveness is obvious enough. Barring the very unlikely supposition that the many things called beautiful owe this shared designation to a mere accident of language, as when we use the word ‘toast’ both for a celebratory drink and for a grilled slice of bread, it does indeed seem likely that they are linked by some single property that runs through all the instances.
In his early, Socratic dialogues Plato was already starting to call this unitary object of definition a ‘form’: the Greek word is eidos or idea. This was not yet a remotely technical term, just a convenient way of picking out the character or property that makes something the kind of thing that it is. What we call Plato’s theory of Forms is expressed with this same term, but by a modern convention we tend for convenience to spell ‘Forms’ with a capital F. This spelling at a stroke turns ‘Forms’ into a technical term. What does the technicality add or make explicit? That question brings us to the main topic of this section. What is a Platonic Form?
The key is separation. The eternal and changeless ‘Forms’, which as we have seen are sought in definitional inquiries and are the potential objects of pure knowledge, exist separately from all their sensible instances, rather than being immanent in them. This is a metaphysical separation, but it has a linguistic counterpart too. Suppose I say, ‘Tom and Bill are large’. The names ‘Tom’ and ‘Bill’ are jointly the linguistic subject, and the word ‘large’ is their linguistic predicate. What correspond to these metaphysically are Tom and Bill themselves, and an actual predicate or property, largeness, that they possess in common. This metaphysical predicate is not their own distinct individual largenesses, but largeness itself, in which they both alike participate. Suppose next that I want to tell you what this shared predicate is or means. What I do, linguistically speaking, is pick out the predicate large and turn it into a subject in its own right. The way to do that in Greek is to employ the expression ‘large itself’: Tom and Bill are large, and as for large itself, it is …. In Greek the expression for ‘large itself’ adds the definite article, ‘the large itself’, and this style of expression – ‘the Large itself’, ‘the Beautiful itself’, and so on – came to be Plato’s most familiar way of referring to Forms.
However, almost as common in Plato’s writings is the same expression but combined with the pronoun ti which serves in Greek as the indefinite article: there is ‘a large itself’, ‘a beautiful itself’, and so on. This is usually his way of putting forward an existential hypothesis about Forms: Socrates is presented as saying (Phd. 74a), hypothesizing (Phd. 100b), or even ‘dreaming’ (Cra. 439c) that there are ‘a Beautiful Itself’, ‘a Good Itself’, and so on: that is, as positing that Forms of these various predicates actually exist.
Why should this existential question arise? To claim that there is, say, ‘a Large Itself’ is to claim that there is such a thing as largeness independently of whatever subjects it happens to inhere in. Or, to put the same metaphysical point in linguistic terms, it is to claim that the predicate ‘large’, as in the sentence ‘Tom and Bill are large’, can be picked out and used as a bone fide subject of predication in its own right. In the case of largeness, this is not really in doubt. As Plato has Socrates point out in the Meno (72d–e) everybody, adult and child, free and slave alike, in so far as they are large, are large in the same way. We know this, he means, and could confirm it if there were any doubt, because the predicates large and small are the objects of a simple and already successful science – that of measurement. But what about a so far undeveloped science, like that of beauty or goodness? For all we know at present, there may be nothing more to being beautiful than being a beautiful sunset, a beautiful painting, and so on, or being beautiful within this or that culture or value-system. That is, beautiful may for all we know be an irredeemably context-dependent predicate. Whether beautiful can also serve as a bona fide subject – whether there is such a thing as the Beautiful Itself, definable and knowable in its own right and independently of all its manifestations – is a question we will not be able to answer affirmatively until a science of beauty has been established.
Even if in this regard, as in others, the precise range of concepts that have Forms remains flexible,Footnote 11 it should be clear that a primary condition for qualifying as a separated Form is to be a bona fide subject of independent truths, not reducible to or dependent on facts about its sensible manifestations. Plato also gives many indications that, whereas facts about those sensible manifestations are contextual, unstable, and contingent half-truths (in a way true, in a way false), about which our opinions are constantly subject to revision, the corresponding facts about the Forms are unqualified truths – independent of context, unchangeable, and, in that they could not have been otherwise, knowable with certainty.
This contrast between two distinct ontological realms is linked by Plato to two competing means of cognitive access: the intellect, and the senses. Consequently, Plato is often, and I think correctly, credited with a ‘two world’ thesis.Footnote 12 There are two worlds: the intelligible world, populated by Forms, and the sensible world, populated by sensible particulars. Inquiry about Forms is pure intellectual inquiry, which must minimize or eliminate the use of the senses. And since knowledge is in its nature permanently true and not subject to revision, the unchanging world of Forms constitutes a suitable object for knowledge. By contrast, the familiar world of sensible particulars is suitable only for opinion: opinion, being in its very nature capable of fluctuating between true and false, is the appropriate mode of cognition for inherently unstable objects. On this basis, Plato operates not only an epistemological distinction between the intelligible world and the sensible world, but also, and directly mapping onto this, an ontological distinction between a world of pure being and a world of pure becoming. Intellectual access to the world of being affords us an understanding of what such things as equality and beauty really and timelessly are, whereas sensory access to the world of becoming does no more than track the ebb and flow of the corresponding predicates – their ‘becoming’, as he calls it in Republic 6–7 and the Timaeus.
Plato is committed to the principle that sensibles not only share their names with the corresponding Forms but also owe their characters to those Forms: if a particular is properly called beautiful, such beauty as it possesses depends, not just linguistically but metaphysically as well, on the Form of Beautiful. It is in fact beauty – the Form – that causes things to be beautiful, and largeness that causes them to be large. Only if you know what beauty or largeness itself is do you know precisely what it is that makes this music beautiful or that building large.
In view of this causal role of Forms,Footnote 13 the radical separation of the two worlds comes at a price. The more separate the two worlds are, the harder it becomes to understand how Forms can have any causal or indeed other impact on the world we inhabit. To his eternal credit Plato, far from shirking this problem, devoted several intricate pages of his own dialogue the Parmenides (127d–134c) to airing it. The wise elder philosopher Parmenides, naturally understood as voicing Plato’s mature perspective, is shown quizzing a very young Socrates, who on this occasion represents Plato’s earlier ‘classical’ theory of Forms, now placed under close critical scrutiny.
Their conversation comes to focus on the question, what does it mean for particulars to ‘participate’ or ‘share’ in these separated Forms? In the end the young Socrates is driven to abandon his initial literal understanding of this ‘participation’, telling Parmenides that the term should instead be understood as meaning likeness. Forms are ideal paradigms, and particulars get their properties in virtue of the degree to which they are likenesses of those paradigms. Although Parmenides proceeds to find a difficulty with this account of the Form-particular relationship as well, the fact is that the likeness model is and remains by far Plato’s favourite way of expressing that relationship, in a range of dialogues of which at least one, the Timaeus, is generally agreed to postdate the Parmenides. We should therefore take the young Socrates’ retreat to a likeness model as, from Plato’s point of view, a mark of progress.
Plato’s idea that Forms are paradigms has often given the impression that a Form is conceived by Plato as an ideal exemplar of the common property represented, rather than as being that property itself. That same impression is strengthened by Plato’s notorious ‘self-predication’ assumption.Footnote 14 To him, that is, it seems blindingly obvious that a property is truly predicable of itself: largeness is large, piety is pious, and so on for every property. As Socrates is already heard saying in Plato’s early dialogue Protagoras (330d–e), it is hard to see how anything else could be pious, if even piety itself is not pious. If piety itself really does have the strongest claim to be pious, it could once again seem plausible that Plato is conceiving piety itself as an ideal model or exemplar which paradigmatically manifests the property in question.
This temptation should be resisted. A Form, being the one thing shared by many diverse but like-named particulars, is a ‘one over many’: not a further particular but a universal. The sense in which the Form of, say, Largeness is a paradigm against which all individual attributions of largeness are to be tested, and approved insofar as they resemble it, is not that largeness is – absurdly – a supremely large thing. It is that largeness itself, a universal, fully satisfies its own definition, and that other things are large precisely insofar as they too satisfy that same definition, that is, insofar as they resemble largeness itself. Largeness itself is definable as the power to exceed, and other things are large precisely insofar as they too, no doubt more episodically, manifest a property that satisfies that same description, namely their own individual power to exceed.Footnote 15
Although the way in which Forms serve as paradigms that sensible particulars imperfectly imitate is, for reasons I have tried to explain, different from the way in which a perfect specimen of some property is a paradigm of it, the notion of Forms as paradigms has proved useful as an aid to understanding why Plato takes the self-predication of Forms – that Beauty is beautiful, Largeness large, and so on – to be an obvious truth. Compare, the paradigmatic role of the standard metre.Footnote 16 In Paris there is a metal bar which serves as the paradigm for what counts as a metre. What we should, strictly speaking, compare to a Platonic Form is not that metre bar itself, but the length of the metre bar. Consider the functional parallelism. Plato sometimes speaks of Forms being ‘present’ in particulars, sometimes of particulars ‘sharing’ or ‘participating’ in the Form, and sometimes of particulars ‘imitating’ or ‘resembling’ the Form. All of these locutions will work equally well for the length of the metre bar. If a piece of string is one metre long, we might say, it has that property insofar as the length of the metre bar is present in it, or insofar as the string shares the length of bar, or insofar as the string, or perhaps rather its length, resembles the length of the metre bar. Under all these descriptions, the string’s being one metre long is both contingent and subject to revision. Contrast that with the way in which the length of the metre bar measures one metre. We don’t even need to check it to know that it is one metre: since it sets the standard, it could hardly fail to meet it. Likewise, it is tempting for Plato to say that Beauty itself sets the standard for what it is for things to be beautiful, in which case it, of all things, can hardly fall short of that standard.
2 Are Forms Concepts? Parmenides 132b–c
The following brief but dense exchange occurs in the ParmenidesFootnote 17 just before Socrates resorts to the equation of Forms with paradigms (Parm. 132b3–c12; see above, pp. 81–83):
‘But Parmenides,’ said Socrates, ‘I suspect that each of these Forms (eidē) is a thought (noēma), and that the only appropriate place for it to come to be is in souls. In this way each would at any rate remain one, and would no longer suffer the consequences mentioned just now.’
‘What about this then?’ said Parmenides. ‘Is each of the thoughts one, yet the thought of nothing?’
‘No, that’s impossible,’ said Socrates.
‘But rather of something?’
‘Yes.’
‘Of something that is, or is not?
‘That is.’
‘Namely of some one thing which that thought thinks, which is set over all the cases and which is a single Idea?
‘Yes.’
‘Then won’t this thing – the thing which is thought (nooumenon) to be one and which is always the same thing set over all cases – be the Form (eidos)?
‘It again appears necessary.’
‘Well then,’ said Parmenides, ‘by the necessity by which you say that other things share in the Forms, does it not seem to you that either each thing consists of thoughts, and everything thinks, or despite being thoughts they are unthinkable?’
‘But that doesn’t make sense either’, he replied.
This is the one place in the corpus where Plato explicitly highlights the view that Forms are conceptual entities. What then does Socrates mean here by his mentalist (as I shall call it) suggestion that Forms are the sorts of thing whose proper place is inside souls or minds?
There has been considerable scholarly uncertainty as to whether these ‘thoughts’ (noēmata) are meant to be acts of thinking, or the things thought. On the latter view, the ‘things thought’ might be either the propositional content of those acts of thinking, for example a definition, or some kind of intentional objects captured, or even created, by those same acts – these last being closest to what we today might term ‘concepts’. Neither the form of the word noēma, with its termination -ma, nor its meagre record of occurrences in other dialogues, is enough to settle the dispute in favour of the latter contents/objects interpretation.Footnote 18 And in fact I believe there is sufficient evidence to confirm that the other view, that Forms are here being viewed as acts of thinking, is the one that Plato has in mind, or at any rate represents his two discussants as having in mind.Footnote 19 Here are three reasons.
First, Parmenides’ closing criticism in the above passage presupposes such an interpretation. Down to this point in their conversation Socrates has naively assumed, with Parmenides’ encouragement, that when particulars ‘share’ or ‘participate’ in a Form, this must mean having some of the Form in them. (It is only at Parm. 132d3–4, in the lines following the current passage, that Socrates will finally abandon that assumption.) As a result, Parmenides is enabled to argue that, if Forms are thoughts, either (1) ‘each thing consists of thoughts, and everything thinks’, or (2) ‘despite being thoughts they [the Forms] are unthinkable’. The meaning of (2) is notoriously obscure, and it can be translated in other ways than the above. But it is at least compatible with the acts-of-thinking interpretation: thus understood, a thought that cannot be thought would be an act of thinking that can never be performed. If a Form were that, it would be forever intellectually inaccessible to us.Footnote 20 And the meaning of (1) positively demands the acts-of-thinking interpretation. Parmenides’ objection makes sense only if he is inferring as follows:
(i) Participants in F-ness have some F-ness in them (Socrates’ assumption).
(ii) F-ness is an act of thinking (Socrates’ hypothesis).
(iii) Therefore, participants in F-ness have some of that act of thinking in them.
(iv) Hence, by generalization, everything that participates in Forms contains parts of many acts of thinking, as many as it contains Forms.
(v) Therefore, everything thinks (reductio ad absurdum).
Second, Parmenides has said, and Socrates agreed, that if a Form is a thought, then it will be the thought ‘of some one thing which that thought thinks’ (132c3–4). That a ‘thought’ (noēma) should itself be said to ‘think’ something is a perfectly sound Platonic usage,Footnote 21 but would scarcely make sense if the thought doing the thinking were identified with the object or propositional content of a thought. This turn of phrase once more steers us away from the contents/objects understanding of noēma, and hence back towards the acts-of-thinking alternative.Footnote 22
Philosophically most important, however, is a third, more positive reason for adopting the acts-of-thinking interpretation. As we heard Socrates put it, if a Form is a thought, ‘the only appropriate place for it to come to be in is in souls’. This should ring a bell. Elsewhere in the Platonic corpus Plato’s principal speaker remarks that a soul is the only thing in which nous – ‘intelligence’, ‘thought’, ‘understanding’, ‘reason’ or ‘intellect’ – can come to be (Soph. 249a6–8, cf. Tim. 30b3, Phlb. 30c9–11). This recurrent motif encourages the expectation that if a specific ‘thought’ (noēma, which we now might render as an ‘act of nous’) can, like nous as a whole, come to be only in a soul, as Socrates and Parmenides take to be obvious, that is a specific application of the very same principle. In which case we may plausibly equate each noēma with some specific activity of nous. If for example the Form of Largeness is such that it can reside only in souls, that will be because it is, along with Smallness, Equality, Oddness, Beauty and many others, one component of the global framework of thoughts or cognitive acts that jointly constitute nous as a whole.
In order to understand Parmenides’ main critique of this proposal in the passage quoted, we need first to consider more generally Plato’s assumptions about the activities and objects of cognitive powers. Take vision, along with its proper object, colour. According to a model prominently used in the Theaetetus,Footnote 23 vision and colour function as a pair of ‘twins’ (Tht. 156a–c). When your eye sees a stone as white, the cognitive process has two matching components: one is the perceived whiteness on the surface of the stone, the other is your eye’s perception, specifically its vision, of that very same whiteness. They are twins because for the stone’s surface to appear white to your eye just is for your eye to be experiencing that whiteness. The twins are interdependent in the strong sense that they are paired aspects of one and the same cognitive process.
Aristotle would later clarify the point in terms of potentiality and actuality: the object’s potentiality to be perceived and the subject’s potentiality to perceive it are two different capacities, but the actualization of the one just is the actualization of the other (De an. 3.2 425b26–426a19).
Aristotle’s potentiality-actuality distinction was not explicitly anticipated by Plato, but a much-debated passage towards the end of Republic 5 (usually dated a little earlier than the Theaetetus) shows that Plato was looking in the same direction. There Socrates sets out to show that knowledge (epistēmē) and opinion (doxa) must have different objects, so that knowledge can be exclusively about Forms, opinion exclusively about sensibles. Every cognitive power is unique, he maintains, in two ways. (a) It has its own proper object: vision discerns colour, for example, and hearing discerns sound.Footnote 24 (b) It has its own unique product. What that product might be is not specified, and to make headway with identifying it we should notice that Socrates conflates (a) and (b) into, in effect, one and the same criterion: ‘Among the properties of a power I look only to the following thing (δυνάμεως δ᾽εἰς ἐκεῖνο μόνον βλέπω), namely both what its object is and what its product is (ἐφ᾽ ᾧ τε ἔστι καὶ ὃ ἀπεργάζεται)’ (Resp. 5.477d1–2). This subtle shift between unity and dualityFootnote 25 shows that Plato is already thinking in the terms that will find an alternative articulation in the Theaetetus twins passage: what makes vision, for example, a distinct cognitive power is that it (a) discerns precisely one object unique to it, colour, and (b) thereby brings about in perceivers the product that it alone can generate, namely their seeing that very same colour. In the case of knowledge, the equivalent roles are taken by (a) the changeless Forms, and (b) the thinking subject’s correspondingly unerring cognition of those Forms.
These examples illustrate an epistemological principle generalized in the Charmides (165c–169a):Footnote 26 no psychological or other power can be internally self-focused, but each must correlate to a distinct object external to itself. In the most typical cases this is because a purely self-focused power could not generate the beneficial ‘product’ expected of it.Footnote 27 For example, medical skill produces health, and the building skill produces a house, both of these being external to them. But even where there is no such evident external ‘product’, Socrates insists, there is certainly still an object, in the case of the skill of counting, for instance, the odd and the even (Chrm. 165e–166b). And that object, he insists at length, is necessarily distinct from the cognitive activity itself.
Returning to our passage in the light of this recurrent Platonic motif, we can see that Parmenides’ first question rested on a thoroughly Platonic assumption. The thought in our souls when we contemplate F-ness cannot itself turn out to be F-ness, because thought, like all other mental powers and activities, requires a further entity, a proper object distinct from itself.
That Platonic principle provides Parmenides with his first move: if Forms are thoughts, the thought each time must be the thought ‘of something’ (Parm. 132b10). From there he and Socrates proceed immediately to the further agreement that this object should not be equated with something ‘that is not’ but with something ‘that is’ (Parm. 132c1–2). What does this add?
The ‘being’ in question seems functionally ambiguous between a thin and a thick understanding. On the thin interpretation, Parmenides’ point could be existential. To think of what-is-not = to think of the non-existent = to think of nothing = not to succeed in thinking at all. Hence any successful thought must be of something that ‘is’, understood existentially. Not only are the elements of this inferential sequence well attested elsewhere in the Platonic corpus (e.g., Resp. 5.478b-c; Euthyd. 283e-284c; Tht. 160a-b; Soph. 237b-239b), they arguably underlay Plato’s own mathematical ‘platonism’ when, as reported,Footnote 28 he postulated a special ‘intermediate’ class of entities for mathematics to be true about, given that its objects could not be either sensibles or Forms. On such an interpretation Parmenides is, to borrow the Theaetetus’ metaphor, establishing that if there is a thought in the soul there must also exist some matching ‘twin’ external to the act of thinking, much as, if there is vision in the eye there must also, externally to the vision, exist its object, the colour of the thing seen. Implicitly, there would be no seeing if the external object, instead of existing, were merely imagined or invented by the perceiver.
On the thicker interpretation, Parmenides may instead, or more probably in addition, mean that the thought’s external twin must ‘be’, not merely as a perfunctory existence-requirement,Footnote 29 but because the sort of ‘thought’ that the young Socrates might expect to play the role of an eternal and unchanging Form would have to have as its proper object something that in its very nature purely is, and in no way is not. That is after all precisely how we are asked to think of ‘knowledge’ (epistēmē) in Republic 5.476e–479b: knowledge is of that which ‘purely is’, by contrast with mere unstable opinion, which has as its objects a range of fluctuating sensible entities, formally analysed as that which ‘at once is and is not’ (Resp. 478d). The Republic 5 argument moreover makes it fairly clear that the being it invokes is fundamentally predicative: being F, where F is a predicate. Opinion is about what ‘at once is and is not’ because when you opine that some sensible object is, say, beautiful, thanks to its predicative instability (dependence on context, viewpoint, etc.) it is only in some ways beautiful, and in others not. Knowledge, by contrast, depends for its own stability on the corresponding stability of its object. When you know how the Beautiful Itself is beautiful, that predication (a case of ‘self-predication’, cf. above, p. 000) is not subject to revision or qualification. Since the Form sets the unchanging standard for what is beautiful, it cannot at any time fail in any respect to satisfy its own proper definition, which by contrast its perceptible participants must frequently fail to satisfy.
This second and thicker interpretation of the Forms-thoughts hypothesis must treat ‘thoughts’ (noēmata) not in the term’s weak sense as covering all acts of cogitation, but as referring to the proper acts of the intellect (nous) when it grasps Being.
Plato may well intend to leave room for readers to make their own choice between the thinner and the thicker reading.Footnote 30 But it is worth noticing one hermeneutic advantage of adopting, or at least including, the thicker reading. Once the twinned nature of cognitive events had been invoked, we saw Socrates quickly concede the necessity that it be the external twin, rather than the corresponding thought within the soul, that we identify with the Form (Parm. 132c3–8). On the thinner interpretation, the text would be offering us no clear reason for his ready concession. For even if we grant that, like every cogitative act, thought about Forms requires the twinning of (a) the thought and (b) its proper object, with the latter being here a mere unspecified ‘something’, nothing immediately follows as to which of (a) and (b) has the stronger claim to be equated with the Form.
In contrast, if we allow the thicker interpretation of ‘be’, Parmenides does use it to specify just what object is properly twinned with the thought of F-ness: it is that single unvarying entity, set over all F things, which ‘is’ F in the strong sense of being what F-ness itself is, in contrast to the many F things that become F in a merely relative, ambiguous, or transient manner. If the external object twinned with our own mental conception of F-ness is agreed to have that kind of ‘being’, any reader of the Republic would recognize it, rather than its mind-dependent twin, as having the primary claim to be the Form.
Thus far, then, we have seen strong reasons to understand Plato in the Parmenides as arguing, contrary to the mentalist proposal, that a Form must be something external to the act of thinking by which we conceive it. True, externality to the act of thinking could in principle allow the Form still to be somehow internal to the mind, perhaps as the thought’s intentional object. But since the proposal that Forms are located in the mind does not recur hereafter, and in fact Socrates’ very next move is to propose that Forms are on the contrary paradigmatic entities ‘established in nature’ (ἑστάναι ἐν τῇ φύσει, Parm. 132d2), it seems clear that the mentalist proposal has now been abandoned.
A further pointer in the same direction is given by Socrates’ originally stated reason for advancing the mentalist suggestion (Parm. 132b5–6): ‘In this way each would at any rate remain one, and would no longer suffer the consequences mentioned just now.’ Whatever consequences mentioned ‘just now’ Socrates may be seeking to avoid, they can hardly fail to include those drawn in Parmenides’ controversial ‘Third Man Argument’ against the Forms, that being the immediately preceding passage of the dialogue, and therefore either the sole or the primary reference of ‘just now’. Significantly, the Third Man Argument, to which we will now turn, generated its unwelcome result, a pluralization of each Form, by treating Forms as something you can ‘look onto with your soul’ (Parm. 132a7). Evidently Socrates’ immediate motive for resorting to the mentalist hypothesis was to relocate the Forms and place them inside the soul, precisely where the soul could not look onto them. The default assumption therefore, to which Socrates must be assumed to return after the failure of the Forms-as-thoughts alternative, is that Forms are objectively real, external, mind-independent entities.
Although there is no room here to discuss the Third Man Argument in detail, a glance at it will help clarify the above distinction between what is in the soul and what can be looked onto by the soul.
First, then, the argument itself (Parm. 132a1–b2):
‘I think it is for the following sort of reason that you believe each Form is one thing. When it seems to you that there are many particular large things, perhaps it seems to you, as you look onto them all, that there is one Form, the same one, thanks to which you judge the Large to be one.’
‘What you say is true’, replied Socrates.
‘But what about the Large itself and the other large things? If you look onto them all in the same way with your soul,Footnote 31 won’t a single Large appear again, because of which all these appear large?’
‘Apparently.’
‘In that case another Form of Largeness will put in an appearance, generated over and above Largeness itself and the things which participate in it. And in addition to all of these again a further one, because of which all of them will be large. And you will no longer have each of the Forms as single, but as infinite in number.’
The emphases added above pick out the roles of the Form of Largeness (i) as the cause of largeness,Footnote 32 and (ii) as among the things that can be seen by the mind’s eye. How do these assumptions generate the regress?
The world contains many cases of largeness, each of them satisfying one and the same definition of this term, which as throughout this chapter I am taking to be ‘the power to exceed’.Footnote 33 When with your mind’s eye you look synoptically at these multiple cases of largeness, you find (at any rate if you share Plato’s view of causation) that what causes, or is responsible for, all these largenesses is a single Form of Largeness. But since this Form itself satisfies the same definition, ‘the power to exceed’, in recognizing the Form’s existence you are increasing by one the number of powers to exceed, or largenesses, seen by your mind’s eye. What in that case makes them all largenesses? Not that same Form again, because it would then be, impossibly, its own cause.Footnote 34 So a second Form of Largeness has to be recognized as the cause of this expanded set of largenesses. And it results in a yet further expansion, and a yet further Form; and so on, indefinitely.
If such is the argument, how does its efficacy depend on the Form’s being external to the mind, so as to be ‘looked onto’ by it? First, the argument turns on the Form’s having its own causal efficacy everywhere, even in contexts where our own minds could be nothing more than bystanders and observers, if indeed even that. Second, if the Form of Largeness were internal to the soul, amounting to no more than our own thought of largeness, it is hard to see how it could itself be counted as another actual case of largeness, to be added to the inventory of largenesses, in the way that the paradox describes. And that, I take it, is why Socrates spotted that, if Forms could somehow be reduced to thoughts, the Third Man Argument’s explosion of largenesses could never get started. As we have seen him put the point, ‘In this way each [Form] would at any rate remain one, and would no longer suffer the consequences mentioned just now’ (Parm. 132b5–6).
3 Forms as a Source of Concepts: Phaedo 74e–75cFootnote 35
What we have been witnessing is Plato’s classical theory of Forms, as viewed critically in retrospect by its own author. The Parmenides has made it very clear that the Forms cannot be reduced to mental entities, but are eternal, objective, structuring entities. Since they are mind-independent, they are neither conceptions – the states of mind whereby we conceive these entities – nor mere concepts, understood as the intentional objects or contents of those states of mind.
Nevertheless, Forms play a key role in our development of conceptions, and it remains to ask what that role is. What is not disputed is that in Plato’s eyes the tasks undertaken by philosophy, such as dividing up reality, are properly exercised in relation to the Forms. But any general theory of conceptions would have to range much wider than this, given that conceptions are not, on any familiar understanding of the term, the sort of thing that only philosophers have at their disposal. Even children and uneducated adults, in order to count as rational beings at all, presumably have to have access to a range of concepts. Do the Forms play any part in this?
Traditionally, the answer has been yes: every human soul contains buried memories of the Forms, and although only successful philosophers may fully recover these memories, everyone draws on them to some extent in the course of forming concepts. Call this the optimistic interpretation. On an alternative, pessimistic interpretation, Plato means to deny that human souls, other than those of philosophers, have any intellectual access at all to the Forms during their incarnate life.Footnote 36 What follows is a partial defence of the optimistic interpretation.
In the myth of Plato’s Phaedrus, Socrates describes a cycle of death and rebirth, in which souls qualify to be reincarnated in a human body only if they have, during their prenatal disembodied state, become acquainted with the Forms (Phdr. 247c3–e6, 249b5–c4, 249e4–250a5-b1), which they can then strive to recollect during their embodied life. Is this recollection process one that begins, as in the pessimistic interpretation, only when intellectual disciplines like mathematics, and ultimately philosophy, are studied? Or is it, as in the optimistic interpretation, already under way in the early stages of life, as the human child learns to understand and articulate very basic concepts: one and many, like and unlike, large and small, good and bad, fair and unfair, and so on, all of which on the one hand have their counterparts in the realm of Forms, and on the other are indispensable components of basic rationality?
It is hard to extract a clear answer from the Phaedrus itself, but consider now the (probably earlier) Phaedo. In a much-discussed passage (Phd. 72e1–77a5), Socrates defends the thesis that all learning is ‘recollection’, namely the recovery of our prenatally acquired knowledge of Forms which was obscured during incarnation but is still present in us. When we encounter sensible cases of equality, he argues, we recognize them as imperfect imitations of something different from them, the Equal Itself, and thereby advance the process of recollecting this, the Form of Equal.
But when does that process occur? According to the pessimists, only when we embark on philosophy, for those few of us who do. According to the optimists, as soon as we start to become rational beings.
The optimistic reading seems to be supported by the following passage (Phd. 74e9–75c3):
In that case, we must have known the Equal before the time when we first saw equal things, and thought: ‘All these are seeking to be like the Equal, but fall short of it.’
‘That’s true.’
‘Now we also agree that we haven’t come to think of it, and indeed that it’s not possible to come to think of it, other than from seeing or touching or any other sense – I count them all as the same.’
‘Yes, because they are the same, Socrates, at least in relation to what the argument aims to show.’
‘Now then, it is from the senses that one must come to think that everything in the reach of the senses both seeks that thing which Equal is and falls short of it. What do we say?’
‘Just that.’
‘Then before we started to see and hear and use the other senses, presumably we must in fact have got knowledge of what the Equal itself is, if we were going to refer to it the equal things deriving from the senses, saying they all are eager to be like it, but are inferior to it.’
‘Necessarily, given what has already been said, Socrates.’
‘Now wasn’t it from the moment we were born that we started seeing and hearing and having use of the other senses?’
‘Certainly.’
‘Right, and we must, as we’re saying, have got the knowledge of the Equal before these?’
‘Yes.’
‘In that case, it seems we must have got it before we were born.’
‘Yes, so it seems.’
Socrates here relies on the premise that ever since birth we have not only been perceiving equal things, but also referring them to that ideal standard of equality, the Form of Equal. Only thus understood can the argument sustain his contention that we must have already had knowledge of the Form before we started perceiving, that is, before we were born.
In Socrates’ view then, from the moment in our earliest infancy when, using the senses, we started the long process of making sense of the world by identifying structures, properties, and relations in it, we were already starting to draw on our innate and intuitive grasp of a priori topic-neutral properties such as like, equal, large, many and good. Our guaranteed (because innate) access to these concepts is what made it all but certain that we would develop into rational beings: no wonder Plato chose to make our access to the corresponding Forms compulsory by building it into the soul’s state at birth. By contrast, empirical items such as bread, gold, and shoes are irrelevant to the argument, because our understanding of them can perfectly well be acquired empirically at any time, if at all. But the trio large, equal, and small is among the things we seem to know about innately, even independently of our sensory experience: to revert to an earlier illustration of the point, that they are transitive properties is something we already know, even prior to and independently of any empirical checking.
In his subsequent work Plato would extend this group’s membership to include Being and Difference, the latter subsuming the function of negation as well. Such additions confirm that the central group of Forms jointly constitute the very stuff of rationality,Footnote 37 accessible at least dimly to all rational beings during their early development.
Forms, according to Plato’s classical theory, are components of the intelligible world. They are also causal factors structuring the sensible world. And they are appropriately stable objects of learning, dialectic, definition, and knowledge. They exist eternally, with no dependence on our or anyone else’s conceiving them, and are therefore not in the final analysis mental entities at all. Nevertheless, they provide all rational beings with the basic tools of thought.
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