Plato: metaphysics and epistemology

Plato: metaphysics and epistemology Robert Heinaman METAPHYSICS The Theory of Forms Generality is the problematic feature of the world that led to the development of Plato’s Theory of Forms and the epistemological views associated with it.¹ This pervasive fact of generality appears in several guises, (1) Normally, one characteristic is exhibited by many individuals. Redness, for example, characterizes many objects. (2) General terms such as ‘is red’ are correctly applied to many objects, and abstract singular terms such as ‘triangularity’ appear to name something without naming any individual. (3) We can think of general characteristics such as redness and of general facts such as that ‘the triangle is a three-sided plane figure’, where what is thought cannot be identified with a red individual or a fact about an individual triangle. (4) I can not merely think of but know general notions such as triangularity and general truths about them. Plato was the first western philosopher to focus attention on these facts, and his Theory of Forms attempts to explain their existence. Although the first philosopher to draw attention to the problem of universals, Plato himself did not use any word that could be translated by ‘universal’. The Greek terms normally used in the middle dialogues’ ‘classical’ Theory of Forms are eidos and idea, which mean shape or form. These terms already appear without their later metaphysical weight in early dialogues, where they signify moral characteristics which Socrates wants to define. In a famous passage of the Metaphysics (987a32–b8) Aristotle wrote, Having in his youth first become familiar with Cratylus and with the Heraclitean doctrines (that all sensible things are ever in a state of flux and there is no knowledge about them), these views he held even in later years. Socrates, however, was busying himself about ethical matters and neglecting the world of nature as a whole but seeking the universal in these ethical matters, and fixed thought for the first time on definition. Plato accepted his teaching, but held that the problem applied not to sensible things but to entities of another kind—for this reason, that the common definition could not be a definition of any sensible thing, as they were always changing. Things of this other sort, then, he called Ideas… This fits what we find in early dialogues where, in asking questions of the form ‘What is X?’ Socrates2 is seeking a general definition stating what X is, not merely what X is like. The correct definition of X should not only be coextensive with X but illuminate the nature of X: the being or reality or essence (ousia) of X. While taking over Socrates’ interest in general definitions, Plato went further by raising the question of ‘what the problem applied to’: what do we define when we truly state, for example, that (1) Virtue is knowledge of good and evil? Further, Plato had a deep interest in mathematics, seeing it as a paradigm of knowledge, and the same question arises for mathematical truths such as (2) The triangle is a three-sided plane figure. Precisely what is the subject-matter of such a statement? I believe the following sort of reasoning lay behind Plato’s answer to this question: Whatever such truths are about, their being about that must explain why they are eternally and changelessly true. By contrast, truths about sensible objects such as (3) Socrates is sitting inevitably become false. The explanation for this feature of (3) seems straightforward: (3) is about Socrates, a changeable object, and it is because Socrates changes that the statement about him changes from true to false. Since (3)’s changeable subject-matter explains its change in truth value, it appears plausible to suppose that what explains the fact that (2) is eternally and changelessly true is that it is about an eternal and changeless subject (cf. Timaeus 2.9b). If so, with what could such a subject be identified? Apart from one brusquely dismissed proposal to be mentioned shortly, Plato believed that the only alternative to Forms which needs to be ruled out consists in sensible objects. Now, as Aristotle informs us, Plato was influenced by a student of Heraclitus named Cratylus who said that the world is in constant flux, and he himself held a similar view of the sensible world. Whatever the exact meaning of Plato’s claim, it certainly entailed that the instability of sensible objects excludes them as the subject-matter of eternal truths. Even if sensible objects sustain the same features for some time, they eventually perish and so could not be what eternal truths are about. If the triangle is a three-sided plane figure even after a particular sensible triangle perishes, the general truth cannot be reporting any fact about it. After its demise, no state of affairs involving the particular triangle exists, so no such state of affairs can be the reality represented by the general truth. So, I take Plato to have reasoned, (2) is about a Form, an eternal and changeless entity, and that is why (2) is an eternal and changeless truth. Similarly, there will be a Form of Virtue underlying a true definition such as (1), thereby justifying Plato’s belief in an objective moral reality which is as independent of human capacities and interests as mathematical reality. A related and absolutely fundamental point for understanding why Plato believed in the Forms lies in their role as objects of thought. Its importance is stressed at the end of the criticism of the Theory of Forms in the Parmenides when, in face of all the alleged problems for the theory, Plato comes down to one bedrock argument that furnishes unanswerable proof for the existence of Forms: If one does not allow Forms of things in view of all the present difficulties and others like them, and does not distinguish some single Form in each case, one will have nothing on which to fix one’s thought, since one is not allowing that in each case there is an Idea that is always the same, and so one will utterly remove the possibility of discourse. (135b–c) Plato sees thought as involving an awareness of entities external to the thinker where these entities furnish the contents of the thought. For, first of all, when I think of triangularity I am thinking about something, my thought has a content. So, Plato (fallaciously) reasons, what I am thinking of exists. Therefore triangularity is a being that I am aware of when thinking of triangularity. And second, to think of triangularity is not to be aware of some thought inside my own mind. Thought is directed toward a content other than itself—a Form (Parmenides 132b–c). So thought, like perception, mentally connects us with a reality outside ourselves, and Plato regularly speaks of thinking as a kind of mental vision. By thinking of triangularity I stand in a relation to a being which is the content of the thought. And since I can think of triangularity when no particular triangles exist, particular triangles could not be the reality I am then related to and aware of in thinking of triangularity. For what is thought when I think of triangularity does not vary with the shifting population of particular triangles. So at no time could the object of thought be identified with sensible objects.³ For Plato, this shows not merely that the object of thought—the Form of triangularity—differs from particular triangles, it proves the Form’s complete independence of them. Hence, Forms are not only eternal and changeless, they exist independently of what happens in the sensible world. The reference to discourse at the end of the passage quoted from the Parmenides indicates that what holds for thought applies equally to language: general words have a meaning or content that must be identified with the Forms. Although Plato distinguishes between words and statements, he does not (yet) distinguish the ways in which they function. Both signify some objective reality which is identified with their content.⁴ Only Forms are objects of knowledge. To see why we must look more closely at Plato’s view of the sensible world. The eternity, changelessness and independence of the Forms are part of what Plato has in mind when, under the influence of Parmenides’ conception of being as an eternal changeless reality, he says that the Forms are real or are in a strong sense to be contrasted with the appearance and becoming characteristic of sensible objects. Being also comprises truth—really being such and such—and when Plato says that knowledge is of being the notion of truth is fused with the idea that a subject S’s being F involves S being F in virtue of its own nature, and therefore being eternally and changelessly F, and hence never being the opposite of F. So the nature of S explains why S really is F. Only what is F in this way is a stable F, a pure F, a true, perfect and real F. A subject cannot be a real F, it cannot be its nature to be F, if it ever appears contrary to F, which Plato (at times) conflates with appearing to be not F. We saw that in early dialogues Plato says that being or reality is displayed in a general definition. Such being or reality—where this now has all the connotations noted above—is found only among the Forms. Beauty, for example, is beautiful in virtue of its own nature, and hence is eternally and changelessly beautiful without any trace of its opposite, ugliness. In contrast, sensibles are never beautiful in virtue of their own nature: they inevitably appear ugly in another respect, or in comparison to another thing, or at another time. If a beautiful object is not ugly at the same time, it will nevertheless eventually become ugly since it is undergoing continuous change. For example, sensible objects constantly change place, and if a beautiful object approaches a more beautiful object the first will be uglier than the second, and hence appear ugly as well as beautiful. Or one may move to a position from where the object appears ugly rather than beautiful. If, unavoidably, A will appear ugly as well as beautiful, then we cannot explain A’s beautiful appearance by saying that it is A’s nature to be beautiful. It is not beautiful in itself, it merely presents an appearance of beauty in virtue of ‘participating’ in a being outside of itself, the Form of Beauty. That is—this is the only content Plato ever gives to participation—the sensible resembles or imitates the nature of Beauty. We must look beyond the sensible object to explain its appearance. It is dependent on the Form which is, by contrast, entirely independent of it. This situation of appearing F without being F applies to all features of sensible objects. There is nothing that they really are. We cannot say that this stuff before us really is snow because changes are constantly going on in the sensible world which will lead to the disappearance of snow. It is not snow in itself, it does not have the nature of snow, or any nature since all its features will eventually disappear or be joined by their contraries. So we must look beyond the snow itself to explain why it is cold. We can say that the stuff before us is cold because it participates in the Form of Cold, or, more interestingly, that it is cold because it participates in the Form of Snow, which always brings along Coldness. But we cannot explain why it is cold by saying that the stuff before us has the nature of Snow, and therefore is cold. At times Plato goes further5 and suggests that the constant change undergone by sensible objects leaves them bereft of any kind of identity between what we call different phases of the ‘same’ object. Plato believes in particular qualities which are peculiar to the object they are found in. Socrates’ health, for example, is peculiar to him and differs from Aristotle’s health. A sensible object is a bundle of such qualities and when the qualities change the numerical identity of the object changes as well, even if we call it the same because of the similarity6 between the earlier and later objects. Not only can we not properly say that this object is healthy, we cannot say that it is Socrates, for that would impute a stability which it does not possess. For the same reason it is misleading to refer to sensible phenomena with the word ‘this’: it suggests permanence and stability that the sensible phenomena are too volatile to merit.⁷ The Timaeus identifies individual qualities with images of the Forms which cannot be legitimately called this or that but should only be derivatively described in reference to their models—Forms—as, for example, ‘such as’ water. One point of this characterization is that the images and sensible objects composed of them are derivative from, dependent on and less real than the Forms they reflect, as images in mirrors or water are derivative from, dependent on and less real than their ordinary models. When shifting phenomena change from air to water to earth, etc., we can, during the second stage, say that the image is such as water since there is a fleeting resemblance to Water. (Similarly we could say that a mirror image of water is ‘such as’ water, imitates or resembles water, without really being water.) But the image’s disappearance shows that we could not have pinned it down as ‘this’ or ‘that’: like mirror images, the phenomena lack any nature which they could be said to be. The Timaeus further develops Plato’s view of the sensible world by introducing the ‘dim and difficult’ notion of space as an entity needed besides Forms and images on the grounds that an image requires a medium or receptacle where it can exist. Space has no feature of its own since that would interfere with its imaging the contrary feature. But since its nature is stable and unchanging, it can properly be spoken of as ‘this’. What we observe in the phenomenal world should be described by saying (e.g.): this (namely, space) is such as fire. An analogue would be the statement that gold is triangular: as an underlying medium gold receives and exhibits the feature without really being that feature and without its own nature being affected by the presence of the shape. Knowledge exists, and its object must plainly be what is, reality. And here all the aspects of being noted above coalesce: truth, essence, eternity, changelessness, stability and intrinsic intelligibility. For Plato, a paradigm case of knowledge would be expressed in the definition of the being or nature of triangularity. Since in knowing that the triangle is a three-sided plane figure one has knowledge of reality, what reality precisely is it that is known? Not a sensible triangle for, as we saw, the changeable character of sensible objects exposes their lack of the being demanded of an object of knowledge: they are not anything but only appear to be and imitate reality. The nature and being of a triangle is not present in but beyond the sensible object and there is nothing there in the sensible to be known. Since sensibles have no natures to be known, the objects of knowledge must be different: the Forms. Nevertheless, we do have mental states related to sensible objects. These, however, are perceptions and opinions or judgements (doxai) based on perception, not knowledge. Lacking any notion of a proposition or sense that could serve as the content of a cognitive mental state, Plato identifies this content with the being in the world that the mental state is about. Since judgement or opinion differs from knowledge—it can be correct or incorrect, it is not based on an account of its object—the entity that is its content, Plato argues, can no more be identical with the being grasped by knowledge (namely, the Forms) than a colour can be what we hear. Still, since opinion does have a content it cannot be directed toward sheer nothingness. So the objects of opinion fall between being and not being. Sensible objects, appearing both to be F and not to be F for many properties, must be the entities that furnish opinions with their content.⁸ Again, the Forms must be changeless and eternal, and as objects of knowledge they must be the natures expressed in definitions. For Plato, even if there were (or are) eternal triangles in the sensible world, there would be a distinct Form of Triangularity because we could not otherwise explain why the triangles have something in common, share one general feature. If it is by reference to the Form of Triangularity that we explain why particular triangles have something in common, then (Republic 597b–c; cf. Timaeus 31a) there must be only one Form of Triangularity. An individual’s being F is explained by its participation in F. If, per impossible, we had two Forms of triangularity, T1 and T2, then if object a were a triangle because it participated in T1 and b were a triangle because it participated in T2, we could not explain why a and b have something in common. To do that we must relate them both to one and the same entity, one and the same Form. To explain how things have features in common, then, we must suppose that for each property there is one and only one Form. We have, Plato believes, the ability to think of ideal standards such as perfect equality, for when we judge that sensible objects are equal we may judge at the same time that they fall short of perfect equality. So to judge is to compare the sensible objects with another entity. For to think about perfect equality—to have that as a content of thought— is for the mind to stand in a relation to a reality outside the mind. The question then arises of how to explain this awareness and our ability to think—from among all the entities that exist—of precisely it. I could no more have become aware of this entity through examining the contents of my own mind than I could have by introspection become aware of Mount Everest. And Plato appears to believe that the explanation of my ability to think of perfect equality must be that at some time or other I experienced it. To perceive sensible equals is not to experience perfect Equality since none of them really is equal: they are inevitably also unequal, the opposite of equal. It is not, Plato thinks, by observing an object that is no more equal than unequal that I can acquire the notion of perfect equality. So it must be through acquaintance with the Form of Equality, which is perfectly equal, that I acquired the ability to think of perfect Equality. So a Form of F-ness is a paradigm of F, it is perfectly F. This is part of a Form’s being in a way that sensibles are not. This idea that a Form of F is itself F has come to be known as ‘selfpredication’. ⁹ Already in the earliest dialogues, where the Theory of Forms is undeveloped, we observe thought and language that naturally evolved into the self-predication assumption. For example, proposed definitions were often expressed as in the following definition of justice: (1) Doing one’s own is just.¹⁰ If the definition is correct, since (2) Doing one’s own=justice it follows that (3) Justice is just. In early dialogues such statements are taken to express self-evident truths.¹¹ A statement of this form is also implied by the assertion that if Beauty is correctly defined as X, then X must be more beautiful than anything else12 and cannot be the opposite of beautiful;¹³ and by an argument that X cannot be the definition of Beauty because it is not beautiful.¹⁴ Assertions of (3)’s form are entailed by Plato’s belief that if an object b explains why an object a is F, b must itself be F15 and somehow impart its own Fness to a. Plato considers it self-evident that if a is F, F-ness is a being, and the presence of F-ness explains why a is F.¹⁶ It follows that F-ness must itself be F. This condition on explanation is important once the Theory of Forms is developed, for Plato uses it and related principles in the Phaedo to mount a rationalist attack on experience of the sensible world as a source of knowledge, and to argue that explanations of phenomena in terms of perceptible and mechanical processes lead to absurdity. Typically, Plato believes, if we use our senses to identify some sensible property, physical process or object X as the explanation of something—Y—in the sensible world, the following absurdities arise: (1) X is contrary to Y, or (2) in other cases the contrary of X appears to bring about Y, or (3) in other cases X appears to bring about the contrary of Y. To suppose that a contrary could be explained by its own contrary is like supposing that we could explain why snow is cold by appealing to the presence in it of something hot. Plato’s explanations of phenomena in terms of participation in Forms avoid these difficulties.¹⁷ The ‘safe and stupid’ explanation of why a sensible object is cold, for example is that it participates in the Form of Coldness. The ‘clever’ explanation appeals to the fact that certain kinds of thing are necessarily associated with one opposite characteristic and exclude another; as Snow, for example, must, in virtue of its own nature, be characterized by Coldness and exclude Hotness. So the clever explanation of why a sensible object is cold could be that it participates in the Form of Snow. Although clearly distinguished from teleological explanations, Plato gives no indication that his preferred explanations differ in kind from those he rejects. But while the latter include what Aristotle would label efficient causes, Plato’s recommended explanations are more like ‘formal causes’. A safe and stupid explanation states what it is for a sensible to be F. The clever explanation’s account of why the snow is cold combines with the snow’s participation in Snow the point that ‘snow’ entails ‘cold’, just as ‘triangle’ entails ‘interior angles equal to 180 degrees’. The important point for self-predication is that Plato’s explanations avoid the alleged difficulties confronting physical, mechanical explanations. The items appealed to possess the characteristic explained and never possess the contrary. Thus, the Form of Snow is cold, and the Form of Coldness is cold. Selfpredication is essential to Plato’s idea of explanation. It is also essential to his account of participation. A sensible object gives the appearance of Beauty, so although it cannot be beautiful, the appearance can only be accounted for if the sensible object ‘participates’ in the Beauty which it cannot be. And for the sensible to participate in Beauty is for it to resemble or imitate the nature of Beauty which it does not possess. If there is resemblance, then there is a shared characteristic.¹⁸ And if this is not strictly true, that is not because the Form of Beauty is not really beautiful, but because the sensible is not really beautiful and only appears to be such as the Form truly is. Resemblance and self-predication are also important for recollection since Plato thinks we are often reminded of and re-acquire knowledge of Forms by observing sensible objects that resemble them. Again, self-predication alone makes sense of Plato’s theory of love. Love is the desire to possess what is beautiful and the supreme object of love is the Form of Beauty. So the Form must be beautiful. How could the object of the most intense and most pleasurable eros not be a beautiful object? As the goal of a passionate longing, the Forms are objects of desire, and to ‘acquire’ them by knowing them is a mystical experience of divine19 beings. All people, most unconsciously, yearn to recapture the vision of the Forms which they enjoyed before birth. This alone did give them and would give them complete satisfaction and happiness. All this makes some sense only if the Forms are perfect paradigms. Because of their greater reality ‘possession’ of the Forms gives true satisfaction in a way in which possession of sensibles does not. And part of that greater reality consists in the Forms being perfectly what sensible objects are only deficiently or in appearance. Similarly, Forms are more real because of their greater ‘cognitive visibility’ in comparison with sensible objects.²⁰ If we want to learn what a property F is, the observation of a sensible F will typically prove of little use since the property will be bound up with its opposite, and so the observation will provide a confused idea of what F-ness is. However, if we could attain a clear view of the Form we would immediately know what F-ness is because it is a ‘pure’ and perfect example of F uncontaminated by its opposite (cf. Philebus 44d–45a). Here again, the greater reality of the Forms depends on their being paradigms. Self-predication, then, is fundamental for Plato’s philosophy. However, it is a mistake, arising, in part, from confusions that helped to make it seem entirely natural. 1 Plato does not distinguish different uses of ‘to be.’ His single Form of Being merges these different uses with the features of true being noted before. So the existential use is run together with the identifying use,²¹ the existential use is conflated with the predicative use,²² and the predicative use is confused with the identifying use.²³ Given the last confusion, since, plainly, Beauty is Beauty, it may also seem self-evident that Beauty is beautiful. 2 Pre-Socratic philosophers did not always properly distinguish between objects and properties. Thus, Anaxagoras spoke of ‘the hot’ and ‘the cold’ on a par with ‘earth’ as elements from which things come to be. If Plato too was not clear on this point, then it would have been natural for him to think of Beauty as a beautiful object.²⁴ The point is not that Plato did not distinguish attributes and objects but that he did not adequately distinguish the kinds of thing which they are. 3 Greek uses expressions formed from the definite article and an adjective such as ‘the beautiful’ to name properties. Occasionally Plato will even use the adjective on its own as the subject of a sentence to refer to a Form. Such expressions lend themselves to being understood as operating in the same manner in which they do operate when applied to sensible individuals, namely as describing the object named. And this danger is especially serious in Plato’s case for (Cratylus 384d–385c) he does not adequately distinguish naming and describing. So he could easily understand terms designating the Form of Beauty—‘the beautiful’ and ‘beautiful’—as describing and not merely naming the Form. 4 The definition (D) The triangle is a three-sided plane figure specifies the condition an individual must satisfy to be a triangle. But even if ‘the triangle’ in (D) names a universal, the rest of the sentence does not describe the universal. That is, (D)—however it should be construed— does not say that the universal triangle is a three-sided plane figure, is a triangle, in the way an individual triangle is. But that is just how Plato understands (D). This connects with a failure to distinguish different types of general predication. Supposing there is a Form of Man we could say that (a) Man is eternal, changeless, etc. Here properties are attributed to the Form just as they are attributed to Socrates when I say he is white, henpecked, etc. Man is an entity that is an eternal thing, etc. But (b) Man is an animal, mortal, etc. makes a different sort of claim. Thus, whereas there may be some plausibility in proposing that (b) means (c) Every man is an animal, mortal, etc., (a) certainly does not mean (d) Every man is a universal, eternal, etc. The predications in (a) are true because they are about a Form: all Forms have those properties. The predications in (b) are true because they are about the specific concept Man. If the two types of predication are not distinguished, one might understand the predications in (b) in the same way as those in (a). Then definitions such as Man is a rational animal may make it seem obvious that Man is a man, Triangularity is a triangle, etc. Plato’s metaphysics is built on the contrast between Forms and sensible objects. These contrasts make Forms more real than sensible objects. Forms are natures existing independently of sensibles: eternal, changeless, divine, immaterial, imperceptible, knowable and intelligible in virtue of their natures. Free of contrary attributes, they are perfectly beautiful, just, etc. and of the highest value. Sensible objects, by contrast, are dependent on Forms: material, perceptible, transient, in constant flux, of little or no value, or evil; lacking intrinsic natures, they are not really anything but bound up with opposites and unintelligible. Being utterly contrary to what is found in the sensible world, Forms do not exist in but apart from the world around us.²⁵ While their images exist in us,²⁶ they exist ‘in themselves’, and this means that they do not exist in us or anywhere ‘here on earth’²⁷ in the ‘corporeal and visible place.’²⁸ They exist in ‘another place,’²⁹ the ‘intelligible place,’³⁰ ‘the place in which the most blessed part of reality exists,’³¹ a place ‘untainted by evils’³²—heaven33or a ‘place beyond heaven.’³⁴ The Parmenides Parmenides 127d–136e presents the puzzling spectacle of Plato putting forward criticisms of his own Theory of Forms. Probably the prevalent view today is that the dialogue documents Plato’s realization of the unacceptable consequences of self-predication, which he therefore abandons. I disagree. Plato portrays a youthful, immature Socrates not yet in possession of the philosophical acumen that would enable him to answer the objections to his underdeveloped theory. But Plato himself, I believe, is not concerned about the objections because, in his view, they arise from confusion or an inadequate understanding of the Theory of Forms. I will only have space to discuss the first version of the Third Man Argument (132a–133a), the ‘TMA’.³⁵ The argument’s validity rests on two assumptions not given in the text: Self- Predication, (SP) A Form of F-ness is F and ‘Non-Identity’, (NI) If all members of a set of objects are F in virtue of participating in a Form of F-ness, no member of that set—that Form of F-ness. The only assumption on the surface of the text is the ‘One over Many Assumption,’ (OM) If several objects are F, there exists a Form of F-ness by virtue of participating in which they are F. Whereas Plato maintains that only one Form exists for any attribute, he appears committed to infinitely many Forms for each attribute. For suppose that sensibles (1) a, b and c are large. Then by (OM) (2) there exists a Form of Largeness: Largeness1. By (SP) it follows that (3) Largeness1 is large. So now we have a new set of large things: (4) a, b, c and Largeness, are large. By (OM), applied to this new set of large objects, (5) there exists a Form of Largeness: Largeness2. And given (NI), Largeness2 differs from Largeness1: since Largeness1 is large by virtue of participating in Largeness2, it cannot be Largeness2. When endlessly repeated, these steps produce an infinite number of Forms of Largeness. Since Plato nowhere explains his attitude toward this argument, we will never know what he thought of it. The question must be addressed on the basis of indirect evidence. Attention has focused on self-predication since that is in fact a mistake. As we saw, self-predication is essential to Plato’s earlier Theory of Forms, so the TMA’s presumption of self-predication does not render it irrelevant to Plato’s position.³⁶ The belief that the argument’s point is to prove the unacceptability of selfpredication runs into the problem that self-predication is present in what is now generally agreed to be a dialogue later than the Parmenides, namely the Timaeus.³⁷ There, despite Parmenides 133a’s rejection of resemblance, sensibles participate in paradigmatic Forms by resembling and imitating them. Resemblance brings along self-predication. That the target is not self-predication is also indicated by a peculiar argument separating the two versions of the Third Man Argument. Socrates proposes that Forms might be thoughts, to which Parmenides objects that then everything is a thought, and hence either everything thinks or else, while being a thought, does not think. The argument assumes that a thought thinks. Further, we saw that one confusion behind self-predication is the failure to distinguish between predications such as (i) Man is eternal and (ii) Man is mortal. If Socrates participates in the Form of Man, then only (ii)’s predicate can be legitimately transferred to Socrates. But when from the proposal that Forms are thoughts Parmenides concludes that (iii) Man is a thought, the predication is of the type that occurs in (i). So one who was clear about the difference between (i) and (ii) would not take Socrates’ participation in Man together with (iii) to imply that Socrates is a thought. But such is Plato’s inference. Now, Plato certainly rejects the idea that Forms are thoughts, so he is probably making what he considers a sound objection against it. If the point of the TMA were to expose and reject self-predication, why would Plato, in the midst of this demonstration, deliberately present a fallacious argument against a view he wants to refute, where the fallacy is of precisely the sort involved in the error of self-predication? But if Plato did not abandon self-predication, how could he respond to the Third Man Argument? By restricting the One over Many Assumption, the only assumption expressly given in the text.³⁸ Platonists in the Academy regularly limited the inference from a set of Fs to a Form of F to cases where the members of the set do not stand in relations of priority and posteriority; and, according to Aristotle, Plato himself accepted this restriction.³⁹ Aristotle reports this view in the Eudemian Ethics (1218a1–8): There is not something common over and above and separate from things in which the prior and posterior exist. For what is common and separate is prior (proteron) since the first (prōton) is taken away when what is common is taken away. For example, if double is first of the multiples, multiple, which is predicated [of particular multiples, namely double, triple, etc.] in common, cannot be separate. For then there will be [a multiple] prior to double. But double is the first multiple and cannot have a multiple prior to it. So there is no Form of Multiple over and above specific multiples. The rationale for this principle assumes self-predication: it is because the Form of Multiple would be a multiple that it would be, impossibly, a multiple prior to double. Ontological priority is in question: if x’s non-existence entails y’s nonexistence, but x can exist without y, then x is prior to y. Aristotle reports that Plato regularly used this notion of priority.⁴⁰ One page before the quoted passage Aristotle points out that a Form of F is, in just that sense, prior to particular Fs: the Form of Good is the first and prior good because if taken away the other goods would be taken away. That is because for them to be good is for them to participate in, and thus depend on, the Form, while the Form is not similarly dependent on the particular goods: being good is its nature, so it is good in itself. Likewise for any other Form. So at step (4) of the argument, (4) a, b, c and Largeness1 are large, Plato can block reapplication of the One over Many Assumption and the inference to a new Form. One subject—the Form—is the first of ‘the larges’ and prior to the others. Of course, if the reason given above was Plato’s justification for thus restricting the One over Many Assumption, then the restriction is unacceptable since it rests on self-predication. In fact, then, but unknown to Plato, the Third Man Argument presents a serious problem for the theory of Forms.⁴¹ Many have detected revision of the Theory of Forms in a discussion of ‘friends of the Forms’ in the Sophist (248a–249d). Some believe Plato is allowing that the Forms can change, some believe that motion is allowed to be real, and some believe that the Forms have become ‘powers’ (dunameis) or potentialities for change—all contrary to what Plato previously believed. Interpretation of the passage is made difficult by its aporetic character, and the entire discussion (236–51) ends in aporia. The Eleatic Stranger, who leads the Sophist’s conversation, examines a dispute between ‘giants’ who define being in terms of matter, and ‘gods’ who explain that being consists of the immaterial and changeless grasped by reason independently of the senses. The latter are called ‘friends of the Forms’ and are often thought to include Plato himself. Hence, when their position is criticized it is thought that Plato is criticizing his own previous position. Before discussing the friends of the Forms, the Stranger criticized the materialists and introduced the following definition of being: x is a being just in case x has a power to act on, or be acted on by, something else. The friends of the Forms might be expected to reject the definition because it admits material objects as beings, but the only explanation given for their rejection is their denial that Forms—the beings—possess a power to act or be acted on. The Eleatic Stranger raises two objections against the friends of the Forms, (1) They allow that Forms are known. But to know is to act, and therefore to be known is to be acted on. Hence, in being known the Forms are acted on, and therefore changed. (2) He cannot accept that intelligence does not belong to ‘what wholly is’. But if intelligence belongs to being, so must life, soul, and hence change, belong to being. Now, to determine Plato’s attitude to this criticism, we need to know: Does Plato accept the Eleatic Stranger’s definition of being? And to answer this we would need to answer the following question: Is the notion of being defined in terms of the capacity to act or be acted on being in the strong sense or the weaker notion applicable to material objects? The Sophist itself fails to settle these questions. But if we look to later dialogues where the earlier contrast between being and becoming is reaffirmed,⁴² and assume that the Sophist does not represent a temporary detour, then we can say the following: (1) If the Sophist defines being in the strong sense, then Plato cannot accept its definition since he later reaffirms that being cannot apply to the sensible world of becoming. (2) If the Sophist is defining being in the weaker sense, then Plato could accept it consistently with his contrast between a stronger notion of being and becoming. For the fact that x is acted on does not, as the Stranger falsely suggests (248e), entail that x is altered. One example of ‘acting’ and ‘being acted on’ was that if x possesses an attribute F, then F acts on x, and x is acted on by F. In this sense the Form of Figure ‘acts’ on the Form of Triangularity, and, according to the Sophist’s doctrine of the communion of Forms, the Form of Being ‘acts’ on the Form of Difference. Obviously, this does not entail that Triangularity or Difference change, and the passage ends with the changelessness of the objects of knowledge reaffirmed (249b-c; cf. Politicus 269d). If it is said that the vehemence with which the Stranger asserts that motion, life, mind and wisdom belong to ‘the wholly real’ shows that he is asserting their being in the strong sense, this is consistent with the earlier Theory of Forms.⁴³ It too asserted the existence of Forms of Soul and Life in the Phaedo.⁴⁴ The Form of Motion is casually referred to in Socrates’ outline of his immature Theory of Forms in the Parmenides (129e), and the Form of Knowledge is mentioned later in the same dialogue (134a–e; cf. Phaedrus 247d–e).⁴⁵ While there is no clear evidence for the suggested alterations in the Theory of Forms, the Sophist does undeniably contain one new development: for the first time Plato speaks of Forms participating in other Forms: the ‘communion of Forms’. Hitherto, Plato was only concerned to give the ontological analysis of the fact behind a true statement that a subject S is F when S is an individual. But in many cases—and many cases of the sort that Plato would be particularly interested in—the subject of a statement asserting that S is F will name a Form. If the case where S is an individual demands explanation, it is obvious that the general case likewise demands an explanation. And this Plato provides for the first time with his doctrine of the communion of Forms. A central passage in the Sophist (251a–257a) presents a series of arguments to distinguish five ‘greatest Kinds’: Being, Sameness, Difference, Rest and Motion. Many have found more sophisticated theories here, but I believe that communion of Forms is the same relation as his earlier notion of participation—in the sense that for a Form S to participate in a Form F is for S to possess F as a property, just as for an individual S to participate in a Form F is for it to have F as a property.⁴⁶ Consequently, self-predication is a feature of the Sophist’s Kinds47 since the ontological analysis of the fact that the Triangle is a figure is: the Kind Triangularity participates in the Kind Figure, and hence is a figure in the same way as particular triangles are. Given that the Kinds are also ‘divine’ (254b), they must be the same Forms which we find in the middle period dialogues. Divinity also characterizes the ‘Henads’ of the Philebus (62a), a very late dialogue mainly concerned with ethical problems but containing important and notoriously obscure passages on metaphysics with Pythagorean overtones absent from earlier works. The obscurity is probably due, in part, to the metaphysics of the Philebus being grounded in Plato’s ‘unwritten doctrines,’⁴⁸ about which our knowledge is very thin. Plato divides ‘all beings’ into the categories of (1) Limit, (2) the Unlimited, (3) the mixture of Limit and the Unlimited, (4) the cause of this mixture. (4) is relatively clear, being identified with intellect, but the rest of the scheme resists interpretation because of the shifting usage of the notions of Limit and Unlimited, and the bizarre diversity of examples from the mixed class. The Limit-Unlimited contrast is associated with the contrast between one ‘Henad’ with a specific number of species, and its indefinitely large range of generable and destructible instances (16c-d). But Limit is later explained in terms of the notion of a numerical ratio or measure (2 5 a), and still later connected to the ideas of moderation and a balanced and good proportion (26a). Correspondingly, the Unlimited is not only associated with the idea of an indefinite range of particular instances but is explained in terms of scales of qualities referred to with pairs of comparative adjectives: hotter-colder, higherlower, etc., which are generally characterized as admitting the more and the less, and as in themselves admitting no definite quantity. Further, the Unlimited also includes pleasure and the life of pleasure. The difficulties are further compounded by Plato’s identification of these different notions of Limit and Unlimited (23c) and by the disparate nature of the examples from the mixed class: it includes a moderate amount of pleasure, the life which combines pleasure and intellect, the art of music, fair weather, health and virtue of character. As these last examples show, Plato’s scheme cannot be interpreted in terms of Aristotle’s notions of form (Limit), matter (Unlimited) and composite (mixture). Nevertheless, it appears that Plato is analysing entities into what can be loosely called ‘formal’ and ‘material’ elements. How do the Forms fit into this classification? If the One of the One-Many problem raised at 13e–15c corresponds to a (perhaps ‘mathematicized’) Form from earlier dialogues, then since the One-Many problem arises for all items in classes (1)–(3) (23e, 24e, 26d), Forms do not fall under any one of these classes but rather there are Forms for all the beings in (1)–(3). So, for instance, the Unlimited will include both the Form of Pleasure and particular instances of pleasure. As in the Sophist, Plato displays greater interest in the relations between Forms than he did before. The Philebus addresses the problem of reconciling the Form’s unity with the fact that it not only has many individual instances but will often be divisible into further species which are themselves Forms. Perhaps 15d– 17a proposes a solution to this problem, but if so it is, like much of the Philebus’ metaphysics, steeped in obscurity.⁴⁹ EPISTEMOLOGY Recollection The recollection theory is Plato’s explanation of our ability to think of and acquire knowledge of general notions and general truths, where general notions are understood as Forms and general truths the facts about Forms.⁵⁰ The theory claims that in this life we can think of and know the Forms only because we experienced them before birth and thereby acquired knowledge of them. This ‘active’ knowledge is lost at birth but remains latent in the soul, and perception of sensibles that resemble the Forms, or teaching by another, or enquiry into the Forms by a dialectical conversation which (ideally) operates independently of the senses, may lead to full recovery of the latent, innate knowledge. To understand why Plato adopted this extravagant theory we must recall his picture of thought as a relation to—as an awareness of— beings outside our minds. Suppose that yesterday you found yourself thinking of my cousin Ruth Collins in Lancaster County, Pennsylvania, a person you never heard of before. As you could not have simply pulled out of yourself the awareness of this person who is a real being existing independently of you, if it could be established that you have had no experience of her since birth, it might be plausible to suppose that you must have somehow experienced her before birth. And how else could we explain your ability to think of her? Of course, we are unable to think about sensible objects we have not encountered since birth. Plato believes, however, that we can think of general notions and general truths which we have never experienced in our present life, and so the problem which does not exist for sensible objects does exist for general notions and general truths. Thus, the Phaedo says we have the ability to think of Equality. Where could it come from? Not merely from perception of sensible equals, for they, unlike the Form, appear unequal as well as equal. This establishes that the Form is a different entity from the sensibles. So even if the sensible equals were perfectly similar to the Form of Equality, our awareness of them on its own could not have made us aware of and able to think of that entirely distinct entity, Equality itself.⁵¹ No more than the perception of several people exactly like Ruth Collins could have given you the ability to think of her. But perception of the sensible equals may revive our latent knowledge, and once we are aware of Equality we may carry out a dialectical enquiry leading to complete knowledge of it. In the Meno, recollection explains a slave boy’s ability to think of a mathematical truth; call it ‘p’. Plato reasons: the slave boy produces this thought that p so it must have already been in him. Since nothing the slave boy experienced since birth could have put it into him, he must have become aware of it before birth (cf. Phaedo 73a–b). What Plato finds puzzling, what requires explanation, is the slave boy’s ability to think of the mathematical fact, and it is by explaining this that the recollection theory explains the slave boy’s ability to make a judgement about and, later,⁵² to know the mathematical fact. This is the more natural for Plato because his picture of thought as an active awareness of some being in the world makes it hard to distinguish thinking and knowing. Now, the correct explanation of the slave boy’s ability is, at one level, straightforward. The sentence asserting that p is composed of words the meaning of which the slave boy already knows. And it is simply a fact about human beings that they can construct new statements and know what they are saying as long as they know the meanings of the words in the statement and can follow the relevant linguistic rules. Only in the Sophist will Plato begin to appreciate the importance of the difference between the ways in which words and statements function. In earlier dialogues, statements are understood to be assigned to beings in the same way as names.⁵³ Related confusions can be found in Plato’s failure adequately to discriminate (1) objects and facts; (2) knowledge of objects and knowledge of facts; (3) propositions and facts. Plato nowhere distinguishes an ontological category of facts as distinct from objects; both are referred to indifferently as ‘beings’. Stating a fact with a sentence or thinking a thought is seen by Plato as a reference to or an awareness of some reality external to the thinker which is, furthermore, identified with the content of the thought, namely the fact in question. What is said is quite naturally identified with the fact—the reality—reported.⁵⁴ So Plato sees the slave boy as someone who has some general mathematical truth, p, as the content of his thought, where this is identified with the fact that p ‘grasped’ by the slave boy’s mind. In thinking that p the slave boy is related to and aware of some part of reality outside himself, and just as I could not think of an object I had never experienced, so Plato believes the slave boy could not think of and be aware of the fact that is the content of his thought if he had never experienced it before. As he has not experienced it since birth, he must have done so before birth. In the Meno the recollection theory is also relevant to the paradox of enquiry raised before Socrates’ examination of the slave boy. The paradox is stated in two ways that are not equivalent: 1 I cannot enquire into something of which I am completely ignorant. 2 I could not know if I came across what I was enquiring into because I could not recognize it as what I was searching for. The recollection theory can answer (2). The slave boy, for example, has latent knowledge of p which, when revived by Socrates’ cross-examination, enables him to ‘recognize’ p. But the recollection theory does not and is not meant to answer (1).⁵⁵ To set up X as an object of enquiry I must actively ‘know’ X, and latent knowledge cannot by itself explain such awareness of X. Once we distinguish between propositions and facts, the solution to (1) is straightforward: I can know what is said by ‘p’ without knowing whether it is the case that p. So I can enquire whether it is the case that p without knowing whether it is the case that p. But with this solution unavailable to him, Plato’s responds to (1) not with an explanation of how enquiry is possible but by arguing that as a matter of fact enquiry can lead to knowledge and so we ought to persist in enquiring into things we do not know. For inasmuch as all nature is akin, and the soul has learned all things, when a man has recalled one piece of knowledge… nothing prevents him from finding out all the other things. (Meno 81c-d) If I learn A, which is similar to B, then I may recollect B. And if B is similar to C then I may recall C, and so on. It is this sort of stepwise enquiry which Socrates conducts here (Meno 82e 12–13).⁵⁶ Dialectic That stepwise procedure of recollection is an example of Plato’s dialectical method. This developed from the negative and destructive Socratic elenchus— the procedure of refutation portrayed in early dialogues— into a method for achieving positive knowledge. The Phaedo contrasts it with empirical investigation which leads to the difficulties mentioned previously, and emphasizes that enquiry should proceed by reason alone. The Forms can only be apprehended by reason, and it will be by thinking about them, by having them in our mental view, that we will acquire knowledge of them, not by turning to the sensibles that only confusingly reflect the natures we wish to know. ‘Dialectic’ is from dialegesthai (‘to converse’) and dialectic is a conversation proceeding by question and answer. The questioner leads the enquiry and begins by asking his interlocutor (possibly himself) a question, typically about how to define some concept. An initial hypothesis is proposed which the questioner attacks by getting his respondent to answer a further series of questions where the answers lead to some difficulty or absurdity. They then go back and, taking this result into account, another answer is proposed. And so on. In early dialogues this procedure produced negative results, but the Phaedo claims that it is the method to follow in order to acquire knowledge of the Forms. In successful enquiry the ability of a proposed definition p to withstand attempted refutations provides partial confirmation of its correctness. And for further confirmation we can select a plausible ‘higher’ hypothesis which would explain p, and deduce the original hypothesis from it. This is not only the method for discovering the truth; the person with genuine knowledge must be able to successfully carry it out. Knowledge of X enables its possessor to ‘give an account’ of X, and, in standard cases, this involves the ability to state and explain the nature of X and to explain why that account is correct. It further involves the ability to defend the proposed definition against objections. These abilities demand expertise and understanding of an entire discipline. A problem is that the method leads to a regress: after unsuccessfully attacking p we further confirm p by deducing it from q; then q must be challenged, and if it survives it must be further confirmed by deducing it from r; and so on. At each stage we are explaining a proposition by another which we do not know, and if we do not know the basis of our explanation we do not know or understand what we purport to explain in terms of that basis. Unlike the Phaedo, the Republic shows some concern for this problem in the famous divided line analogy, where Plato criticizes mathematicians because they fail to scrutinize critically their assumptions, cannot explain why they are true, and hence do not know them; and therefore also do not know the conclusions derived from them. Dialecticians avoid this failing by critically examining assumptions which they can explain and defend. The backwards regress is said, vaguely, to end in apprehension of an unhypothesized beginning: the Form of the Good. Plato does not elaborate, but since the Good is the first principle, there must be nothing more basic in terms of which the Good can be explained or defined. Knowledge of it will have to consist in some sort of intuition. This is probably related to the Phaedo’s best method of explanation, which was abandoned as too difficult in favour of the ‘safe and stupid’ and ‘clever’ forms of explanation mentioned above. Plato clearly believes that the proper explanation of a phenomenon is a ideological explanation of why it is best for things to be thus and so, and therefore a proper explanation presupposes some account of what the good is. In the Phaedo ideological explanation is presented as an alternative explanation of a fact about the sensible world which can be less adequately explained by a clever or safe and stupid explanation in terms of participation in Forms. But in the Republic, where the concern is with Forms alone, it appears rather that, for example, a mathematical theorem q is explained in terms of the mathematician’s starting-point p, which is in turn—eventually—explained in terms of the Good. The Good is also the ultimate explanation of q via its explanation of p. Similarly, in the Republic the being of other Forms, and not merely sensible phenomena, will ultimately be explained by reference to the Form of the Good (Republic 509b). Later, the Timaeus identifies the contrast between ideological and mechanical explanations of features of the sensible world with a contrast between Reason and Necessity, and now some things are explained by one factor, some by the other, and some by both. Reason has priority over Necessity, acts to produce what is best and is solely responsible for anything that is intrinsically good such as order and proportion. At the cosmic level it is represented by the ‘Demiurge,’ the creator who looks to the Forms and tries to embody them in disorderly matter. Necessity is responsible for randomness, disorder and evil in the material world, but also acts in subordination to Reason to explain features which are necessary conditions for and concomitant causes of certain instrumental goods, much like Socrates’ bones and sinews in the Phaedo (99a).⁵⁷ In later dialogues58 dialectic involves less argumentation and greater interest in classification. The Republic’s conception of a master science establishing the starting-points of subordinate disciplines disappears, and is apparently not required for understanding an area of enquiry. For all Plato explicitly says, distinct disciplines are now autonomous. The procedure called ‘collection and division’ does not provisionally posit a hypothesis and then subject it to critical scrutiny. Rather, it standardly begins when undefined species are unified under a defined genus. This genus is divided into species, which are in turn divided into subspecies, etc., until indivisible species are reached. Conjoining the divisions thus passed through yields definitions of the items at the end of the chains. Dichotomy—the division of a genus into two species—may be followed when the aim is to define a particular Form, since the remaining species will then be irrelevant. But when we want clarification of a genus the number of divisions made at any stage should match the natural, objective divisions in the subjectmatter. However, collection and division does not exhaust the content of Plato’s later ‘dialectic’. It comprises (Sophist 253b–d): 1 dividing things according to Kinds; 2 producing definitions of Forms; 3 not identifying distinct Forms or distinguishing identical Forms; 4 knowing what Forms can and cannot combine. (1) often aims at (2), and the misidentification of distinct Forms (violating (3)) may result from failure to properly divide a genus (cf. Politicus 285a). But that is not how misidentification of the Greatest Kinds is avoided in the Sophist (254b– 257a), nor is it obvious how (4) is connected with division. Sophist 254bf. aims for (3) and (4) but uses arguments characteristic of the earlier dialectical method, and makes no use of the sorts of divisions which occur at the beginning of the dialogue. Perhaps Plato thought that when, unlike with many of his own examples, philosophically important Forms were investigated, then the sort of argumentation found in the Sophist passage might be required.⁵⁹ The Theaetetus and the Sophist The Theaetetus represents Plato’s most sustained investigation into the nature of knowledge. Structured around an attempt to define knowledge, it, like the early dialogues, ends in frustration. But scholars have been quick to find positive lessons which we are meant to draw from the discussion.⁶⁰ The dialogue divides into three sections which consider proposals to define knowledge as (1) perception, (2) true judgement, and (3) true judgement with an account. (3) resembles contemporary definitions of knowledge in terms of justified true belief, but one difference is that all three suggestions define knowledge not as a disposition but as a mental event: perception or judgement, where judgement occurs when the soul says something to itself (180e–190a, Sophist 265e–264a). (1) Because knowledge is infallible and of what is, if knowledge is perception then perception is infallible and of what is. Since x may (e.g.) appear warm to A and cold to B, (1) entails a Protagorean relativism validating both perceptions: what A perceives is for A and what B perceives is for B. The object is not warm or cold in itself: no objective reality independent of the perceptions exists that could falsify them. Less straightforwardly, Plato connects (1) to a Heraclitean doctrine of constant flux. If what a sensible object x is for A is nothing more than how x appears to A, then x lacks an intrinsic nature—it is nothing in itself—and hence, in the strong sense of ‘being’, x is nothing. Given the connection between ‘being’ and permanence, x also lacks stability and constantly changes. For sensible objects are continuously changing place so as to present different appearances to different perceivers. The refutation of (1) initially attacks the relativism and flux doctrines which it is said to imply. Of several objections raised against Protagoras, the main difficulty is that his position is self-refuting. Protagoras’ ‘Man is the measure’ doctrine was not that it appears to Protagoras that what appears to any person A is for A, but that, absolutely, what appears to A is for A. But most people reject this, that is, for most people it appears that it is not the case that what appears to A is for A. So if what appears to them is for them, Protagoras’ doctrine does not hold for them. Protagoras’ absolute claim is false. As for the flux doctrine, if everything continuously changes in every respect, no object can be accurately called anything since ‘it is always slipping away while one is speaking’. So nothing we might call ‘perception’ is any more perception than not perception, and therefore, on the proposed definition of knowledge, nothing is any more knowledge than not knowledge.⁶¹ Finally, Plato attacks the definition directly by arguing that no perception can ever be an instance of knowledge. The argument has aroused much interest because Plato is often, mistakenly, taken to be marking an important contrast between the objects of perception and judgement.⁶² He first distinguishes the subject of perception from the senses through which the subject—the soul— perceives colour, sound, etc. A single subject is aware of the different kinds of sense object and observes relations between them. Further, anything perceived through one sense cannot be perceived through a different sense. For example, I cannot hear a colour. So if anything is common to different kinds of sensible object, the soul cannot ‘grasp’ it by perception. Now, ‘being’ is a common notion applicable to different kinds of sensible object: both a sound and a colour are. So the soul grasps ‘being’ not through a sense but on its own. But to know is to know the truth, and knowing the truth is grasping being, i.e., awareness of what really exists or is the case. Since perception cannot grasp being it cannot put us into contact with the truth, and therefore it can never be knowledge. Plato’s argument rests on an ambiguity in the notion of ‘grasping being’. When the common notions are first introduced, to grasp being is to understand the meaning of ‘being’ or what being is: being itself (not an object like red or a fact that has being) is not an object of perception but an object of thought. However, when in the passage’s final argument it is claimed that to attain truth one must grasp being, the claim has plausibility only if grasping being is equivalent to grasping an object that really exists or a fact that is the case. And perception’s inability to grasp what being itself is provides no reason to believe that perception cannot make us aware of what really exists. On the contrary, Plato himself affirms shortly afterwards (188e–189a) that if one perceives x, then x exists. (2) The definition of knowledge as true judgement is quickly dismissed: true judgement can turn out to be true by luck, and then it is not knowledge. (3) The final definition meets this point by suggesting that knowledge is true judgement ‘with an account’. But the notion of an account is unclear, and Socrates attempts to explain it in terms of a metaphysical theory he heard in a dream. The theory says there are simples and complexes. There is no account of the simples which can only be named and so are unknowable. Complexes are knowable and expressible in an account which is a weaving together of names. Even at this abstract level the dream theory faces two objections. First, a complex either is or is not identical with its elements. If it is, then since its elements are unknowable, it is unknowable too. If it is not, then it does not have the elements as parts, and, since nothing else could be part of the complex, it must be simple and hence (according to the theory) unknowable. Second, if we consider simples and complexes such as syllables and their letters, the letters are knowable independently of any account of them. Both arguments have plausibly been supposed to be meant to apply to the problem of knowledge of Forms. If a Form F is defined in terms of A, B and C, the knowledge of F expressed in the definition presupposes knowledge of A, B and C. And if A, B and C are known by knowing their definitions, the same problem recurs. Either there is an infinite regress and knowledge does not exist, or some kind of knowledge does not involve an account—a definition—of the thing known. This last seems to be the sort of knowledge needed of the Republic’s unhypothesized beginning, but Plato never clarifies what kind of knowledge it could be. Although the final argument against the dream theory seems to show that knowledge does not need an account, Plato proceeds to consider different interpretations of ‘account’. The serious suggestions—and it is important to bear in mind that the item known is an object—are that knowledge of X requires (1) the ability to analyse X into its elements or (2) the ability to give a mark distinguishing X from everything else.⁶³ Against (1) Socrates objects that a person might correctly judge that the first syllable of ‘Theodoras’ contains ‘t’ ‘h’ and ‘e’, but on another occasion, when writing the name of Theaetetus, incorrectly judge that that same syllable contains the elements ‘t’ and ‘e’. Then he did not know the syllable ‘t-h-e’ the first time even though he correctly analysed it into its elements. Knowledge is infallible. Against (2) Socrates objects that the ability to give a distinguishing mark of X is presupposed in having a true judgement about X: otherwise one would not have a true judgement about X to begin with. So (2) adds nothing to the idea of having a true judgement about X.⁶⁴ With this the discussion comes to an end. One puzzle is the question of why Plato neglects the notion of giving an account which he himself uses in other dialogues when discussing knowledge. If being able to give an account includes the abilities to explain why something is so and to defend the claim in question, then some of the Theaetetus’ difficulties are overcome. Another problem arises from the dialogue’s use of sensible objects as objects of knowledge. Does Plato now countenance knowledge of the sensible world, or is the negative conclusion of the dialogue rather meant to reinforce the lesson that we cannot explain the nature of knowledge when its objects are disregarded? It seems the Theaetetus cannot be intended as a demonstration that an account of knowledge must fail if it does not bring in Forms as the object of knowledge, for if that were Plato’s aim the neglect of his own interpretation of ‘account’ would only too obviously undermine his argument. And we’ve already seen that some objections against the proposal that knowledge be defined in terms of judgement apply equally well when its objects are taken to be Forms. For example, accounts of Forms are as vulnerable to the epistemological regress as accounts of anything else.⁶⁵ None of the objections against proposed definitions of knowledge turn on the objects used in the examples not being of the right kind. The one firm conclusion of the dialogue is about the sort of state knowledge is, not the nature of its object: knowledge must be sought in judgement rather than perception (187a). Despite this conclusion—which could be supposed to be undermined by the rest of the dialogue—one might still see the Theaetetus as reinforcing Plato’s view that Forms are the sole objects of knowledge, where knowledge must be contrasted with judgement, not explained in terms of it. After all, it is clear that the Theaetetus cannot represent Plato’s abandonment of his earlier view, given that later dialogues are still emphatically contrasting perception and judgement (doxa) with knowledge on the basis of a difference in their objects. Thus, the Timaeus (27d–28a, 51d–51a) asserts: Being (i.e. Forms) is grasped by intelligence (noēsis) with an account (or reason, logos), while becoming (the sensible world) is grasped by judgement (doxa) with perception. Yet, in direct contradiction of this, the Theaetetus considers definitions of knowledge that state that it is perception or a kind of judgement (doxa). So, perhaps, Plato takes the Theaetetus’ failure as confirmation of the Timaeus’ view on the objects of knowledge. But this interpretation faces serious problems, the answers to which are far from clear. For example: why should the difficulties which afflict proposed definitions of knowledge in terms of judgement (doxa) disappear when knowledge is defined as a kind of thought (noēsis)? Lacking the notions of proposition and sense, Plato can only identify the contents of thought with beings—facts or objects—in the world. Taking statements to name facts in the way that words name objects, Plato is inclined to construe stating or judging what is false as stating or judging where there is no content to be stated or judged. False judgement appears impossible. Likewise, for Plato, if I think of X I am thereby related to a being in the world which is the content of the thought. And how could I think of X—that being which furnishes the content of my thought— if I was not aware of X, if I did not know X? And if I know Y as well as X, I would never say to myself that X is Y, i.e., I could not judge falsely that X=Y. While if Y is unknown to me it could never enter into any judgement I made, so again I could not falsely judge that X=Y. These problems from the Theaetetus are attacked with the wax tablet and aviary models, which begin to make headway towards over-coming some of the obstacles to an account of false judgement in so far as they provide for the possibility of an object entering into thought via different routes. But it is the Sophist which presents Plato’s solution,⁶⁶ a solution which does not build on the Theaetetus. The main philosophical section of the Sophist begins with the assertion that in order to show how false judgement is possible, Parmenides’ assertion ‘Never shall this be proved, that things that are not are’ must be refuted. For a false statement says that what is not (=Not Being) is. The main point needed to overcome Parmenides’ dictum is that ‘Not Being’ or ‘What is Not’ does not signify contrary to being, i.e. non-existence, but different from being. Focusing on the ‘greatest Kinds’—Being, Difference, Sameness, Rest and Motion—Plato, after explaining how some can participate in and hence be the others, points out that each is different from the others, and hence can be said to not be each of the others. So Not Being exists. Next, we must be clear about the fact that a statement has two kinds of parts that function in different ways. The name signifies the being in the world that the statement is about, while the verb signifies what is said about the subject, namely the being in the world that is the attribute ascribed to the subject. ‘Theaetetus is sitting’ is true if sitting ‘is with respect to Theaetetus’, i.e. if sitting=one of his attributes. And then ‘Theaetetus flies’ is false if flying ‘is not with respect to Theaetetus’, i.e. is different from every attribute that is with respect to Theaetetus. The fact that in this false statement what is not is said of Theaetetus does not mean that nothing is said about Theaetetus. For here what is not is not the non-existent or non-existence67 but flying—a being. Plato’s solution marks a major advance when he clearly signals the difference between the ways in which words and statements function. But with no clear notion of sense as distinct from reference, he still has nothing to say on the question of what could constitute the content of a false statement. NOTES 1 My understanding of the Theory of Forms owes most to Ryle [10.43] and Frede [10.74]. See also Graeser [10.76], Ross [10.92]; Wedberg, ‘The Theory of Ideas’, in [10.97], 28–52; Bostock [10.67], 94–101, 194–201, 207–13. Crombie [10.36] can be consulted on all subjects covered by this chapter. I am very grateful to Christopher Taylor for his extensive and helpful comments on earlier drafts of this chapter. Any discussion of the topics I discuss is bound to be controversial and some alternative interpretations can be found in works cited in the notes and bibliography. Limitations of space compel these references to be highly selective. 2 I assume the generally agreed view that the earliest dialogues closely reflect the methods and beliefs of the historical Socrates, but that in middle period dialogues the character of Socrates expresses views which go far beyond those of Plato’s teacher. 3 Cf. the argument ‘from things that are no more’ from Aristotle’s On Ideas in [10. 63], 81–2. Note that the point in the text applies just as much to ‘horse’ and ‘finger’ as it does to ‘beauty’ and ‘one’. Some believe Republic 523–5’s distinction between concepts that do and do not give rise to thought shows that Forms are not needed for concepts such as ‘horse’ which, like the concept of ‘finger’, do not give rise to thought. But the passage only indicates that perception of particular fingers may suffice, epistemically, for recollection of the Form of Finger. The latter is an object of thought as distinct from perceptible fingers as the perceptible and ‘oppositeless’ squares and circles drawn in the sand are distinct from their corresponding Forms which are the objects of the mathematician’s thought (Republic 510d–511a). 4 Cratylus 431b–c; cf. 432e, 385b–c. Similarly with the philosopher Parmenides: what is required for thought was not distinguished from what is required for speech. 5 Symposium 207d–208b: the relation between the different phases of ‘one‘ life is the same as that between a parent and its offspring. See also Cratylus 439d; Theaetetus 154a, 159d–160a; Timaeus 49c–e. Contrast Phaedo 102e. 6 Even in this most extreme statement of the doctrine of flux, Plato allows that the later and earlier objects share many characteristics. Hence, he does not accept the Theaetetus’ wild version of Heracliteanism which says that sensibles always change in every respect. 7 Timaeus 49d–e. For other views on flux, see Bolton [10.65], Irwin [10.80]. 8 For a different interpretation, see Fine, ‘Knowledge and Belief in Republic V–VII’, in [10.101], 85–115. 9 This topic is thoroughly examined in Malcolm [10.85]. 10 Hippias Major 289d, 291d, 292c–d, 297e, 304d; Charmides 161a–b; Laches 192c– d. 11 Hippias Major 292e; Protagoras 330c–e. 12 Hippias Major 291c. 13 Hippias Major 291d. 14 Hippias Major 296c–d. 15 Lysis 217c; Charmides 160e–161a, 169d–e; Hippias Major 291c; Gorgias 497e; Meno 87d–e; Phaedo 68d–e, 100e–101b; Republic 335d–e, 379a–c; Parmenides 131c–d; Philebus 65a. 16 Hippias Major 287c. 17 While Plato allows that physical conditions and phenomena are necessary conditions for the items he explains in other terms, the Phaedo (99a–b) denies them the title of ‘explanations’. In the Timaeus (46c–d), however, he calls them secondary or co-operative causes or explanations. 18 Parmenides 139e, 148a. 19 See, for example, Symposium 211e, Republic 500c, Phaedo 84b, Pbaedrus 250a, Sophist 254b, Philebus 62a. 20 See Vlastos [10.98], 58–75. For the ideas in the paragraph before last, see [10.98], 43–57. 21 Timaeus 38b. 22 Republic 478b12–c1 with 478d–479d. 23 Phaedo 74c1–2. Plato equates two questions: (1) Is Equality ever unequal? (2) Is Equality ever Inequality? Had he seen the difference, he should also have seen (2)’s irrelevance to his argument. He is trying to show that sensible equals differ from Equality because they possess a feature Equality lacks. But sensible equals no more appear to be Inequality than Equality does. 24 On this point see Frede [10.74], 51–2. 25 Timaeus 52a, c; Symposium 211a–b. 26 Phaedo 102d–e, 103b; Republic 501b; Parmenides 132d. 27 Theaetetus 177a. 28 Republic 532c–d. 29 Phaedo 80d. 30 Republic 5080, 509d, 517b. 31 Republic 526e. 32 Theaetetus 177a. 33 Republic 592b. 34 Phaedrus 247c–e. 35 Very briefly on the other objections: the first questions the range of Forms but does not present any positive objections. The second falsely assumes that Forms exist in sensible objects. The last objection mistakenly infers from the statements that (for example) the Form of Master is master of Slavery itself and not of any particular slave, and a particular master is a master of a particular slave and not of Slavery itself, that there can be no relations between individuals and Forms. 36 For another view, see Allen, ‘Participation and predication in Plato’s middle dialogues’, in [10.64], 43–60, and in Vlastos [10.97], 167–83; H.F.Cherniss ‘The relation of the Timaeus to Plato’s later dialogues’, in [10.64], 360–7; Nehamas [10. 87]. 37 In a famous paper (‘The Place of the Timaeus in Plato’s dialogues’, in Allen [10. 64], 313–38) G.E.L.Owen argued that the Timaeus should be dated prior to the Parmenides. This provoked H.F.Cherniss’s response in the article cited in n. 36. Owen’s thesis ‘must be pronounced a failure’ Vlastos [9.93], 264). See Brandwood [10.34], and, more briefly, ‘Stylometry and chronology’, in Kraut [10.41], 90–120. 38 The only author I have come across who notes the relevance of the following point to the Third Man Argument is Cherniss [10.71], 520. 39 [10.63], 84. Cf. Philebus 59c; Aristotle, Nicomachean Ethics 1096a17–19, ps.- Aristotle, On Indivisible Lines 968a9–14. This restriction on the One over Many Assumption was a commonplace among the Neoplatonists. See Proclus, In Parmenidem, V, 125, Cousin=684, Stallbaum; Plotinus, Enneads VI, 1.1. Ammonius, In Porphyrii Isagogen, ed. A. Busse, Berlin, 1891, 28.10–12; 29.18–19; 82, 5–10; Olympiodorus, In Categorias, ed. A.Busse, Berlin, 1902, 58.35–7; Asclepius, In Metaphysicorum Libras A–Z Commentaria, ed. M.Hayduck, Berlin, 1888, 226. 21–2. 40 Metaphysics 1019a2–4. 41 For further discussion see Vlastos, ‘The Third Man Argument in the Parmenides’, in [10.64], 031–63; Strang, ‘Plato and the Third Man’, in [10.58] I, 184–200; Allen [10.19]. 42 Timaeus 27d–28a, 51d–52a; Philebus 59a–c. Cf. Politicus 269d. 43 But possibly Plato is referring to the demiurge of the Timaeus or the world soul (cf. Timaeus 30b, Philebus 30c). 44 Phaedo 106d refers to the Form of Life. Keyt [10.81] convincingly argues the Phaedo’s commitment to Forms for substances such as Snow and the Soul. 45 Sophist 248a–249d is discussed in Keyt [10.82]. 46 I defend this view in [10.78]. For other views see Ackrill in [10.64], 199–206 (=[10.58]1, 201–9); and a sometimes inaccurate survey of alternative accounts in Pelletier [10.89]. 47 I argue that the text of the Sophist bears this out in [10.77]. For other views, see, e.g. Vlastos, ‘An Ambiguity in the Sophist’, in [9.87], 270–308; Frede [10.73]. 48 Aristotle, Physics 209b15. The unwritten doctrines are views attributed to Plato by Aristotle and ancient commentators which are, at least frequently, not clearly expressed in Plato’s writings. The Philebus’ notions of Limit and the Unlimited may be connected to Plato’s generation of Forms from the One and the Great and the Small in his oral teachings (Aristotle, Metaphysics 987b18–21). On the unwritten doctrines, see, for example, Cherniss [10.70], Gaiser [10.75], Krämer [10. 83], Robin [10.91], Vlastos, ‘On Plato’s oral doctrine’, in [9.87], 379–403. 49 For discussion of the Philebus, see Hackforth [10.25]; Gosling [10.26]; Sayre [10. 93], ch. 7; Striker [10.95]. 50 At least this is so in the Phaedo where Forms and the recollection theory are said to stand and fall together (76e). Since we do not experience Forms in the world around us, the Phaedo in effect offers an explanation of a priori knowledge, where the knowledge is prior not to all of the soul’s experience, but to its experience since birth in its present life. It is doubtful, however, that Plato is thinking of Forms in the earlier Meno, where they go unmentioned and we recollect things seen ‘here’ (81c6) in the present life. A related difference between the dialogues is that in the Meno, where knowledge is a kind of opinion (98a), both latent opinion and latent knowledge explain the slave boy’s performance. While in the Phaedo, where Forms alone are recollected and are ‘unopinable’ (adoxaston, 84a), references to latent opinions disappear. For general discussion of Plato’s epistemology, see, for example, Gulley [10.102] and the papers on Plato in [10.101]. 51 It doesn’t matter whether x is or is not like y, or, in the first case, whether x does or does not (73a) fall short of y; the important point is that ‘as long as while you are seeing something else (allo) from this vision you think of something else (allo)’ (74c–d) it is recollection. 52 In the dialogue the slave boy does not recover active knowledge of p (85c–d), so what he actually does there which requires explanation in terms of recollection must be something else. 53 Cratylus 431b–c. 54 The confusion persisted into this century. ‘Moore and Russell were constantly perturbed by whether or not to identify true propositions with facts, which they took to be fully part of the real world, or merely to regard the one as corresponding to the other, whether to admit the existence of false propositions, and similar problems, and constantly changing their minds on these points’ (M. Dummett, Frege: Philosophy of Language, London, Duckworth, 1973, p. 153). 55 There are good reasons to reject Gail Fine’s suggestion that Plato answers (1) with the slave boy example by saying that, even though the enquirer lacks knowledge in any sense, he has true beliefs about the subject of enquiry (‘Inquiry in the Meno’ in [10.41], 200–26). First, the purpose of the slave boy example is to demonstrate the truth of the recollection theory (81e, Phaedo 72e–73b), not to solve the paradox of enquiry. Further, her attempt to explain away the references to the slave boy’s knowledge as allusions to his past or future knowledge (n. 40) is refuted by the reference to ‘the knowledge which he now has’ at 85d9. Likewise Phaedo 73a is clearly saying that the slave boy could not have spoken the truth if knowledge had not been in him then. This is also the presumption of Republic 518b-d. There is no contradiction with Meno 85b-c’s statement that the slave boy does not have knowledge since this denies that he has current, revived knowledge of p, not that he has latent knowledge of p. 56 For different views of the recollection theory, see the papers reprinted in [10.10]. 57 This paragraph is based on Strange [10.94]. Some other works on the Timaeus: Cornford [10.23], Brisson [10.68], Mohr [10.86], Taylor [10.96]. For Plato’s dialectical method in the middle dialogues the classic work is Robinson [10.105]. See also Sayre [10.106]. 58 In particular, the Phaedrus, the Sophist, the Politicus and the Philebus. 59 For discussion of Plato’s later dialectic, see Ackrill [10.99]; Sayre [10.106]; Stenzel [10.107]. 60 Some works on the Theaetetus: Cornford [10.20]; McDowell [10.21]; Burnyeat [10. 22]; Bostock [10.100]. 61 One important issue of interpretation concerning the Theaetetus is the question of whether Plato revises his earlier views of the sensible world. For the famous debate between Owen and Cherniss (referred to in n. 37), see Allen [10.64], 332–5 and 349–60. 62 The standard view holds that Plato is saying that to know one must truly judge that something is the case (grasping being either is this judgement or is presupposed by it in virtue of ‘is’), and that such an intentional content cannot be delivered by perception. But Plato uses singular terms and ‘that’ clauses indifferently to refer both to objects of judgement and objects of perception. (Judgement: 185c–d, 186a– d; 185a–b, 186b. Perception: 184b, 184d–185a; 185b–c.) Furthermore, on the standard view it is inexplicable that Plato blatantly ignores the point for the rest of the dialogue where many examples of objects of knowledge and judgement are individuals. Before, during and after 184–7 both things and facts are objects of the knowledge which the dialogue attempts to define, and this is one source of the difficulties troubling Plato’s discussion. 63 Unlike present day epistemologists, Plato does not speak here of the justification of belief in a proposition. 64 This argument brings out Plato’s inability to clearly distinguish thinking of X and knowing X: to think of X is already to know X. 65 Burnyeat in [10.22], 238. 66 For further discussion of the Sophist’s solution, see McDowell [10.103] and Frede ‘The Sophist on false statements,’ in [10.41], 397–424. 67 Here I am assuming a view of Not-Being in the Sophist which not all will accept. This issue is discussed in Malcolm [10.84]; Frede [10.73] Owen ‘Plato on Not-Being’, in [10.58] I, 223–67; Heinaman [10.79]; Brown [10.69]. GENERAL BIBLIOGRAPHY FOR CHAPTERS 10–12 Complete Greek Text 10.1 Burnet, J. Platonis Opera, 5 vols, Oxford, Clarendon Press (Oxford Classical Texts), 1900–7. A new text is in preparation; vol. I, ed. E.A.Duke et al., appeared in 1995. A complete Greek text with English translation is published by the Loeb Classical Library (London and Cambridge, Mass., Harvard University Press). 12 vols (various editors). Complete Translations 10.2 Cooper, J. (ed.) Plato. Complete Works, Indianapolis, Ind. and Cambridge, Hackett, 1995. 10.3 Hamilton, E. and Cairns, H. (eds) The Collected Dialogues of Plato, New York, Bollingen Foundation, 1961. 10.4 Jowett, B. The Dialogues of Plato, 4th edn, rev. D.J.Allan and H.E.Dale, 4 vols, Oxford, Clarendon Press, 1953. Translations of Selected Works 10.5 Allen, R.E. The Dialogues of Plato, 2 vols, New Haven, Conn., Yale University Press, 1984 and 1991. (First 2 volumes of projected complete translation.) 10.6 Matthews, G. Plato’s Epistemology, London, Faber and Faber, 1972. Contains translations of passages from Meno, Phaedo, Republic, Parmenides, Theaetetus, Sophist. 10.7 Saunders, T.J. (ed.) Early Socratic Dialogues, Harmondsworth, Penguin, 1987. Contains translations of Ion, Laches, Lysis, Charmides, Hippias Major, Hippias Minor, Euthydemus. Translations of Separate Works (some with Greek text) (Listed in probable order of composition by Plato) 10.8 Guthrie, W.K.C. Plato: Protagoras and Meno, Harmondsworth, Penguin, 1956. 10.9 Sharples, R.W. Plato: Meno, Warminster, Aris and Phillips, 1985. Greek text with facing translation and commentary. 10.10 Day, J.M. (ed.) Plato’s Meno in Focus, London, Routledge, 1994. Contains a translation of the Meno with a collection of articles. 10.11 Hackforth, R.M. Plato’s Phaedo, Cambridge, Cambridge University Press, 1955, repr. Indianapolis and New York, Bobbs-Merrill. Translation and commentary. 10.12 Gallop, D. Plato, Phaedo, Oxford, Clarendon Press, 1975. Translation with philosophical commentary. Revised version of translation with notes, Oxford and New York, Oxford University Press, 1993 (World’s Classics). 10.13 Rowe, C.J. Plato: Phaedrus, Warminster, Aris and Phillips, 1986. Greek text with facing translation and commentary. 10.14 Grube, G.M.A. rev. C.D.C.Reeve Plato: Republic, Indianapolis, Ind., and Cambridge, Hackett, 1992. Translation with notes. 10.15 Waterfield, R. Plato, Republic, Oxford and New York, Oxford University Press, 1994. Translation with notes (World’s Classics). 10.16 Halliwell, F.S. Plato: Republic V, Warminster, Aris and Phillips, 1993. Greek text with facing translation and commentary. 10.17 Halliwell, F.S. Plato: Republic X, Warminster, Aris and Phillips, 1988. Greek text with facing translation and commentary. 10.18 Cornford, F.M. Plato and Parmenides, London, Routledge and Kegan Paul, 1939. Contains a translation of Parmenides with commentary. 10.19 Allen, R.E. Plato’s Parmenides, Oxford, Blackwell, 1983. Translation and analysis. 10.20 Cornford.F.M. Plato’s Theory of Knowledge, London, Routledge and Kegan Paul, 1935. Contains translations of Theaetetus and Sophist with commentary. 10.21 McDowell, J. Plato, Theaetetus, Oxford, Clarendon Press, 1973. Translation with philosophical commentary. 10.22 Burnyeat, M. The Theaetetus of Plato, Indianapolis, Ind. and Cambridge, Hackett, 1990. Contains translation of Theaetetus by M.J.Levett, with introduction by M.Burnyeat. 10.23 Cornford, F.M. Plato’s Cosmology, London, Routledge and Kegan Paul, 1937. Contains translation of Timaeus with commentary. 10.24 Rowe, C.J. Plato: Statesman, Warminster, Aris and Phillips, 1995, Greek text with facing translation and commentary. 10.25 Hackforth, R. Plato’s Examination of Pleasure, Cambridge, Cambridge University Press, 1958. Contains translation of Philebus with commentary. 10.26 Gosling, J.C.B. Plato, Philebus, Oxford, Clarendon Press, 1975. Translation with philosophical commentary. 10.27 Saunders, T.J. Plato: The Laws, Harmondsworth, Penguin, 1970. Other translations (of some of the above and of other dialogues) are published by Hackett, Oxford University Press (Clarendon Plato Series and World’s Classics), Penguin and (in French) Flammarion. Most contain notes/or commentary. Bibliographies 10.28 Cherniss, H.F. ‘Plato, 1950–59’, Lustrum 4 (1957): 5–308, and 5 (1960): 321–648. 10.29 Brisson, L. ‘Platon, 1958–1975’, Lustrum 20 (1977): 5–304. 10.30 Brisson, L. and Ioannidi, H. ‘Platon, 1975–1980’, Lustrum 25 (1983): 31–320 (corrections in vol. 26 (1984)). 10.31 Brisson, L. and Ioannidi, H. ‘Platon, 1980–1985’, Lustrum 30 (1988): 11–294 (corrections in vol. 31 (1989)). Concordances 10.32 Ast. F. Lexicon Platonicum, 2 vols, Leipzig, Weidmann, 1835–6; repr. Bonn, Rudolf Habelt, 1956. 10.33 Brandwood, L. A Word Index to Plato, Leeds, W.S.Maney and Son, 1976. Chronology 10.34 Brandwood, L. The Chronology of Plato’s Dialogues, Cambridge, Cambridge University Press, 1990. 10.35 Ledger, G.R. Re-Counting Plato, Oxford, Clarendon Press, 1989. General surveys of Plato 10.36 Crombie, I.M. An Examination of Plato’s Doctrines, 2 vols, London, Routledge and Kegan Paul, 1962. 10.37 Friedländer, P. Plato, trans. H.Meyerhoff, 3 vols, London, Routledge and Kegan Paul, 1958–69. German original Berlin, de Gruyter, 1954–60. 10.38 Gosling, J.C.B. Plato, London and Boston, Routledge and Kegan Paul, 1973. 10.39 Grube, G.M.A. Plato’s Thought, London, Methuen, 1935; repr. 1958; 2nd edn, London, Athlone Press, 1980, with new bibliography by D.J.Zeyl. 10.40 Guthrie, W.K.C. A History of Greek Philosophy, vols IV and V, Cambridge, Cambridge University Press, 1975 and 1978. See [2.13]. 10.41 Kraut, R. (ed.) The Cambridge Companion to Plato, Cambridge, Cambridge University Press, 1992. Contains substantial bibliography. 10.42 Rowe, C.J. Plato, Brighton, Harvester, 1984. 10.43 Ryle, G. ‘Plato’, in P.Edwards (ed.) The Encyclopedia of Philosophy, New York and London, Macmillan Inc. and The Free Press and Collier Macmillan, 1967, vol. VI, pp. 314–33. Other Relevant Works 10.44 Adkins, A.W.H. Merit and Responsibility, Oxford, Clarendon Press, 1960. 10.45 Annas, J. An Introduction to Plato’s Republic, Oxford, Clarendon Press, 1981. 10.46 Burkert [1.43]. 10.47 Dodds [2.28]. 10.48 Dover, K.J. Greek Popular Morality in the Time of Plato and Aristotle, Oxford, Blackwell, 1974. 10.49 ——Greek Homosexuality, London, Duckworth, 1978; 2nd edn, 1989. 10.50 Easterling, P.E. and Muir, J.V. (eds) Greek Religion and Society, Cambridge, Cambridge University Press, 1985. 10.51 Irwin, T.H. Classical Thought, Oxford, Oxford University Press, 1989. 10.52 Kahn [9.40]. 10.53 Lloyd [2.37]. 10.54 Mikalson, J.D. Athenian Popular Religion, Chapel Hill, NC, University of North Carolina Press, 1983. 10.55 Ober, J. Mass and Elite in Democratic Athens, Princeton, NJ, Princeton University Press, 1989. 10.56 Patterson, R. Image and Reality in Plato’s Metaphysics, Indianapolis, Ind., Hackett, 1985. 10.57 Szlezák, T.A. Platon und die Schriftlichkeit der Philosophie: Interpretationen zu den frühen und mittleren Dialogen, Berlin, de Gruyter, 1985. 10.58 Vlastos G. (ed.) Plato: A Collection of Critical Essays, 2 vols., Garden City, NY, Doubleday, 1971. 10.59 ——[9.87]. 10.60 ——[9.93]. 10.61 ——[9.94]. 10.62 Watson, G. Plato’s Unwritten Teaching, Dublin, Talbot Press, 1973. BIBLIOGRAPHY FOR CHAPTER 10 Metaphysics 10.63 Alexander of Aphrodisias, On Aristotle Metaphysics 1, trans. W.Dooley, London, Duckworth, 1990. 10.64 Allen, R.E. (ed.) Studies in Plato’s Metaphysics, London, Routledge and Kegan Paul, 1965. 10.65 Bolton, R. ‘Plato’s distinction between Being and Becoming’, Review of Metaphysics 29 (1975): 66–95. 10.66 Bostock, D. ‘Plato on “is not” (Sophist 254–9)’, Oxford Studies in Ancient Philosophy 2 (1984): 89–119. 10.67 ——Plato’s Phaedo, Oxford, Clarendon Press, 1986. 10.68 Brisson, L. Le Même et l’Autre dans la structure ontologique du Timée de Platon, Paris, Klincksieck, 1974. 10.69 Brown, L. ‘Being in the Sophist: a syntactical enquiry’, Oxford Studies in Ancient Philosophy 4 (1986): 49–70. 10.70 Cherniss, H.F. The Riddle of the Early Academy, Berkeley and Los Angeles, Calif., University of California Press, 1945. 10.71 ——Aristotle’s Criticism of Plato and the Academy, Baltimore, Md., Johns Hopkins University Press, 1935; repr. New York, Octagon Books, 1964. 10.72 Fine, G. On Ideas: Aristotle’s Criticism of Plato’s Theory of Forms, Oxford, Clarendon Press, 1993. 10.73 Frede, M. Prädikation und Existenzaussage, Göttingen, Vandenhoeck and Rupprecht (Hypomnemata 18), 1967. 10.74 ——‘Being and Becoming in Plato’, Oxford Studies in Ancient Philosophy, suppl. vol. (1988): 37–52. 10.75 Gaiser, K. Platons Ungeschriebene Lehre, Stuttgart, E.Klett, 1968. 10.76 Graeser, A. Platons Ideenlehre, Bern and Stuttgart, Paul Haupt, 1975. 10.77 Heinaman, R. ‘Self-predication in the Sophist’, Phronesis 26 (1981): 55–66. 10.78 ——‘Communion of Forms’, Proceedings of the Aristotelian Society NS 83: (1982– 3): 175–90. 10.79 ——‘Being in the Sophist’, Archiv für Geschichte der Philosophie 65 (1983): 1–17. 10.80 Irwin, T. ‘Plato’s Heracliteanism’, Philosophical Quarterly 27 (1977): 1–13. 10.81 Keyt, D. ‘The fallacies in Phaedo 1028–107b’, Phronesis 8 (1963): 167–72. 10.82 ——‘Plato’s paradox that the immutable is unknowable’, Philosophical Quarterly 19 (1969): 1–14. 10.83 Krämer, H.J. Arete bei Platon und Aristoteles, Heidelberg (Abh.d.Akad., Phil.-hist. Kl., 1959, 6), 1959. 10.84 Malcolm, J. ‘Plato’s analysis of TO ov and TO JIT) ov in the Sophist’, Phronesis 12 (1967): 130–46. 10.85 ——Plato on the Self-Predication of Forms, Oxford, Clarendon Press, 1991. 10.86 Mohr, R. The Platonic Cosmology, Leiden, E.J.Brill, 1985. 10.87 Nehamas, A. ‘Plato on the imperfection of the sensible world’, American Philosophical Quarterly 12 (1975): 105–17. 10.88 ——‘Self-predication and Plato’s Theory of Forms’, American Philosophical Quarterly 16 (1979): 93–103. 10.89 Pelletier [4.50]. 10.90 Penner, T. The Ascent from Nominalism, Dordrecht, D.Reidel, 1987. 10.91 Robin, L. La Théorie platonicienne des Idées et des Nombres d’après Aristote, Paris, Félix Alcan, 1908; repr. Hildesheim, Olms, 1963. 10.92 Ross, W.D. Plato’s Theory of Ideas, Oxford, Clarendon Press, 1951. 10.93 Sayre, K.M. Plato’s Late Ontology, Princeton, NJ, Princeton University Press, 1983. 10.94 Strange, S. ‘The double explanation in the Timaeus’, Ancient Philosophy 5 (1985): 25–40. 10.95 Striker, G. Peras und Apeiron, Göttingen, Vandenhoeck and Rupprecht (Hypomnemata 30), 1970. 10.96 Taylor, A.E. A Commentary on Plato’s Timaeus, Oxford, Clarendon Press, 1928. 10.97 Vlastos [10.58], vol. 1. 10.98 ——[9.87]. Epistemology 10.99 Ackrill, J.L. ‘In defence of Platonic division’, in O.P.Wood and G.Pitcher (eds) Ryle, Garden City, NY, Doubleday, 1970, London, Macmillan, 1971, PP. 373–92. 10.100 Bostock, D. Plato’s Theaetetus, Oxford, Clarendon Press, 1988. 10.101 Everson, S. (ed.) Companions to Ancient Thought 1: Epistemology, Cambridge, Cambridge University Press, 1990. 10.102 Gulley, N, Plato’s Theory of Knowledge, London, Methuen, 1962. 10.103 McDowell, J. ‘Falsehood and not-being in Plato’s Sophist’, in Schofield and Nussbaum [see 3.34], pp. 115–54. 10.104 Moravcsik, J.M.E. ‘The anatomy of Plato’s divisions’, in Lee, Mourelatos and Rorty [see 3.43], pp. 324–48. 10.105 Robinson [9.74]. 10.106 Sayre, K.M. Plato’s Analytic Method, Chicago, University of Chicago Press, 1969. 10.107 Stenzel, J. Plato’s Method of Dialectic, trans. D.J.Allan, Oxford, Clarendon Press, 1940. 10.108 Vlastos [9.93].