Plato (Aristocles)

Ancient Philosophy Πλάτων Plato (Aristocles)

Nicholaos Jones Autumn 2011

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Lecture 14: Plato - Meno The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. - A.N. Whitehead, Process and Reality (Free Press: 1979, p.39) Platonic Dialogue Plato's Meno begins with Meno asking Socrates whether virtue is teachable. Meno: Can you tell me, Socrates, is virtue something acquired by teaching? Or is it something acquired not by teaching, but by practice? Or is it something acquired neither by practice nor by learning, but something human beings possess by nature or in some other way? (70a) Socrates replies that he doesn't know the answer to Meno's question. He reasons that, since he does he know what virtue is, he cannot know whether it is teachable (71b). But he offers to inquire, with Meno, about the nature of virtue (71d). Meno replies with a list of virtues: for a man, helping to govern the city by benefiting friends and harming enemies; for a woman, managing the household; and so on (71e). But rather than go on with his list, Meno describes the pattern: "for each of the affairs and stages of life, and in relation to each particular function, there is a virtue for each of us--and it is the same way, I think, Socrates, for vice" (72a). This does not satisfy Socrates. Socrates does not want to know examples of virtuous actions. And he does not want to know a generalization from these examples to a pattern they all share (72a-c). He wants to know the form of virtue, that because of which each example is an example of a virtue (72c). This form of virtue is the same among different instances of virtue; it is what makes each instance an instance of virtue (72d-e). Socrates goes on to argue that there really is a form of virtue: 1. Anyone who is temperate and just is good; and anyone who is intemperate and unjust is not good (73a-b). 2. So "all human beings are good in the same way" (73c). 3. If virtue were not the same in all human beings, humans would not all be good in the same way (73c). 4. So virtue is the same in all human beings. Socrates and Meno proceed to inquire into what this form of virtue is. The dialogue ends with Socrates leaving for a different appointment (100b). They never quite answer Meno's question.

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Despite leaving Meno's question unresolved, Plato's dialogue exhibits several interesting arguments. Before we get into the details, however, it is worth noting something about the structure of the Meno. For many of Plato's dialogues have the same form as the Meno: 1- Some Athenian claims to be an expert on some X, such as piety, knowledge, beauty, love, friendship, or virtue. 2- Socrates asks the person to tell him about the form of X, what makes X-things X. 3- The person offers a series of examples but does not answer the question. 4- Socrates uses a method of question-and-answer to help the person articulate their answer. (This is known as Socratic elenchus.) 5- The conversation ends with no firm answer, having revealed everyone to be confused about the form of X. There are historical records that provide evidence for the existence of a person, Socrates, who roamed Athens discoursing with fellow citizens in the way he appears to in Plato's dialogues. (If you want to know what happened to Socrates, read Plato's Apology and Crito.) But most contemporary scholars maintain that, rather than Plato being an impartial recorder of what Socrates said on various occasions, Plato uses the dialogues to develop his own philosophical views. Those views are heavily indebted to Socrates, because Plato was one of the Athenians who followed Socrates around town. And it is likely that, in the dialogues, Plato is not only engaging with other philosophers of his time but also struggling to make sense of what Socrates was doing when doing philosophy. Already, early in the Meno, we can catch a glimpse of Plato's theory of forms. This is Plato's theory about what Socrates was asking people to discuss. A form is, roughly, that which many different things share, which makes them things of the same kind. So, for example, the form of virtue is that which different virtuous actions share, which makes them all instances of virtue. We can infer, from the opening section of the Meno, that Plato takes forms to have two properties. First, they are common to different things. But second, and more subtly, forms are non-linguistic. Specifically, forms are not definitions. Different virtuous actions might all be called virtuous because they satisfy some definition of "virtue." But the definition does not reveal what makes them all virtuous actions, because it does not reveal what it is about an action which guarantees that the action satisfies the definition. Forms might be the objects of definition; but they are not themselves definitions. This makes the nature of forms somewhat mysterious. We'll have to keep our eyes open for more hints from Plato about what these forms are supposed to be, and how (if at all) we can know about them. Meno's Paradox At 80d-e, Meno raises an objection to Socrates' demand that he reveal the form of virtue. This has come to be known as Meno's Paradox: 3

Meno: [H]ow are you going to inquire about [the form of virtue], Socrates, when you do not know at all what it is? For what sort of thing, from among the ones you do not know, will you take as the object of your inquiry? And even if you do happen to bump right into it, how are you going to know that it is the thing you did not know? (80d) Meno's argument amounts to a set of rhetorical questions; Socrates usefully rephrases it as a series of claims, making it an argument in the formal sense of "argument": Socrates: [I]t is not possible for a person to inquire about what he knows, or about what he does not know. After all, he wouldn't inquire about what he knows--since he knows it, and there is no need to inquire about something like that--or about what he does not know-since he does not know what he is to inquire about (80e) Here's the problem: Socrates and Meno feel that they can recognize instances of virtuous behavior; but they do not know the form of virtue, what virtue means. And this is puzzling, because it's not clear how we could know that this action is virtuous unless we already knew what it is that makes action virtuous. Meno's Paradox, if sound, establishes that inquiry is impossible. This entails that learning is impossible, because learning proceeds through inquiry. And this, in turn, entails that we cannot acquire new knowledge. There's no question that there's something amiss with Meno's Paradox, given that even Socrates and Meno agree that they can identify new actions as virtuous or vicious. But the argument puts, in concrete form, a challenge for Socrates to explain how this can happen. We can rephrase Meno's Paradox as a formal argument, to get clear about its structure and its premises: 1. 2. 3. 4.

Either you know what you're inquiring about, or you don't. If you know what you're inquiring about, inquiry is unnecessary. If you don't know what you're inquiring about, inquiry is impossible. Hence, inquiry is either unnecessary or impossible.

In "Meno's Paradox of Inquiry and Socrates' Theory of Recollection," Ross Harman argues that premise #3 is false: We might not know the object of our inquiry, but that does not mean that we do not know the methods of inquiry which are necessary to find out this object. For example, in my college, there are code-locks on doors, and one must know the correct code in order to pass through the door. I want to go to the computer room, but I have no idea what the code is. However, I have a very simple way of finding out: at the Porter’s Lodge there is a list of codes, and I only have to go there and ask, and I will immediately be told the correct code for the door. In this instance, I started off not knowing something, but my ignorance did not

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render me helpless to inquire; I had in mind a very simple method of inquiry, I followed this inquiry through to its conclusion, and I reached the knowledge that I desired (31). Harman's counterexample provides a case in which someone doesn't know what he's inquiring about and yet nonetheless inquires about it. But one might reject this counterexample for the reason that, whereas knowing a door code is a kind of aposteriori knowledge obtained through sensory experiences, knowing a form is a kind of apriori knowledge that cannot be so obtained. Others maintain that the argument commits the fallacy of equivocation, changing the meaning of the phrase "what you're inquiring about," and that once we remove the equivocation, the argument fails. There are two things Meno might mean by "what you're inquiring about:" (Q) the question you wish to answer; (A) the answer to that question. In sense (Q) Meno and Socrates' inquiry is an inquiry about what the form of virtue is; in sense (A), their inquiry is an inquiry about x, where x is the form of virtue. Premise #3 is true, when read in sense (Q): if you don't know the question you're inquiring about, inquiry is impossible. But it seems to be false when read in sense (A): if you don't know the form of virtue, say, it seems that you can do things that will lead you to discover that form. Premise #2 is, however, true when read in sense (A): if you know the form of virtue, there is no need to inquiry about it. But it seems to be false when read in sense (Q): if you don't know the question you're inquiring about, inquiry is necessary, at least for discovering the question. There does not seem to be any one sense to the phrase "what you're inquiring about" that makes both premise #2 and premise #3 true. So the argument is unsound: if all the premises are true, the argument is not valid due to equivocation; but if the argument is made valid by avoiding equivocation, at least one premise is false and so the argument is not sound. But not everyone maintains that the paradox is fallacious in this way. Consider, for example, this version, which seems to be free from equivocation: 1. Either you know the answer to the question you are asking, or you don't. 2. If you know the answer to the question you are asking, then you cannot learn anything by asking the question. 3. If you do not know the answer to the question you are asking, then you cannot recognize a correct answer when you encounter one, and so you cannot learn the correct answer (because learning requires recognition). 4. Hence, in either case, you cannot know answers to questions you ask. If something like this argument succeeds, Socrates' entire method of doing philosophy--the Socratic elenchus--fails. But even if the argument itself is unsound, the challenge it presents remains: what, if anything, bridges the gap between input, from our senses, about virtuous actions, and output, from our minds, about the common form of those actions? How can we know that particulars have certain properties (such as being virtuous) without first having knowledge of what those properties (such as virtue) are?

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Lecture 14 Topics for Class Discussion 1. What is the difference between a virtuous action and the form of virtue? Why is the form not a definition? 2. What is Socrates' argument that there exists a form of virtue? Is it persuasive? 3. What is Meno's Paradox? Is it fallacious? Is it persuasive? 4. Given that forms are neither actions we can observe with our senses nor definitions we can create with our minds, is there any plausible way to think we could come to know about forms? Are there any other objects of knowledge that resemble forms? How do we know about those objects?

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Lecture 15: Plato - Meno The Problem of Creativity Meno's Paradox purports to show that we cannot know anything unless we have learned it already. Socrates' conversation with the slave boy makes this paradox worse, because it suggests that we cannot learn anything new unless we already know it. Socrates succeeds in getting the boy to prove a geometrical theorem (that the square twice as large as a given square has a side equal to the diagonal of the given square), despite the boy's claim of not knowing the length of the side of a square which is twice as large as some given square. Socrates reiterates facts the boy already knows, Socrates has the boy prove the theorem which he did not know, an accomplishment the boy thought beyond his powers. I've never been able to follow the geometry example in the dialogue (82b-85c), so I'll give a different one. Consider the proposition that 1 is equal to 0.999… repeating. This seems like it is not true. But you can come to know it by recollecting things you already know. Let's give the label "x" to the number 0.999… repeating, for convenience. So we have the equation x = 0.999…. Now let's go through the process of remembering that x = 1, in which case we will have recollected that 1 = 0.999…. Recall that multiplying both sides of an equation by the same amount preserves equality. (Doesn't it?) Let's multiple both sides of our equation by 10. So 10x = 9.999…. (Right?) Recall that subtracting the same number from both sides of an equation preserves equality. (Doesn't it?) Let's subtract x (0.999…) from both sides of our equation. So we get 9x = 9. (Right?) Recall that dividing both sides of an equation by the same number preserves equality, provided the number is not zero. (Doesn't it?) Let's divide both sides of our equation by 9. So x = 1. (Right?) Recall that equality is transitive: if x = y and x = z, then y = z. (Isn't it?) We have x = 1 and x = 0.999… repeating. (Right?) So 1 = 0.999… repeating. (Right?) Voila! This is just what Socrates does with the slave boy. The boy comes to "have knowledge without being taught by anyone but only questioned, since he [has] recovered the knowledge from inside himself" (85d). This is a bit puzzling: how can the slave boy be aware of something of which he is not aware? How can you exhibit knowledge of something that you have not encountered in your past experience? Put this together with Meno's Paradox, and we have a tight knot: it's not clear how we can come to know something we haven't experienced in the past; and it's not clear how our experience could lead us to knowing something we didn't already know. 7

Socrates' Theory of Recollection (Anamnesis) Socrates makes an observation: the slave boy comes to know the geometrical theorem through reliance on knowledge he already has within himself, and "recovering knowledge himself from within himself is recollection" (85d).1 Plato takes this to support what scholars call the theory of recollection (or, in the Greek, anamnesis = unforgetting): acquiring knowledge is not learning something we don't already know, but rather remembering something we have forgotten that we know. For example, yesterday I left my house and made sure that the stove was turned off. Then, not ten minutes later, I forgot whether I turned off the stove. Someone asked me whether I had, and while in some sense I knew that the stove was off, in another sense I did not--I had to take a minute to recollect my stove's condition. So, by taking a minute to recollect, I learned something I already knew. That's the basic idea of the theory of recollection. Socrates states this idea in the Phaedo: When people are questioned, if you put the question well, they will always answer correctly; and yet, unless they had knowledge and the correct account already within them, they could not do this (73a). Learning is an illusion, and the source of the illusion is the frailty of memory. This solves the problem of learning and Meno's Paradox in one fell swoop. We produce new knowledge by remembering rather than learning. And inquiry is necessary despite our already knowing the answers to the questions we are asking, because inquiry prompts recollection. Factual Relativity and Modern Linguistics Plato's theory of recollection is not at all how we, today, would answer Meno's Paradox and the problem of learning. Memories are memories of what have been observed or inferred, and remembering occurs only after we have learned something. Learning, we think, comes from observation and inferences based on those observations; learning precedes remembering, not vice versa. Plato, surely, is aware of this. But consider this: one can memorize multiplication tables without learning anything about multiplication; one can memorize moral rubrics and 1

Socrates infers from this that the soul must be immortal: if the boy recollected the piece of geometrical knowledge (or you recollected the piece of arithmetical knowledge), he must have that knowledge in him. But the series of question and answers did not put that answer in him. So he must have had it in him before he was born, because he did not get the knowledge in his present life. So his soul, that which has knowledge, must have been in a state of knowledge before he was born. But then the knowledge must have always been in his soul, which entails that his soul must be immortal (86a-b). We are not really going to discuss Plato's doctrine of the soul's immortality. 8

adages without learning anything about virtue. Understanding, in both mathematics and morality, seems to be something that must come from within a person--it must be recollected, in a special sense of "recollection." Recollection in this sense does not tell us about empirical matters of fact, such as when Athens became a democracy or what Socrates' wife was named. But mathematical truths, and the nature of virtue, are not empirical matters of fact: we do not come to know them by observation. We never observe perfect triangles; but we know the what properties perfect triangles have (else we could not recognize when something is close enough to a perfect triangle to be called a triangle). We never observe a virtue untainted by vice; but we know what virtue is (else we could not recognize examples of virtuous actions). Plato develops this line of thought in the Phaedo, so we'll set it aside for the moment. For now, it might be helpful to have some contemporary problems for which a kind of theory of recollection seems to provide a good answer. One problem is that observation is something over and above the raw data of perception. Observation involves construction: even experts can disagree about what they observe. This means that the "facts" which observation reveals are not neutral--they involve theoretical baggage, assimilation of perceptual data into some kind of conceptual framework. When the frameworks differ, the facts which are observed also differ. I see the sun rising and setting; you see the earth moving around the sun. I see some bubbles popping up in a chamber; a physicist sees a photon traveling through space. If observation is "relative" in this way, it is not clear how we can come to know something we do not already know through observation, because it is not clear how something that is "relative" (observation) can provide knowledge of something that is not (mathematical theorems, the nature of virtue). The theory of recollection does not have this problem: recollection directly connects us to the knowledge we are seeking, without going through problems involving the relativity of observation. A second, less abstract problem that the theory of recollection solves concerns how we come to acquire language. Noam Chomsky presents the problem like this: The most striking aspect of linguistic competence is what we may call the "creativity of language," that is, the speaker's ability to produce new sentences, sentences that are immediately understood by other speakers although they bear no physical resemblance to sentences which are "familiar." This is the same problem that Plato is addressing in the Meno: how can we exhibit knowledge that we have not already learned some time in the past? In Chomsky's case, the problem takes the form: how can we produce new, grammatical sentences that we have never learned some time in the past? Chomsky solves this problem by postulating an innate sense of grammar, a sense that we do not learn from our experience but that we have within us innately. Chomsky does not posit that we have immortal souls containing this grammatical knowledge; instead, he takes this grammatical knowledge to be hard-wired into our brains. But this is Plato's theory of recollection in modern garb, shorn of reference to souls. For Plato and Chomsky agree that we 9

come into the world with knowledge that is not acquired by experience or observation. Both agree that our knowledge vastly exceeds our learning history. In the case of language, the number of grammatical sentences we can create far exceeds the number we have heard or read. In Plato's case, our knowledge of mathematics and forms far exceeds the number of mathematical theorems or forms we can recall. The Indictment of Sophistry Plato develops the theory of recollection, and the theory of forms, in the Phaedo. Prior to the end of the Meno, however, Socrates and Meno are interrupted by Anytus, who turns the conversation to the topic of the sophists. Some sophists, like Protagoras, claim to be able to teach what virtue is; others, like Gorgias, claim only to make people clever at speaking about virtue. If the theory of recollection is correct, however, then there is a third way: helping people to remember the nature of virtue, without teaching it to them, and without merely settling for cleverness in using words. Socrates, Meno, and Anytus end up condemning the sophists. The argument, in brief, is that the sophists might help people to express true beliefs, but they do not give people knowledge, because true belief that is not "tied down" is not knowledge (97c-98a). This discussion produces a defense of the value of knowledge over opinion (even true opinion), and an analysis of the difference between knowledge and opinion. The indictment of sophistry amounts to the charge that, whole sophistry might give a person persuasive opinions, and even persuasive opinions that are true, it does not give a person knowledge, true opinions that are "tied down." What does give knowledge is, according to Plato at the end of the Meno, divine inspiration. We need to wait for later dialogues until we have some account for Plato's way of understanding this inspiration differs from Hesiod's way.

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Lecture 15 Topics for Class Discussion 1. Why might Socrates say that the slave boy comes to "have knowledge without being taught by anyone but only questioned?" Is he correct to think so? 2. How does the theory of recollection explain how the slave boy produces knowledge of a geometrical theorem? How does it explain how we produce knowledge of the forms? 3. What, according to Socrates, is the difference between knowledge and opinion? Is his argument for the value of knowledge over opinion persuasive? 4. How does a Socratic investigation into the nature of virtue differ from a sophistical one? Why might Plato think that a Socratic investigation can provide knowledge but a sophistical one cannot? 5. How might Plato's notion of divine inspiration differ from Hesiod's? What, if anything, does Plato's notion of divine inspiration provide that Hesiod's does not? 6. Supposing that the forms are what-is, how might Plato/Socrates respond to Gorgias' argument that we cannot communicate this knowledge to others because the forms are external to us but we cannot communicate something that is external to us?

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Lecture 16: Plato - Phaedo Soul The Phaedo begins with Socrates speaking to some friends in prison while awaiting his execution. The main thesis that Socrates undertakes to prove in the dialogue is that the soul is immortal. He repeats an argument from the Meno, that the soul must exist before birth because knowing requires recollection. He also adds a few more: that the soul must be immortal, because the soul brings life to the body and so cannot admit death (must be deathless); and that the soul is simple and therefore indecomposable and therefore indestructible. But, interesting as these arguments might be, we are going to skip them. Plato overlooks the alternative, taken by Chomsky more recently, that we can have knowledge prior to sense experience by having that knowledge hard-wired into our bodies. We'll focus, instead, on developments to the theory of recollection and the theory of forms. The Meno leaves us with some pressing questions about forms. Socrates claims that we recollect when we come to have a form in mind in response to sense perception. But it's not clear what it is to have a form in mind, and so it's not clear what recollection is. Socrates says that recollection is "a process of recovering that which has been forgotten through time and inattention." But it's not clear what has been forgotten, because it's not clear what a form is. From the Meno (and other dialogues, such as the Euthyphro), we know that the main task of philosophy, as Plato conceives it, is to discover forms that make things be of various kinds. We also know that these forms are objective, independent of how people view things of various kinds; and that this objectivity extends to the realm of normativity, such as justice, virtue, and beauty. All of this puts Plato into conflict with the sophists, who maintain that all knowledge is relative. As Protagoras says, "Man is the measure of all things." Plato disagrees: Forms are the measure of all things, and forms are independent of men. Socrates' discussion about the soul involves saying more about what these forms are and how we come to know them. Background on Forms There is no one dialogue in which Plato lays out a theory of forms. His theory, if indeed there is a coherent theory, is scattered across many dialogues. So it's worth pausing to collect together some details on what these forms are supposed to be. Since Socrates is always asking his interlocutors to give a definition (of, say, virtue), it is tempting to infer that a form is a definition. This would be a mistake. Suppose Socrates asks you what the definition of virtue is. You give him some words. But how do you know whether the definition you have given is correct? You have to at least understand the words in your definition. But how do you do that? By giving more definitions? But then you need to at least understand the words in those definitions. Thinking of an answer to Socrates' requests for definitions as a series of words leads to either circularity or an infinite regress.

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Plato's theory of forms offers a way out of this puzzle. Knowing that a definition is correct involves a kind of knowing that is not propositional (a matter of more definitions) but, instead, a kind of knowing by acquaintance, direct awareness of the object of the definition. We know, say, that a definition of virtue is correct by being directly acquainted with virtue itself. Accordingly, even if a correct answer to the Socratic question "What is X?" involves giving a definition, it involves something else too, namely, coming to an awareness of X itself. But why think that this awareness isn't merely a matter of convention, a matter merely of what people think? Because the question "What is X?" presupposes that there is a single correct answer. Socrates doesn't ask "What is X to you?" He asks "What is X, period, full stop?" If that question makes sense (and Socrates is going to argue that it does), then we have a correct definition when we have a series of words that correctly describes X. Since different people can come to know the same correct definition, and others can have incorrect definitions, the object of this definition must be independent of what people think. And since the object of this definition isn't something we can access with our senses (our senses only tell us about particulars), it must be a kind of abstract entity known by the mind. That's just what Plato thinks the forms are: abstract, mind-independent entities, mental acquaintance with which provides knowledge of what makes particular things be of the same kind. (Note: The Greek word for forms is eidos, and sometimes people translate this as "ideas." But that's a misleading translation, because ideas are mind-dependent whereas eidos are not.) The Imperfection Argument (74a-76e) The Phaedo fleshes out the properties of forms: unchanging (78c-d), eternal (79d), intelligible but not perceptible (79a), divine (80a, b), incorporeal (80a, b), causes of being (100c), unqualifiedly what their instances are only with qualification (75c). A concise summary occurs at Phaedo 80c, which lists the properties that forms share with souls: "divine, deathless, intelligible, uniform, indissoluble, always the same as itself." Timaeus 37e-38a adds that forms are not temporal; Phaedrus 247c, that they are not spatial. The Phaedo also provides some arguments that forms have these properties. The first is known as the Imperfection Argument. This argument purports to show not only that forms are always the same as themselves, but also that they are not perceptible and that they exist. Socrates begins the argument by recalling that forms are supposed to be distinct from the objects which have the forms. Socrates: "…we say that there is something that is equal. I do not mean a stick equal to a stick or a stone to a stone, or anything of that kind, but something else beyond all these, the Equal itself" (74a). That is: considering two sticks that are equal in length, the form that makes them equal in length, the Equal itself, is something other than the sticks. (What is it? It is the equality of the sticks.) Next, he provides an argument for this claim, based upon the variability of perceptions. 13

Socrates: "…do not equal stones and sticks sometimes, while remaining the same, appear to one to be equal and to another to be unequal?" --Certainly they do. "But what of the equals themselves? Have they ever appeared unequal to you, or Equality to be Inequality?" -Never, Socrates. "These equal things and the Equal itself are therefore not the same" (74bc). That is: the form that makes sticks equal in length equal in length, the Equal, is distinct from equal things. For while equal things sometimes appear to be unequal, the Equal itself never does -- it is always the same as itself. The same is true of all other forms: Beauty itself never appears to be ugly; Good itself never appears to be bad; the Square itself never appears to be round. And the reason each form never appears to be what it is not is that each form is always the same as itself. (This is one way in which the forms are unchanging: they do not change how they appear when people change their perspectives.) So the Equal cannot be an equal thing, because the Equal always appears to be equal but equal things something do not appear to be equal. From this, Socrates argues that it is not possible to abstract knowledge of the Equal from our sensory perceptions of equal things. For we never experience, with sensory perception, objects that are really, precisely equal; and this means that we must have knowledge of the Equal from something other than our perception of equal things, lest we be unable to recognize that equal things have the Equal in them. (And this means, in turn, that we could not abstract our knowledge of the Equal from our knowledge of equal things, because we would not know how to do so -- we need to be able to recognize equal things as equal before we can rely upon equal things to generalize a concept of equality.) Socrates: "Whenever someone, on seeing something, realizes that that which he now sees wants to be like some other reality but falls short and cannot be like that other since it is inferior, [we agree] that the one who thinks this must have prior knowledge of that to which he says it is like, but deficiently so" (74d-e). For example, when we see two equal sticks, we realize that they are not exactly, precisely equal to each other. For we realize that two sticks might appear equal in length to one person but unequal to another. Yet, even though they "fall short" of being equal, we perceive them to be imperfectly equal, close enough to being equal but "inferior" to the Equal itself. Socrates sums up his intermediate conclusion: "Our sense perceptions must surely make us realize that all we perceive through them is striving to reach that which is Equal but falls short of it" (75b). Finally, from the facts that the Equal must be distinct from equal objects and that we perceive equal objects as imperfectly equal, Socrates concludes that the Equal itself exists. For in order to perceive that two sticks are imperfectly equal, we must have in mind something that is perfectly equal, something with respect to which the equal sticks approximate but fall short. But if we have in mind something that is perfectly equal, then there is something that is perfectly equal, namely, the Equal itself. Because if the Equal itself did not exist, there would 14

not be something we have in mind when we have in mind that which is perfectly equal. (Socrates mixes into his argument here an implicit reference to the theory of recollection. This is relevant in the following way: if our knowledge of the Equal precedes our knowledge of equal things, then we know the Equal. But we can only know that which exists. So the Equal exists.) Chomsky Again, and Impoverished Stimuli The linguist Noam Chomsky makes a Plato-friendly observation. When we classify the physical shapes that we experience, we classify them as inexact representations of geometrically perfect figures rather than as exact representations of geometrically imperfect figures. For example, when we see two squares drawn on the board, we classify them both as imperfect representations of a square rather than as perfect representations of distinct figures. This makes sense. Our geometric concepts would be pretty useless if every time someone drew a square, we needed a new concept to identify what they had drawn. Having one concept that we use to identify different drawn figures, and using that concept in a way that allows different objects to be classified as the same kind of object despite slight differences, makes the concept useful. This is similar to the point Plato makes: when we realize that sticks can be classified as equals despite slight differences in how they are perceived by people, we realize that our concept of the Equal is one that applies to many perceived objects imperfectly rather than a concept that applies to only one perceived object perfectly. Chomsky concludes from this observation about concepts that our sensory perceptions are "impoverished." We never experience perfect squares, or perfect circles, etc. But we have the concept of a perfect square, and of a perfect circle; and we use these concepts to classify different things as being of the same kind. This raises the question of how we could acquire these concepts, given that we never experience anything to which they literally apply. If we need to have the concept before we can recognize distinct objects as being of the same kind, then we do not acquire the concept by abstracting from experience. Plato has it that the only other alternative is that the concept is innate; Chomsky agrees. (While Plato says that the concept is innate by virtue of being possessed prior to birth, Chomsky does away with this theory of recollection, allowing that the concept is innate by virtue of being hard-wired as a matter of biology.) This doesn't leave us with forms being concepts, however, at least not if concepts are merely mental phenomena. For the squares, or the sticks, would have something in common even in the absence of mental phenomena. If concepts are mental, this means that there must be something mind-independent to which the concepts refer. That's what Plato calls the forms.

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Lecture 16 Topics for Class Discussion 1. At the beginning of the Phaedo, Socrates says, "any man who has the spirit of philosophy will be willing to die." What does he mean by this? Why does he believe it? 2. Why might Plato suppose that forms are not definitions? Why might he suppose they are not ideas in our minds? 3. Given the properties that Plato attributes to forms, do the forms respect Parmenides' principles about what-is? 4. What is the Imperfection Argument? What does it show? Is it valid? Is it sound? How might Gorgias respond?

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Lecture 17: Plato - Phaedo Misology and Misanthropy (89d-91c) A misanthrope is a person who hates people. A misologue is a person who hates logos, a person who hates arguments. Given that Socrates is led to his views about forms (and souls) by argument, that for every argument there seems to be a counter-argument, and that there are competing ways to come to form views (such as through appeals to authority or testimony by others), Socrates addresses the concern that giving arguments is a waste of time. He thinks it's not, and his caution against misology provides a defense of argumentation as a path to knowledge. Here is how Socrates sees the cause of misology: Socrates: "it is as when one who lacks skills in arguments puts his trust in an argument as being true, then shortly afterward believes it to be false--as sometimes it is and sometimes it is not--and so with another argument and then with another. You know how those in particular who spend their time studying contradiction in the end believe themselves to have become very wise and that they alone have understood that there is no soundness or reliability in any object or in any argument, but that all that exists simply fluctuates up and down as if it were in the Euripus and does not remain in the same place for any time at all" (90b). Socrates has in mind those who find one argument persuasive, and then an argument for the opposite thesis, and so on repeatedly. But what he goes on to say will apply equally well to those who never find any argument persuasive, who think from the get-go that argumentation is a waste of time because none ever seem to survive scrutiny. For this person Socrates would find to be equally pitiable, by virtue of being deprived of truth and knowledge of reality: Socrates: "It would be pitiable … when there is a true and reliable argument and one that be understood, if a man who has dealt with such arguments as appear at one time true, at another time untrue, should not blame himself or his own lack of skill but, because of his distress, in the end gladly shift the blame away from himself to the arguments, and spend the rest of his life hating and reviling reasonable discussion and so be deprived of truth and knowledge of reality" (90d). Socrates' point here is that encounters with unsound arguments do not warrant concluding that argumentation itself is flawed. For if one was persuaded by an unsound argument, that's one's own fault; and if one was not persuaded, that's as it should be. The misologue, however, makes a mistake, blaming his unsatisfactory encounters with arguments on argumentation itself rather than his own poor skill in discerning good arguments from bad ones. The proper response, however, is not to blame argumentation, but to take steps to develop skills in discerning good arguments from bad and finding true premises.

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Socrates: "We should not allow into our minds the conviction that argumentation has nothing sound about it; much rather should be believe that it is we who are not yet sound and that we must take courage and be eager to attain soundness, you and all the others for your whole life to come…" (90e-91a). The Search for Causes (96b-101e) After considering some objections to the thesis that the soul is immortal, Socrates engages with the way in which Anaxagoras and Empedocles did philosophy. This engagement extends to all the pre-Socratics, because they are all concerned to "know the causes of everything, why it comes to be, why it perished, and why it exists" (96a). This concern is the concern of what, today, we might call natural science. Socrates thinks the pre-Socratics were doing natural science all wrong. Socrates maintains that any answer to the question of why something comes to be, or why it perishes, or why it exists at all -- in short, any answer to a question asking after the cause of something -- must involve saying what the best way is for the thing to be (97c). For he accepts, following Anaxagoras, that Mind is the cause of everything (Mind is similar to what Heraclitus referred to as logos) and that Mind "direct[s] everything and arrange[s] each thing in the way that is best" (97c). Hence, to know why something is the way it is amounts to knowing why the way it is is the best way for it to be. The reason that something exists instead of not existing is, accordingly, that it is better for it to exist than to not exist; the reason that the planets move is that it is best for them to move. (There are affinities here to Leibniz's later idea that this world is the best of all possible worlds.) But, when reading the pre-Socratics, Socrates notices that they do not identify what is best when discussing causes. They say that contraction of muscle causes sitting; that moving air causes speech; and so on. But, Socrates maintains, contraction of muscle does not explain why I am sitting; the motion of air does not explain why I am speaking. What does explain these things is what is best: I am sitting because I judged it to be better to sit than to stand; I am speaking because I judged it to be better than silence. The cause of my sitting or standing is some purpose I am trying to achieve, and this purpose causes my actions when I judge it to be for the best. Now Socrates realizes that I could not sit without contracting my muscles, and I could not speak without moving air. But identifying these things as causes amounts to "not being able to distinguish the real cause from that without which the cause would not be able to act as a cause" (99a-b). My judgment that it is better to sit than to stand could not produce my sitting if my muscles did not contract. But the cause of my sitting is my judgment about what is best and not my muscle contractions. So Socrates argues. Dissatisfied with the pre-Socratics' methods of discovering causes, Socrates says he took up his pursuit of the forms.

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Socrates: "if someone tells me that a thing is beautiful because it has a bright color or shape or any such thing, I ignore these other reasons--for all these confuse me--but I simply … cling to this, that nothing else makes it beautiful other than the presence of, or the sharing in, or however you may describe its relationship to that Beautiful we mentioned, for I will not insist on the precise relationship, but [I will insist] that all beautiful things are beautiful by the Beautiful" (100d-e). Socrates' idea is that the cause of the beauty in beautiful things is the Beautiful; that the cause of bigness in big things is the Big; that the cause of goodness in good actions is the Good; and so on. He thinks that, in so identifying causes, there is no way he can go wrong -- he will avoid the uncertainty that plagues the pre-Socratics and satisfy his search for that which makes things for the best. Forms, Particulars, and Participation (102b-104c) At this point in the Phaedo, Phaedo raises an objection. Suppose that Simmias is taller than Socrates and shorter than Phaedo: Phaedo > Simmias > Socrates. Then, with respect to Socrates, Simmias is tall; and with respect to Phaedo, Simmias is short. So Simmias is both tall and short at the same time. But this is absurd. One might imagine that there is no genuine problem here, because "tall" and "short" are comparative terms. Simmias being tall is just his being taller than one person; and his being short is his being shorter than another; and there is no contradiction in saying that a person is both taller than one person and shorter than another at the same time. This reply is not open to Plato. Plato endorses a theory according to which x is F if and only if x participates in, or has a share of, or partakes of, the form F. So, for example, the statue is beautiful because the statue has Beauty in it; and volunteering is good because volunteering has Good in it. Comparative sentences, of the form do not fit into this schema nicely, because participating in a form is not a relational property. When something has a form, it has it independently of other things, because forms are in things categorically rather than merely hypothetically. So if the statue is beautiful to me, that is because it has Beauty in it; and if it has Beauty in it, it possesses Beauty in itself, regardless of its relation to other things. There is an intellectual economy to Plato's attempt to reduce relational properties to intrinsic properties. For if we maintain that x is F compared to y entails that x is F, then we need only postulate the existence of F, and we do not need to postulate relational forms such as F-inrelation-to-y. Reducing relational properties to intrinsic properties minimizes the number of forms we need to postulate in order to explain things in the way Socrates wants to explain them.

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Here's another way to put think about this. It does not seem correct to treat relational properties as absolute properties. As Thomas Mann puts it in Doctor Faustus, relational properties raise … the problem of the absolute good and beautiful … the good and beautiful without reference to the evil and ugly--the problem of quality without comparison. Where comparison falls away … the measure falls away too, and one cannot speak of heavy or light, of large or small. One might suppose that being tall requires being tall in relation to something else, and that being short requires being short in relation to something else, so that relational properties (such as tall and short) are irreducibly relational. But, given what he says about the explanatory role of forms in 100d-e, Plato is committed to the covariance of predication and form participation: Predication-Participation Schema: x is F if and only if x participates in the form F. If Simmias is taller than Socrates and if (the relational property) being taller than Socrates does not reduce to (the intrinsic, absolute property) being tall, the Predication-Participation Schema entails either that Simmias participates in the absolute form Taller-Than-Socrates or that Simmias participates in the irreducibly relational form Taller-Than. But the forms are complete, and this requires that a form be such that it gives something a property when the thing participates in the form--or, linguistically, that a form be such that when the form is predicated of a thing, the result is a complete sentence. This means that cannot be such a thing as the form Taller-Than. For if there were, then Simmias participating in this form entails that Simmias is taller than. But "Simmias is taller than" is an incomplete sentence, which means that TallerThan is an incomplete form. Hence, if being taller than Socrates does not reduce to being tall, the Predication-Participation Schema entails that there are both relational and non-relational forms, such as the Divisible-By-Two and the Even. Plato rules out the possibility of relational forms--given their already mysterious nature, it seems better to postulate as few as are required for explaining causes in terms of forms. This leads naturally to the idea that x is F compared to y only if x is F. And this amounts to a reduction of relational properties to absolute or intrinsic properties, contrary to the idea that "Where comparison falls away … the measure falls away too, and one cannot speak of heavy or light, of large or small." Phaedo's objection amounts to the claim that Socrates' reduction of relational properties to intrinsic properties must fail. If Simmias being taller than Socrates entails that Simmias is tall, and his being shorter than Phaedo entails that Simmias is short, then Simmias is both tall and short. But nothing can be one thing and its opposite at the same time. Socrates' reply to this objection is subtle. He accepts that the Tall itself cannot be the Short, because of the principle that forms never admit their opposites. He accepts that Simmias has both the Tall and the Short. But he denies the supposition, made by Phaedo, that when Simmias has the Tall, he simultaneously has the Short. 20

Now it seems to me that not only Tallness itself is never willing to be tall and short at the same time, but also that tallness in us will never admit the short or be overcome, but one of two things happens: either it flees and retreats whenever its opposite, the short, approaches, or it is destroyed by its approach. It is not willing to endure and admit shortness and still be other than it was, whereas I admit and endure shortness and still remain the same person and am this short man. But Tallness, being tall, cannot venture to be small (102d-103a). The idea seems to be that, since no form can be its opposite, the Tall flees from Simmias when Simmias is compared to Phaedo, to be replaced by the Short; and the Short flees from Simmias when Simmias is compared to Socrates, to be replaced by the Tall. Hence, even though no form can be its opposite, an opposite thing can come from an opposite thing: tall Simmias can come from short Simmias, and vice versa. This is possible in Simmias' case because, as Socrates notes, Simmias is not taller than Socrates by virtue of being Simmias and he is not shorter than Phaedo by virtue of being Simmias (102c). As we might put it today, it is not Simmias' nature to be taller than Socrates and shorter than Phaedo; his tallness and shortness is an accidental property rather than an essential property. So he can lose the Tall or the Short without ceasing to be Simmias. Socrates goes on to add the caveat that not everything can become its opposite in every respect (104a-105c). For example, the number two cannot admit the form Odd, because it is in the nature of the number two to be even. This caveat allows Socrates to argue that the soul cannot become dead because the nature of the soul is living; but a body can become dead, because living is accidental to bodies.

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Lecture 17 Topics for Class Discussion 1. What is Socrates' argument against misology? Is it persuasive? How might Gorgias respond to the idea that there could be a true and reliable argument? What would Plato's reply be? 2. Why does Socrates think that the pre-Socratics were searching for causes in the wrong place? What is Socrates' alternative, and why does he think it is superior? Does Socrates' method do what he criticizes the pre-Socratics for not doing? 3. What is Phaedo's objection to Socrates' theory of forms? How does the objection's argument go? How does Socrates respond to this objection? Is the response successful?

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Lecture 18: Plato - Republic 5 The Republic is probably Plato's most famous dialogues. It's certainly the one for which he has gotten most grief. In the 20th century, Karl Popper, in The Open Society and Its Enemies, criticized the Republic for advocating what Popper saw as a totalitarian nightmare of deceit, violence, racism, and eugenics. There is scholarly disagreement about whether Popper correctly characterizes Plato's views or, instead, imposes on Plato a superficial and overly literal interpretation. But we are going to ignore Plato's political philosophy, using the Republic to focus, instead, on the development of his metaphysics and epistemology. For a hint about why one might find plausible an alternative reading of Plato, I'll just note that the opening line of the Republic -- "I went down to the Piraeus yesterday" -- uses the same verb phrase, kataben = I went down, that Homer uses to describe Odysseus' descent to the underworld in Book 11 of the Odyssey, and that this suggests, to some scholars, that Plato intends the Republic to be the result of descending from lofty academic considerations of forms into how one might apply philosophy to practical, real-world issues. Moreover, going down to the underworld is a theme in Book 7 of the Republic, with the famous cave allegory. We'll build up to that. Forms and Knowledge Recall that, in the Meno, Plato distinguishes between knowledge and true belief: true belief that is not "tied down" is not knowledge (97c-98a). In the Republic, Plato spells this out a bit more, using his theory of forms to elaborate on the difference. Socrates: What about someone who believes in beautiful things but does not believe in the beautiful itself, and would not be able to follow anyone who tried to lead him to knowledge o fit? Do you think he is living in a dream, or is he awake? Just consider. Isn't it dreaming to think--whether asleep or awake--that a likeness is not a likeness, but rather the thing itself that is like? Glaucon: I certainly think that someone who does that is dreaming (476c). A form, according to Plato's theory, is something that many objects of the same kind have in common, something that makes each of those objects to be of the same kind. So consider some collection of beautiful things--beautiful sounds, colors, shapes, and so on. These all have something in common: they are all beautiful. But what makes them all beautiful? Socrates, in the passage above, envisions two options: either the beautiful things are all beautiful because of the beautiful itself and their common participation in this form, or else the beautiful things are all beautiful because the things themselves are similar apart from their sharing in the beautiful itself. Socrates suggests that the latter option is incoherent: if x is beautiful and y is beautiful, then the reason they are both beautiful must be because they both have beauty and not because x, considered apart from having beauty, is similar to y, also considered apart from its having beauty. Glaucon agrees to describe those who adopt the incoherent view as "dreaming."

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Socrates goes on to characterize those who accept that beautiful things are beautiful by virtue of participating in Beauty, and that the form Beauty is distinct from beautiful things, as being "awake" (476c-d). And he characterizes those who are awake as having knowledge, and those who are asleep as having merely belief. Socrates: So, because this person knows these things [that forms exist and are distinct from particular objects], we would be right to describe his thought as knowledge; but the other's we would be right to describe as belief, because he believes what he does [namely, that beautiful things resemble each other because of the things but not because of their common participation in Beauty] (476d). The conclusion here seems to be that knowledge of the world requires knowledge of forms, and that those who are ignorant of the forms can have at most true beliefs about the world. But this requires that there really is a difference between knowledge and belief, and Plato hasn't really established this beyond gesturing to the metaphor of "tying down." Knowledge, Belief, and Ignorance Plato has Socrates give an argument that knowledge differs from belief. He starts by distinguishing knowledge from ignorance: 1. Whoever knows knows something (ti) rather than nothing (476e). 2. If someone knows something, what the person knows is something that is (on ti) rather than something that is not (mē on ti) (476e). 3. "What completely is, is completely an object of knowledge; and what in no way is, is not an object of knowledge at all" (477a). 4. If anything is and is not, it lies between what is completely and what in no way is (477a). 5. Knowledge deals with what is; ignorance (agnōsia), with what is not (477a). 6. So something between knowledge and ignorance deals with what is and is not (477a). Next, he states two theses: that belief differs from knowledge by virtue of being a different power, and that belief and knowledge deal with different things because of their different powers (477b). He then provides an argument for these theses: 7. Powers (dunameis) are a kind of thing by which we are able (dunametha) to do what we are able to do, and by which everything else can do what it can do (477c). 8. Powers are distinguished by what they deal with and what work they do (477c-d). 9. Knowledge is a power (477d). 10. Belief (doxa) is a power (because it is that by which we are able to believe) (477e). 11. Knowledge is infallible; belief is fallible (it can be in error) (477e). 12. So knowledge and belief are different powers (from 8 and 11). 13. So knowledge and belief deal with different things (from 8 and 12). 14. So belief must deal with something other than what is (from 5 and 13).

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Socrates and Glaucon take this argument to establish that belief differs from knowledge. This leaves open the possibility that belief differs from knowledge by virtue of being ignorance. Since this would be an absurd result, Socrates goes on to argue that belief also differs from ignorance. 15. Whoever believes believes something (478b). 16. What is not is nothing rather than something (478b). 17. So belief does not deal with what is not (from 15 and 16). 18. So belief differs from ignorance (478c, from 5, 8, and 17). Socrates and Glaucon take this to establish that belief is neither knowledge nor ignorance (478c). They proceed to establish that belief lies between knowledge and ignorance, noting that belief is more obscure than knowledge but clearer than ignorance, and less clear than knowledge but more obscure than ignorance (478c). Having previously established that what is and is not lies between what is and what is not, they infer that belief, being set between knowledge and ignorance, deals with what is and what is not (478d). CLEAR——————————————————————————OBSCURE what is knowledge

what is & is not belief

what is not ignorance

Objects of Knowledge and Belief Merely distinguishing knowledge from belief does not show that those who lack knowledge of forms lack knowledge altogether. Plato returns to this earlier topic, with an argument that those who lack knowledge of forms have only belief. He supposes, for the sake of argument, that there are no forms. (He does this, because he is arguing against someone who denies that forms exist and yet claims to have knowledge of what is.) 19. For anything that we perceive with our senses to be F, sometimes it seems to be F and something it seems to be not F (479a-b). 20. Hence, our senses tell us that what we perceive is both F and not F (479b). 21. So attitudes, formed on the basis of sensory perceptions, are "somehow rolling around between what is not and what completely is" (479d). 23. Therefore, attitudes formed on the basis of sensory perceptions are beliefs rather than knowledge, dealing with objects that both are and are not (479d). The upshot here is that, if we rely only on our sensory perception, we can have at most true beliefs about the world, because the objects of perception change and appear differently to different people. Objects of knowledge, accordingly, must be unchanging and "always the same in every respect" (479e). Since the only thing that fits this bill is the forms, it follows that knowledge requires knowledge of forms (479e-480a).

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Lecture 18 Topics for Class Discussion 1. Why, according to Plato, does knowledge differ from ignorance? Is his argument persuasive? 2. Why, according to Plato, does knowledge differ from belief? Is his argument persuasive? 3. Why, according to Plato, does ignorance of forms make knowledge impossible? What assumptions about the requirements for knowledge are required to make this thesis plausible? Are those assumptions true? 4. In what way is believing like dreaming and knowing like being awake, according to Plato's analysis of the difference between belief and knowledge? 5. In the Meno, Plato says that knowledge is true belief that is tied down, and that we obtain knowledge through divine inspiration. In light of Plato's analysis of knowledge in Republic 5, what might "tying down" amount to, and what is the content of "divine inspiration"?

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Lecture 19: Plato - Republic 6&7 Being Informed The Meno says that knowledge is true belief that is "tied down," bound by an explanatory account (aitias logismos: 98a). The Phaedo says, in effect, that forms are what do the tying down (96+). This entails that knowledge of forms is necessary for any knowledge at all, and Republic 5 develops the details of how the forms figure into knowledge. One might notice that Plato never really gives an explicit, straightforward argument for the existence of these forms. But we can make one for him, that seems to fit the way he invokes forms. The basic idea appeals to a plausible criterion for existence: If X is part of a significant and informative explanation of some phenomenon Q, then X has real existence. Plato has given, in the Meno and the Phaedo, several phenomena for which postulating the forms provides a significant and informative explanation: our ability to have knowledge of the form , our ability to "learn" or recollect (new) knowledge on the basis of inference, the apparent fact that sometimes things that are different have something in common, the apparent fact that similarities among things are features of the things themselves, and the apparent fact that the way things are in themselves does not depend on the way we use words. Republic 5 argues, moreover, that only the forms fit the requirements for being objects of knowledge. So the forms provide a unified explanation for all these phenomena: both how it is possible for us to have knowledge (rather than only ever true belief), and how it is possible for things to resemble each other apart from the way we choose to speak about them. Given that this explanation is significant and informative, and that there does not appear to be a better competitor explanation, it follows that a sort of "inference to the best explanation" warrants the conclusion that forms exist. Now it is, of course, open to someone, such as Gorgias or Protagoras, to deny the phenomena Plato takes the forms to explain. One might, for example, deny that different things can have something in common, or that what different things have in common is something about the things rather than how we speak of the things, or that how we speak of the things does not determine what the things are in themselves. But, if Plato's argument in Republic 5 is correct, this seems to entail that we cannot have knowledge of anything. A sophist bite this bullet, too. But there are costs: resting content with true belief alone does not explain the different between, say, someone able to regurgitate a mathematical theorem and someone who understands why the theorem is true. The Line Analogy In Republic 6, Plato uses the famous line analogy to support the idea that knowledge differs from belief, and he further distinguishes between kinds of knowledge and kinds of belief. This 27

provides further support for the idea that the forms explain a genuine phenomenon, namely, the difference between knowledge and belief; and in doing so, the analogy clarifies Plato's ideas about the nature of forms. The analogy relies upon a distinction between visible and intelligible realms. The visible realm is the collection of objects to which our sensory perceptions provide access. The intelligible realm is the collection of objects to which only our minds provide access. The divided line analogy occurs over the course of 509d-511e, and I'll quote from those passages selectively: Picture them [sc. the visible and intelligible realms] as a line cut into two unequal sections and, following the same proportion, subdivide both the section of the visible realm and that of the intelligible realm. Now you can compare the sections in terms of clarity and unclarity. The first section in the visible realm consists of likenesses, by which I mean a number of things: shadows, reflections (on the surface of water or on anything else which is inherently compact, smooth, and bright), and so on. You should count the other section of the visible realm as consisting of the things whose likenesses are found in the first section: all the flora and fauna there are in the world, and every kind of artifact too. If the mind wants to explore the first subdivision [of the intelligible realm], it can do so only by using those former originals as likenesses and by taking things for granted on its journey, which leads it to an end-point, rather than to a starting-point. If it wants to explore the second subdivision, however, it takes things for granted in order to travel to a starting-point where nothing needs to be taken for granted, and it has no involvement with likenesses, as before, but makes its approach by means of forms alone, in and of themselves. [The second subdivision of the intelligible realm] is what reason grasps by itself, thanks to its ability to practice dialectic. When it takes things for granted, it doesn't treat them as starting-points, but as basic in the strict sense -- as platforms and rungs, for example. These serve until it reaches a point where nothing needs to be taken for granted, and which is the starting-point for everything. Once it has grasped this starting-point, it turns around and by a process of depending on the things which depend from the starting-point, it descends to an end-point. It makes absolutely no use of anything perceptible by the senses: it aims for forms by means of forms alone, in and of themselves, and it ends its journey with forms. Imagine a line segment AB divided into unequal sections, AC and CB. And imagine that these unequal sections are themselves divided into unequal sections of the same ratio, as AD and AC within AC, and as CE and EB within CB. |--------|----------------|----------------|--------------------------------| A D C E B

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AC is the visible realm; CB, the intelligible realm. The elements of AD are likenesses of likenesses, such as paintings and shadows; the elements of DC are likenesses, objects that we perceive around us with our senses. (Why likenesses? Because they both are and are not; they imperfectly participate in the forms.) The elements of CE are visible forms, objects the study of which involves visualization but which are not perceived through vision (such as triangles, circles). And finally, in EB, there are the forms, objects perceived and studied through the mind alone. Plato gives different names to the states of mind we have when perceiving objects in each of these regions: from left to right, he calls the states imagination (eikasia), confidence (pistis), thought (dianoia), and understanding (nous). Imagination and confidence are kinds of belief; thought and understanding, kinds of knowledge. That there are different objects for different objects of (sensory or intelligible) perception suggests that there are different states of mind involved in perceiving these objects. The Cave Analogy (Notes borrowed from < http://faculty.washington.edu/smcohen/320/cave.htm>.) In Republic 7, Plato offers another famous analogy, the allegory of the cave. Plato realizes that many people form beliefs and speak without acknowledging the existence of the forms. The point of the cave analogy is to explain what mistake people make when they deny the existence of the forms, and to suggest a reason for this mistake. In the allegory, Plato likens people untutored in the Theory of Forms to prisoners chained in a cave, unable to turn their heads. All they can see is the wall of the cave. Behind them burns a fire. Between the fire and the prisoners there is a parapet, along which puppeteers can walk. The puppeteers, who are behind the prisoners, hold up puppets that cast shadows on the wall of the cave. The prisoners are unable to see these puppets, the real objects, that pass behind them. What the prisoners see and hear are shadows and echoes cast by objects that they do not see. Here is an illustration of Plato’s Cave:

From Great Dialogues of Plato (Warmington and Rouse, eds.) New York, Signet Classics: 1999. p. 316.

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Such prisoners would mistake appearance for reality. They would think the things they see on the wall (the shadows) were real; they would know nothing of the real causes of the shadows. So when the prisoners talk, what are they talking about? If an object (a book, let us say) is carried past behind them, and it casts a shadow on the wall, and a prisoner says "I see a book," what is he talking about? He thinks he is talking about a book, but he is really talking about a shadow. But he uses the word "book." What does that word refer to? Plato gives his answer at line (515b2). The text here has puzzled many editors, and it has been frequently emended. The translation in Grube/Reeve gets the point correctly: Socrates: And if they could talk to one another, don't you think they'd suppose that the names they used applied to the things they see passing before them? (515b) Plato's point is that the prisoners would be mistaken. For they would be taking the terms in their language to refer to the shadows that pass before their eyes, rather than (as is correct, in Plato's view) to the real things that cast the shadows. If a prisoner says "That's a book," he thinks that the word "book" refers to the very thing he is looking at. But he would be wrong. He's only looking at a shadow. The real referent of the word "book" he cannot see. To see it, he would have to turn his head around. Plato's point is that the general terms of our language are not "names" of the physical objects that we can see. They are actually names of things that we cannot see, things that we can only grasp with the mind. When the prisoners are released, they can turn their heads and see the real objects. Then they realize their error. What can we do that is analogous to turning our heads and seeing the causes of the shadows? We can come to grasp the Forms with our minds. Plato's aim in the Republic is to describe what is necessary for us to achieve this reflective understanding. But even without it, it remains true that our very ability to think and to speak depends on the Forms. For the terms of the language we use get their meaning by "naming" the Forms that the objects we perceive participate in. The prisoners may learn what a book is by their experience with shadows of books. But they would be mistaken if they thought that the word "book" refers to something that any of them has ever seen. Likewise, we may acquire concepts by our perceptual experience of physical objects. But we would be mistaken if we thought that the concepts that we grasp were on the same level as the things we perceive.

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Lecture 19 Topics for Class Discussion

1. What is the line analogy? Give examples of each part, and the state of mind that corresponds to each part. 2. What is the cave analogy? How do the different stages of the prisoner's mental state correspond to the different segments of the line and the different states of mind for those stages? 3. If sensory perception yields only belief, and thought aided by visual imagery yields only knowledge of visual forms, how is one supposed to know about the forms themselves?

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Lecture 20: Plato - Parmenides Zeno Against Forms The first part of the Parmenides is a critique of the theory of forms. Zeno argues that if there are many things, then they are both like and unlike, which is impossible (127e). This is an argument you might recall from our discussion of Melissus. Socrates replies that things being both like and unlike is not contradictory at all, because it happens all the time as things come to share in both likeness and unlikeness: Socrates: But tell me this [Zeno]: don't you acknowledge that there is a form, itself by itself, of likeness, and another form, opposite to this, which is what unlike is? Don't you and I and the other things we call 'many' get a share of those two entities? And don't things that get a share of likeness come to be like in that way and to the extent that they get a share, whereas things that get a share of unlikeness come to be unlike, and things that get a share of both come to be both? And even if all things get a share of both, though they are opposites, and by partaking of them are both like and unlike themselves, what's astonishing about that? (129a) Socrates is, in effect, accepting that the many which we perceive with our senses are both like and unlike, because they participate in both Likeness and Unlikeness. This does not mean that the many do not exist; it means, instead, as the argument in Republic 5 shows, that the many which we perceive with our senses are objects of belief but not objects of knowledge. (Why suppose that a thing can be both like and unlike at the same time? Perhaps because it is like in a different respect than it is unlike. But then why suppose we cannot know about the thing? Perhaps because there is no using our senses to get past all the various respects, to perceive the thing as it is in itself rather than as it is from some perspective or other.) Socrates then notes that, whereas objects of the sensible realm can have opposite qualities, objects in the intelligible realm -- the forms -- cannot. For while matter can admit both one form and its opposite, no form can admit its opposite (129b-e). And since no form can admit its opposite, Socrates takes Zeno's argument against a multiplicity of forms to fail (130a). So the forms, at least as understood in the Phaedo and the Republic are immune to Zeno's arguments for monism over pluralism. Parmenides against Forms Having made this claim, Parmenides intervenes in order to argue that the theory of forms is unintelligible, full of problems and contradictions. There are many objections, and we'll consider only two. While Plato offers, in the second part of the Parmenides (not in your textbook) a refutation of the first, we must wait until Aristotle to find a refutation of the second. Aristotle's refutation involves rejecting one of the fundamental principles of Plato's theory of the forms; and Parmenides' objections amount to extracting unfavorable

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consequences from the conjunction of these principles. So before getting to the objections, we will be well served by making explicit the basic principles of Plato's theory of forms. The Phaedo and the Republic reveal that Plato does not only maintain that forms exist, but that he accepts certain principles regarding their nature. This means that he has a theory of forms. One principle, which he uses to explain the cause of something being an F, is Causality: Things that are F, other than the F itself, are f by virtue of participating in the F. (Phaedo 100c-101c) Causality captures the idea that forms are what make things to be the kinds of things they are. A second principle, which seems to be based on the idea that forms reside in the intelligible realm while things that participate in forms reside in the visible realm, is Separation: The F is itself by itself, separate from and hence not identical with the things that participate in the F. (Phaedo 75c-d, 100b; Republic 476b, 480a) Separation explains why we do not perceive the forms with our senses: we perceive sensible things with our senses, but forms are separate from sensible things. A third idea, that forms are what many different things have in common, supports a third principle: One-over-Many: For any plurality of F things, there is a form, F, participation in which makes each member of the plurality to be F. (Republic 596a) In the Republic (597c-d), Plato infers from One-over-Many a further principle, namely Uniqueness: For any property F, there is exactly one form of F. (By the way, Uniqueness and One-over-Many jointly entail Causality. Neat!) Uniqueness means that each form is distinct from every other form, and should not be confused with a separate principle, which Plato also endorses, according to which forms are things that can be counted: Oneness: Each form is one. Each form is one in the same sense that a person is one among many (Parmenides 129c-d). In addition to being countable, Plato seems to maintain that each form can be predicated of itself: the beautiful is beautiful, the just is just, and so on. Self-Predication: For any property F, the F is F. (Phaedo 100c, 102e)

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Finally, Socrates' response to Zeno's objection indicates that Plato's theory of forms endorses two further principles: Sensible Impurity: Sensible things can (and often do) have contrary properties. Form Purity: Forms cannot have contrary properties. Parmenides' criticisms of Plato's theory all rely upon showing that these principles either lead to puzzling results or contradict each other. The first, concerning the extent of forms (130a-e), concerns a tension between Separation and Self-Predication. For Self-Predication entails that there are forms for humans and mud; and Separation entails that these forms must be separate from every sensible thing. But it's difficult to see how humans and mud could be non-sensible. Plato could bite the bullet here, maintaining that humans and mud (their forms, at least) are non-sensible. But Parmenides has stronger objections. One which exercises Aristotle (see Metaphysics 990b) is known as the Third Man argument. The Third Man Argument (132a-b) Parmenides begins the argument by noting that, according to Plato's theory of forms, Oneness is supposed to follow from One-over-Many. For if the many F are all F by virtue of participating in the form, F, then there is one form "over" the many F things; and this entails that this form, F, is something that can be counted, since it is "one" over many. But, Parmenides notes, One-over-Many seems to be inconsistent with Oneness when taken as part of Plato's larger theory of forms. Consider a plurality of large things: A, B, C. By One-overMany, there is a form by virtue of which A, B, and C are large. Call it Largeness. By SelfPredication, Largeness is large. So there is a further plurality of large things: A, B, C, Largeness. By One-over-Many, there is a form by virtue of which each of these things are large. Call it Largeness-2. So Largeness participates in Largeness-2. Now this would not be a problem, if Largeness were identical to Largeness-2. But it can't be, because Separation entails that forms are separate from, and hence not identical to, things that participate in them. So we have two forms of largeness, Largeness and Largeness-2. Things get worse. Using the same reasoning, we can see that there are infinitely many forms of largeness. This infinite regress is problematic, because Uniqueness entails that largeness has only one form. And, what's worse, even if the infinitely many forms of oneness are all forms of one form (and this somehow does not violate Uniqueness), the form of largeness would be both one and many; and this conflicts with Form Purity (and undermines the response to Zeno). So the Third Man Argument identifies one of two inconsistent subsets of principles in Plato's theory of forms: I- One-over-Many, Self-Predication, Separation, Uniqueness; II- One-over-Many, Self-Predication, Separation, Form Purity. 34

Lecture 20 Topics for Class Discussion 1. What are the basic principles of Plato's theory of forms? What was Plato's motivation for accepting each of those principles? 2. What is the Third Man argument? In what way does it undermine Plato's theory of forms? 3. What strikes you as a reasonable solution to the Third Man argument?

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Lecture 21: Plato - Parmenides The Greatest Difficulty (133a-134e) The last objection Parmenides makes against the theory of forms, and probably the most worrisome, is that if the forms exist in the intelligible realm, independent of the changing objects of the visible realm, then there is no intelligible relation between the forms and the changing objects. There is, as we might say today when talking about mind-body relations in Descartes, an unbridgeable gap between form and matter. For if the forms are as Socrates takes them to be, "they cannot even be known" (133b). His argument goes like this: 1. 2. 3. 4. 5. 6. 7.

Each form is "itself by itself" (133c). So no form is in us (from 1). Knowledge that belongs to us is of truth that belongs to our world (134a). So whatever we know is something that belongs to our world. But the forms do not belong to our world (133c-d). So the forms are neither in us nor in our world (from 2, 5). So we do not know the forms (from 4, 6).

In terms of the principles for Plato's theory of forms, this objection is attacking Separation, according to which forms are separate from things which participate in forms. Separation provides the warrant for the claim that no form is in us, and for the claim that the forms do not belong to our world -- the forms are separate from our world, and hence they are not identical to things in our world. We can try to clean up the reasoning in the dialogue in the following way: A. B. C. D.

Forms are not in us (from Separation). If X is knowledge in us and X is what it is in relation to Y, then Y is in humans. Knowledge is what it is in relation to what it is knowledge of. So we do not know forms.

C and B together entail that if X is knowledge is in us, then the object of X (what it is that X is knowledge of) is in us. Since, according to A, forms are not in us, knowledge of forms is not in us. The motivation for premise B is a more general principle, namely If X is in us and X is what it is in relation to Y, then Y is in us. Parmenides' discussion of masters and slaves provides support for this principle: A human master is a master only in relation to a human slave. So being a master is in (some) humans, and those who are masters are what they are in relation to slaves. But slaves are not forms; a master is what he is in relation to slaves rather than the form slave, because there are no 36

masters if there are no slaves. And slavery is something that is in us, because some people are slaves. Similarly, some people have knowledge; there is knowledge in them. But knowledge is always knowledge of something, and so knowledge is always knowledge in relation to something, namely, the object of knowledge. (There is no knowledge without an object.) Hence, by the principle, the objects of knowledge must also be in us. Parmenides for Forms Curiously, Parmenides takes his argument to show that only a very gifted person, or a prodigy, could know about forms: Parmenides: The forms inevitably involve these objections and a host of others besides--if there are those characters for things, and a person is to mark off each form as 'something itself.' As a result, whoever hears about them is doubtful and objects that they do not exist, and that, even if they do, they must by strict necessity be unknowable to human nature; and in saying this he seems to have a point; and, as we said, he is extraordinarily hard to win over. Only a very gifted man can come to know that for each thing there is some kind, a being itself by itself; but only a prodigy more remarkable still will discover that and be able to teach someone else who has sifted all these difficulties thoroughly and critically for himself (134e-135b). Parmenides here seems to give a friendly ear to theses that resemble Gorgias', that the forms do not exist (that's Zeno's objection) and that, even if they do, they are not knowable (that's Parmenides' objection). But he is not being ironic or sarcastic, because despite the objections, he agrees that forms exist and are knowable: Parmenides: if someone, having an eye on all the difficulties we have just brought up and others of the same sort, won't allow that there are forms for things and won't mark off a form for each one, he won't have anywhere to turn his thought, since he doesn't allow that for each thing there is a character that is always the same. In this way he will destroy the power of dialectic entirely (135b-c). Those who destroy the power of dialectic by denying the existence of forms are the sophists, for whom the measure of things is man rather than the things themselves. Parmenides thinks the sophists are mistaken, and he gives a very simple argument: i. Thought requires something stable to be the object of thought. ii. If there are no forms, there is nothing in objects that is stable. iii. So if there are no forms, there is no thought. Without forms, Parmenides argues, our minds are a Heraclitean flux of perpetually changing contradictions and there is no possibility of intelligent thought or discourse. (In contemporary 37

language, we might put the point like this: intelligent thought requires concepts; so if there are no concepts, there is no intelligent thought.) The Magic of Dialectic Parmenides holds out hope to Socrates that there is, in fact, a way to know the forms. (This is the second part of Parmenides, which is not in your textbook.) Parmenides gives a detailed characterization of what he has in mind, with reference to Zeno: in the case of … Zeno's [hypothesis] about the many, you should inquire not only what will be the consequences to the many in relation to themselves and to the one, and to the one in relation to itself and the many, on the hypothesis of the being of the many, but also what will be the consequences to the one and the many in their relation to themselves and to each other, on the opposite hypothesis. Or, again, if likeness is or is not, what will be the consequences in either of these cases to the subjects of the hypothesis, and to other things, in relation both to themselves and to one another, and so of unlikeness; and the same holds good of motion and rest, of generation and destruction, and even of being and not-being. In a word, when you suppose anything to be or not to be, or to be in any way affected, you must look at the consequences in relation to the thing itself, and to any other things which you choose,—to each of them singly, to more than one, and to all; and so of other things, you must look at them in relation to themselves and to anything else which you suppose either to be or not to be, if you would train yourself perfectly and see the real truth. In the remainder of the dialogue, Parmenides uses this method to examine his own hypothesis that what-is is one. We will not consider the argument here; it is dense, lengthy, and pretty much a whirlwind of rigorous argumentation. Samual Rickless, in his Stanford Encyclopedia of Philosophy entry on Parmenides, summarizes the conclusions Parmenides reaches in the dialogue as follows: What Parmenides' criticisms reveal is that … Plato's middle period theory of forms is internally inconsistent. It turns out that there are three principles the abandonment of which would eliminate all inconsistencies apart from the Greatest Difficulty: [Form Purity], Uniqueness, and No Causation by Contraries. Careful logical analysis of the second part of the dialogue then reveals that the Deductions establish not only that the forms posited by the middle period theory exist, but also that Purity-F, Uniqueness, and No Causation by Contraries are all false. It is then reasonable to suppose that Plato meant the reader to recognize that the proper way to save the forms is by abandoning these three basic assumptions. And, importantly, this can be done without abandoning the most important principles at the heart of the middle period theory, namely One-over-Many and Separation. The aptly-named Greatest Difficulty is then left as a challenge for future work.

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Lecture 21 Topics for Class Discussion 1. What is the "Greatest Difficulty" objection to Plato's theory of forms? Is it persuasive? 2. Why does Parmenides maintain that forms must exist? What is his argument? Is it persuasive?

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Lecture 22: Plato - Timaeus Knowledge and Belief, Again The textbook provides an excerpt from the Timaeus, beginning with a rehearsal of the difference between knowledge and belief (or understanding and opinion). Knowledge grasps that which always is, the Forms; and belief grasps that which becomes, things in the sensible realm. In a passage not in our text, the dialogue also rehearses the argument from the distinction between knowledge and belief to the existence of forms: If understanding and true opinion are distinct, then these “by themselves” things definitely exist - these Forms, the objects not of our sense perception but of our understanding only. But if - as some people think - true opinion does not differ in any way from understanding, then all the things we perceive through our bodily senses must be assumed to be the most stable things there are. But we do have to speak of understanding and true opinion as distinct, of course, because we can come to have one without the other, and the one is not like the other . . . Since these things are so we must agree that (i) that which keeps its own form unchangingly, which has not been brought into being and is not destroyed, which neither receives into itself anything else from anywhere else, nor itself enters into anything else anywhere, is one thing. It is invisible - it cannot be perceived by the senses at all, and it is the role of understanding to study it. (ii) The second thing is that which shares the other’s name and resembles it. This thing can be perceived by the senses, and it has been begotten. It is constantly borne along, now coming into being in a certain place and perishing out of it. It is apprehended by opinion, which involves sense perception. . . . This discussion establishes some principles that get put to work later in the dialogue, namely: (1) that some things are, without ever becoming; (2) that some things become, without ever being; (3) that a thing always is if and only if it is grasped by the understanding through a rational account; and (4) that a thing becomes if and only if it is grasped by opinion through unreasoning sense perception. Cosmological Framework Having established these principles, the dialogue goes on to establish a framework for theorizing about the origin and structure of the universe (kosmos). 1. The universe is a thing that has become (28c). The reason for this is that the universe is visible, tangible, and has a body; and that these features entail that the universe is perceptible and therefore grasped through opinion through unreasoning sense perception. So it follows, via (4) above, that the universe is a thing that becomes.

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That the universe is a thing that becomes is taken to entail that there is a cause of the universe (28a, c), because every becoming must have a cause -- there is no uncaused change. So 2. The universe has been caused to become by something. This raises the question of what this cause is. And Plato's answer is that the cause is a Craftsman. (Sometimes scholars refer to this as the Demiurge.) It is interesting to note that the Demiurge is not a ruler, as in the Abrahamic religious tradition, but rather a laborer. In Plato's Universe, Gregory Vlastos notes, That the supreme god of Plato’s cosmos should wear the mask of a manual worker is a triumph of the philosophical imagination over ingrained social prejudice. ... But this divine mechanic is not a drudge. He is an artist or, more precisely, what an artist would have to be in Plato’s conception of art: not the inventor of new form, but the imposer of pre-existing form on as yet formless material [namely, the "receptacle"] (26-27). It is not entirely clear why the cause of the universe must be a Craftsman, something with intelligence, rather than some unthinking event. But Plato adopts an important assumption, namely: 3. The universe is supremely beautiful (29a). (Why does he adopt this? It is difficult to say. Perhaps because the universe is the most unified perceptible thing and unity correlates with beauty. Perhaps not.) Given that this is so, the cause of this beauty is either intelligent or unintelligent. Plato does not consider unintelligent causes of supreme beauty to be feasible, and so concludes that the cause must be intelligent. Accepting that the cause of a supremely beautiful universe is an intelligent Craftsman, the question arises of how the Craftsman creates the universe. Just as craftsman from everyday life create their works in accordance with a model of some sort, Plato takes the Craftsman to create the universe in accordance with a model, which he calls the Living Thing. The universe, on this account, is an image of the Living Thing; and since the Craftsman is supremely good and the universe is supremely beautiful, Plato infers that the Living Thing must itself be something that always is (29a), namely, a kind of form (or a constellation of forms). 4. The universe is a work of craft fashioned after an eternal model. This conclusion is significant for the proper method of cosmological inquiry. For the conclusion means that the universe has a teleological structure to it and that this structure is something to be grasped by the understanding through a rational account (via principle (3), above). And this means that, if we want to understand the kosmos, we should do so through reason alone. Sensory perceptions are therefore irrelevant to cosmology. This marks a departure from preSocratic methods of cosmological thinking, which seem to reserve some role (however small)

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for sensation. But it fits Melissus' conclusion that sensory perception does not provide knowledge of what-is. Timeaen Cosmology: Global Properties of the Universe The remainder of our excerpt from the Timaeus provides a cosmogony. (This cosmogony is partial, because our textbook does not provide the entire dialogue. The rest of the Timaeus offers an account of the heavenly bodies, human beings and other animals, the structure of matter, and the coming to be of the elements.) Unlike the cosmogonies of the pre-Socratics and Hesiod, this one is deduced apriori, from general principles. These arguments provide a rational account for understanding the universe. And this is possible because the object of understanding is not the universe itself but rather the Living Thing, the eternal and unchanging model of the universe (30a-d). The universe is unique, because it is based on a unique model, the Living Thing (31a). It is also spherical, because spheres are the most complete shape (33b). And it moves by spinning upon itself, because it has no need of any other kind of motion (34a) but must move in some way (since it is something that becomes). Finally, because it moves of its own accord, it must have a soul (34b).

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Lecture 22 Topics for Class Discussion 1. What is the Demiurge, and how does it differ (if it does differ) from what the Abrahamic tradition refers to as God? What is the argument for the existence of the Demiurge? Is the argument persuasive? 2. What is the Living Thing? What properties does it have as a whole? What is the account for why it has these properties? Is the account persuasive? 3. What is the relation between the Living Thing, the Demiurge, and the universe (kosmos)?

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Lecture 23: Plato - Timaeus Timeaen Cosmology: Properties of the Universe's Parts The ingredients of the universe include: -

fire, because the universe is visible and nothing is visible without fire (31b); earth, because the universe is tangible, only solids are tangible, and nothing is solid without earth (31b); air and water, because solids (fire and earth) require two intermediate "middle terms" for combination (32b).

These elements are arranged proportionally: air is to water as fire is to air; water is to earth as air is to water (32b-c). That is, fire:air :: air:water, and air:water :: water:earth. (Observe how "air:water" is the "middle term" relating fire to earth. There is also a numerological explanation for the requirement of two middle terms in your textbook.) The ordering in this proportionality preserves Empedocles' ordering of the four elements (fire-air-water-earth). A part of the dialogue not in your textbook improves upon Empedocles' theory by offering an account of what composes these four elements: because all bodies are three dimensional and hence bound by surfaces, and because every surface bound by straight lines is divisible into triangles, and because every triangle is divisible into right triangles, Plato infers that each element is composed of right triangles (53c-d). There are two kinds of right triangles, scalene and isosceles. So, Plato infers, all bodies are constructed from scalene and isosceles triangles. He even describes the composition arrangements (54d-55c). Here, for example, is fire:

And here is earth:

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And air:

And water:

This makes Plato's atomism simpler than Democritus', because Democritus postulates an infinite number of atomic shapes while Plato allows his Demiurge to work with only two. Plato's atomism also respects Parmenides' cosmological principles, because the triangles themselves do not change--only their arrangement changes. Plato even provides an account of how changing arrangements result in elements changing into each other, thereby improving upon the Ionians (who allow the elements to change into each other entirely, with nothing at all staying the same) and Empedocles (who does not allow elements to change into each other and does not explain how changes of unchanging elements produce changes we observe). When two fire molecules combine, they create an air molecule; when five fire molecules combine, they create a water molecule; five air molecules can combine to create two water molecules; two air and one fire can combine to create one water; and three fire and one air can combine to create one water. The molecules can also split apart. So we have these equations (note the heavy influence of Pythagorus' idea that the world is number):

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1A = 2F, 1W = 5F, 2W = 5A, 1W = 2A+1F, 1W = 3F+1A. Only earth cannot change into other elements, because of its "atomic" structure. Timeaen Cosmology: Time and Space Because the Living Thing is eternal but the universe is not, the universe, unlike the Living Thing, changes. This allows Plato to provide an account of time. [The Demiurge] began to think of making a moving image of eternity: at the same time as he brought order to the universe, he would make an eternal image, moving according to number, of eternity remaining in unity. This, of course, is what we call "time." (37d) "This" apparently refers to the moving of the universe (the image of the Living Thing). Time is celestial motion. Plato restates this point later in the dialogue: [The Demiurge] brought into being the Sun, the Moon, and five other stars, for the begetting of time. These are called "wanderers" [planêta], and they stand guard over the numbers of time. … And so people are all but ignorant of the fact that time really is the wanderings of these bodies (38d, 39d). (Aristotle later abstracts time from motion, defining time as the number that measures motion rather than motion itself.) One consequence of Plato's definition is that the forms exist "outside" of time, because the forms do not move/change. Since the forms do not change, the universe cannot be forms. So what does change? What receives the forms? Plato's answer here is: the receptacle. Perhaps this is something like empty space, or Democritus' void, or Hesiod's Chaos, or Anaximander's to apeiron. It's not clear.

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Lecture 23 Topics for Class Discussion 1. What explanation does Plato give for why the basic elements of the world are earth, air, water, and fire? How does it compare to Empedocles? 2. In what way is Platonic cosmology atomistic? How does this compare to Democritus? 3. In what ways does Plato's cosmology improve upon those of his predecessors? What problems does it solve? What problems remain? What new problems arise?

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