Plato's Theory of Knowledge Ralph Wedgwood 0. Introduction In his middle-period dialogues, Plato worked out at least the rough outlines of a distinctive theory of knowledge. According to the chronology that seems most plausible, he first sketched the outlines of this theory in Meno; then he revised and developed the theory further in Phaedo and the Republic; and finally, in Theaetetus, he probed the theory in depth, by subjecting it to a series of searching questions. In this essay, I shall propose an interpretation of the version of the theory that is presented in Phaedo and the Republic, although I shall also consider what seems to be the slightly earlier version of the theory that we find in Meno. Unfortunately, I shall not be able to pay more than the most glancing attention to Theaetetus. My interpretation will focus, as narrowly as possible, on Plato's view on the question, "What is knowledge?" I shall touch only briefly on Plato's views on related questions, such as "What is belief?" and the like. My interpretation of Plato's view on this question will be at least in part conjectural: although I shall show that it fits much of the textual evidence, I shall not be able in the available space to check this interpretation against all the relevant textual evidence, nor shall I be able to argue in detail that this interpretation is preferable to all alternatives. The primary goal of this essay is just to put this interpretation forward for consideration. No contemporary scholar of ancient philosophy has studied Plato's epistemology in greater depth than Gail Fine.1 The debt that my interpretation owes to her work is both obvious and immense. I shall admittedly disagree with her on one crucial point: I shall accept a version of the traditional interpretation of Republic 476e–480a, according to which what in that passage is called "knowledge" (epistēmē or gnōsis) consists in a kind of grasp of the Forms, whereas – at least typically – what in that passage is called "opinion" (doxa) consists in a kind of grasp of some perceptible concrete things. On many other points, however, I shall accept Fine's interpretation. Moreover, I shall also follow her methodology – which involves not just the most rigorous philosophical analysis, based on a painstakingly close reading of the primary texts, but also an attempt to bring Plato into a dialogue with contemporary epistemologists, in a way that looks more for continuities between Plato's thinking and that of our contemporaries than for contrasts or dissimilarities. While it is agreed on all sides that it is important to avoid anachronism, I strongly agree with Fine's belief that a consideration of such contemporary ideas is often helpful in understanding Plato's thought. Briefly, my interpretation of Plato's theory of knowledge is the following. 1. Plato is a kind of contextualist about words like 'knowledge'. The heart of Plato's theory is an account of four different levels of cognitive mental states, which he illustrates with the image of the four segments of the Divided Line (Republic 509d– 1 See the papers collected in Fine (2003), and also Fine (2004 and 2008). 2 511e). But as Plato explicitly admits, sometimes he uses his principal term for "knowledge" ('epistēmē') to cover both of the upper two levels, and sometimes just for the highest level. There are also indications that his usage of other Greek words for 'know' (such as 'eidenai' and 'gignōskein') and of the term 'doxa' ('belief' or 'opinion') varies with context as well. I shall explain the sense in which this makes Plato a contextualist below. 2. Plato assumes that knowledge is a factive mental state, belonging to the inclusive genus of cognitive states that also includes all kinds of belief or opinion. As I shall argue, one distinguishing feature of knowledge, in his view, is that it must satisfy the condition that contemporary epistemologists call "adherence". Indeed, he may think that genuine knowledge must satisfy adherence to the highest degree – that is, in effect (as I shall explain), genuine knowledge must be utterly indefeasible. If he does think this, it would explain why he also holds that all genuine knowledge is a priori – which, he speculates, is best explained by the Theory of Recollection. 3. It is also plausible that Plato thinks that every truth that can be known is necessary. Together with the explanation of knowledge that is based on the Theory of Recollection, this guarantees that genuine knowledge also satisfies the condition that contemporary epistemologists call "safety". Indeed, knowledge is safe to the highest degree – that is, infallible. If, as seems plausible, Plato assumes that all truths that are necessary in this way are in some sense aspects of the Forms, this vindicates the traditional interpretation that he holds that all genuine knowledge consists in a grasp of some aspect of the Forms. 4. For Plato, knowledge always requires at least some grasp of the explanation of the truth that is known. The truth about the Forms constitutes an intelligible explanatory system of necessary truths; and the different levels of knowledge correspond to the different degrees to which the thinker grasps this explanatory system of necessary truths. It may be that all adult human beings have at least a rudimentary grasp of some fragments of this system of these necessary truths. But no human being has yet achieved the highest level of knowledge, which would consist in a coherent synoptic grasp of the whole system of necessary truths. 5. We can use our understanding of Plato's terminology to show how the texts support this interpretation. As Plato admits, he switches between using 'epistēmē' strictly, to refer to the highest level of cognition, and using it more loosely, to refer to both of the two upper levels together. In some other dialogues, he uses 'doxa' as a generic term for the genus of which all four levels are species; but in the Republic, he mostly uses 'doxa' for mere belief – a cognitive mental state that falls short of counting as "epistēmē" – though what this means depends on how in turn the term 'epistēmē' is being understood. Moreover, Plato sometimes allows himself to use some of the Greek words for 'know' (such as 'eidenai' and 'gignōskein' and their cognates) in an idiomatic sense, to stand for what in fact, according to his official theory, is just a true belief of a relatively reliable kind (in his terminology, confidence or pistis). In what follows, I shall take these five points in turn. 3 1. Plato's contextualism There are two famous passages where Plato contrasts knowledge and opinion: Meno 98a, and Republic 476e–480a. But later in the Republic, this duo of contrasting states is elaborated into a quartet, when Plato gives an account of four different levels of cognitive state, illustrating these states by the image of the four segments of the Divided Line (509d–511 e). The names that he gives to these four states there are: intellection (noēsis), thought (dianoia), confidence (pistis), and imagination (eikasia). It is natural to wonder how the pair discussed earlier (knowledge and opinion) is related to the quartet that is discussed later (intellection, thought, confidence, and imagination). Plato answers this question explicitly, in a slightly surprising way, in a passage in the middle of the description of the education of the guardians in Book VII. In this passage, Socrates contrasts "dialectic" – which is his name for the highest form of intellectual inquiry – with five other branches of learning (namely, arithmetic, the two-dimensional geometry of planes, the three-dimensional geometry of solids, astronomy or the fourdimensional geometry of motion, and harmonic theory), and makes the following comment about these other branches of learning (533d–534a): From force of habit, we have often called these branches of learning kinds of "knowledge". But they need another name, clearer than "opinion" and darker than "knowledge". We defined it as "thought" somewhere before. But I don't suppose we will dispute about names, with matters as important as these before us to investigate. ... It will be satisfactory, then, I said, to do as we did earlier and call the first portion "knowledge", the second "thought", the third "confidence", and the fourth "imagination". The last two together we call "opinion", while the first two we call "intellection". Opinion is concerned with becoming; intellection with being. And as being is to becoming, so intellection is to opinion; and as intellection is to opinion, knowledge is to confidence and thought to imagination. Here Plato clearly characterizes both the two lower levels (confidence and imagination) as species of "opinion" (doxa). This characterization would be pointless if doxa were in fact a wide genus that included all four levels of cognition. So this is one of the passages in the Republic where he uses the term 'doxa' for mere belief – that is, for a kind of cognition that falls short of knowledge. However, he also explicitly admits that his terminology is not invariant between different contexts: he says that earlier he called both of the two upper levels kinds of "knowledge" (epistēmē), though here he now prefers to use this term more strictly, so that it refers only to the uppermost level. Moreover, without explicitly taking note of the fact, he also switches around his use of the term 'intellection' ('noēsis') as well. When he gave the image of the Divided Line at the end of Book VI (509d–511 e), he used the term 'intellection', not to refer to the upper two levels together, but just to refer to the highest level alone. Here, however, in Book VII, he explicitly uses the term 'intellection' for both of the two upper levels together. So, in effect, Plato has switched around the terms 'intellection' (noēsis) and 'knowledge' (epistēmē) between the discussion of the Divided Line in Book VI and this later passage at 534a. It is clearly more charitable for us to interpret this switch as deliberate, rather than as a mere slip on Plato's part. 4 By switching his terminology around in this way, Plato seems to be warning us against assuming that the same word always expresses the same concept and refers to the same entity. On the contrary, we need to look at the underlying structure of the concepts that are being expressed, and not just at the terminology that is being used. Fundamentally, there are these four levels of cognition, which following Fine (1990) I shall refer to as L1, L2, L3, and L4; and there are also the various genera to which these four levels of cognition belong. Our fundamental task as epistemologists is to understand these different species and genera of cognitive states, not to worry about the terminology that we use to refer to them. With respect to the terminology itself, however, Plato is in a sense a contextualist. In different contexts, he uses cognitive terms like 'epistēmē' to refer to different mental conditions – sometimes using the terms to refer a more restricted condition, which includes only L4 (the highest level of cognition), and sometimes to refer to a more inclusive condition, which includes both L3 and L4 (the upper two levels) together. We shall later see evidence that he also uses the other Greek words for 'know' (such as 'eidenai' and 'gignōskein') in a similarly flexible way as well. Admittedly, the text does not definitively establish whether Plato is a full-fledged contextualist, like such contemporary philosophers as Keith DeRose (2009), among others. To be such a full-fledged contextualist, he would have to think that cognitive terms like 'epistēmē' are not ambiguous, but have a single univocal meaning, and that in using the terms so that their extension shifts between contexts in this way, he is using the terms strictly in accordance with this univocal meaning. In other words, according to contextualism, it is part of the univocal meaning that cognitive terms like 'epistēmē' have that their extension shifts between contexts in this way. Nonetheless, the text is at least compatible with Plato's being a contextualist in this full-fledged sense; and so I have taken the liberty of referring to Plato's flexible use of this cognitive vocabulary as "contextualist". Finally, it is also fairly clear that Plato's use of the term for "belief" or "opinion" ('doxa') varies with context as well. Sometimes, as at this point in the Republic, he uses it for mere belief – that is, for the kind of belief that falls short of counting as knowledge. But in other contexts, he uses it more broadly for the genus of which all four levels are species. This seems to be the usage that we find in the second half of Theaetetus, where both of the two definitions that Plato considers – that knowledge is true belief (187b), and that it is true belief accompanied with an account (201c–d) – clearly imply that knowledge is a species of belief. On the relation between knowledge and belief, it is not Plato's view but only his terminology that changes between Republic and Theaetetus. In both works it is assumed that there is a wider genus of cognitive states, and that both knowledge and mere belief are species of this wider genus. The only difference in the terminology is that sometimes (as in Theaetetus) Plato uses the word 'doxa' for the wider genus, and sometimes (as in the Republic) Plato restricts the word for the species of belief that falls short of knowledge. We shall return to this understanding of Plato's terminology in the last section, when we survey some of the evidence for and against the interpretation that will be defended 5 here. As we shall see, this understanding of Plato's terminology will help us to evaluate this evidence in a more precise and discriminating way. 2. Adherence, indefeasibility, and the a priori Towards the end of Meno, Socrates makes the following suggestion about the difference between knowledge and mere true belief (97e–98a): True opinions are also a fine thing and altogether good in their effects so long as they stay with one, but they won't willingly stay long, and instead run away from a person's soul, so that they are not worth much until one ties them down by reasoning out the explanation. And that is recollection, Meno my friend, as we agreed earlier. And when they've been tied down, then for one thing they become items of knowledge, and for another, permanent. And that's what makes knowledge more valuable than correct opinion, and knowledge differs from right opinion by being tied down. Here, Plato suggests that knowledge differs from mere true opinion because true opinions "run away", while knowledge is "permanent". According to Bernard Williams (1978, 38), this suggestion should not be interpreted as the "the blankly psychological proposition (in any case, surely, very dubious) that one is more disposed to forget what one merely believes than what one knows". Instead, it should be interpreted as the "point ... that knowledge cannot rationally be rendered doubtful" – whereas mere beliefs can be "rationally rendered doubtful". For a belief to be "rationally rendered doubtful", I assume, is for the belief to be given up because it is rationally undermined or defeated. Let us also assume that in all the cases that concern us, the belief in question will be given up if and only if (and because) it is rationally undermined. In effect, then, the suggestion is that knowledge (unlike mere belief) cannot be rationally undermined. Williams interprets this suggestion as implying that knowledge "cannot" be rationally undermined. This interpretation is plausible – at least on some understanding of 'can'. Plato is presumably not suggesting merely that knowledge is "permanent" in the same way as a belief that by a strange fluke just happens never to be undermined. Instead, the suggestion is that whereas with mere beliefs, it could easily happen that these beliefs are rationally undermined, it could not easily happen that any genuine knowledge is rationally undermined. To say that it could "easily happen" that a belief is undermined is to say that there are possible worlds that are sufficiently similar to the actual world (in the relevant respects) in which the belief is undermined. Presumably, when a belief is rationally undermined, it is undermined by new information or new reflections. There seem to be two ways in which this could happen: 1. The true belief might have been unjustified all along, and the new information or reflections might prompt the believer to think more rationally, and to give up the belief. 2. The true belief might originally have been rational and justified, but the new information might defeat that original justification. 6 Cases of the first kind (1) are true beliefs that were never justified at all; such cases were never cases of justified true belief (JTB). Cases of the second kind (2), however, involve a JTB whose justification is later defeated. According to Plato, the fact that the belief "ran away" or was rationally undermined in this way shows that it was never a piece of knowledge in the first place. Thus, if we agree with Plato's judgment on cases of this second kind, we must conclude that they are cases in which a JTB fails to count as knowledge – or in the terminology that has become common after the work of Edmund Gettier (1963), they are "Gettier cases". However, these cases are importantly different from the cases that were originally discussed by Gettier (1963). In each of the original Gettier cases, the believer might easily have had a belief, in a very similar way to the way in which the believer actually believes the particular proposition in question, even if the proposition that the believer would then have believed were false. As many contemporary epistemologists would say, the belief in question fails to be safe.2 The problem with cases of type (2) is different: it is not that the believer might too easily have believed something false; it is that the justification of the belief in question might too easily have been defeated. Thus, the closest parallel to the cases that Plato has in mind are cases like the "assassination case" that was first presented by Gilbert Harman (1973, 143f.). In this case, there is a JTB that fails to count as knowledge, because there is a mass of (misleadingly) defeating evidence in the believer's environment, and it is simply a fluke that the believer does not encounter this defeating evidence. But this defeating evidence – we may suppose – consists entirely of "undercutting" (rather than "rebutting") defeaters. So if the thinker had encountered this defeating evidence, she would simply have given up on having any beliefs about the topic in question: she would not have come to believe the proposition's negation. In other words, this belief fails to count as knowledge, not because the believer could too easily have come to believe something false, but because the belief could too easily have been rationally defeated even if it were true. That is, on this approach, for you to know p, there must be no possible world that is sufficiently similar to the actual world, in which p is true, but your belief in p is rationally defeated or undermined. This condition on knowledge is broadly akin to the fourth of the four conditions that were imposed on knowledge by Robert Nozick (1981, 176–8) – the condition which has more recently come to be known as "adherence".3 For a thinker's belief in a true proposition p to "adhere" to the truth is for the belief to be such that, in all the relevantly similar possible worlds in which the proposition p is still true, the thinker would still believe p. In effect, this idea of a belief's "adhering" to the truth across the relevantly similar possible worlds seems equivalent to giving an explicitly modal gloss on Plato's talk of the belief's being "permanent". 2 For seminal discussions of the idea that knowledge involves safety, see Sainsbury (1997), Sosa (1999), and Williamson (2000). 3 For a systematic discussion of adherence, see Bird (2003). 7 It is clear that a belief in a proposition p can be safe without adhering to the truth in this way. This will happen whenever there is no relevantly similar world in which the corresponding belief that the believer has is false, but there is a relevantly similar world in which although p is true, the believer encounters misleading undermining evidence, and so does not believe p in that world. What adherence requires, then, is that there must be no relevantly similar worlds in which the thinker encounters misleading undermining evidence in this way. Now, the term 'relevantly similar' as it appears in this statement of adherence is presumably a context-sensitive term: in some contexts, the term might have an inclusive extension, so that many worlds count as "relevantly similar"; in other contexts, the term might have a more restricted extension, so that many fewer cases count as "relevantly similar". Depending on how inclusive the term's extension is, the adherence condition will vary in strength. At one extreme, it might in effect be the condition that there is no possible world whatsoever in which the thinker encounters such misleading defeating evidence. At the other extreme, it might merely be the condition that the thinker does not in fact encounter such misleading defeating evidence in the actual world. In between these extremes, adherence requires that the thinker should encounter no such misleading defeating evidence in a range of possible worlds besides the actual world, but not that the thinker should encounter no such defeating evidence in any possible world whatsoever. There is no evidence that Plato is aware of this issue with the interpretation of adherence. However, it may be that, at least implicitly, he interprets adherence as the strongest of these conditions – that is, as the condition that there is no possible world in which the thinker's knowledge would be rationally undermined, or in other words, as the condition that knowledge is indefeasible. If all genuine knowledge is indefeasible in this way, then this would guarantee that all genuine knowledge must satisfy adherence to the highest degree. If Plato does assume that all genuine knowledge is indefeasible in this way, then this could explain one of the most striking claims that he does seem to make – the claim that all genuine knowledge is a priori. Most philosophers would accept that all of our empirical justification for beliefs about mind-independent reality is defeasible; there is always the possibility of new experiences that would defeat any such empirical justification. So, on this assumption, if any knowledge about mind-independent reality is indefeasible, that knowledge must be a priori. There is much textual evidence in favour of interpreting Plato as regarding all genuine knowledge as a priori. First, in Meno (81d) he declares that "seeking and learning are in general recollection"; and at 86b, he seems to treat "what we happen not to know at present" as the same as "what we do not remember". There are many controversial issues surrounding the interpretation of the Theory of Recollection, but it is clear that when we "recollect" something, we in some way "retrieve" a truth that is already contained within the soul. In this sense, recollected knowledge is not derived from our sensory experience of the external world; it is knowledge that we possess purely by exploiting the resources that are already, antecedently to sensory experience, contained within the soul. In other words, it is a priori. 8 Another passage where Plato insists on the a priori character of genuine knowledge is in Phaedo (65a–66e). For the attainment of wisdom (phronēsis), the bodily senses are said to be a positive "hindrance" (65a). Sight and hearing and the other bodily senses "hold no truth"; and when the soul attempts to inquire into anything with the body, it is "utterly deceived" (65b). Instead, it is "through reasoning that any of the things that are become manifest" to the soul (65c). He seems to equate this kind of reasoning with thinking (dianoeisthai, 65e); and he says that the truth of these things is not seen through the body, but it is whoever of us who has prepared himself for thinking most fully and precisely of each object of inquiry itself who would come closest to knowing (gnōnai) each thing (65e). Finally, the prominence of mathematics and philosophy in Plato's conception of knowledge also encourages the conclusion that he thought that all genuine knowledge is a priori. Admittedly, there are some striking passages where he seems to allow for knowledge of truths – such as the road to Larissa (Meno 97a) – that would be knowable only empirically if at all; we shall return to the issue of how to understand these passages in Section 5 below. But the general picture that seems to emerge is that the paradigmatic examples of knowledge are mathematics and philosophy – which are plausibly taken to be a priori. To sum up, according to Plato, knowledge is a factive cognitive state, which (a) adheres to the truth, and (b) is a priori – perhaps because it must adhere to the truth to the highest degree, or in other words, must be completely indefeasible. 3. Necessity, safety, and the Forms How could it be that all the truths that we ever come to know are already contained within the soul itself, waiting to be recollected? This is never fully explained in Meno, but it seems to have something to do with the fact that the soul is imperceptible, immaterial, and eternal (existing for all of time – past, present, and future), and so in some way "akin" to the Forms, as Plato argues at length in Phaedo (78b–80c). It also seems that the Forms collectively are the source of an intelligible system of necessary truths, which somehow articulates the nature of the Forms. So, presumably, one of the main ways in which the soul is "akin" to the Forms is in somehow reflecting this system of necessary truths. This explains why all knowable necessary truths about the nature of the Forms are somehow built into the nature of the soul itself – even though, for most of the time, at least while we live an embodied human life on earth, these truths are inaccessible to consciousness (or as Plato suggests, have been forgotten). How exactly can we retrieve these truths that are built into the soul itself? Some philosophers might propose that we can sometimes retrieve such necessary truths though a kind of inference: perhaps one can sometimes "recollect" a truth p by means of a process of inference whose conclusion is p. But this proposal would suffer from the following defect. The capacity for knowledge-yielding inferences of a certain sort is itself a mental state that has a certain kinship with the knowledge that those inferences are valid. So this capacity would itself demand explanation – and the explanation of how we possess this capacity will itself have an affinity to the explanation of how we know the very necessary truths that are in question. So any explanation based only on the appeal to such a capacity for inference is superficial, and fails to get to the heart of the matter. 9 At all events, Plato's account of how recollection works is not just based on such an appeal to inference. When Socrates interrogates the slave in Meno (82b–85b), what happens seems just to be that Socrates asks the slave a question, and then the correct answer to the question pops up in the slave's head. By asking these questions, Socrates gets the slave consciously to focus on certain propositions. So Plato's picture seems to be this: for at least some of these necessary truths, when we consciously focus on these truths, we immediately come to understand and know them. This seems to be suggested by his remark (Republic 508d) that "when the soul focuses on something illuminated by truth and what is, it understands, knows, and apparently possesses understanding...". In other words, given that these truths are already built into the soul, sometimes simply focusing consciously on these truths is sufficient for "recollecting" them. As I understand it, this account of what it is to "recollect" a truth does not appeal to any kind of "direct acquaintance" with the truth in question. Instead, the account appeals to truths that are buried deep in unconscious propositional memory, and then awoken into conscious knowledge. A perceptual reading of Platonic recollection would be quite misguided. (Indeed, it may be that one of the chief functions of recollection is to explain our capacity for inferring necessary truths. As I shall tentatively suggest in the next section, Plato may think that whenever recollection provides us with any kind of knowledge, what we recollect is never a single truth all by itself, but rather an argument, which involves both certain premises and a conclusion that follows from them.) It is part of this account of how a priori knowledge is possible that it is knowledge of aspects of the Forms – that is, of necessary truths. There is no hint anywhere else in Plato's middle-period writings of any other account of how a priori knowledge might be possible. So it seems plausible that Plato held not only that all genuine knowledge is a priori, but also that it is all knowledge of necessary truths. This necessitarianism about knowable truths is inherited by Aristotle, who argues in the Posterior Analytics I.33 (88b30–89b9) that the knowable truths are always necessary truths, while the objects of "opinion" (by which Aristotle means mere opinion, the kind of belief that falls short of being knowledge) are contingent propositions – or as Aristotle puts it, "what is true or false but can also be otherwise" (89a3).4 I have already suggested that Plato may think that genuine knowledge must be indefeasible, and so satisfy the "adherence" condition to the highest possible degree; at least, this would provide one possible explanation of why he thinks that all genuine knowledge is a priori. This raises the question of whether he also thinks that knowledge must satisfy safety to the highest degree. For a belief to satisfy safety to the highest degree would be for it to be impossible to have a belief in a false proposition on any basis that is similar to the basis of the belief in question. In that sense, for a belief to satisfy safety to the highest degree is for it to be based on an infallible basis for the belief in question. (It is striking that at 477e, Plato says that knowledge is "infallible" – anamartēton – although there are admittedly several possible interpretations of that term in this context.) As we have seen in considering the Theory of Recollection, whenever anyone has genuine knowledge of a truth, Plato would say that the basis for this 4 See the interpretation of Aristotle's account of the distinction between knowledge and belief that is given by Fine (2010). 10 knowledge is precisely that the truth in question was already built into the knower's soul. So, for a belief that has a basis of this sort to be maximally safe, it would have to be impossible for any false proposition to be built into the soul in this way. If the only truths that can be built into the soul in this way are necessary truths that constitute aspects of the Forms, then it will be impossible for any false proposition to be built into the soul in this way. So, if Plato accepts the sort of necessitarianism about knowable truths that I have described, then he would in effect be committed to the conclusion that all genuine knowledge satisfies safety in the highest degree. The view that Plato accepts this sort of necessitarianism about knowable truths is also supported by the traditional interpretation of the Republic according to which it argues that all knowledge concerns the Forms. As Socrates says at 529b–c: I can't conceive of any branch of learning that makes the soul look upward except that which concerns what is and what is invisible, and if anyone attempts to learn any of the sensible things, whether by gaping upward or squinting downward, I'd claim – since there's no knowledge to be had of such things – that he never learns anything.... In this passage, the reference to "what is and what is invisible" is clearly a reference to the Forms, while "sensible things" – that is, perceptible concrete things – are explicitly said to be unknowable. As I shall argue later in this section, the same point – that the "objects" of knowledge are the Forms – is also made in the famous passage at the end of Book V (476d–480a). It is not immediately clear what it might mean to say that the "objects" of knowledge are Forms. Plato uses a variety of different expressions to capture this idea of the "object" of a cognitive state. Often, he uses the preposition 'epi', apparently in the sense of towards or in reference to. For example, he says that "knowledge" (gnōsis) is "towards what is" (477a), that opinion is "positioned towards something else" (477b), and that the person who has an opinion "bears the opinion towards something" (478b) – although he also uses phrases without 'epi', as when he says, "We had to assign ignorance to what is not, and knowledge to what is" (478c). It would be a mistake, I think, to identify the "object" of these cognitive states, which Plato is trying to indicate with these phrases, with the content of the state that is indicated by the noun clause that is the grammatical direct object of the cognitive verb. Instead, I propose, Plato is trying to offer an explanatory analysis of the cognitive state: he is suggesting that the state is ultimately or fundamentally explained by a kind of cognitive connection with or grasp of this "object". However, just because the "object" of these cognitive states is an entity like a Form or a perceptible concrete thing, it does not follow that these states do not also have propositions as their contents: the "object" of the state may be distinct from its propositional content. In fact, Plato is perfectly happy to fill in his specifications of pieces of knowledge by noun clauses that indicate propositions, as when he says that "knowledge (epistēmē) is by nature towards what is, to know how it is (gnōnai hōs esti)" 11 (477b).5 So, it seems plausible that Fine (1990) was right to argue that the kind of knowledge under discussion here is ordinary propositional knowledge. Thus, on the interpretation that I am proposing, according to Plato all the propositional knowledge that one has is fundamentally explained by one's having a kind of cognitive connection with or grasp of the Forms. Since it also seems that both the existence and the intrinsic character of the Forms are metaphysically necessary, if one knows a proposition solely because of having an appropriate kind of cognitive connection with the Forms, that proposition would be surely have to be a necessary truth. Thus, if I am right to accept a version of the traditional interpretation of the end of Book V, according to which the "objects" of knowledge are the Forms, and the "objects" of opinion are perceptible concrete things, this passage supports the conclusion that all genuine knowledge for Plato is knowledge of necessary truths. By contrast, on my interpretation, according to Plato all belief or opinion is explained by some kind of cognitive connection with or grasp of concrete perceptible things. The idea here may be that all opinion is ultimately explained by some kind of sensory experience, which Plato may view as essentially consisting in a kind of cognitive connection with concrete perceptible things. It is clear why all the beliefs that we would regard as empirically justified would in his view be explained by sensory experience. But he may also have thought that even those beliefs that we would regard as irrational or unjustified are best explained by the thinkers' somehow misreading or being misled by their sensory experiences. (Perhaps even beliefs in necessary falsehoods – like Meno's slave's initial belief that the square whose sides are double in length is also double in area (82e) – are also in Plato's view explained by sensory experience.) What reason is there for accepting this interpretation of the end of Book V? Clearly, one of the passage's main goals is to explain the difference between three cognitive conditions – knowledge, ignorance, and opinion – in terms of a corresponding difference in their "objects".6 It seems clear that these three cognitive conditions are understood to be disjoint: no particular token state can be an instance of more than one of these three types. Ignorance is clearly disjoint from both knowledge and opinion: to be ignorant of a certain domain is to be cognitively connected to nothing in that domain (478b–c) – this is the sense in which the "object" of ignorance is "what is not". In this way, being ignorant of a domain excludes both having opinion and having knowledge within that domain. Since the term 'opinion' in this passage seems to refer to "mere opinion", no token state can be both a state of knowledge and a state of "opinion" – that is, a cognitive state that falls short of knowledge. It follows that these three kinds of cognitive condition are disjoint. Since Plato seems to be aiming to explain the differences between these three types of states in terms of corresponding differences between their objects, the sets of the objects 5 Admittedly, the exact interpretation of this sentence is disputed. But on any plausible interpretation, the clause that I have translated 'how it is' (hōs esti) indicates that it is part of the knowledge in question that it in some way involves predicating or describing its object – that is, in effect, it involves a proposition. 6 In this way, Plato's approach is parallel to the way in which Aristotle in De Anima II.6 (418a6–25) explains the differences between the different senses by identifying the different "special objects" of the senses. 12 of these three types of state would also have to be equally disjoint. The set of the objects of ignorance would have to be the empty set, since as we have seen, being ignorant about a domain involves being cognitively connected to nothing within that domain; and every pair consisting of the empty set and any other set is disjoint. Since the Forms and the perceptible concrete things are also disjoint non-overlapping sets, one way to interpret the passage as identifying three disjoint sets for each of these three cognitive conditions would read it as identifying the empty set for ignorance, the set of Forms for knowledge, and the set of perceptible concrete things for opinion. Ultimately, however, there is a simpler and more powerful reason for accepting a version of the traditional interpretation of this passage. As we have seen, Plato claims that knowledge has as its object, or is "towards", "what is" (477a); in a parallel way, he concludes, opinion has as its object, or is "towards", what is "intermediate between what purely is and what in every way is not" (478e). The text (479a–c) also seems to make it clear that Plato identifies (a) what is with the Forms (for example, as Plato says, "the Beautiful itself"), which are delighted in and loved by the philosophers, and (b) what is intermediate between what is and what is not with the concrete perceptible things (as he says, "the many beautiful things"), which are delighted in by the "lover of sights and sounds". The conclusion that Plato draws at 480a, apparently making the very same use of the preposition 'epi' as earlier at 477a–b, is that the "objects" of knowledge are the Forms (like "the Beautiful itself"), while the "objects" of opinion are the perceptible concrete things (like "the many beautiful things"). So shall we say that the latter (i.e. the philosophers) delight in and love the things that knowledge is towards, while the former (i.e. the lovers of sights and sounds) delight in and love the things that opinion is towards? It is admittedly far from clear exactly what Plato means by saying that perceptible things are "intermediate between what is and what is not" (478d–e). It may have to do with the fact that the existence and character of perceptible things is contingent, and so every such thing exists and has a certain intrinsic character in one possible world, and either does not exist or does not have that intrinsic character in another world. But at all events, the important point for our purposes is that in this passage he endorses the view that the "objects" of knowledge are the Forms. As I have explained, what this seems to mean is that all genuine knowledge is ultimately explained by our cognitive connection with or grasp of the Forms, and so must be knowledge of metaphysically necessary truths. In this way, then, it seems to me that a version of the traditional "Two Worlds" (TW) interpretation of Plato's theory of knowledge is correct. Several objections have been raised against this TW interpretation – and especially by Fine (2003). I shall consider these objections to the TW interpretation in Section 5 below. 4. Explanation and the levels of knowledge So far, it seems as if Plato is defending an extreme conception of knowledge, according to which all knowledge must consist in a priori knowledge of necessary truths – perhaps because all knowledge must be both indefeasible and infallible. So how can it also be that – as I have claimed – Plato is also a kind of contextualist about knowledge? 13 The answer is that Plato also thinks that knowledge must meet a further condition. This condition is in a way analogous to the "justification" condition that later epistemologists imposed on knowledge. It is the condition that knowledge requires a grasp of the explanation of the truth that is known.7 The point that knowledge must satisfy this condition is made at several points. In Meno (98a), it is said that knowledge is "tied down by reasoning out the explanation" (aitias logismōi); in Phaedo (76b), it is said that "a man who has knowledge would be able to give an account of what he knows"; in the Republic (534b), it is said that the person who cannot give an account "to that extent" (tosouton) lacks understanding (nous) concerning the thing in question; and in Theaetetus (201c-d), the suggestion that knowledge is "true belief accompanied by an account" seems to be treated as the most promising of the accounts of knowledge under consideration. Some contemporary contextualists like Stewart Cohen (1999) hold that justification comes in degrees, so that it is only the context in which the term 'know' is used that determines how much justification a person needs for a proposition for it to be true to say in that context that the person "knows" the proposition. In an analogous way, as I shall argue, Plato thinks that there are levels of knowledge, where each of these levels corresponds to the degree to which the person grasps the explanation of the truth that is known; and in different contexts words like 'know' can be used more or less strictly. When the term is used less strictly, it refers to all levels that involve any degree of grasp of the explanation of the truth that is known; but when the term is used more strictly, it refers only to the highest degree of grasping this explanation. Plato's account of the different levels of knowledge is made most explicit in his discussion of the Divided Line (Republic 509d–511e). Strictly speaking, this analogy is only part of an extended discussion, the overall goal of which is to convey the central role of the Form of the Good both in knowledge and in reality. Unfortunately, I will not be able to explore the role of the Form of the Good in any detail; I shall simply focus on what this passage tells us about the nature of knowledge. As we have seen, the four segments of the line correspond to two different kinds of opinion – imagination (L1) and confidence (L2) – and two different kinds of knowledge – thought (L3) and intellection (L4). In interpreting the distinction that is drawn here between these two levels of knowledge (L3 and L4), it seems best to assume that both levels of knowledge satisfy all the conditions on knowledge that I have identified so far: that is, both levels of knowledge involve a priori knowledge of necessary truths. Similarly, both levels of opinion (L1 and L2) involve beliefs, which are fundamentally explained by sensory experience – which Plato seems to regard as consisting in a kind of cognitive connection with concrete perceptible things. Plato's account of the analogy at 509d implies that the four segments of the Divided Line have certain proportions to each other. Let the lengths of the four line-segments be, respectively, l1, l2, l3, and l4. Plato tells us explicitly that the following three ratios are all the same: l1/ l2 = l3/ l4 = (l1 + l2) / (l3 + l4). 8 It follows by elementary algebra that l2 = l3. It is in 7 For a revealing exploration of this point, see Burnyeat (1980). 8 This interpretation is clearly supported by Plato's use of the phrase 'ton auton logon' at 509d5; it does not matter whether we follow the Oxford Classical Text in reading 'anisa' at 509d4 or the various ancient and modern critics who have suggested amending the text to 'an' isa'. 14 my judgment preposterously implausible to suggest that Plato might somehow have failed to notice this simple mathematical fact. Moreover, even if – quite unaccountably – Plato himself failed to notice this fact, there were plenty of brilliant mathematicians at the Academy who would have pointed it out to him. So it seems to be an important feature of this image that the length of the line-segment that represents confidence (L2) is equal to the length of the line-segment that represents thought (L3). Most scholars hold that it is also part of Plato's image that the divisions of the line are unequal. In other words, the ratio in accordance with which the line is divided (l1 + l2) / (l3 + l4) ≠ 1, and in consequence, l1 ≠ l2, l3 ≠ l4 and (l1 + l2) ≠ (l3 + l4). It is not totally clear what these unequal divisions are meant to convey. But one reasonable speculation is that it is meant to indicate that opinion (that is, L1 and L2 together) – in the sense of mere opinion, the kind of belief that falls short of knowledge – is inferior to knowledge (L3 and L4 together), and that in a similar way, imagination (L1) is inferior to confidence (L2), and thought (L3) is inferior to intellection (L4). Since as we have seen, the line-segment that represents confidence (L2) is equal in length to the line-segment that represents thought (L3), what seems to be suggested is that confidence (L2) is not inferior to thought (L3) in the way in which opinion in general is inferior to knowledge in general. In short, there is a "good kind of belief" and a "second-rate kind of knowledge", and neither of the two – at least as Plato now thinks of things in the Republic – is inferior to the other. The distinction between imagination and confidence is sketched extremely briefly in the discussion of the Divided Line. On the whole, however, the view of many commentators seems plausible: imagination (L1) is a state that involves uncritically taking sensory experiences at face value, without any deployment of an ability to discriminate between reliable and misleading appearances; confidence (L2), on the other hand, is a state that involves some deployment of a reliable discriminatory ability of this sort.9 In fact, it seems clear that the same distinction is explained again much later, in Book X (602c–603b), when Plato distinguishes between two kinds of belief that are involved when we see something that "looks crooked when seen in water and straight when seen out of it ..." (602c). Cases of this kind, he argues, reveal that there are two kinds of belief -clearly implying that both kinds involve a part of the soul's "believing" something (doxazon). It seems plausible to me that Plato's reason for implying that the superior kind of belief in these cases counts as belief, rather than as knowledge, is because its content is a contingent fact about concrete perceptible items, rather than on necessary truths about the Forms. The inferior kind of belief is the one that uncritically takes sensory appearances at face value; this kind of belief is attributed to an "inferior" part of the soul (603a). The other kind of belief somehow "places confidence in measurement and calculation" (603a); because it "places confidence" in such measurement and calculation it is attributed to the "best part of the soul". It is striking that Plato uses the term 'pisteuon' for 'places confidence' – a term that is obviously cognate with the term that he uses for the L2 kind of belief, 'pistis'. This makes it plausible that this superior kind of belief is what was 9 This is in effect how Fine (1990) interprets the distinction. 15 earlier called confidence (pistis): that is, it is a belief about contingent concrete things that involves a reliable ability to discriminate veridical from misleading appearances. Presumably, exercising this ability will often involve a sort of "measurement" or "calculation". Such measurement or calculation presumably involves some application of mathematical reasoning to concrete perceptible things; this sort of reasoning would presumably only be possible for those who possess at least some degree of knowledge (if only the lower L3 kind of knowledge, thought). The distinction between the two levels of knowledge is explained in somewhat greater detail. The lower kind of knowledge is illustrated in the Republic (510c–d) by the examples of the kinds of mathematics that had been developed in Plato's time. We know from Meno that this sort of mathematics (even the very rudimentary grasp of this sort of mathematics that Meno's slave achieves in the course of his discussion with Socrates) involves recollection: the soul consciously focuses on certain necessary truths, and because these necessary truths about the Forms are already built into the soul, the soul comes to have a priori knowledge of those truths. What Plato says here is that L3-level knowledge (thought) has two limitations compared to L4-level knowledge (intellection). First, even though it is concerned with abstract mathematical objects, it still makes use of concrete visible objects as images (this point is made three times, at 510b, 510d and 511a). Secondly, it cannot avoid relying on "hypotheses" instead of on the ultimate "unhypothetical" explanatory first principle (510b–c and 511a–b). The first point might seem puzzling: if L3-level mathematical knowledge really is a priori knowledge of necessary truths, why does it still use perceptible things as "images"? It seems that Plato must be assuming that while we are only at this level of knowledge, we still need images of this sort – such as figures and diagrams and the like – to focus clearly enough on the relevant truths in order to recollect them. (It seems clear that in his discussion with Meno's slave, Socrates draws diagrams in order to help the slave to focus on the relevant questions.) By contrast, if we ever acquired complete L4-level knowledge of the whole intelligible system of truths, then we would somehow be able to focus on each of these truths without any such reliance on images. It is because of this feature of L3-level knowledge that it still has some kinship with opinion: although it is a state that is fundamentally explained by the soul's cognitive connection to the Forms, it still has a kind of dependence on the soul's connection to perceptible concrete particulars. The second difference between L3-level and L4-level knowledge concerns the degree to which the thinker grasps the explanatory system of necessary truths. L3-level knowledge involves relying on "hypotheses" and deriving "conclusions" from such hypotheses, but failing to provide any "further" explanation of these hypotheses. Presumably, these "hypotheses" and "conclusions" are themselves necessary truths that belong to the whole explanatory system of necessary truths that flow from the nature of the Forms. So, whenever we have any level of a priori knowledge of these necessary truths, we must grasp at least a small argument in which some of these truths are "hypotheses" and others are "conclusions" that logically follow from them. If you grasp an argument in which a true conclusion follows from some true hypotheses, you can be said to have at least some grasp of an explanation of this conclusion. But if you cannot derive these hypotheses from any "further" principles, you have no "further" explanation of these hypotheses. This raises a problem about how you can be said to 16 "know" these hypotheses, given that (as we have seen) Plato insists that to know a truth, one must have some grasp of its explanation. The solution to this problem proposed by Fine (1990) seems plausible to me: there is still a sense in which I grasp a kind of explanation of these hypotheses, since these hypotheses are in a way explained by their explanatory power in relation to the truths that follow from them. So L3-level knowledge involves grasping at least a small argument involving these necessary truths, and so having a limited though genuine insight into the explanation of the truths in question. L4-level knowledge, by contrast, involves a complete grasp of the whole explanatory system of necessary truths, including the ultimate "unhypothetical first principle of everything", which Plato seems to identify with the Form of the Good.10 To achieve L4-level knowledge, a few one-off bits of recollection would not be sufficient. One would have to use what Plato calls "dialectic" (511b) in order to fit all of these recollected truths together in the right way, and thereby to achieve a grasp of the whole explanatory system of necessary truths. It seems clear that Plato thinks that anyone who has any grasp of mathematics at all has L3-level knowledge, while L4-level knowledge has perhaps never yet been achieved by any actual human being. This reveals that it is in a way an oversimplification on Plato's part to write as though there were exactly two levels of knowledge. If one's grasp of this explanatory system of necessary truths comes in degrees, there is a huge indeterminate number of levels of knowledge, extending all the way from the most rudimentary grasp of tiny fragments of the explanatory system of truths through intermediate levels to a comprehensive grasp of the whole system. Indeed, there is some – admittedly somewhat equivocal – evidence that Plato thinks that virtually everyone possesses at least certain very elementary kinds of L3-level knowledge. When the argument for the Theory of Recollection is presented in Phaedo (72e–77a), it starts out from the assumption, which is enthusiastically accepted by Simmias, that "we know what the Equal itself is" (74b) – where the phrase "the Equal itself" clearly refers to the Form of the Equal. However, Simmias explicitly denies having the kind of knowledge of the Equal itself that would involve being able to give an account of it "properly" (axiōs, 76b); we may take this as the claim that Simmias does not have L4-level knowledge of the Form of the Equal.11 Nonetheless, with respect to the L3-level knowledge of the Equal itself that Simmias does have, Socrates and Simmias seem to agree that he got that knowledge from perceiving concrete perceptible objects like "equal sticks and stones" (74b), and that we have been having the relevant kind of perceptions "from the very moment we were born" (75b). The implication seems to be that Simmias started to acquire the kind of knowledge of what the Equal itself is that he actually has not long after he started having perceptions of this kind. This kind of knowledge may be plausibly identified with a possession of the concept of equality. So it may be that for Plato, certain particularly elementary pieces of L3-level knowledge are necessary for even possessing the basic mathematical concepts that we have; and since the other examples of Forms that he cites in Phaedo and the Republic are the Forms of ethical qualities like the Good and the Just and the like, Plato 10 For an illuminating discussion of Plato's conception of the "unhypothetical", see Bailey (2006). 11 For a seminal discussion of this part of Phaedo, see Ackrill (1997, Essay 1). 17 may also think that certain rudimentary pieces of L3-level knowledge are also necessary for possessing the fundamental ethical concepts too.12 At all events, we know that even Meno's untutored slave recollects certain necessary mathematical truths; in so doing, according to the theory that Plato develops in Phaedo and the Republic, the slave recollects certain aspects of the Forms – certain small fragments of the complete intelligible system of necessary truths. According to the interpretation of this theory that I am proposing here, in recollecting these truths, the slave acquires some rudimentary pieces of L3-level a priori knowledge of necessary truths. But the kind of grasp of mathematical truth that the slave achieves in this passage is, of course, as Plato presumably knew, fairly widespread. So, on my interpretation, at least some basic pieces of L3-level knowledge are widespread. Some readers may think that this implication of my interpretation – that according to Plato, some rudimentary forms of a priori knowledge of necessary truths are widely shared – is incompatible with the view, which Plato seems to endorse, that nonphilosophers are "in reality deprived of knowledge of each thing that is" (Republic 484c). However, it is open to me to interpret this occurrence of the word 'gnōsis' ('knowledge') as referring to something like L4-level knowledge. This is one example of a pattern that I shall explore in more detail in the following section: once we understand the flexible way in which Plato uses his terminology, the apparent obstacles to my interpretation will disappear. 5. Cognitive terms in context In this final section, I shall try to show how my interpretation of Plato's theory and of his use of terminology can explain some puzzling features of the relevant texts, and also answer some of the key objections that are raised against my interpretation. First, we can now see why in Phaedo, Simmias seems to contradict himself on the issue of whether people like him have knowledge of Forms like the Equal itself – with Simmias saying at 74b that "we know what the Equal itself is", and clearly implying at 76b that he does not know what the Equal is. In the first passage, Simmias is referring to rudimentary L3-level knowledge, while in the second passage, he is referring to complete L4-level 12 This interpretation of this passage in Phaedo is emphatically denounced by Dominic Scott (1999), who claims that it involves Plato in "appalling difficulties" (114); according to Scott, "recollection only starts with the process of philosophizing, and thus only a rather limited number of people recollect" (96). However, Scott's arguments are not persuasive: his suggestion that only philosophers recollect seems incompatible with the indisputable point that according to Plato, Meno's untutored slave recollects certain truths of mathematics before Socrates' and Meno's eyes; the kind of grasp of elementary mathematics that the slave achieves is certainly not confined to philosophers. Scott regards it as an "absurdity" (106) to read Plato as claiming that any ordinary thinkers are aware of the way in which ordinary concrete perceptible objects "fall short" of the Forms. But in fact, it is not implausible to suggest that, at least at the time when he wrote Phaedo, Plato believed that even Meno's slave is implicitly aware of the difference between a necessary truth (like the theorem that the square on the diagonal is double the area of the original square) and any contingent truth about the perceptible diagram before him; and this implicit awareness of this difference is, I suggest, precisely what Plato means by speaking of our awareness of how concrete perceptible objects "fall short" of the Forms. 18 knowledge. So there is no contradiction between these statements when they are correctly understood. As I have explained, my account of Plato's theory of knowledge is a version of the traditional TW interpretation. I shall now address some objections to the TW interpretation. One such objection that might be raised is that Plato's ontology is not in fact divided into just two worlds – the world of the Forms and the world of perceptible concrete things. There are other items in his ontology – most notably, souls, which as we have seen are "akin" to the Forms in being imperceptible and eternal, but are clearly not themselves identical to Forms, like the Equal itself or the Beautiful itself. In fact, however, this point is quite consistent with my version of the TW interpretation. My argument for this interpretation only needs the assumption that the Forms and the concrete perceptible things constitute disjoint sets of items: the two sets do not need to be exhaustive as well as disjoint. Moreover, on my version of this interpretation, Plato's claim that the Forms are the "objects" of knowledge and concrete perceptible things the "objects" of belief does not imply that beliefs can only be about concrete perceptible things. It implies that all our beliefs are ultimately explained by our sensory experiences, which consist in a cognitive connection to such concrete perceptible things. As I shall explain, this allows for both knowledge and beliefs about the soul. First, there are presumably some necessary truths about the soul as such, which can be known a priori (for example, it seems that according to Plato, we can know a priori that the soul is immortal). These beliefs are explained by our cognitive connection with the Forms (presumably including the universal Form of the Soul as such). Secondly, our beliefs in any contingent truths (and in any false propositions) about souls must in Plato's view be ultimately explained by sensory experiences – which consist in a kind of cognitive connection with concrete perceptible things. So Plato is committed to the view that all beliefs in contingent truths (and in false propositions) about souls are in this way empirical. Admittedly, this view is not obviously correct; but it certainly does not seem obviously wrong either. At one point, Fine (1990) enumerates five objections to the TW interpretation. I shall now defend my interpretation against these five objections. First, Fine (1999, 215) objects that according to the TW interpretation, "the objects of knowledge and belief are ... disjoint; one cannot move from belief to knowledge about some single thing." On my interpretation, however, the "object" of a belief must be distinguished from the belief's content. So, in principle, one could have an unjustified belief in a necessary truth – which would be ultimately explained by one's sensory experiences, which consist in one's cognitive connection with perceptible concrete things – and then move from this unjustified belief to knowing the truth. In addition, one can also move from L3-level knowledge to L4-level knowledge of a necessary truth, and from L1-level belief to L2-level belief in a contingent truth. As we have seen, in some texts, Plato uses the term 'doxa' as a generic term for the genus of which all four levels are species. So when we are using the term 'doxa' in this way, it will be correct to describe someone who moves from L3 to L4 as moving from a kind of doxa to epistēmē. In Meno, the slave's recollections of mathematical truths are described as "beliefs aroused in him in a dream-like way" (85c). In the Republic, these dream-like 19 beliefs – since they are the results of genuine recollection, and so explained by the slave's cognitive connection with the Forms – would have to count as L3-level cognitive states, of an elementary and rudimentary kind. It is certainly possible in Plato's view to move from L3-level beliefs of this kind to L4-level knowledge. Secondly, Fine (1999, 215f.) objects that the TW interpretation implies that Plato "radically rejects the Meno's account of knowledge, according to which true beliefs become knowledge when they are adequately bound to an explanatory account. For the Meno, knowledge implies true belief; on TW, knowledge excludes true belief." However, it is only when the term 'doxa' is used in the narrower way, to refer to L1 and L2 taken together, that it excludes knowledge. When it is used in the broader way, it refers to the genus of which all four levels are species. When the term 'belief' is used in the larger sense, knowledge – even according to the Republic – does not exclude true belief. Thus, my version of the TW interpretation is entirely compatible with Meno's account of knowledge. The reader may suspect that the TW interpretation conflicts with Meno's account of knowledge in a different way. The TW interpretation restricts knowledge – strictly so called – to a priori knowledge of necessary truths, explained by our cognitive connection to the Forms. But in Meno, one of the examples that Plato gives, seemingly as one of the centrepieces of his discussion of knowledge, is the case of someone's knowing the road to Larissa (97a). But the truth about which road leads to Larissa is evidently a contingent truth (if the bridges and tunnels had been built in different locations, the road in question might not have led to Larissa at all), and it is also a truth that can surely only be known empirically. In fact, however, if we analyse the dialectical context of this example, it is not clear that Plato does commit himself to the assumption that one can genuinely know the road to Larissa. At this point, Socrates is raising an objection to the premise that he invoked earlier that "only someone with knowledge (phronimos) can guide correctly". Proponents of this premise will presumably accept that it is possible to "guide" travellers to Larissa; and so proponents of this premise are committed to the assumption that it is possible to know the road to Larissa. But Socrates rebuts this premise by pointing out that one can also guide correctly if one has mere correct belief (97b). So, Socrates need not accept the assumption that anyone can genuinely know the road to Larissa: for Socrates, it is an entirely live possibility that the only condition that ever enables anyone to guide travellers to Larissa is mere correct belief, and not knowledge. The most that Socrates need accept – purely for the sake of argument – is that if anyone (perhaps per impossibile) knew the road to Larissa, then they would be able to guide travellers successfully. So, when read carefully, the text of Meno does not commit Plato to recognizing the possibility of anyone's knowing the road to Larissa.13 13 At one point in Theaetetus (201b6), Socrates seems to presuppose – at least for the sake of argument – that an eyewitness can know (eidenai) the truth "about what happened to people who have been robbed of their money or have suffered other acts of violence". In this way, it seems to me that in Theaetetus, Plato is exploring the possibility of broader conception of knowledge than the one that he developed in Republic and Pheado. 20 Thirdly, Fine (1999, 216) objects that the TW interpretation implies that "Plato is quite sceptical about the limits of knowledge; ... no one can know items in the sensible world." Fundamentally, this point is correct: according to my version of the TW interpretation, no one can know any contingent truths at all – including contingent truths about the sensible world. However, the difference between L1 (imagination) and L2 (confidence) – that is, between the inferior and superior levels of belief – is of great importance to Plato. An L2-level belief flows from the deployment of a reliable ability to distinguish between misleading and veridical appearances; if such a belief is also true, it is at least fairly close, if not identical, to what contemporary reliabilists like Alvin Goldman (1986) would categorize as full-blown knowledge. It is not surprising, then, that algebraically the ratios of the segments of the Divided Line suggest that L2-level belief is in no way inferior to L3level knowledge. So Plato is not denying that we can have reliably true beliefs about the sensible world. This hardly makes him into a radical sceptic about our cognitive relations with the sensible world. Fourthly, Fine (1999, 216) objects that "this sceptical result would be quite surprising in the context of the Republic, which aims to persuade us that philosophers should rule, since only they have knowledge, and knowledge is necessary for good ruling. If their knowledge is only of Forms – if like the rest of us, they only have belief about the sensible world – it is unclear why they are specially equipped to rule in this world." However, it seems that mathematical knowledge can underwrite an ability for "calculation and measurement", and one of the main ways in which someone can acquire an ability for reliably discriminating between misleading and veridical appearances is by having such an ability for calculation and measurement. In other words, having L4-level mathematical knowledge will help the philosopher-kings to have good L2-level beliefs rather than bad L1-level beliefs. So this is why those who have knowledge of necessary truths are better equipped to rule in the world of contingent sensible things. Still, it is unfortunately true, in Plato's view, that beliefs about contingent concrete things can never be infallible in the same way as a priori knowledge of necessities. But Plato explicitly accepts this. This is why in the end the kallipolis will decline, when the philosopher-kings (in spite of their knowledge of all the necessary truths) form some mistaken beliefs about contingent perceptible matters (546b–c). So, Plato's restriction of genuine knowledge to a priori knowledge of necessary truths is not surprising in the context of the Republic. Finally, Fine (1999, 216) objects that "the text of the Republic seems to contradict TW. At 506c, Plato says that he has beliefs about, but no knowledge of, the Form of the good; and at 520c he says that the philosopher who returns to the cave will know the things there, i.e. sensibles." The first point is easy for my account to handle. When Socrates says at 506c that he has doxa without epistēmē, he is using the term 'doxa' in its broad sense, to refer to the genus of which all four levels of cognitive states are species, and he is using 'epistēmē' in its narrow sense, to refer to L4 (intellection) alone. The point of this passage, then, is that Socrates has some kind of doxa (perhaps an elementary form of L3-level awareness) of the Form of the Good, but that this falls far short of the kind of L4-level knowledge that the philosopher-king would have. The second point is less easy for my version of the TW interpretation to handle. But Fine (2008) has herself emphasized that in the Apology Plato uses some of the Greek cognitive 21 verbs for knowledge (such as 'eidenai' and 'gignōskein' and their cognates) in an idiomatic way, to refer to what by the lights of Plato's official theory is only a reliably true belief – that is, an L2-level belief (confidence or pistis). It seems plausible to me that something similar is happening with Plato's use of these terms in the Republic as well. If L2-level beliefs are not in fact inferior in value to L3-level knowledge, it is not too misleading for Plato sometimes to use these terms in this idiomatic way. With the term 'epistēmē' and its cognates, there are a couple of passages where Plato seems to use these terms in other idiomatic senses. First, these terms sometimes refer to expert know-how – that is, to an expert's knowledge of how to do something. We find this usage in a couple of places, especially in Republic IV: first, in an ironic passage at 420e ("We know how to order the farmers to be clothed in purple and gold..."); then at 422c ("the rich have more knowledge and experience of boxing than of warfare"); and, finally, in the passage where Socrates defines what it is for the city to be wise (428c–e), which moves, in a way that is reminiscent of the early Socratic dialogues, from speaking of knowledge of the crafts of building and metal-working and farming, to speaking of the knowledge that enables the guardians to deliberate about what is good and bad for the city as a whole. Secondly, a more specialized idiomatic use of the verb 'epistasthai' refers to knowing a text or a story by heart, as when Socrates says that he knows Aesop's fables by heart (Phaedo 61b), or asks Glaucon whether he knows the beginning of the Iliad by heart (Republic 392e). Otherwise, however, in the middle-period dialogues, the term 'epistēmē' and its cognates seem to refer principally to some level or other (according to context) of a priori knowledge of necessary truths.14 In these ways, I propose, we can answer Fine's objections to the TW interpretation. The TW interpretation is much less outré than generally supposed. Plato's goal in classifying cognitive states is to "carve at the joints" (as he puts it in Phaedrus 265e). In his view, the distinction between a priori knowledge of necessary truths and our somewhat-reliably true beliefs about contingent matters marks a crucial "joint" – that is, a crucial dissimilarity between two different kinds of cognitive states. He is willing to allow that in ordinary language we use terms like as 'eidenai' and 'gignōskein' to refer to the latter as well as the former; and in some contexts, he is willing to slip into that form of speech too. But what is of fundamental importance to him is not what terminology we use, but the essential nature and differences between these different kinds of cognitive states. My fundamental conclusion, however, is that Fine is right on the most important point of all. Plato is not concerned with utterly different questions from contemporary epistemologists, nor is he defending a fantastic pre-modern theory that nowadays no one 14 This is especially clear of the occurrences of 'epistēmē' and its cognates in Phaedo 73c, 74c, 75e, and 76d. I would read the occurrences of these terms in Meno 85c and Republic 426d and 522c–d as referring to a priori knowledge of necessary mathematical truths, and the occurrences in Meno 93b, Republic 409b, 505a, 536a, and 579e as referring to a priori knowledge of necessary ethical truths. (Nothing about Plato's own views of knowledge can be inferred from Phaedo 96b or Republic 488d or 598c, since in these passages these terms appear in direct or indirect speech, expressing views that Plato rejects.) 22 could take seriously. He is brilliant and insightful epistemologist, with whom we can still have a productive dialogue today.15 References Ackrill, J. L. (1997). Essays on Plato and Aristotle (Oxford: Clarendon Press). Bailey, D. T. J. (2006). "Plato and Aristotle on the Unhypothetical", Oxford Studies in Ancient Philosophy 30: 101–26. Bird, Alexander (2003). "Nozick's fourth condition", Facta Philosophica 4: 141–51. Burnyeat, Myles (1980). "Socrates and the Jury: Paradoxes in Plato's Distinction between Knowledge and True Belief", Aristotelian Society Supplementary Volume 54: 173–206. Cohen, Stewart (1999). "Contextualism, skepticism, and the structure of reasons", Philosophical Perspectives 13: 57–89. DeRose, Keith (2009). The Case for Contextualism. 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