John La Farge, The Relation of the Individual to the State: Socrates and His Friends Discuss ‘The Republic’, as in Plato’s Account; color study for mural (1903). Photograph by Pharos (2017), Wikimedia, Public Domain, https://commons.wikimedia.org/wiki/File:The_Relation_of_the_Individual_to_the_State-_Socrates_and_His_Friends_Discuss_%22The_Republic,%22_as_in_Plato%27s_Account;_Color_Study_for_Mural,_Supreme_Court_Room,_Saint_Paul,_Minnesota_State_Capitol,_Saint_Paul_MET_187194.jpg

8. Surfing the Third Wave: Plato’s Metaphysical Elevator, the Powers Argument, and the Infallibility of Knowledge, Book V

Socrates regards the last of the Three Waves, ‘whether it is possible for this constitution to come into being’ (5.471c), as ‘the biggest and most difficult one’ (5.472a). The constitution he refers to is not a written document as in the US or even a collection of documents as in the UK; it is the conceptual organization of the ideal city itself. ‘Constitution’ translates the Greek word πολιτεία (politeia, whence the English word ‘politics’), which is in fact the Greek title of the Republic. Socrates thinks that the ideal polis is indeed possible, but the condition of its being made real is as bold as it is famous and controversial:

Until philosophers rule as kings or those who are now called kings and leading men genuinely and adequately philosophize, that is, until political power and philosophy entirely coincide, while the many natures who at present pursue either one exclusively are forcibly prevented from doing so, cities will have no rest from evils, Glaucon, nor, I think, will the human race. And, until this happens, the constitution we have been describing in theory will never be born to the fullest extent possible or see the light of the sun. It is because I saw how very paradoxical this statement would be that I hesitated to make it for so long, for it is hard to face up to the fact that there can be no happiness, either public, or private, in any other city. (5.473c–e)

Glaucon’s reaction to Socrates’ inspirational little speech might not be what Socrates was hoping for: he thinks people will think that Socrates is either crazy or dangerous. So Socrates has his work cut out for him.

Philosopher-Kings and Political Animals (5.471c–474c)

There is a lot going on in this famous paragraph. One crucial point is that political power and political wisdom are not merely separated in the non-ideal city that Socrates and company inhabit but are in fact at odds with each other. If those with political power lack political wisdom, they will lack the virtue necessary to perform well their function, governing. Even if those in power reject Thrasymachus’ self-interested conception of ruling and aim to act for the city’s benefit rather than their own, they are likely to get things wrong as often as they get them right if they merely have beliefs about what is best for the city; what they need is knowledge. And those who possess this knowledge—true philosophers—have little interest in getting their hands dirty in politics, preferring a life of intellectual inquiry over political activity. Socrates thinks that this division between political power and political wisdom must be overcome, perhaps even by force, if the ideal city is to be made real. But the force in question will turn out to be the force of rational persuasion, rather than physical compulsion (thus reprising the force–persuasion theme raised in the Republic’s opening scene.)

Socrates doubles down on the importance of marrying political power and philosophy. Not only is their union the necessary condition for realizing this ‘theoretical model of a good city’ (5.472e), but it is also required for human happiness itself: ‘there can be no happiness, either public, or private, in any other city.’ It is this claim, Glaucon thinks, that people will find ridiculous or worse. But Socrates’ claim has more going for it than Glaucon first thinks. Socrates is suggesting that humans, being essentially social creatures, cannot fully flourish in defective cities or when living in Thoreau-like solitude. When Aristotle says early in his Politics that ‘a human is by nature a political animal’,1 he is not saying that humans love to argue about politics or anything like that but rather that we are the kind of animal that lives in a polis, a view that Socrates surely agrees with. And many readers who are uncomfortable with Plato’s community-first ethos might find that their own conceptions of a good human life involve active engagement in a community, even if only one made up of their family and friends. Socrates will have something to say in Book VI about how one can live reasonably happily in an unjust and thus unhappy city, but only in a just city can a person fully flourish and be as happy as it is possible for a human being to be.

Socrates’ solution to the Third Wave prompts the issue which will organize the remainder of Book V as well as Books VI and VII: ‘we need to define […] who the philosophers are that we dare to say must rule’ (5.474b). This project of distinguishing philosopher from non-philosopher will take us into the deep end of the philosophical pool, so to speak, since the distinction will be twofold, drawing on Plato’s metaphysics (his account of the ultimate nature, structure, and constituents of reality, which will involve the famous theory of the Forms) and epistemology (his theory of knowledge). Metaphysics and epistemology are intimately related in Plato’s thought, as we will soon see when we examine the marquee argument of Book V, the Powers Argument. It is fair to say that this is the most intellectually challenging part of the Republic, but also the most intellectually rewarding, I think.

Philosophers and Non-Philosophers

The epistemological distinction between philosophers, who should govern, and non-philosophers, who should not, is that philosophers have knowledge of what is best for the city, while non-philosophers have belief or opinion (δόξα [doxa, whence our word ‘orthodoxy’: correct belief]). Indeed, at the end of Book V, Socrates distinguishes between φιλόσοφος (philosophoi), lovers of wisdom, and φιλόδοξοι (philodoxai), lovers of belief. We met the distinction between knowledge and belief back in Book IV, where it was put to use in explaining the cardinal virtues of wisdom and courage. The distinctive virtue of the guardian-rulers is wisdom, which is knowledge of what is best for the city as a whole. Courage, the distinctive virtue of the auxiliaries, is a matter not of knowledge but of belief—unshakably true belief about what is appropriately feared, but something falling short of knowledge. An auxiliary will believe without doubt that dishonor and enslavement are worse than death, but they need not know why this is the case in order to perform their function well (although they may have true beliefs about why). Plato will have more to say about how knowledge differs from belief in Books VI and VII, especially in the analogies of the Divided Line and the Cave. For now, it is enough to note that the distinction is at the heart of Socrates’ response to the Third Wave: philosophers have knowledge while non-philosophers only have belief.

The metaphysical distinction between philosopher and non-philosopher will turn out to be intimately related to this first, epistemological distinction, since it is a distinction between the objects of knowledge and belief. The word ‘metaphysics’ often conjures up thoughts of crystals, incense, New Age healing, etc., but this is not the philosophical sense. Philosophically speaking, metaphysics concerns the ultimate nature, structure, and constituents of reality. Where natural scientists try to discover and explain causal connections between events, metaphysically minded philosophers want to understand what causation itself is. They want to know what kinds of things exist: is everything that exists physical, or do non-physical things exist? For example, is the human mind something fully physical, reducible without remainder to the brain? Or is it something non-physical? If minds are non-physical, how do they interact with the body, which is decidedly physical? These are not the kinds of metaphysical questions that Plato asks; they assumed a central place in Western metaphysics with the thought of René Descartes (1596–1650). But hopefully they give the reader a sense of what sorts of concerns are addressed by metaphysics.

We have beliefs about the particular things that make up our everyday world, on Plato’s view, but we have knowledge of the Forms—the timeless essences of the particulars.2

A brief jump ahead to the beginning of Book X will be helpful in getting clearer about what the Forms are. There, Socrates reminds Glaucon that their ‘usual procedure […] [is to] hypothesize a single Form in connection with each of the many things to which we apply the same name’ (10.596a). There must be something, Plato thinks, that all just actions have in common, that all courageous actions have in common, that all red things have in common. Grasping this common feature—the essence or the Form, the real definition—is the task of philosophy, for Plato. His example in Book X is rather mundane: beds. ‘The form’, he says, ‘is our term for the being of a bed’ (10.597a), where ‘being’ means what the thing is: its essence, what it is to be a bed. So far, assuming a common feature seems like a reasonable, innocuous assumption. While there are many particular beds and many particular just actions, there is a single, unifying Form or essence of bedness and one of justice. So where particulars are many, Forms are one.

Another crucial difference between Forms and particulars is that particulars are ever-changing. ‘Of all the many beautiful things’, Socrates asks, ‘is there one that will not also appear ugly? Or is there any one of those just things that will not also appear unjust? Or one of those pious things that will not also appear impious?’ (5.479a) Although Plato does not share the subjectivist view that beauty is in the eye of the beholder, the beauty example is a helpful one. The sky to the west is beautiful right now, but in an hour, after the sun has set, it no longer is. Nor is it beautiful to my color-blind friend. The bouquet of flowers on the dining room table will not evoke ‘oohs’ and ‘ahs’ in two weeks. Thus, beauty seems both temporal and perspectival. As we saw in Book I, returning the weapon you have borrowed is usually just, but in a particular set of circumstances (say, its owner is deranged) it is not. Telling the truth is usually the right thing to do but sometimes the demands of kindness trump the demands of honesty. That fox seems big when standing next to the squirrel, but small when standing next to the bear. And so on. Being ever-changing and unstable are hallmarks of concrete particulars. Bob Dylan captures something of Plato’s point when he sings, ‘He not busy born is busy dying.’ I hope my non-existence is a long way off in the future, but every day I live I am one day closer to my death—hence, I seem to be both living and dying, just as every beautiful thing seems both beautiful and not beautiful.

The Forms are altogether different, on Plato’s view. Unlike the many particular beautiful things, the Form of beauty is permanent, stable, unchanging: ‘the beautiful itself’, Socrates says, ‘remains always the same in all respects’ (5.479a). It is the only thing that is always and everywhere beautiful. The same goes for the Forms of justice, piety, redness, bigness, whatever. While the world of particulars is in constant flux, the world of the Forms is stable and unchanging. We experience particular things and events via our senses, but the Forms ‘are intelligible but not visible’ (6.507b): we perceive them with our minds, not our senses.

One of Plato’s ways of referring to the Form of something drives this point home: the Form of a thing is the ἰδέα—literally, the idea—of the thing. We cannot see or taste or touch or smell or hear ideas; we can only think them. But the word ‘idea’ can be misleading, since for Plato the Forms are not psychological entities like thoughts or feelings, which depend for their existence on someone having them, as ‘idea’ might suggest. Unlike ordinary thoughts and ideas, which cannot exist without thinkers thinking and having them, Plato’s Forms are mind-independently real, not depending for their existence upon thinkers thinking them. This is one of the most distinctive features of the Forms. It is one thing to claim that there is a common essence shared by particular things; it is another to claim that these common essences or Forms are not dependent, psychological entities but are instead mind-independently real. While the shadow my hand casts is real, it seems somehow less real than my hand, since its existence depends on the presence of the hand. Ideas and thoughts and feelings and moods seem similar to shadows in this regard: they are dependent entities, depending on conscious subjects for their existence. Plato does not deny this. But the Forms are not dependent psychological entities. It turns out that the Forms depend upon the Form of the good—goodness itself—but they are decisively unlike our ordinary ideas and thoughts. If this all sounds a bit weird, thinking about numbers can be helpful. Although the two coffee cups on the table are concrete particular objects, the number two is an abstract object, capable of being instantiated in space and time by infinitely many pairs of concrete particular objects but it is not itself a concrete particular—at least on a plausible philosophy of mathematics known, perhaps unsurprisingly, as Platonism. One reason for thinking of mathematical objects as mind-independently real is that doing so helps us make sense of other beliefs many of us have about these objects. It will seem to many readers, for example, that the Pythagorean Theorem is timelessly true and would still be true even if no person ever thought of it. We should resist the temptation to say that numbers and the Forms have always existed, because ‘always existed’ is a temporal notion, and the idea here is that such entities are outside of time.

Plato’s Metaphysical Elevator

We can think of Plato’s metaphysics via the metaphor of an elevator, as in this diagram.

Level 4 The Form of F is more real than the many particular Fs.

↑

Level 3 The Form of F is real: it is a non-spatiotemporal,mind-independent entity.

↑

Level 2 There is a form of F (the real definition of F), which all particular F things have in common.

↑

Level 1 The many particular F things are real: they are spatiotemporal, mind-independent entities.

At Level One we find the everyday objects making up the world we experience through our five senses: trees, squirrels, rocks, picnic tables, etc. Most readers, I assume, think these objects are metaphysically real, existing independently of our minds and still there when we close our eyes or when we no longer exist. This is a plausible, commonsense philosophical view, though of course not all philosophers hold it. The great Irish philosopher George Berkeley (1685–1753), for one, thought that what we ordinarily take to be mind-independently real things are in reality mind-dependent ideas. We are tempted to think of them as mind-independently real because they seem to persist in our absence, but, he thought, this is only because God continues to think them when we do not. Berkeley’s motto was esse est percipi: to exist is to be perceived. This seems right for headaches, for example, which require someone to perceive them; they are not floating around in space, waiting to land on an unfortunate victim. So while some philosophers will not even get on Plato’s elevator at the first floor, most of us will.

At Level Two we find those real definitions or essences that Socrates is forever seeking, the trait or property that all F things have in common: chairness, justice itself, etc. Most readers, I suspect, will take Plato’s elevator to Level Two. We think that the many particular things we experience through our senses come in clusters unified by common properties: there are red things, round things, beautiful things, just and unjust actions and social arrangements, etc. Ascending to Level Two results from agreeing with Socrates that there is ‘a single form in connection with each of the many things to which we apply the same name’ (10.596a). Indeed, the Republic is the search for the Form of justice, as many of Plato’s dialogues are searches for the Forms or essences of various virtues such as piety, courage, temperance, etc. But at level two, we find forms, rather than Forms, since they are not mind-independently real, existing in their own right.

Not everyone will follow Plato to Level Two, however. The great twentieth-century philosopher Ludwig Wittgenstein (1889–1951), for one, declined the invitation, thinking that the search for one commonality was misguided and inevitably futile. If we consider the wide variety of games—card games, board games, ball games, party games, computer games, etc.—we will see, Wittgenstein thought, that there need not be features common to everything we call a game:

Or is there always winning and losing, or competition between players? Think of solitaire. In ball games there is winning and losing; but when a child throws his ball at the wall and catches it again, this feature has disappeared […] Think now of games like ring-a-ring-a-roses; here is the element of amusement, but how many other characteristic features have disappeared! And we can go through the many, many other groups of games in the same way; can see how similarities crop up and disappear.3

Instead of an essence shared by all games, Wittgenstein finds ‘a complicated network of similarities overlapping and crisscrossing’, which he dubs a family resemblance. Not everyone accepts Wittgenstein’s view; Bernard Suits, for one, thought he had found the essence of game. But it is worth noting that contemporary psychology and cognitive science seem to side with Wittgenstein over Plato. According to prototype theory, first articulated by the cognitive psychologist Eleanor Rosch in the early 1970s, our concept of, say, bird, involves a cluster of features, some more important than others, with certain examples serving as prototypes.4 If you want to give someone an example of a bird, you are likelier to offer a robin or cardinal as an example than you are to offer a penguin, because penguins lack one of the prototypical—but not necessary—traits of we associate with birds, namely the ability to fly.

Even though Wittgenstein would not ascend to Level Two, preferring family resemblances to essences, many readers will follow Socrates there. It is at Level Three, though, where Platonism really starts to kick in, for Level Three involves a commitment to the real, mind-independent existence of these Forms or common properties. At Level Three, we discover essences and Forms; we do not invent them. It is one thing to regard the Form or essence of justice or kindness or chairness as a psychological entity, a conceptual construct having no mind-independent existence in its own right. It is another thing entirely to regard the Form as mind-independently real, something that is to be discovered rather than invented. You can ascend to Level Two while thinking that the Forms are like ordinary ideas and thoughts, not real in themselves but rather depending for their existence on thinkers thinking them. But ascending from Level Two to Level Three requires a considerable jump in what philosophers call ‘ontological commitment’, a fancy-sounding but precise phrase indicating which kinds of things one is prepared to say exist in their own right. Few people, for example, are ontologically committed to unicorns or the tooth fairy: most of us do not regard them as mind-independently real. And while most of us think that our thoughts and feelings are ‘real’ in an everyday sense—the sense which contrasts ‘real’ with ‘imaginary’ or ‘hallucinatory’—we do not regard them as real in the sense of existing in their own right, mind-independently. Many people who find the ascent to Level Two unproblematic and obvious will balk at ascending to Level Three. Why go there, after all? It seems needlessly complicated or metaphysically profligate to posit the real, mind-independent existence of Socrates’ real definitions.

Many readers are familiar with Ockham’s Razor, which in one formulation tells us that the simplest explanation of a phenomenon is usually correct. Perhaps less familiar is the ontological formulation of the Razor, which bids us not to multiply entities beyond necessity: non sunt multiplicanda entia sine necessitate. In short, if you do not need to posit the existence of certain things or kinds to make sense of your experience, then don’t; be metaphysically frugal and parsimonious. No doubt this metaphysical or ontological simplicity is related to explanatory simplicity: explanations involving fewer kinds of entities will probably be simpler. It is as though there is an ontology tax that philosophers are keen to avoid paying. Most of us find ontological commitment to ships and shoes and sealing wax unproblematic because it is difficult to make sense of our everyday experiences without a commitment to the real existence of the spatiotemporal objects that we sit on, stub our toes on, eat, etc. But many readers will resist ontological realism about Plato’s Forms, feeling they can understand and explain their experiences without appeal to them.

The journalist Hunter S. Thompson once wrote, ‘When the going gets weird, the weird turn pro’.5 If so, then Level Four is where one loses one’s amateur standing. For those ascending to Level Four go beyond ontological commitment to the real, mind-independent existence of the Forms that typified Level Three. On Level Four, the Forms are not merely mind-independently real but are more real than the spatiotemporal particulars that are instances of them. The idea that the essence of chairness is more real than the chair one is sitting on is, well, pretty weird. Many people will get off the Platonic elevator at Level Two, being philosophically unwilling, perhaps for Ockham-inspired reasons, to ascend to Level Three. But of those who go to Level Three, few, I suspect, will be willing to go all the way to Level Four, and readers might be forgiven for thinking that Socrates has gotten into the drugs reserved for the rulers of the city (5.459c). But—bad jokes aside: the drugs are not those kinds of drugs, anyway—his reasons for ascending to Levels Three and Four are philosophical rather than psychedelic, and it is to those philosophical reasons that we now turn.

Marrying Metaphysics and Epistemology: The Powers Argument (5.476d–480a)

The metaphysical and epistemological distinctions are intimately related, for Plato. In what I call the Powers Argument, he starts with epistemology and ends up at metaphysics, arguing that the distinction between knowledge and belief requires allegiance to the Forms, since knowledge and belief, being different powers, must have distinct kinds of objects. The Powers Argument is crucial to addressing the Third Wave, since it will help ‘define […] who the philosophers are that we dare to say must rule’ (5.474b), but its implications go beyond this, as it attempts to give good reasons to ride the Metaphysical Elevator all the way up.

The epistemological and metaphysical distinctions fit together this way: concrete particular things are the objects of belief, while the Forms are the objects of knowledge. A non-philosopher has beliefs about the many particular things and activities that make up the furniture of our everyday world: chairs, just actions, cats, sunsets. They ‘believe[] in beautiful things, but do[] not believe in the beautiful itself’ (5.476c). The philosopher, by contrast, is ‘able to see and embrace the nature of the beautiful itself’ (5.476b), the Form or essence in virtue of which all particular beautiful things are beautiful. A non-philosopher can have a true belief that a sunset is beautiful but never knowledge of this. Indeed, ‘there is no knowledge of such things’ (7.529b), as the Forms and not particulars are the proper objects of knowledge, on Plato’s view. But perhaps something that falls short of knowledge but is more than true belief—knowledge with an asterisk—is possible where particulars are concerned. If so, a philosopher might know* that this particular sunset or that particular painting is beautiful by grasping the Form of beauty and seeing that the painting or sunset is an instance of—participates in, as Plato often puts it—the Form, if only temporarily. Such a philosopher would know why the sunset is beautiful, which is beyond the cognitive capacities of a non-philosopher, who lacks access to the Form of beauty and thus never ascends above true belief.

The Powers Argument’s crucial concept, which gives it its name, is the concept of a power (δύναμις [dunamis, whence the word ‘dynamic’]). Sight, hearing, touch, taste, and smell are ordinary examples of powers, which we might also call ‘capacities’ or ‘faculties’. Animals typically have the power of sight; rocks do not. Even though powers are what enable us to see, hear, touch, taste, and smell the world, powers themselves are not the kinds of things we can see, hear, touch, taste, and smell. We distinguish them, Socrates says, by what they do and what they are ‘set over’ (5.477d)—by their functions and their objects: ‘What is set over the same things and does the same I call the same power; what is set over something different and does something different I call a different one’ (5.477d). Talk of knowledge and belief as powers, analogous to sight and hearing, might make this first premise sound odd to modern ears, but this is how Socrates conceives of them. The second premise is the claim that knowledge and belief are different powers, which Glaucon regards as obviously true to ‘a person with any understanding’ (5.477e). From these two premises Socrates concludes that knowledge and belief must have different objects. This conclusion seems innocuous enough, but we will soon see that it is anything but.

Having established, he thinks, that knowledge and belief must have different objects, Socrates then tries to determine what these different objects are. Knowledge’s object, Glaucon agrees, is ‘what is’ (5.478a). There is a trifold ambiguity here that we should be aware of. In the existential sense, ‘what is’ means what exists, what is real. Someone who asks, ‘Is there a god?’, is using ‘is’ in the existential sense. In the epistemic sense, ‘what is’ means what is true, what is the case. News anchor Walter Cronkite’s signature sign-off, ‘And that’s the way it is’, employed ‘is’ in the epistemic sense. In the predicative sense, ‘is’ serves to link subject and predicate: the sky is blue, Jonas Starker is a great cellist, etc. So ‘what is’ means what is …, where the dots are filled in with some predicate: what is red, what is beautiful, what is just, etc.

Plato does not make explicit which sense of ‘is’ Glaucon has in mind when he says that knowledge’s object is ‘what is.’ To get a sense of the argument without becoming ensnared in scholarly controversy, I propose that we read ‘what is’ in the existential sense, given the metaphysical implications of the argument. Taken this way, when Socrates says that ‘knowledge is set over what is’ (5.478a), he is saying that the objects of knowledge—what we know when we know something—exist: they are real. And the Forms exist, so they are objects of knowledge. Ignorance, by contrast, has as its object ‘what is not’ (5.477a, 478c): what does not exist. (It is odd to think of ignorance as a power or capacity, since it does not enable its possessor to do anything, as powers usually do, but let us set aside this minor point.) Since belief is in between knowledge and ignorance, ‘darker than knowledge but clearer than ignorance’ (5.478c), its objects will be intermediate between what is and what is not. Thus the objects of belief ‘participate in both being and not-being’ (5.478e): they straddle both existence and nonexistence, not fully real but not unreal, either. In short, the objects of belief are the particulars of everyday experience.

To summarize: knowledge and belief, being different powers, must have different objects. Indeed, they have very different kinds of objects: knowledge’s objects are the timeless Forms, while belief’s objects are the spatiotemporal particulars that make up our everyday world. So there are two metaphysically different worlds: the world of the Forms and the world of particulars. The world of the Forms is the world of reality while the world of particulars is the world of appearance—but not, I hasten to add, a world of illusion. Plato is very careful with his language here, emphasizing that those things we think of as being beautiful really only appear beautiful, since they also appear ugly. ‘Is there any one of those just things’, Socrates asks, ‘that will not also appear unjust? Or one of those pious things that will not also appear impious?’ (5.479a) Plato is not claiming that our everyday world is illusory in the sense of not being real. It is just not as real as the world of the Forms. It is smack dab in the middle, metaphysically, more real than complete non-existence, but less real than complete existence.

Problems with the Powers Argument

That is a lot to take in, so let us pause and restate the argument in premise-conclusion form, in order to grasp its structure more clearly, which should help us analyze it:

P1	x and y are the same power if and only if
	(a) x and y have the same objects and
	(b) x and y have the same function. (5.477d)
P2	Knowledge and belief are different powers. (5.477b,e)
C1	So, knowledge and belief have different objects and different functions. (5.478a)
C2	So, knowledge and belief have different objects.
P3	Knowledge’s object is what is. (5.478a,c)
P4	Belief is intermediate between knowledge and ignorance. (5.478d)
P5	Ignorance’s object is what is not. (5.478c)
C3	So, belief’s object is what is and what is not. (5.478d)

(A minor detail regarding C1: Grube’s translation does not quite square with the Greek text here, which is better captured by C2—which logically follows from C1. I do not think anything rides on Grube’s addition, but some readers, especially brave souls wrestling with the Greek text, will want to know this.) Let us work backwards, starting with C3. We have already noted that for Plato particular things are bundles of opposites, simultaneously beautiful and not beautiful, just and not just, etc.: ‘each of them always participates in both opposites’ (5.479b). But Socrates now takes this to imply that these particular things are ‘intermediates between what is not and what purely is’ (5.479d). This is something new. It is one thing to claim that predicates like ‘…is beautiful’ both apply and do not apply to one and the same particular object—that the particular thing participates in both beauty and non-beauty. But why would this imply that any particular ‘participates in both being and non-being’ (5.478d), that it somehow both exists and does not exist? There seems to be something a little fishy here. Socrates seems to slide from the predicative sense of ‘is’, where it links subjects and predicates, to its existential, existence-asserting sense. That is, he seems to slide from

(Predicative) Any particular thing both is beautiful and is not beautiful

to

(Existential) Any particular thing both is and is not,

as if he simply crossed out the occurrences of ‘beautiful’ in (Predicative).

Bertrand Russell once wrote that employing the same word to express such different senses was ‘a disgrace to the human race’.6 Russell’s hyperbole is no doubt tongue-in-cheek, but there is a serious point in the background: philosophy often requires attention to linguistic subtleties like the distinction between the senses of ‘is’. In this portion of the argument, Socrates seems to elide the distinction between the predicative and existential senses, drawing a conclusion employing the latter from a premise employing the former. I stress that he seems to me to be doing this; I am not insisting that he actually does so. Such insistence would violate the principle of charity, which requires us to interpret texts and utterances in ways that maximize their truth and reasonableness and logical validity. But sometimes even very smart people make logical blunders, and the principle of charity does not require us to pretend otherwise. If this were a different book, aimed at a different audience, we would explore this question in depth and detail. Some people are sufficiently fascinated by issues like this as to become Plato scholars, and no doubt some of those scholars are rolling their eyes or at least arching their eyebrows at what I have said here. But—and here I am on firm logical ground—this is not a different book than it is, so I tentatively suggest that we view this apparent equivocation between senses of ‘is’ as a heuristic device to help us think critically about the argument and move on.

These concerns about whether Socrates makes this predicative-to-existential slide fade into the background when we see how problematic the first part of the argument is, the derivation of C1 from P1 and P2. Glaucon thinks that C1 ‘necessarily’ (5.478a) follows from P1 and P2, but his confidence is misplaced, since the conclusion does not follow necessarily at all. Since the conclusion could still be false even if we assume that the premises are true, the argument is invalid. To see this, consider a parallel example. Two Constitutional conditions of eligibility to be President of the United States are (a) that one be at least thirty-five years old and (b) that one be a natural-born citizen. From the fact that my friend Geoff is not eligible to be President, it does not follow that he is not at least thirty-five and that he is not a natural born citizen; what follows is that either Geoff is not at least thirty-five years old or Geoff is not a natural-born citizen. Both negative conclusions might follow, as they do in the case for my cat Frobisher, who, despite having been born here, is not a citizen of the US and is well shy of thirty-five. But all we—and Socrates—are entitled to is the or. If I know that Geoff is well past thirty-five, I can then conclude that he is not a natural-born citizen (he is, in fact, Canadian). But until I know that, I am jumping to a conclusion I am not entitled to draw. What Socrates should conclude from P1 and P2 is that either knowledge and belief have different objects or they have different tasks. It might be that both their objects and tasks differ, but Socrates is not entitled to conclude that. To get to C2, the conclusion that knowledge and belief have different objects, from C1, which now functions as the premise that they either have different tasks or different objects, he has to show that knowledge and belief do not have different tasks. But without doing this, he is jumping to a conclusion—C2—that he is not entitled to.

So Plato, in the person of Socrates, has committed one of the gravest of philosophical sins: he has given a logically invalid argument. But even if we could fix the logical invalidity, switching the ‘and’ in C1 to an ‘or’, it is difficult to see how Socrates can get to C2. Powers differ more often by having different tasks or functions than by having different objects. Shepherds and butchers, for example, share a common object, sheep, but they have different tasks in relation to that object: shepherds seek to nurture sheep while butchers seek to turn them into lamb chops. On a common conception of education (though one we will see Plato calling into question in Book VII), teaching and learning have the same object, knowledge, but have different tasks or functions with respect to that object: teaching seeks to impart or instill knowledge while learning seeks to acquire it. And so on.

Perhaps the trouble is thinking of knowledge and belief as powers or capacities. Plato thinks that each of the senses has a distinct object: sight’s object is color, hearing’s is sound, etc. In the Theaetetus, a dialogue roughly contemporary with the Republic, Socrates says, ‘what you perceive through one power, you cannot perceive through another’ (185a). Cases of synesthesia aside, this has the ring of truth, though it seems to have the odd implication that we cannot see and smell and taste the same object, when it seems clear that we can: I see the coffee, smell it, taste it, etc. But Socrates could respond that we see the coffee’s color, smell its aroma, feel its heat, etc. These various sensations are synthesized or integrated into a unified sensory impression, but the various senses are modular, operating independently. We perceive the coffee by or through perceiving its sensible qualities. But, a critic might insist, it is not the case that these powers ultimately have different objects; instead, they have a common object: the coffee. It is true that their intermediary objects are different properties or qualities of that object—we see color, smell aroma, etc.—but there is a common object that those various sensory qualities belong to. So we have reason to be skeptical of the first premise of the Powers Argument. And even if we give Socrates the benefit of the doubt and take him to be talking of the various intermediate objects of these powers, not the ultimate object, we might wonder what reason we have to think of knowledge and belief as analogous to powers in having unique objects.

Most contemporary philosophers would agree with the spirit of P2, since they think that knowledge and belief are different cognitive or epistemic states, though they would be unlikely to think of them as ‘powers’. Few, though, would agree with Plato’s conclusion that knowledge and belief have different kinds of objects. As discussed earlier, on the JTB (Justified True Belief) conception of knowledge, to know something is to have a belief that is not only true but is also justified, which (on a plausible account of what it is to be justified in believing something) requires good reasons for having the belief. Most contemporary philosophers would regard C2 as false, since knowledge and belief, though different, have the same objects: propositions. In the first sentence of the Gettysburg Address, Lincoln speaks of the Founders’ dedication to ‘the proposition that all men are created equal.’ If he had said it in French (‘la proposition que tous les hommes sont créés égaux’) he would have expressed the same proposition. Even though we express propositions in language, at heart propositions are conceptual entities rather than linguistic ones, and the same proposition can be expressed in different languages. Lincoln believed in the proposition of fundamental human equality, while Plato, we have seen, did not. Both Anna, who grew up in Wisconsin and has looked at her share of roadmaps and atlases, and Bryce, a ‘Coastie’ with a vague picture of the geography of North America who has trouble locating Wisconsin on a map (for him the Midwest is a vague ‘blobject’), believe the proposition that Wisconsin is east of the Mississippi River. On the JTB conception, Anna knows this while Bryce does not. Though Bryce’s belief is true, he does not have good reasons for it, since when pressed the only reason he offers is, ‘I just think it is’. Though Anna and Bryce are in different cognitive and epistemic states, their objects are the same, the proposition that Wisconsin is east of the Mississippi River.

Or so say most contemporary epistemologists. That most contemporary philosophers think C2 is false does not make it false, of course, but in the next section we will see reason to think they are probably right about this.

Plato’s Fallible Conception of Infallibility

So why does Plato have someone as smart as Socrates make such a logically flawed argument? It may be that the argument accurately reflects Socrates’ reasoning, which Plato faithfully reproduces, though that seems unlikely. Perhaps this is one of those instances of Plato’s intentionally having Socrates make a bad argument in hopes of engaging the reader in philosophical dialogue, since the yes-men Socrates is talking with do not seem up to the task. That is certainly possible, but here it does not ring true—at least to me. In those instances in Book I when the bad arguments seem intentional—e.g., in Socrates’ first refutation of Polemarchus—there was a substantive philosophical point that Plato seemed to want his readers to work out for themselves (that virtues are not crafts or skills). But given how much is at stake here—reasons for believing in Plato’s Forms, for taking Plato’s Elevator to the Third and Fourth Levels—it is an odd time for such a lesson. Perhaps Plato has independent reasons for believing C2, that knowledge and belief have different objects, and this makes him less attentive than he should be to the quality of the reasons he offers here in support of this belief. It is a common enough human failing, but it is surprising to see Plato falling victim to it here.

Those independent reasons for thinking C2 is true can be found in the discussion Socrates and Glaucon have about P2. Glaucon agrees—as we all should—that knowledge and belief are different. ‘How could a person with any understanding’, he asks, ‘think that a fallible power is the same as an infallible one?’ (5.477e) The idea that belief is fallible should ring true: we regularly believe things that are not true. We think they are true, of course, and sometimes insist that they are. After all, we probably would not believe them if we knew they were false, since to believe something is, at least in part, to take it to be true. But while I can believe things that are false, I cannot know things that are false. I might believe that Orson Welles directed The Third Man or that Edward Albee wrote Desert Solitaire, but I cannot know these things, since they are false. On the JTB conception, remember, my beliefs count as knowledge only if they are true (though being true is not enough: those true beliefs also have to be justified). For contemporary philosophers, that is the sense in which knowledge is infallible and belief is fallible: I can believe things that are false but I cannot know things that are false.

Plato seems to have a different understanding of the infallibility of knowledge, one that goes beyond the view that we cannot know things that are false and holds that we cannot know things that could be false. In other words, the objects of knowledge must not only be true, they must be necessarily true. While a contingent truth could be false, a necessary truth cannot possibly be false: it must be true. The candidates for such things are few, but the truths of mathematics offer the most intuitively plausible examples of necessary truths. Although it is not completely uncontroversial, I think that the Pythagorean Theorem is necessarily true, that it was true even before anyone thought of it and would be true even if no one ever thought of it, even if no creatures capable of understanding geometry had ever existed. That the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides is not merely a mind-independent truth, it is a mind-independent truth that could not be false. Given the nature of right triangles, there is no way the square of the hypotenuse could not equal the sum of the squares of the other two sides. If there are two mittens and one stocking cap on the table, it is mind-independently true there are three things on the table: it does not matter whether I am looking at them or not; there are three things on the table. But it is merely a contingent truth that there are three things on the table; I could have just as easily kept my stocking cap on (it is cold in here!), in which case there would only be two items on the table. So while it is true that there are three items on the table, it is a contingent truth. But that three is the sum of one and two is a necessary truth: it cannot be otherwise. And here it is important not to confuse numbers with numerals, which are our names for numbers. We could use the word ‘two’ to name the number three and the word ‘three’ to name the number two—heck, we could call two ‘Ethel’ and three ‘Fred’. The English sentence ‘two plus one is three’ is only contingently true, since which words attach to which objects is a contingent fact of English. But the proposition it expresses, that the sum of two and one is three, is necessarily true, regardless of which names or numerals we use to designate the numbers.

The crucial difference between these two conceptions of the infallibility of knowledge is that the contemporary conception of infallibility is a claim about the nature of knowledge, while for Plato it is a claim about the objects of knowledge:

Contemporary:	Necessarily, if someone knows that p, then p is true.
Plato:	If someone knows that p, then p is necessarily true.

A lot rides on where ‘necessarily’ appears—or as linguists and philosophers would say, on its scope. There is a world of difference between

Not Trying I am not trying to hear what they are saying

and

Trying Not I am trying not to hear what they are saying.

Not Trying is true so long as I am not making an effort to hear what they are saying (e.g., I am not leaning in, putting my ear to the wall, etc.); if I hear what they are saying, perhaps the fault is theirs and not mine, since I was not eavesdropping. But Trying Not requires that I make an effort to not hear them (e.g., I cover my ears, change locations, etc.).; if I hear what they are saying, I have failed in my attempt to not hear them—perhaps I should have tried harder. Similarly, the difference between the contemporary and Platonic conceptions of the infallibility of knowledge is a difference in the scope of the adverb ‘necessarily’. On the contemporary account, what is necessarily true is a claim about the nature of knowledge, that if I know that p, then p is true—so I can have knowledge only of things that are true. On the account I am attributing to Plato, it is the proposition known that is necessarily true: if I know that p, then p is necessarily true—so I can have knowledge only of necessary truths, never of merely contingent truths.

If Plato understands the infallibility of knowledge as I have suggested, it is no wonder that he thinks that knowledge and belief must have different objects. Only the Forms, Plato thinks, have the necessity required of objects of knowledge, since only the Form of beauty is completely beautiful; particular beautiful things are too awash in contingency and opposition to make the grade. (The self-predication of the Forms—the view that the Form of beauty is beautiful, the Form of justice is just—is of great interest to Plato scholars, but it is an issue we need not tangle with here. Suffice it to say that there are problems with this view: if the Forms are self-predicating, then the Form of beauty is beautiful and the Form of justice is just. That might seem just fine, but then the Form of bigness is big and the Form of smallness is small, the Form of redness is red and the Form of squareness is square—all of which are odd implications for entities that are not spatiotemporal.)

Most of the truths of our everyday lives—our names, where we parked the car, our favorite flavor of ice cream, how many (if any) children we have—are contingent truths, not necessary truths: they could have been otherwise. My parents could have named me Ivan instead of Sean; I parked the car in the street but I could have parked it in the driveway or in the garage, etc. Things could be different than they are. On the ordinary conception of knowledge, I know that my name is Sean and that I have two cats. But on the stronger understanding of the infallibility of knowledge that Plato seems to have, I do not know these things, since they are only contingently and not necessarily true and thus not proper objects of knowledge. This will strike many readers as quite counter-intuitive; most of us feel quite confident that we know our names (though where we parked the car might be a different matter entirely, especially for garageless city-dwellers).

So it is plausible that Plato’s view about the infallibility of knowledge is what accounts for his belief that knowledge and belief must have different objects. And it might help explain why he does not seem aware of the weaknesses of the actual argument he gives to support that belief. But there are still the facts that the Powers Argument is logically invalid and its key first premise is false. It is certainly the marquee argument of Book V, intended to provide good reasons to accept Plato’s distinctive metaphysics. Of course, Plato’s metaphysics might still be correct: the conclusion of an invalid argument can still be true. But as things stand, there is a gaping hole in the middle of the Republic.

Some Suggestions for Further Reading

Readers looking for an excellent introduction to metaphysics by one of the best contemporary philosophers will find it in Peter Van Inwagen, Metaphysics (4th ed.) (Boulder: Westview Press, 2014).

Readers interested in a good, brief introduction to epistemology should see Jennifer Nagel, Knowledge: A Very Short Introduction (New York: Oxford University Press, 2014), https://doi.org/10.1093/actrade/9780199661268.001.0001.

For an overview of Plato’s metaphysics and epistemology, interested readers should see Allan Silverman, ‘Plato’s Middle Period Metaphysics and Epistemology’, in the ever-helpful Stanford Encyclopedia of Philosophy (https://plato.stanford.edu/entries/plato-metaphysics/).

For an advanced discussion of some of the issues treated in this chapter, interested readers might start with Gail Fine, ‘Knowledge and Belief in Republic V’, in Plato 1: Metaphysics and Epistemology, ed. by Gail Fine (New York: Oxford University Press, 2000), pp. 215–46. Gregory Vlastos, ‘A Metaphysical Paradox’, in Plato’s Republic: Critical Essays, ed. by Richard Kraut (Lanham, MD: Rowman & Littlefield, 1997), pp. 181–95, is an accessible discussion of Plato’s two-worlds metaphysics by one of the twentieth century’s leading Plato scholars.

For readers interested in Wittgenstein’s philosophy, his Philosophical Investigations, 3rd ed., trans. by G. E. M. Anscombe (Oxford: Basil Blackwell, 1973) is a good place to start. Bernard Suits, The Grasshopper: Games, Life, and Utopia, 3rd ed. (Peterborough, ON: Broadview Press, 2014) is of great interest in itself and also for its anti-Wittgensteinian analysis of the concept of a game.

Readers interested in Berkeley’s philosophy might start with George Berkeley, Principles of Human Knowledge and Three Dialogues Between Hylas and Philonous, ed. by Roger Woolhouse (Harmondsworth: Penguin Classics, 1988). Jonathan Bennett’s helpful modernization can be found at Early Modern Texts (http://www.earlymoderntexts.com/).

Readers interested in the philosophy of mathematics might start with Stewart Shapiro, Thinking about Mathematics: The Philosophy of Mathematics (New York: Oxford University Press, 2000). Philosophy of Mathematics: Selected Readings, ed. by Paul Benacerraf and Hilary Putnam, 2nd ed. (Princeton: Princeton University Press, 1983) is a classic collection of essays on this fascinating and difficult area of philosophy.

Plato’s Theaetetus is a Socratic dialogue especially focused on epistemology. The Parmenides explores the complexities of the theory of the Forms, among other things. There are excellent translations of both in Plato: Complete Works, ed. by John Cooper (Indianapolis: Hackett Publishing, 1997). Hackett also offers stand-alone translations along with informative, detailed introductions.

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