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A. Knowledge vs. Belief

• Background: the over-arching theme of the Republic is the search for a proper understanding of justice (“morality” in our translation). This leads to many other topics, such as an attempt to define justice, temperance, courage, and wisdom (the four “cardinal virtues”) and a discussion of the ideal political order. We pick up the discussion toward the end of Book V, where Socrates claims that in the ideal political order philosophers will be kings or kings will be philosophers (473c-d).
  
• That raises the question: what is a philosopher? The obvious answer is that he is someone who loves the whole of knowledge (475b). But then how is a philosopher different from an avid theatre-goer, or anyone else driven by curiosity? Socrates’ answer is that the merely curious never get beyond the level of the sensible objects in front of them; they are unable to “approach Beauty Itself and see Beauty as it actually is” (476b). Consequently they mistake semblance for reality, like people living in a dream; they have only belief (doxa) whereas one who apprehends the Forms has knowledge (476c-d).
  
• Here Socrates is correlating the distinction between knowledge and true belief in the Meno with that between the Forms and sensible objects in the Phaedo. The rest of Book V explains his reasoning in more detail. Here are the key steps:
  
• Knowledge must be of “what is” or “being” (to on) (476e). Note: the translation “something real” is misleading. It assumes that Plato is using the existential sense of “to be,” whereas the context (esp. 479b) makes it clear that he is using the predicative or veridical sense. (Cf. the notes on Parmenides.) This is important, for the book’s translation makes what he is saying seem less plausible than it really is.
  
• Therefore, “what is not” or “non-being” (to me on) is “entirely inaccessible to knowledge” (477a). It is the proper object or “field” of incomprehension (478c).
  
• Besides the faculty of knowledge there is also the faculty of belief (doxa). But different faculties must have different objects (478a). Since belief is intermediate between knowledge and incomprehension, its object must be intermediate between being and non-being.
  
• Does anything fit that description? Yes: sensible objects. As explained in the Phaedo, no sensible object is ever fully and completely—i.e., in all respects, to all observers, at all times—beautiful or ugly, just or unjust, double or half, large or small. Therefore sensible objects both are and are not. They “mill around somewhere between unreality and perfect reality” (479d).
  
• It follows that one whose attention is limited to sensible objects has only belief, not knowledge. He is a “lover of belief,” whereas a philosopher—a lover of wisdom—is one whose attention is fixed on being (480a). Cf. the statement of the Symposium (204b) that Eros is a philosopher!
  

  B. The Myth of the Sun

• What is the Good (not “goodness”)? Some identify it with knowledge—but when pressed they say it is knowledge of the Good, which is circular (505c-d). Others say it is pleasure, but this is refuted by the fact that there are bad pleasures (505c).
  
• The best general description is that the Good is that which “everyone, whatever their temperament, is after, and which is the goal of all their activities” (505d). But this tells us very little.
  
• Socrates does not claim to be able to say what the Good itself is, but he does offer to describe its child (506d-e). This child is the sun. The Good begot the sun as a kind of counterpart (analogon) to itself in the visible world (508b). There are two main points of similarity:
  
  1. The sun is the source of light and thereby confers upon the eye the ability to see. In the same way, the Good is the source of truth and being (to on) and thereby confers upon the mind the capacity for knowledge. (508b-d)
     
  2. The sun is the source of generation, growth, and nourishment in the visible world. In the same way, the Good is the source of reality (to einai) and being (ousia) in the intelligible world. (509b-c)
     
• Why does the Good have this unique role? Why not, for example, Beauty or Justice?
  
• Regarding (1), the answer goes back to the argument in the Phaedo that to understand something fully one must understand how it is for the best. That is why things apprehended apart from the Good are seen as if in twilight, and can be the objects only of belief rather than knowledge (508d).
  
• Intelligibility is closely linked to reality, especially in the “intelligible world.” So to some extent (1) explains (2). Cf. the elementary fact that we often regard something that is especially good as especially real; e.g., we say of an especially exciting and well-played game that it was a real game.
• Cf. the following: ‘Knowing an object as an instance of X-ness, as an image of the idea of X, requires us to know what an X ought to be as well as what the various X’s happen to be. Such knowledge would depend on our ability to perceive the Idea of X in its necessary relation to the Idea of the Good . . .’ (David Melling, Understanding Plato, p. 102). The point is that Forms are not abstractive descriptions of the way things actually are, but norms of ideal order; therefore they derive their intelligibility from their connection to the Good.
  
• Since the Good is the source of knowledge and truth, it is beyond them in value and dignity (508e-509a). Likewise, since it is the source of being it is itself “beyond being” (epekeina tes ousias) (509b). This is a fateful saying that will have a profound influence on both pagan Neoplatonism and Jewish, Christian, & Islamic philosophy.
  

  C. The Myth of the Line

• The Line both summarizes what was said in Book V and adds some powerful new ideas. One of its purposes is to drive home the deficiencies of thinking at each level as compared to those above it. For example, suppose your only knowledge of spheres were through viewing their shadows and reflections (level A). You would have some understanding of spheres, but it would be very defective. Much better would be to view the spheres themselves (level B); even then, however, you would not know the definition of a sphere or what mathematical principles determine its characteristics. To do so requires the kind of discursive thought (dianoia) represented by level C. Best of all would be just to “see,” without proofs or exercises, how the properties of a sphere follow from the fundamental axioms of geometry. That is the immediate intuitive knowledge (noesis, from the same root as nous) represented by level D.
  
• Alongside the distinction among different types of thought there is a corresponding distinction among the objects of each type of thought. (See the diagram on p. 271.) Some points to note:
  • Region C is not a separate realm of “mathematical objects.” It is composed of ordinary visible objects (the same as in Region B) taken in a special way—namely, as likenesses of something higher (510b). An example is the way a mathematician takes a particular triangle drawn on the board, which in itself is a physical object, as a diagram representing all triangles (510d-511a).
    
  • Socrates explains later that the segments of the line are in mathematical proportion (534a). The ratio of A to B also holds between C and D and (A+B) and (C+D). This symbolizes the fact that the relation of A to B—i.e., of image to archetype—is also the relation of C to D and of A+B (the entire visible realm) to C+D (the entire intelligible realm).
    
  • Thus, the Myth of the Line is the first clear statement of an important claim: sensible objects are images of the Forms. We will return to this point in the Timaeus.
    
  • Finally, Socrates adds that the intelligible realm is the realm of “Being” whereas the sensible realm is the realm of “Becoming” (534a). These terms are first introduced during the Myth of the Cave (518c). They do not imply that the main defect of the sensible realm as compared to the intelligible realm is the fact that it undergoes change. Undergoing change is just one aspect of the general fact that sensible objects both “are” and “are not.”
    

  D. The Myth of the Cave

• The Myth of the Cave is a vivid summary of all that has been said so far. One caution: the Cave and the Line do not match quite as neatly as the diagram on p. 274 suggests. In particular, the shadows in the cave correspond, not to images in the sensible world, but to sensible objects (region B of the Line). Apparently the objects higher up in the cave that cast the shadows do not match anything on the Line.
  
• Why are they included? Simply because Plato wants to drive home the point that our ordinary knowledge of sensible objects is a knowledge of shadows. The Phaedo has already argued that physical science does not provide full understanding or penetrate to the essence of things. Now Plato takes this further to assert that most so-called expertise really deals only with appearance rather than reality.
  
• The contrast of Being and Becoming also has a moral dimension. Plato has already suggested that to be fixated on sensible objects is a kind of false love (Republic V) and degrades and contaminates the soul (Phaedo). Now he adds that it as a form of imprisonment. To turn away from sensible objects and toward the intelligible realm is an act of liberation. That explains why it is painful and may not always be welcome; we have grown accustomed to our chains!
• To achieve this liberation requires the conversion of the soul, i.e., a turning of the focus of one’s life away from one direction and toward another. Hence Plato has a distinctive conception of education. Education is not the introduction of knowledge into the soul; rather, it is the attempt to turn the innate faculty of understanding away from Becoming and toward Being (518b-d).
  
• Note the role that habits and early upbringing play in this process. Socrates says that education should begin by “knocking off” at an early age “the inevitable consequences of incarnation” (519a-b). Presumably he has in mind teaching the child habits of self-discipline and self-denial. Aristotle will make a similar point in Book II of the Nicomachean Ethics.
  
• Finally, note the role of the Good (i.e., the sun in the world beyond the cave). Socrates says explicitly that one who has escaped from the cave will eventually be able to behold the Good (516b). Thus, although the Good is beyond our present understanding, it is not intrinsically unintelligible to the human mind. This is one point on which Neoplatonists such as Plotinus will differ from Plato.
  

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