1. Plato’s Republic Theory of Forms
陳斐婷 清華大學哲學研究所專任助理教授

2. Challenges to Plato’s Theory of Forms

3. 1. The Compresence of Opposites
Argument from Opposites To prove that little b and big B are not identical: little b can share in opposite properties—both ugliness and beauty—whereas big B cannot.
Challenge to Plato The Form of the Different is the same as itself, and the Form of the Same is different from other Forms. (Plato’s Sophist)

4. 2. Problem of Separation
Problem of separation The Largeness itself (i.e., the Form of Largeness) exists in the intelligible world. The largeness in us (i.e., the property of largeness that we possess) exists in the visible world.
Challenge to Plato Is the Largeness itself the same as the largeness in us? Are Forms immanent characters in sensible particulars? “But Socrates did not make the universals or definitions separate; his successors (sc. for instance, Plato), however, did separate them, and beings of this sort they called ‘Forms.’” (Aristotle’s Metaphysics M4, 1078b30-32)

5. 3. The Third Man Argument
1. If a number of things, a, b, c, are all F, there must be a single Form F-ness, in virtue of which a, b, c are all F. 2. F-ness is not identical to any of a, b, c. 3. F-ness is F. 4. Therefore, a, b, c, and F-ness are all F. 5. If a, b, c, and F-ness are all F, there must be another Form, F1-ness, in virtue of which a, b, c, and F-ness are all F. 6. And this goes on forever.

6. More about the Cave

8. Does the Cave correspond to the Line?
Clearly the cave and fire correspond to the visible world, and the world outside the cave to the realm of thought. But how detailed is the correspondence?
The state of the bound prisoners: imagination (εἰκασία) Seeing the puppets: belief (πίστις) Seeing reflections outside the cave: thought (διάνοια) Seeing the real things outside the cave: intellect (νόησις) The sun: the Form of Good

9. Does the Cave correspond to the Line?
“Firstly, While the Line stresses the passage from the world of sense to that of thought, and by making this a case of the image/original relation stresses its continuity with what happens within those worlds, the cave stresses the sharp division between them. The journey out of the Cave is unlike anything that happens in the Cave or out of it; there are, as in the Sun figure, two worlds, contrasted and not continuous. This is pointed up by the Cave’s insistence on the inexplicable nature of the conversion to enlightenment; the prisoner’s release from bonds is an unexplained intervention, not an extension of anything done before. The Line, on the other hand, presents each move to more clarity as a comprehensible example of something done before: a move from image to original.” (Annas, 254)

10. Does the Cave correspond to the Line?
Secondly, how can the prisoners be in a state of εἰκασία, as they must be if correspondence with the Line is to be maintained?
“The whole cave is an image, an extended metaphor. The shadows are literally shadows and metaphorically are any ordinary opinions about things like justice, taken over unreflectively and based on acquiescence in the way things appear rather than effort to find out how they really are.” (Annas, 256)

11. The Cave: not just the philosopher’s struggle for enlightenment
“Sun, Line and Cave are philosophically frustrating; they point us in too many directions at once.” (Annas, 256)
First, “Plato’s Cave brings out how much an individual is encouraged to make false choices, and to do things he can recognize to be unworthy of him, if he lives in a society that positively rewards false and superficial values and encourages intelligent people to make only a cynical use of their abilities. This is a point which it is easy to miss in the Cave if we are concentrating on the philosopher’s struggle for enlightenment.” (Annas, 258)

12. Impersonal nature of the knowledge of the Good
Second, “we tend to think that wisdom is built on self-knowledge, and that the beginnings of wisdom are found in facing facts about oneself. We find it natural to think that the false consciousness of the prisoners, their failure to recognize the state they are in, is due to ignorance of the ways in which their lives are deformed by the manipulations of others. They are ignorant of themselves…. [But] Plato does not think in this way. The prisoners are ignorant of their real nature and real needs, but no role at all is played in the intellectual awakening to these needs and natures by particular facts about individuals. The knowledge that the prisoners wake up to is impersonal; individual scrutiny of self plays no role at all.” (Annas, )

13. Impersonal nature of the knowledge of the Good
“Plato see no intellectual value in particular facts about particulars. The prisoner’s mysterious release from bonds is to be achieved by abstract and impersonal studies like mathematics. The ascent out of the Cave offers no personal interest or fulfillment, not even the satisfaction of having shed inauthentic roles…. The culmination of the whole journey is comprehension of the Form of the Good—and this is precisely not what is good for the seeker, or good for others, or good in relation to anything or anyone, but simply and unqualified good, in a way that is completely impersonal and indifferent between individuals.” (Annas, 259)
But why should future philosophers ever in the first place see the importance of studies of such an abstract kind, not directed to any self-promoting end?

14. Problem of the impersonal Good
“…If we recall the main argument, Socrates showed that justice was the harmonious state of a person’s soul, as part of an argument to show that justice was worth having for the person…. Reason in the soul knows what is best for all the soul’s parts, including personal aspirations and particular desires. Now we find, however, that this knowledge requires an abandonment of one’s personal concerns. The Good that is the supreme object of knowledge has nothing to do with one’s own good; it is the purely impersonal Form of Good. But how can the knowledge that produces harmony in my soul, caring for all my concerns, require me to turn away from the world I share with others and concentrate on what is simply just and good, not just or good for me? How can the knowledge developed by mathematics…make my soul harmonious?” (Annas, 260)

15. Problem of the impersonal Good
“This problem can be restated in terms of a distinction between two conceptions of what the philosopher is like. For the developments of Sun, Line, and Cave have made the philosopher’s knowledge appear to be no longer practical, but rather theoretical…” (Annas, 260)
“It is completely unclear how such knowledge [mathematics] could ever have application to matters concerning the two lower parts of the soul, which are concerned with particular and personal things…” (Annas, 262)
But knowledge is only of Forms, which requires a wholesale downgrading of our originally accepted beliefs.
These are very different ways of looking at the rule of reason. Why does Plato not see that they are very different?

16. Aristotle’s response
“The problem comes because Plato is being over-ambitious and treats two very different things as parts of a single project.” (Annas, 265)
Aristotle reacts sharply against Plato in a way we find sympathetic (Nicomachean Ethics Book 6); he clearly distinguishes practical reasoning from theoretical, and insists that a person outstanding in one may be undistinguished in the other. Theoretical reasoning concerns universals, whereas action and practical choice are inevitably conerned with particulars.

17. The Guardians’ progress is the journey out of the Cave
“It is in terms of the distinction between the practical and contemplative conceptions of the philosopher, and his assimilation of them, that we can best understand a famous problem [sc. why the philosophers should return to the Cave] that besets Plato in the Republic. The Guardians’ progress is the journey out of the Cave; so if they are to rule others they must leave the studies that they excel in and find pleasant and rewarding, and go back down in to the Cave.” (Annas, 266)

18. Why should the philosophers return to the Cave?
The philosophers owe it to the city for their privileged upbringing (520a-c); rulers who don’t want to rule are better than those who do (520d).
“The real ground is stated at 519e-520a, and is repeated at 520e in the claim that we are making a ‘just order to just people.’ The Guardians know what is just because they have the knowledge that is based on the Form of Good. Their return is demanded by the justice that prescribes disinterestedly what is best for all (519e-520a). The do not go down because it is better them; they would be happier and better off doing philosophy. … They go down because they realize that that is best—simply best, not best for any particular group of people. ” (Annas, )

19. Why should the philosophers return to the Cave?
“They are not seeking their own happiness. … They take a wholly impersonal attitude to their own happiness, along with everybody else’s; and this is because their judgments are made in the light of the impersonal Good, the separated Form which is what is simply good, not good relative to anything. They can act in the light of what justice requires because they can detach themselves from their own personal standpoint; for they have experienced the enlightenment which the Cave portrayed as a turning away from one’s own personal concerns towards the light of abstract studies and the separated Forms.” (Annas, 267)

20. Conflict between the impersonal Good and the agent-centered theory of justice
But why should I, as a philosopher, do what justice requires?
“The Republic began from the inadequacy of act-centered theories, which presented justice as a set of arbitrary and external demands. The discussion of the state, and of the soul’s parts and virtues, allowed Plato to show that justice is not this, but is a state of the person that is clearly in their interests, because it is the condition for psychic health and unity. But the central books seem to have undermined this claim, by showing that the knowledge required to be just is knowledge of what is impersonally just. … However, Plato made Socrates accept the strongest form of Glaucon’s challenge: show me that it is in my interests really to be…just.” (Annas, 267)

21. Conflict between the impersonal Good and the agent-centered theory of justice
Solution? Many scholars try to rescue Plato from this problem by pointing out that the Guardians themselves do not perceive the requirements of justice as conflicting with their interests, and so they can think of their own happiness impersonally and accept without resentment its sacrifice to the requirements of impersonal goodness. They do not see the sacrifice of going down into the Cave as a real sacrifice, really against their interests.
Problem of the above solution This only raises the question, why in that case I should want to be a Guardian or a philosopher? Why ever should it be in my interests to want to do that?

22. Conflict between the impersonal Good and the agent-centered theory of justice
If the philosophers suffer real loss, then then justice is not their own interests, and Plato set out to show that justice was in the agent’s interests.
If the philosophers do not suffer real loss, then justice seems to demand an ideal, impersonal viewpoint which it is not in the interests of any actual people to adopt. “We thought that Plato’s account had the virtue of taking seriously the claims of justice on us as we are; now justice demands that we positively stop being human. The more the Guadians’ justice requires that they conform their own viewpoints to that of impersonal reason and impersonal goodness, the more any actual person is driven to ask why…there is any reason for him, or her, to be just.” (Annas, )

23. Summary of problems of the Cave
Does the Cave correspond to the Line?
Impersonal nature of the knowledge of the Good
Problem of the impersonal Good
Why should the philosophers return to the Cave?
Conflict between the impersonal Good and the agent-centered theory of justice

24. Philosophy, dialectic, and mathematics

25. The propaedeutic studies
The Guardians’ knowledge (a) arithmetic 521d-526c (b) plane geometry 526c-528b (c) solid geometry 528b-e (d) astronomy 528e-530d (e) harmonics 530d-531c
Why does knowledge of goodness need to be developed through mathematics? (next week)
Dialectic 532d-535a (next week)
The Guardians are not to begin studying philosophy at once, since this would have destructive effects (537e-539d) if it is begun too young : old truth are thrown out with nothing to replace them.

26. Plato’s “hypothetico-deductive” approach
Some concepts provoke the mind into recognizing Forms, and among these is that of oneness or unity. “Plato is here treating ‘one’ as a predicate that applies to its object in the same way as ‘long’ or ‘thick.’” (Annas, 273) But this makes these units look rather like Forms then things between Forms and particular things.
Plato’s insistence on a purely mathematical approach to studies like astronomy and harmonics has often led him to accusations that he is “anti-scientific” (530b-d). But what is usually meant is that he is anti-empiricist, and more precisely anti-inductive.
Modern scientific approach: look at the facts of experience and inductively work out hypotheses to explain them.
Plato’s “hypothetico-deductive” approach: putting forward a hypothesis and then testing its application to observed facts.