Goodness And Beauty In Plato

In the first part of this paper I argue that beauty and goodness are at least coextensive for Plato. That means that at least with respect to concrete particulars, everything that is good is beautiful and everything that is beautiful is good. Though the good and the beautiful are coextensive, there is evidence that they are not identical. In the second part of the paper I show significance of this relation. In ethics it implies that the good is the right. It also allows one to see how platonists can believe that goodness exists in mathematics. And it explains the usefulness of mathematics in moral education.


Introduction
In this paper I would like to explore the relation between goodness (to agathon) and beauty (to kalon) in Plato. In the first place it will be argued that the evidence suggests that at the very least Plato believed there was a biconditional relation between goodness and beauty. That is, everything that is beautiful is good and everything that is good is beautiful. However, the evidence concerning the relation between beauty and goodness almost always has to do with concrete particulars, as opposed to Forms. In other words, it is almost always the case that where Plato speaks about the relation between beauty and goodness he is speaking about concrete particulars, whether these be particulars. Of course, what we would perhaps most like to know is how beauty and goodness are related at the level of the Forms. In particular we would like to know whether there are two Forms or one, i.e. whether the Form of the Good is the same as the Form of the Beautiful. Unfortunately, Plato says next to nothing about this, and thus the most we can do is speculate about the relation of the Forms.
In the final analysis, I will argue that the evidence suggests that there are two Forms, and that the Form of the Good is distinct from the Form of the Beautiful. However, it seems that this was not at all a major concern of Plato and that he was much more concerned to show the closeness, if not virtual identity, between beauty and goodness, than he was to explore the question concerning the identity or difference between their Forms.
But, having shown the biconditional relation between beauty and goodness in Plato, the question becomes, what are we to make of this? What are the consequences of this for Plato's thought? I want to argue that this fact has consequences for two areas of Plato's thought: ethics and mathematics. As it does for Aristotle, to kalon for Plato has above all to do with mathematics and mathematical concepts.
The consequences of this for Plato's ethics turns out to be that goodness in ethics has to do with the instantiation of mathematical concepts such as measure and proportion. To be ethically good is to instantiate such things as equality, moderation, and due proportion in one's actions. On the other hand, the coextension of beauty and goodness resulted for Plato in the collocation of goodness in mathematics as well. Because beauty exists in mathematics, and everything that is beautiful is good for Plato, it seems he concluded that goodness exists in mathematics as well.
In this respect, as in so many others, it is instructive to compare Aristotle's views with those of Plato. At Metaphysics M, Aristotle explains he understanding of the relation between beauty and goodness. At 1078a31 he states, Now since the good and beautiful are different (for the former is always in action, while the beautiful is found also in motionless things), those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a very great deal about them; for it is not the case that if they do not name them but prove their results and accounts, that they do not speak about them. The chief forms of beauty are order, proportion, and definiteness, which the mathematical sciences demonstrate most of all. And since these (e.g. order and definiteness) are causes of many things, evidently they mean that such a cause as the beautiful is a cause in a way. But we shall speak more plainly elsewhere about these matters. 1 Setting aside many of the intriguing questions about this passage, 2 we can at least see that In this paper, then, I will argue that Plato and Aristotle had remarkably similar understandings of beauty (to kalon), but this passage from Aristotle shows that they differed in their understanding of goodness. For Aristotle goodness, as the final cause, always has to imply some sort of desire, but this seems not to have been true all the time for Plato.

Coextension
In this section we will try to show that Plato believes a biconditional relation holds between beauty and goodness at least at the level of con- good, followed by evidence which directly supports a biconditional relation.
But first a word about these terms biconditional and coextensive. For the purposes of this essay I take these terms to imply the same thing.
In other words, to say that there is a biconditional relation between beauty and goodness is to say both A. If something is good then it is beautiful, and B.
If something is beautiful then it is good. This is the same as to say that beauty and goodness are coextensive. That is, everything which falls under the extension of goodness falls under the extension of beauty and vice versa. Notice that neither of these imply that goodness and beauty and identical. If two objects are essentially identical, then they must have the same extension. But it is not the case that if two objects are coextensive, they are essentially or "intensionally" identical-intensional identity being taken as the linguistic correlate of essential identity.
To borrow an example from Quine, whatever has a heart has a kidney, but it is not the case that having a heart is essentially the same as having a kidney.
Several texts indicate Plato thinks everything good is also beautiful. The first is at Symposium 200a-201b where Socrates tries to prove to Agathon that Love is neither beautiful nor good. In order to prove that Love is not good, Socrates asks Agathon, "Don't good things also seem beautiful to you (τἀγαθὰ οὐ καὶ καλὰ δοκεῖ σοι εἶναι; 201c)?" Agathon agrees, and Socrates goes on to argue that if Love needs and desires beautiful things and good things are beautiful, then Love will need and desire good things, and therefore Love cannot be good either (201c). If we can take Socrates' question here as evidence of his own belief then this would support the view that Plato believes that what is good must also be beautiful.
The next text is from the Timaeus. When Timaeus turns to the care of body and mind, he states, "Now all that is good is beautiful, and what is beautiful is not ill-proportioned (πᾶν δὴ τὸ ἀγαθὸν καλόν, τὸ δὲ καλὸν οὐκ ἄμετρον: 87c Here Socrates uses the hidden assumption that whatever is beautiful cannot be harmful. The implication is that whatever is beautiful is beneficial and therefore, given our aforementioned connection between benefit and goodness, whatever is beautiful is also good.

Evidence for a Biconditional Relationship between Goodness and Beauty: Hippias Major 297b-c.
In the Hippias Major, during the refutation of the beneficial as a possible answer to the question "What is beauty?" Socrates presents strong evidence of a biconditional relation between goodness and beauty. The argument is that if the beautiful is the beneficial then the beautiful is not good and the good is not beautiful. It is taken as obviously absurd to say that the good is not beautiful and the beautiful is not good, and therefore the beautiful cannot be the beneficial. But if it is obviously absurd to say that the good is not beautiful and the beautiful is not good then the correct belief must be that what is good is beautiful and what is beautiful is good.
The argument against this is as follows: The beneficial is the maker (τὸ ποιοῦν) of the good (296e). As such, it is the cause (αἴτιον) of the good. But the effect of a cause insofar as it is an effect, is an effect, not a cause. Therefore, since the beneficial is the maker and cause of the good, it must differ from the good. And this conclusion is unacceptable to both interlocutors. The conclusion of the argument is: good and the good is beautiful. And this is the biconditional thesis.

Evidence for a Difference between the Goodness and Beauty in Plato
It was said at the beginning that while a good deal of evidence seems to support the view that Plato thinks goodness and beauty are coextensive (at least at the level of concrete objects), it is probably unsafe to infer from this that therefore Plato

Significance of beauty in Ethics:
The Good is the Right.
Let us now try to see the significance of the biconditional thesis in ethical contexts, and in the next section we will look at its significance in mathematical contexts. In order to see how the biconditional thesis plays out in the ethical context we must return to our earlier stated claim that to kalon refers to a sort of essential rightness.
We may, perhaps, see this most clearly in the claims of the earlier poets to see death in battle as somehow paradigmatically beautiful. So, in the  474c-d, rev.). 31 What we see here is how in the Greek mind the beautiful was so easily separated from any sense of benefit, and yet it was still held to be laudatory in some sense. It was Plato's project then to argue that this beauty, which marked essential rightness, was in fact the most beneficial thing for the agent.

Significance of Beauty in Mathematics: Goodness in Mathematics
The second effect or result of the bicondi-  But knowing what we now know about the relation between goodness, beauty, and mathematics in Plato's thought, we may now suggest an answer.

Mathematics in Ethics
Socrates may be thinking that if Callicles, or anyone else studied geometry and mathematics, they could not help seeing the beauty in it. And this sort of beauty is real beauty for Plato, this is the true food and nourishment of the mind. Once Callicles saw this real beauty, he would make the pursuit of truth his real goal and no longer be interested in getting the greater share of material goods. In addition to this, Callicles might wish to imitate the beauty he saw in mathematics, and instantiate that beauty into his actions. Plato's thought might be that to instantiate this beauty into one's soul and actions is to be become truly good and happy.

Conclusion
In this paper I have argued, first, that 'beautiful' is at least as good as any other translation of kalos. Secondly, I have argued that this beauty seems to supervene, for Plato, on a notion of es- sential rightness, whereas his sense of goodness has more to do with benefit. We then moved on to try to show that while there is evidence that the Forms of beauty and goodness were distinct, still it seemed that there was a great deal of evidence that beauty and goodness were coextensive, at least at the level of sensible particulars. The consequences of this thesis in Plato's ethics is that he seems to assimilate goodness to beauty, more than the other way around, that is, he seems to start with the accepted understanding of beauty and argue that that is what constitutes human goodness.
In mathematics, this thesis showed the way in which Plato or platonists could have thought that goodness exists in mathematics. Since beauty and goodness are coextensive, and since beauty clearly exists in mathematics most of all, it would follow that goodness must exist in mathematics as well.