Socrates reveals his problem
Socrates is happy that Hippias came to reminisce on beautiful things, because this is a subject that interests Socrates greatly and with good reason. Recently, according to the latter, while criticising the beauty or ugliness of part of speeches, he claims to have been harassed by an acquaintance, who reproached him for not really knowing the definition of beauty.
Thus embarrassed by this exposure, Socrates claims to be delighted that finally one as competent as Hippias will be able to provide his opinion on the nature of beauty. The great Sophist, flattered, does not object; and is goaded on by Socrates, who offers to reprise the discussion, playing the part of the harasser. This role-play on the part of Socrates adds to the comic nature of dialogue, by allowing him to address and mock Hippias in ways which otherwise would not have been acceptable.
Hippias's three responses
First definition: beauty is a pretty girl. Hippias by his first response shows that he understood nothing of the needs of his interlocutor: "For be assured, Socrates, if I must speak the truth, a beautiful maiden is beautiful." (287e). Socrates estimates this to be, with his usual irony, a brilliant answer. But cannot they say that a lyre, a horse or even a pot is beautiful? The most beautiful of pots of course would not stand up to comparison with a beautiful girl, but then in turn what is the beauty of a girl in comparison to that of a goddess?In short, there is an infinite number of beautiful things besides beautiful girls. In any case, this is not really the question; it is not a question of knowing what is beautiful and what isn't, but rather to define beauty and to say what makes beautiful things "beautiful".
Second definition: beauty is gold. The second response offered by Hippias is not much more inspired: "This that you ask about, the beautiful, is nothing else but gold... For we all know, I fancy, that wherever this is added, even what before appears ugly will appear beautiful when adorned with gold."(289e)No doubt, replies Socrates, but what to make then of the great statue of Athena at the Parthenon? This masterpiece of Phidias is mostly made of ivory and precious stones, and not of gold. Yet the statue is magnificent. Besides, gold any other precious metal only gives rise to beauty if it is properly used. In the case of the pot, for instance, who is to say whether a wooden spoon or a golden spoon would be better to stir with, or which would be more beautiful?
Third definition: beauty is to be rich and respected. This time Hippias thinks that he understands: Socrates wants to know what no man will ever find ugly. But once again his conclusion disappoints: "I say, then, that for every man and everywhere it is most beautiful to be rich and healthy, and honoured by the Greeks, to reach old age, and, after providing a beautiful funeral for his deceased parents, to be beautifully and splendidly buried by his own offspring." (291d-e)A very comic scene follows, where Socrates shows his fear of the beating with a stick he would receive from his harasser if he had given that answer. What then of Achilles or Heracles? Was it beautiful for these two heroes, sons of the immortals, to be buried before their parents, before the gods? Was there no beauty in their lives because they were not buried by their offspring? Beauty in this sense then applies to ordinary men, but it would be ugliness for heroes. The definition is thus incorrect.
Socrates's three responses
First definition: beauty is that which is appropriate. Tiring of the errors of Hippias, Socrates offers a definition in his turn, which he holds came from his famous harasser: the beautiful is simply that which is appropriate. This response pleases Hippias. But further examination is needed: first of all, is it the appropriateness which makes things beautiful, or does it simply make them appear to be beautiful? The second hypothesis is tempting: even a ridiculous man, dressed in nice clothing, will appear more beautiful. But inside he would still be ridiculous; thus appropriate and beautiful are not the same. Hippias suggests that appropriateness provides at the same time the reality and the appearance of beauty. But then, nothing could be less sure; if everything was that simple, citizens and politicians would no longer have to quarrel to decide which action was the nicer.
Second definition: beauty is that which is useful. For a second time, Socrates proposes a solution: if it is beautiful, is it useful?
But here again problems surface: it is through power that men make things useful. Nevertheless, as is well known, power can as much serve evil as it serves good. And there is difficulty in qualifying actions as bad or good. Which in turn requires that the definition be refocused; beauty is only usefulness applied to good ends, or those that are "favourable". Identifying the beautiful and the favourable leads to a paradox: the favourable procreates the beautiful, as a father procreates a son. Since the favourable and the beautiful are thus considered to be one and the same, they arrive at the finding that beauty is the reason of goodness. In logic, a cause and an effect are two different things, as a father is different from the son. And thus they must conclude that Beauty is not good, and good is not beauty; an assertion which pleases neither Socrates nor Hippias.
Third definition: beauty is the pleasure that comes from seeing and hearing. To conclude, Socrates brings out a final definition; at first glance quite amazing: "[what] if we were to say that that is beautiful which makes us feel joy; I do not mean all pleasures, but that which makes us feel joy through hearing and sight?" This hypothesis, while appealing, contains according to Socrates himself a fundamental flaw; that it ignores the beauty of the more noble pleasures, drawn from the studious occupations or the study of laws. On the other hand, it seems striking that only the senses of sight and hearing are taken into account. Is this a way to submit to common opinion, which is that touch, taste and smell are somehow more shameful and base than the other senses? Finally, it is not simply because pleasure comes from seeing or hearing that it is beautiful. Socrates throws himself into a series of very complex considerations: taking into account pairs of objects, in the Majority of cases the term which they apply to both objects (A and B are beautiful, A and B are just) can apply also to an object taken separately (A is beautiful and B is beautiful). But in some rare cases it can happen that it this is not the case, notably when the sum of A and B forms an even number and A and B, taken in isolation, are two odd numbers. In the case of beauty, it is the first category that is appropriate, because if a pair of two objects is beautiful, it stands to reason that each of them is. But a new paradox appears, since the beautiful, in discreet definition, must belong to both pleasures of sight and hearing, taken jointly, and cannot belong to only one of them. The definition, as a result, proves to be flawed.
Exhausted by the many ultimately useless subtleties they have considered, Hippias berates Socrates and urges him instead of "with mere talk and nonsense" to seek beauty in "the ability to produce a discourse well and beautifully in a court of law or a council-house or before any other public body before which the discourse may be delivered."
Socrates, taking his leave, pretends to feel bad about the situation, cornered between the attacks of Hippias and those of his mysterious opponent. His only certainty, he concludes with a sense of humour, is that from now on he better understands the Greek proverb "beautiful things are difficult"
Literary and philosophical impact
It may strike the reader as surprising that the definition identifying the beautiful the useful is refuted, given that this corresponds quite well with the historical view of Socrates. But as in Charmides, Lysis and Euthyphro, Hippias Major has an "anatreptic" or self-defeating virtue, that is the purpose of the author is to defeat commonly held opinions, without necessarily offering a resolution, something which is saved for subsequent texts (in a sense, the philosophical equivalent of a cliffhanger).
In terms of philosophical development, Hippias Major is not much more advanced that the other early dialogues. The concept of "Good in and of itself", although only obliquely, makes its first appearance in this work. Nevertheless platonic thought is not yet fully developed: there is, for instance, no trace of the concept of "reminiscence" enunciated in "Meno" and "Phaedrus", where souls acquire the knowledge of the concept of "Beautiful" and "Good" in the course of their wanderings in the afterlife.
It is on the literary