PLATO (428-348 BCE)

Precondition for beauty: proportions among constituent parts

Timeaus 87cd

Everything that is good is fair, and the fair is not without proportion...the due proportion of mind and body is the fairest and loveliest of all. ... he who is careful to fashion the body, should in turn impart to the soul its proper motions, and should cultivate music and all philosophy, if he would deserve to be called truly fair and truly good. And the separate parts should be treated in the same manner, in imitation of the pattern of the universe.

Timeaus 32c

G-d placed water and air in the mean between fire and earth, and made them to have the same proportion so far as was possible (as fire is to air so is air to water, and as air is to water so is water to earth); and thus he bound and put together a visible and tangible heaven. And for these reasons and out of such elements which are in number four, the body of the world was created, and it was harmonized by proportion, and therefore has the spirit of friendship.

Philebus 64e

Socrates: There is no difficulty in seeing the cause which renders any mixture either of the highest value or of none at all.

Protarchus: What do you mean?

...

Soc.: He knows that any want of measure and symmetry in any mixture whatever must always of necessity be fatal, both to the elements and to the mixture, which is then not a mixture, but only a confused medley which brings confusion on the possessor of it. ..And now the power of the good has retired into the region of the beautiful; for measure and symmetry are beauty and virtue all the world over.

Philebus 66ab (summation)

Socrates: Then, Protarchus, you will proclaim everywhere...that pleasure is not the first of possessions, nor yet the second, but that in measure, and the mean, and the suitable, and the like, the eternal nature has been found...In the second class is contained the symmetrical and beautiful and perfect...

Philebus 51d (regarding beauty)

Protarchus: Once more, Socrates, I must ask what you mean.

Socrates: My meaning is certainly not obvious, and I will endeavour to be plainer. I do not mean by beauty of form such beauty as that of animals or pictures...but...understand me to mean straight lines and circles, and the plane or solid figures which are formed out of them...for these I affirm to be not only relatively beautiful, like other things, but they are eternally and absolutely beautiful...When sounds are smooth and clear, and have a single pure tone, then I mean to say that they are not relatively but absolutely beautiful and have natural pleasures associated with them.

Symposium, 187a

Anyone who pays the least attention to the subject will also perceive that in music there is the same reconciliation of opposites; and I suppose that this must have been the meaning of Heracleitus...for he says that The One is united by disunion, like the harmony of the bow and the lyre. Now there is an absurdity in saying that harmony is discord or is composed of elements which are still in a state of discord. But what he probably meant was that harmony is composed of different notes of higher or lower pitch which disagreed once, but are now reconciled by the art of music; for if the higher and lower notes still disagreed, there could be no harmony... For harmony is a symphony, and symphony is an agreement...