You cannot prove an aesthetic proposition. Ergo, all propositions regarding beauty, its definition, its criteria, and its essence are subjective; that is, a matter of opinion (what Locke would call an "indifferent matter"). This position is implicit in the latin motto, De gustibus non est disputandum.
According to Wikipedia, "De
gustibus non est disputandum is a Latin maxim meaning 'In matters of
taste, there can be no disputes' (literally, 'There is no disputing of
This agrees with what Locke means by indifferent matters.
And hence also the notion from analytic philosophy that logic cannot prove aesthetic propositions.
Of course, things become controversial when this exclusion is applied to moral, internal, and external/empirical propositions. As I suggest to my students, propositions that are not analytic* and therefore cannot be proven with logic are matters of politics and poetic speculation. They are not the material of philosophy, but of myth.
Consider Frank Zappa's mythological elaborations, presented as audio extrapolations, in the following propositions:
1) Beauty is a Lie
2) Beauty is a French
Of a short cloth
Elsewhere, however, Zappa
suggests that beauty (or some thing we might call "beauty") can be
achieved in a composition by likening the composition to a mobile, and
subjecting it to the physical rules which govern mobile construction.
Under this paradigm, the components of a composition should move around
and balance like the arms and weights of a turning mobile.
* "A triangle has three sides" is an analytic proposition. It can be proven with logic and hence is a proper matter for philosophical discussion. Of course, this relegates philosophy to the examination of some pretty mundane subjects; ergo, to kill time between arguing over analytic propositions, analytic philosophers can occupy themselves explaining to students why philosophers have nothing to contribute to our understanding of moral, internal, external/empirical, and aesthetic propositions--the point of departure, incidentally, for all highbrow activity. Non est ad astra mollis e terris via.