To which (or a similar question) the father of Guyal of Sfere replied: "Beauty is a luster which love bestows to guile the eye. Therefore it may be said that only when the brain is without love will the eye look and see no beauty."
My buddy Haszari—and yes, I really do know where he is sitting and whence he sees what he sees: about 30 seconds down the hallway from my office—responded to my last post with the 'beauty is in the eye of the beholder' rote, which is related to what I wrote, but is is also a non sequitur; defining, as it does, a different space of meaning altogether. His response maps more into Jack Vance's fictional response by Guyal's much-tried father.
For what beauty 'is' requires a definition—at least if we want to talk about it and understand mutually what it is we're talking about! Where it exists, if you will, may well be an entirely different question that will complete our understanding of it, but it is different entirely to the 'what'.
Thing is 'beauty', like everything else, doesn't just exist in a vacuum. It's a linguistic term and stands for something, and—yeah, I know you know that by now!—every half-decent General Semanticist will tell you, as I do, that every word describing an object or a concept requires a definition that links it to that which is points at.
The other thing is that literally everything in the conceptual universe—that is, the universe we experience cognitively—is indeed in the 'eye of beholder'. Hence the rote about beauty being there is without any significant semantic content, except in the sense that it says that 'beauty' is a concept of sorts and therefore is one of those things which is in the eye of the beholder. Big deal.
Of course, the purpose of the beauty-rote is merely to put it into a place where the concept itself becomes essentially inaccessible to any inspection outside the scope of the individual. Now, it may be true that the experience and awareness of what beauty is and does, is potentially sufficiently different between people, so that talking about it is pointless. But then...well, then there's really no point in talking about it, and why should anybody ever say to anybody else "You're beautiful!" or point at something and say "Isn't this beautiful?" unless it were not to make a statement about an actual 'property' of something—a lover, a sunrise—but merely an enumeration of instances of individually perceived 'beauty', that hopefully conveys to the person it's being conveyed to, something about what the speaker considers 'beautiful'.
But that's not what we do when we make those declarations! We presume the pre-existence of some understanding of the concept; a shared definition of sorts. 'Art' presumes such a shared definition, no matter how much 'in the eye of the beholder' it may be. The concept of 'beauty', much as the concept of 'love' is a cultural binding element, and it will serve to distinguish this culture from that one. It is a shared personal experience of some sort, which is given the name 'beauty'. While this experience when applied to certain things—like, for example, objects of 'art', or just human faces and shapes—may differ even between persons inside the same culture, there is something there nonetheless that we all sense we share. And when someone tries to define it, as that, possibly fictitious, line from Next, then we should acknowledge it for what it is. Not necessarily something complete or all-encompassing; but nonetheless and attempt to delineate the nature of something that serves to bind people together—usually in a positive way.
And, as definitions go, this one was good. Just like the reply of Gyual's father, though it kind-of avoided a direct reply; which could not be given to the question as it was obviously intended by the questioner. But at least Gyual was perceptive enough not ask what beauty 'is'. Instead he posed the question from an existentialist point of view: "Where does beauty vanish when it goes?" (This is the original quote.)
What something 'is' defines itself mostly, as some would argue—including I—by what it does or what effect it has on those objects or people it affects. And here, too, the longer I think about it, the more I actually like that definition that prompted my buddy to pen his last comment.
And look what he got in response!