See my first two posts on beauty as introduction to the question: Is beauty objective? and attempting to define our goal in aesthetics.
Here I shall endeavor a slightly different approach: metaphysics.
Classical ontology (the study of being) can be divided into three branches.*'
1. The study of "being as being," that is, not studying the shape or size or color or function of the keyboard I am typing on, but studying the simple existence of the keyboard itself. This study asks, "What makes it something rather than nothing?"
2. The study of general principles of being, "general features that are true of all things whatsoever. "Medieval philosophers characterize all the different transcendentals to stand for all those features that characterize all the different kinds of entities that exist. The notions of existence, unity, truth and goodness have been taken by some to be examples a transcendental. Everything that is, say a carbon atom, a person, a number or a property of being green, is such that it exists, is a unity (i.e., is one entity in some sense), and is true and good." *''
3. The study of the fundamental categories or 'kinds' of existing things that all other particular existing things fall into. What are the fundamental categories? Persons? Substances? Properties? Physical massive objects? This is different from the study of transcendentals in that an existing thing, say attributes, may or may not be a substance, may or may not be a relation, may not be a physical massive object, but it still must exemplify the transcendentals of unity, existence, goodness etc.
*I here draw from JP Moreland in the Philosophical Foundations...
Why Transcendentals Still Matter
Invoking transcendentals to explain existing things has fallen somewhat out of fashion, but the force of the simple argument remains strong. All things have unity, or are unities. Even to say "a thing is not a unity" linguistically presupposes that we know what we mean by "thing," and we know that it is one, ie it is not "things" nor is it "no-thing." What is unity, then? Is it a property like other properties? If so, how does it come to be so universally predicated? Whether we resort to the classical posit of transcendentals, the empirical observable fact of unity demands an explanation.
Drawing from tradition, there are three major transcendentals that tend to stick together in a group: goodness, truth, and beauty. That is, everything that exists, has some share of all three, by virtue of its existence. Though this schema may sound unfamiliar to the modern mind, it has immense explanatory power and the advocacy of many centuries of intelligent thinkers. Ancient, medieval, and modern thinkers make use of this scheme. Immanuel Kant, to take one modern instance, takes these three transcendentals as his touch-point in three major works of philosophy Critique of Pure Reason, Grounding for Metaphysics of Morals, Observations on the Feeling of the Beautiful and Sublime, etc.
If Beauty is Real, Why Is It So Hard to Identify?
This dual-hypothesis (the existence of transcendentals in general and beauty in particular) helps us to address one of the primary complaints against the notion that beauty is real and objective and knowable and communicable. Namely, the difficulty (impossibility?) of answering the question, "Is object x beautiful or not?"
For instance, one of the ways we know truth is real and objective is that it is possible to find propositions, mathematical equations, and so on about which we can answer the question "Is this true or not?" 3x3=9 is a true statement. "The sky is blue during the day most of the time in most parts of the world" is true. "The sky is never pink" is false.
Further, one of the ways we can know goodness is objective is to find actions that are morally good (as well as objects that are good in a more general sense.) Giving money to the financially less fortunate is (in most cases) morally good. The sun is more generally a good thing, for the earth and for all life on the earth. These are, I hope, not very controversial statements.
Does the precedent hold for beauty? Surely there are some objects that are uncontroversial beautiful... Niagra falls, the Grand Canyon, a simple rose. None but the agenda-driven skeptic cares to assert that these objects are not-beautiful, though they may want to call them 'not certainly beautiful.' No one, that I have met, cares to assert even for the sake of argument, that they are ugly. But why can't we ground the intuition that the Grand Canyon is "beautiful"? We cannot seem to describe clearly something beautiful in contradistinction to something we do not generally intuit as beautiful, such as a rat, a clod of dirt, a basic oscillating fan. Therefore, the argument goes, beauty is probably not (or if it is real, it is not knowable.)
The above argument seems to hold only if we consider 'beauty' to be a property that is contrarily either had or not had by things. If, however, it is a transcendental as classically understood, this both accounts for the fact that we think some things actually are beautiful and for the fact that "nailing down" this property is difficult. Why? Because beauty is not the kind of thing that is either had or not had, like roundness or whiteness. Rather, it is had by everything to some extent or another, like existence or unity.
Beauty as a Transcendental
Like any other transcendental, beauty is predicable of every existing entity. Roses are not only beautiful, but they exist, and exist as a unity. Chairs likewise are unities, have existence, and have some predication of beauty, and so on.
This produces a set of new conundrums, but solves the basic problem of the seeming slippery identity of beauty.
For instance, is a dead rat beautiful? The answer must be a qualified "yes," in the sense that a dead rat has a greater share of beauty than, say, a dead and decaying horse... (For the sake of propriety we shall not continue further in that direction.) But a dead rat has far less a share of beauty than a living animal, which has less a share than a human being. Someone might jump in and ask, "Which humans are the most beautiful?" This is an interesting question, but so specified that it should wait until we have established more securely the thesis that beauty is a transcendental (and that answering such questions is (in theory) possible!) With beauty as a transcendental, we can expect a) that every existing thing has some share, more or less, of it's qualities, and b) that with enough education and training, we will be able to scientifically determine which objects are more beautiful and which are less so, with a fair degree of specificity, is possible. Just as mathematicians can discover true equations and more elegant and clear true equations, so aestheticians, assuming they exist, can instruct us about beauty.