"Beauty is a sense of harmony" (Ayn Rand)
Beauty is universally popular. Beautiful people are considered virtuous, sexy, interesting, and wise. Beautiful music is considered profound and philosophical. Beautiful paintings are considered full of deep meaning. It's as if we like the concept beauty so much that we pile everything into it we think of as good.
That is, we make the concept wrong.
To make a concept, you combine a range of similars by finding an essential commonality, which you specify in a definition. Then you assign a word, which lets you mentally treat the range as a unit.
If you find the essential by looking for the common denominator of a range, then the concept helps sort reality out into a manageable number of units, so you can think about how things are related, and convey your thoughts to others.
If you find the essential by consulting your feelings, then the concept is personal to you alone. You wonder why the only relationships you know are relationships to you alone, and why everybody misunderstands what you try to tell them.
According to Ayn Rand, the essential of beauty is harmony. To find what the word beauty refers to, look among sensations, and pick out the one you get from a face in harmony with itself, a sound harmonious with others, a painting in which everything fits together, and the like. If you use the essential of harmony, then when you have esthetic arguments about the limits of the range, you will know what the argument is about.
Since virtue is action in harmony with reality, it can justly be called beautiful. But to include it in the concept beauty would make no sense. The essential of virtue is not harmony, but rationality. Beauty is desirable, and the essential of "sexy" is desirability, so beauty is often sexy. But they have different essentials, and belong in separate concepts. To include in the concept beauty all that is often included, you have to use the essential: "things I like."
If beauty includes all things I like, then instead of sorting things out, I throw them all into one concept. I end up in a muddle, and annoyed at the refusal of others to see what I mean. I lose the ability to examine things separately, while keeping sight of the relationships among them.
If you want to analyze why an object has beauty, don't get lost in metaphor. Don't look for the deeper meaning of a beautiful flower arrangement, or the deeper wisdom behind a beautiful face. Look for the ways one element is in harmony with the other elements, and with the context in which you see it, and with your expectations.
Beauty is objective and contextual. It is not in the eye of the beholder, but in the relationship among elements of an object, and the relationship between an object and its context. It is a sense of harmony.
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