The Kabbala describes Beauty as the synthesis of opposites, and associates it with Truth. Our human faculties for beauty and truth map nicely to this.
The perception of beauty seems to be related to pattern recognition in the human brain. The brain tries to match inputs with stored patterns and when it succeeds, chemicals are released as a kind of self-reward. So maybe this feeling of beauty results from successfully recognizing one pattern in terms of another. And that might also be associated with a feeling that something is true.
We like to think of beauty as a subjective quality, while truth is some kind of absolute that resides in subjects like math and science. But if we examine matters closely, we recognize that even in these subjects, truth is contingent and synthetic, or approximate and tentative. It is difficult to think of many places where we deal with truth in another way. While we may feel there is some external truth, what we do and experience is much more connected with truth and beauty as feelings. So they seem closely related, though not identical.
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