A Quote by Karl Wilhelm Friedrich Schlegel
Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry.
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First of all, the art of living; then as my ideal profession, poetry and philosophy, and as my real profession, plastic arts; in the last resort, for lack of income, illustrations.
There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depends heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood.
What we cannot express by the art of thinking, by the art of science or philosophy or logic, we can and should express by the poetic, visual, or some other arts.
Dancing and building are the two primary and essential arts. The art of dancing stands at the source of all the arts that expressthemselves first in the human person. The art of building, or architecture, is the beginning of all the arts that lie outside the person; and in the end they unite. Music, acting, poetry proceed in the one mighty stream; sculpture, painting, all the arts of design, in the other. There is no primary art outside these two arts, for their origin is far earlier than man himself; and dancing came first.
Art, in the widest sense of the word, is the instrument Hellenism has used and would use for that purpose. All the arts, poetry, music, ritual, the visual arts, the theatre, must work singly and together to create the most comprehensive art of all, a humanized society, and its masterpiece, the free man.
Poetry is a mystic, sensuous mathematics of fire, smoke-stacks, waffles, pansies, people, and purple sunsets.
There are areas of philosophy that are important, but I think of them as being subsumed by other fields. In the case of descriptive philosophy, you have literature or logic, which, in my view, is really mathematics.
So if the worth of the arts were measured by the matter with which they deal, this art-which some call astronomy, others astrology, and many of the ancients the consummation of mathematics-would be by far the most outstanding. This art which is as it were the head of all the liberal arts and the one most worthy of a free man leans upon nearly all the other branches of mathe matics. Arithmetic, geometry, optics, geodesy, mechanics, and whatever others, all offer themselves in its service.
May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life.
Poincaré was a vigorous opponent of the theory that all mathematics can be rewritten in terms of the most elementary notions of classical logic; something more than logic, he believed, makes mathematics what it is.
The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.
We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry.
Most of the arts, as painting, sculpture, and music, have emotional appeal to the general public. This is because these arts can be experienced by some one or more of our senses. Such is not true of the art of mathematics; this art can be appreciated only by mathematicians, and to become a mathematician requires a long period of intensive training. The community of mathematicians is similar to an imaginary community of musical composers whose only satisfaction is obtained by the interchange among themselves of the musical scores they compose.
Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.
It is a mistake to suppose, with some philosophers of aesthetics, that art and poetry aim to deal with the general and the abstract. This misconception has been foisted upon us by mediaeval logic. Art and poetry deal with the concrete of nature, not with separate 'particulars,' for such rows do not exist.
What does that represent? There was never any question in plastic art, in poetry, in music, of representing anything. It is a matter of making something beautiful, moving, or dramatic - this is by no means the same thing.
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