Abstract
In the old days all of us studied philosophy because the twin concepts of liberal education and core curriculum were fixed in place and philosophy was part of what you should know if you were to be considered educated. And, in the beginning of Philosophy 101, we learned the four classical questions with which the subject deals:
What is truth?
What is reality?
What is justice?
What is beauty?
These four questions, our professor said, go by the appellations of the cognitive, the metaphysical the ethical and the aesthetical What philosophy is all about, he told us, is to bring meaning to these great and fundamental issues and to establish progress and procedures toward their resolution.
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Notes
Lynn Steen, ed., Mathematics Today, p. 10.
Thomas Munro, Toward Science in Aesthetics (New York: Liberal Arts Press, 1956), p. 3.
Arthur Berger, P. W. Prall, in Aesthetic Analysis (New York: Crowell, 1936), p. ix.
Nicholas Wolterstorff, Works and Worlds of Art (Oxford: Clarendon, 1980), p. v.
John Keats, “Ode on a Grecian Urn.”
Henri Poincaré, The Foundations of Science (New York: Science Press, 1929), p. 386.
Ibid., p. 385.
Ibid., p. 391.
Seymore A. Papert, “The Mathematical Unconscious,” in On Aesthetics and Science, ed. Judith Wechsler (Boston: Birkhauser, 1988), p. 106.
G. H. Hardy, A Mathematician’s Apology, p. 92.
Ibid., pp. 85, 90.
Papert, “The Mathematical Unconscious,” p. 106.
Ibid., p. 111.
Ibid.
Ibid., p. 112.
Ibid., p. 118.
Herman Weyl, “Symmetry,” in The World of Mathematics, Vol. 1, ed. James R. Newman (New York: Simon & Schuster, 1956).
James Jeans, “Mathematics and Music,” in The World of Mathematics, Vol. 4, ed. James R. Newman (New York: Simon & Schuster, 1956).
Gustav Fechner, Vorschule der Aesthetik. (Leipzig: Breitkoph & Hartel, 1876).
I. C. McManus, D. Edmondson, and J. Rodger, “Balance in Pictures,” British Journal of Psychology, 76 (1985), pp. 311–324.
George David Birkhoff, “Mathematics of Aesthetics,” in The World of Mathematics, Vol. 4, ed. James R. Newman (New York: Simon & Schuster, 1956).
George Stiny and James Gips, Algorithmic Aesthetics (Berkeley: University of California Press, 1978).
Mortimer Adler, Six Great Ideas (New York: Macmillan, 1981).
George Dickie, The Art Circle (New York: Haven, 1984).
Will Durant, The Story of Philosophy (New York: Pocket Library, 1954), p. xxvii.
Allan Bloom, The Closing of the American Mind (New York: Simon & Schuster, 1987), p. 271.
Norman Bryson, Vision and Painting (London: Yale University Press, 1983).
Roger Scruton, “Recent Aesthetics in England and America,” in Aesthetics and Art Education, eds. Ralph A. Smith and Alan Simpson (Chicago: University of Illinois Press, 1991), p. 43.
Arthur Danto, Connections to the World (New York: Harper & Row, 1990).
Harold Bloom, as quoted in L. S. Klepp, “Everyman a Philosopher,” New York Times Magazine, Dec. 2, 1990, p. 117.
Arthur Danto, “The Artworld,” The Journal of Philosophy, 61 (1964), pp. 571–584, p. 572.
Ibid., p. 573.
Ibid., p. 581.
Eugene F. Kaelin, “Why Teach Art in the Public Schools?” in Aesthetics and Art Education, eds. Ralph A. Smith and Alan Simpson (Chicago: University of Chicago Press), p. 165.
Danto, “The Artworld,” p. 571.
Dickie, The Art Circle, p. 11.
Ibid., p. 66.
Ibid., p. 67.
Ibid., p. 84.
Ibid., p. 80.
Paul Halmos, as quoted in Mathematics Today, Steen, ed., p. 1.
Richard Wollheim, Art and Its Objects (New York: Harper & Row, 1968).
R. G. Collingwood, The Principles of Art (London: Clarendon, 1938), p. 130.
Hardy, A Mathematician’s Apology, p. 61.
Howard Nemerov, as quoted in Doug Anderson, “Poet in Prose,” New York Times Book Review, April 28, 1991, p. 15.
David Hilbert, as quoted in Morris Kline, Mathematics in Western Culture (New York: Oxford, 1953), p. 397.
Poincaré, as quoted in Kline, Mathematics in Western Culture, p. 397.
C. P. Snow, as quoted in Hardy, A Mathematician’s Apology, p. 37.
Edward Bullough, “Psychical Distance as a Factor in Art and an Aesthetic Principle,” British Journal of Psychology, 5 (1912), p. 87–118.
Donald Sherburne, A Whiteheadean Aesthetic (New York: Yale, 1961), p. 108.
James L. Jarrett, The Quest for Beauty (Englewood Cliffs, NJ: Prentice Hall, 1957), p. 111.
Bullough, “Psychical Distance,” p. 92.
Ibid., p. 93.
Ibid., p. 94.
Ibid., p. 95.
Ernest Hemingway, Death in the Afternoon (New York: Scribners).
Ortega y Gasset, The Dehumanization of Art and Notes on the Novel (Princeton, NJ: Princeton University Press, 1948), p. 12.
Ernest Nagel and James R. Newman, Godel’s Proof (New York: NYU Press, 1958), p. 24.
Martin Gardner, Mathematical Puzzles and Diversions (New York: Simon & Schuster, 1959), p. 47.
Angus E. Taylor, Advanced Calculus (Boston: Ginn, 1955).
Martin Gardner, 2nd Book of Mathematical Puzzles and Diversions (New York: Simon & Schuster, 1961), p. 57.
George B. Thomas, Calculus and Analytic Geometry (Reading, MA: Addison-Wesley, 1951).
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© 1992 Jerry P. King
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King, J.P. (1992). Aesthetics. In: The Art of Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-6339-0_6
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