Abstract
This chapter explores problems of the mechanism of aesthetic induction. The aesthetic induction has conceptual problems as wells as significant explanatory anomalies. In particular, historical evidence supports the existence of historical constants—properties whose preferences remain relatively unchanged throughout history, fact which contradicts the aesthetic induction.
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Notes
- 1.
As a matter of fact, from today’s perspective, it is difficult to see how properties such as tractability by mechanistic analogy, abstractness or being visualizing can be regarded as aesthetic qualities of theories. This is precisely because the appreciation of such properties is determined by contingent historical circumstances. Different historical contexts influence what properties are seen as aesthetically appealing by a scientist living in such contexts. Our contemporary context is one in which tractability by mechanistic analogy or being visualizing seem simply deprived of any aesthetic appeal. This fact supports my labelling them contingencies.
- 2.
McAllister claims that if there is any relation between beauty and truth such a relation must be established empirically.
- 3.
The compilation was inspired by the mathematician Paul Erdos, who used to say that God had a book that contained all the most beautiful mathematical proofs. Erdos used to exclaim “This is a proof from the Book” whenever he found a proof he considered extraordinarily beautiful.
- 4.
In a proof by cases one divides the statement to be proven into a finite number of mutually exclusive cases, and then shows and documents independently that in each case the statement holds.
Bibliography
Aaboe, A. (1963). Episodes from the early history of mathematics. New York: MAA.
Aigner, M., & Ziegler, G. M. (2004). Proofs from the book. Berlin/New York, Springer.
Alperson, P., & Kivy, P. (2004). The philosophy of music: Formalism and beyond. In P. Kivy (Ed.), The Blackwell guide to aesthetics (pp. 254–275). Malden: Blackwell
Appel, K., & Haken, W. (1976). Every planar map is four colorable. Bulletin of the American Mathematical Society, 82(5), 711–713.
Appel, K., & Haken, W. (1977). Every planar map is four colorable. Part I: Discharging. Illinois Journal of Mathematics, 21(3), 429–490.
Appel, K., & Haken, W. (1986). The four color proof suffices. The Mathematical Intelligencer, 8(1), 10–20.
Appel, K., Haken, W., & Koch, J. (1977). Every planar map is four colorable. Part II: Reducibility. Illinois Journal of Mathematics, 21(3), 491–567.
Ax, A. F. (1953). The physiological differentiation between fear and anger in humans. Psychosomatic Medicine, 15(5), 433–442.
Balaguer, M. (2001). Platonism and anti-platonism in mathematics. New York: Oxford University Press.
Benacerraf, P. (1973). Mathematical truth. The Journal of Philosophy, 70(19), 661–679.
Brady, E., & Levinson, J. (2001). Aesthetic concepts: Essays after Sibley. New York: Oxford University Press.
Budd, M. (1992). Music and the emotions: The philosophical theories. Psychology Press. London: Boston.
Cohen, T. (1973). Aesthetic/non-aesthetic and the concept of taste: A critique of Sibley’s position. Theoria, 39(1–3), 113–152.
Colyvan, M. (2003). The indispensability of mathematics. New York: Oxford University Press.
Cooper, A. A. (1964). Third earl of shaftesbury. Characteristics of Men, Manners, Opinions, Times, 1711, 397–400.
Damasio, A. (2005). Descartes’ error: Emotion, reason, and the human brain. London/New York: Penguin (Non-Classics).
De Clercq, R. (2005). Aesthetic terms, metaphor, and the nature of aesthetic properties. The Journal of Aesthetics and Art Criticism, 63(1), 27–32.
de Villiers, M. (2004). The role and function of quasi-empirical methods in mathematics. Canadian Journal of Math, Science & Technology Education, 4(3), 397–418.
Dirac, P. (1980). Why we believe in the Einstein theory? In B. Gruber & R. S. Millman (Eds.), Symmetries in science. New York: Plenum.
Dreyfus, H. L., & Wrathall, M. A. (2006). A companion to phenomenology and existentialism (Vol. 35). Malden: Wiley-Blackwell.
Ekman, P., & Davidson, R. J. (Eds.). (1994). The nature of emotion: Fundamental questions (1st ed.). New York: Oxford University Press.
Feigl, H. (1970). Beyond peaceful coexistence. In R. H. Stuewer (Ed.), Historical and philosophical perspectives of science (Number 5 in Minnesota studies in the philosophy of science, pp. 3–11). Minneapolis: University of Minnesota Press.
Feynman, R. P., & Weinberg, S. (1999). Elementary particles and the laws of physics: The 1986 Dirac memorial lectures. New York/Cambridge: Cambridge University Press.
Feynman, R. P., Leighton, R. B., & Sands, M. (2011). The Feynman lectures on physics, Vol. I: The new millennium edition: mainly mechanics, radiation, and heat. New York: Basic Books.
Field, H. H. (1980). Science without numbers: A defence of nominalism. Princeton: Princeton University Press.
Franks, J. (2010). Cantor’s other proofs that R is uncountable. Mathematics Magazine, 83(4), 283–289.
Frege, G. (1980). Frege against the formalists. In M. Black & P. Geach (Eds.), Philosophical writings: Translations (3rd ed., pp. 162–213; 2nd ed., 1970, 1969, 1966, 1960; 1st ed. 1952). Oxford: Blackwell.
Frijda, N. H. (1986). The emotions. Cambridge/New York: Cambridge University Press.
Goldman, A. (1995). Aesthetic value (Focus series). Boulder: Westview Press.
Goodman, N. (1968). Languages of art: An approach to a theory of symbols. Indianapolis: The Bobbs-Merrill Company.
Gow, J. (2010). A short history of Greek mathematics. Cambridge: Cambridge University Press.
Guyer, P. (2004). The origins of modern aesthetics: 1711–35. In P. Kivy (Ed.), The Blackwell guide to aesthetics (pp. 15–44). Malden: Blackwell.
Hardy, G. H. (1992). A mathematician’s apology. Cambridge/New York: Cambridge University Press.
Hillman, D. J. (1962). The measurement of simplicity. Philosophy of Science, 29, 225–252.
Hungerland, I. C. (1962). The logic of aesthetic concepts. Proceedings and Addresses of the American Philosophical Association, 36, 43–66.
Hutcheson, F. (1973). Francis Hutchenson: An inquiry concerning beauty, order, harmony, design (Vol. 9). The Hague: Martinus Nijhoff Publishing.
Kaku, M., & Thompson, J. T. (1997). Beyond Einstein: The cosmic quest for the theory of the universe. Oxford: Oxford University Press.
Kivy, P. (1975). What makes “Aesthetic” terms aesthetic? Philosophy and Phenomenological Research, 36(2), 197–211.
Kivy, P. (1980). The corded shell: Reflections on musical expression. Princeton: Princeton University Press.
Kivy, P. (1989). Sound sentiment: An essay on the musical emotions, including the complete text of the corded shell. Philadelphia: Temple University Press.
Kivy, P. (1991). Music alone: Philosophical reflections on the purely musical experience. Ithaca: Cornell University Press.
Kivy, P. (1993). The fine art of repetition: Essays in the philosophy of music. Cambridge/New York: Cambridge University Press.
Kivy, P. (1997). Philosophies of arts: An essay in differences. Cambridge/New York: Cambridge University Press.
Kivy, P. (2002). Introduction to a philosophy of music. Oxford: Oxford University Press.
Kline, M. (1990). Mathematical thought from ancient to modern times, Vol. 1 (1st ptg. ed.). New York: Oxford University Press.
Kline, M. (1990). Mathematical thought from ancient to modern times, Vol. 2. New York: Oxford University Press.
Kline, M. (1990). Mathematical thought from ancient to modern times, Vol. 3. New York: Oxford University Press.
Kuipers, T. A. F. (2000). From instrumentalism to constructive realism: On some relations between confirmation, empirical progress, and truth approximation. Dordrecht: Springer.
Kuipers, T. A. F. (2002). Beauty, a road to the truth. Synthese, 131(3), 291–328.
Lakatos, I., Worrall, J., & Zahar, E. (Eds.). (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge/New York: Cambridge University Press.
Langer, S. K. K. (1957). Philosophy in a new key: A study in the symbolism of reason, rite, and art (Vol. 17). Cambridge: Harvard University Press.
Laudan, L. (1978). Progress and its problems: Towards a theory of scientific growth. Berkeley: University of California Press.
Lazarus, R. S. (1991). Emotion and adaptation. New York: Springer.
LeDoux, J. (1996). Emotional networks and motor control: A fearful view. Progress in Brain Research, 107, 437–446.
LeDoux, J. E. (1998). The emotional brain: The mysterious underpinnings of emotional life. New York: Simon & Schuster.
LeDoux, J., & Bemporad, J. R. (1997). The emotional brain. Journal of the American Academy of Psychoanalysis, 25(3), 525–528.
Le Lionnais, F. (1971). Les grands courants de la pensée mathématique. Marseille: Cahiers du Sud.
Le Lionnais, F. (2004). Great currents of mathematical thought: Mathematics: Concepts and development (Vol. 1). Mineola: Dover.
Levenson, R. W. (1994). The search for autonomic specificity. In P. Ekman & R. J. Davidson (Eds.), The nature of emotion: Fundamental questions (pp. 252–257). New York: Oxford University Press.
Livio, M., & Grunwald, E. (2006). The equation that couldn’t be solved: How mathematical genius discovered the language of symmetry. The Mathematical Intelligencer, 28(4), 63–64.
Marenbon, J. (2003). Boethius. Oxford/New York: Oxford University Press.
McAllister, J. (1996). Beauty and revolution in science. Ithaca: Cornell University Press.
McAllister, J. (1998). Is beauty a sign of truth in scientific theories? American Scientist, 86(2), 174–183.
McAllister, J. W. (2005). Mathematical beauty and the evolution of the standards of mathematical proof. In M. Emmer (Ed.), The visual mind II (Vol. 2). Cambridge: MIT.
McWeeny, R. (2002). Symmetry: An introduction to group theory and its applications. Mineola: Dover.
Montano, U. (2010). Beauty in mathematics. PhD thesis, [s.n.], S.l. University of Groningen, The Netherlands.
Montano, U. (2012). Ugly mathematics: Why do mathematicians dislike computer-assisted proofs? The Mathematical Intelligencer, 34(4), 21–28.
Nahin, P. J. (1998). An imaginary tale: The Story of i [the square root of minus one]. Princeton: Princeton University Press.
Nahin, P. J. (2006). Dr. Euler’s fabulous formula: Cures many mathematical ills. Princeton: Princeton University Press.
Nahin, P. J. (2011). Dr. Euler’s fabulous formula: Cures many mathematical ills. Princeton: Princeton University Press.
Newton, I. (2003). Newton’s philosophy of nature selections from his writings. Whitefish, Mont. Kessinger Publishing.
Newton-Smith, W. (1981). The rationality of science. Boston: Routledge.
Ortony, A. (1991). Value and emotion. In G. Mandler, W. Kessen, A. Ortony, & F. I. M. Craik (Eds.), Memories, thoughts, and emotions: Essays in the honor of George Mandler (pp. 337–353). Hillsdale: Erlbaum.
Ortony, A., Clore, G. L., & Collins, A. (1990). The cognitive structure of emotions. Cambridge/New York: Cambridge University Press.
Popper, K. R. (2002). The logic of scientific discovery. London/New York: Routledge.
Robinson, J. (2005). Deeper than reason: Emotion and its role in literature, music, and art. New York: Oxford University Press.
Robinson, J. (2005). Deeper than reason: Emotion and its role in music literature and art. London: Claredon.
Rota, G. (1997). The phenomenology of mathematical proof. Synthese, 111(2), 183–196.
Rota, G.-C. (1997). The phenomenology of mathematical beauty. Synthese, 111(2), 171–182.
Rota, G. C. (2005). The phenomenology of mathematical beauty. In M. Emmer (Ed.), The visual mind II (pp. 2–13). Cambridge: MIT.
Russell, B. (2004). Mysticism and logic. Mineola: Dover.
Sibley, F. (1959). Aesthetic concepts. The Philosophical Review, 68(4), 421–450.
Snow, C. P. (2012). The two cultures. Cambridge/New York: Cambridge University Press.
Solomon, R. C. (2005). Subjectivity. In T. Honderich (Ed.), The Oxford companion to philosophy new edition (2nd ed.). Oxford/New York: Oxford University Press.
Stuewer, R. H. (Ed.). (1970). Historical and philosophical perspectives of science (Volume 5 of Minnesota studies in the philosophy of science). Minneapolis: University of Minnesota Press.
Swinnerton-Dyer, P. (2005). The justification of mathematical statements. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 363(1835), 2437–2447.
Thagard, P. (2005). Why is beauty a road to the truth? Poznan Studies in the Philosophy of the Sciences and the Humanities, 84(1), 365–370.
Thomas, R. S. D. (2007). The comparison of mathematics with narrative. In B. Kerkhove & J. P. Bendegem (Eds.), Perspectives on mathematical practices (Volume 5 of Logic, epistemology, and the unity of science, pp. 43–59). Dordrecht: Springer.
Tymoczko, T. (1979). The four-color problem and its philosophical significance. The Journal of Philosophy, 76(2), 57–83.
Weber, K. (2009). How syntactic reasoners can develop understanding, evaluate conjectures, and generate counterexamples in advanced mathematics. The Journal of Mathematical Behavior, 28(2), 200–208.
Weber, K., & Alcock, L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56(2), 209–234.
Weinberg, S. (1994). Dreams of a final theory. New York: Vintage Books.
Wells, D. (1988). Which is the most beautiful? The Mathematical Intelligencer, 10(4), 30–31.
Wells, D. (1990). Are these the most beautiful? The Mathematical Intelligencer, 12(3), 37–41.
Wright, C. (1994). Truth and objectivity. Cambridge/London: Harvard University Press.
Zajonc, R. B. (1984). On the primacy of affect. American Psychologist, 39(2), 117–123.
Zajonc, R. B. (1998). Emotions. In D. T. Gilbert, S. T. Fiske, & G. Lindzey (Eds.), The handbook of social psychology (Vol. 2, pp. 591–632). Boston: McGraw-Hill
Zajonc, R. B. (2001). Mere exposure: A gateway to the subliminal. Current Directions in Psychological Science, 10(6), 224–228.
Zangwill, N. (2003). Beauty. In J. Levinson (Ed.), The Oxford handbook of aesthetics. Oxford/New York: Oxford University Press.
Zangwill, N. (2010). Aesthetic judgment. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Fall 2010 ed.). http://plato.stanford.edu/archives/fall2010/entries/aesthetic-judgment/.
Zangwill, N. (2011). Music, essential metaphor, and private language. American Philosophical Quarterly, 48(1), 1.
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Montano, U. (2014). Problems of the Aesthetic Induction. In: Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics. Synthese Library, vol 370. Springer, Cham. https://doi.org/10.1007/978-3-319-03452-2_4
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