Chapter Seven— Numbers, Systems, Functions—and Essences
1. Many of the ideas in Part III and Part IV have appeared in two of my articles. See Cassedy, "Mathematics, Relationalism"; and "Paul Valéry's Modernist Aesthetic Object," Journal of Aesthetics and An Criticism 45 (1986-87): 77-86. [BACK]
2. Ernst Cassirer, Philosophy of Symbolic Forms, vol. 3, The Phenomenology of Knowledge, trans. Ralph Manheim (New Haven: Yale University Press, 1957), pp. 357-405. [BACK]
3. Immanuel Kant, Kritik der reinen Vernunft, "B" edition, p. 75; "A" edition, p. 51; English translation, Critique of Pure Reason, trans. Norman Kemp Smith (New York: St. Martin's Press, 1965), p. 93. [BACK]
4. See Tony Rothman, "The Short Life of Evariste Galois," Scientific American 246 (1982): 136-49. The New York Times ran an amusing editorial on Rothman's deflation of the Galois story, April 4, 1982. [BACK]
5. Ernst Cassirer, "The Concept of Group and the Theory of Perception," Philosophy and Phenomenological Research 5 (1944): 1-36. This is an English translation of an original French version, "Le concept de groupe et la théorie de continue
la perception," Journal de Psychologie (July-December 1938): 368-414. Cassirer also wrote a shorter and simpler version of this paper as a lecture, which he was working on the morning of the day of his death. The lecture is titled "Reflections on the Concept of Group and the Theory of Perception" and is published in Symbol, Myth, and Culture: Essays and Lectures of Ernst Cassirer, 1935-1945, ed. Donald Phillip Verene (New Haven: Yale University Press, 1979), pp. 271-91. [BACK]
6. Cassirer mentions Poincaré's theory in "The Concept of Group, p. 3. [BACK]
7. Roman Jakobson, "Verbal Communication," Scientific American 227 (September 1972): 72—80. This passage occurs on p. 72. [BACK]
8. Jakobson, "Verbal Communication," p. 76. [BACK]
9. Distinctive features are treated in Roman Jakobson and Morris Halle, "Phonology and Phonetics," in Jakobson, SW, 1:464—504, and, in the same volume of SW, "The Revised Version of the List of Inherent Features," 1:738-42. [BACK]
10. Ernst Cassirer, "Structuralism in Modern Linguistics," Word 1 (1945): 99-120. [BACK]
11. Jean Piaget, Le structuralisme (Paris: Presses Universitaires de France, 1968); English translation, Structuralism, trans. Chaninah Maschler (New York: Basic Books, 1970). [BACK]
12. Michel Serres, Hermès ou la communication (Paris: Minuit, 1968). [BACK]