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Self-Reference in Logic and Mulligan Stew
Published online by Cambridge University Press: 02 April 2024
Extract
The novel has always provided a vehicle for commenting on various aspects of human existence. We are familiar with the political novel, the historical novel, or the metaphysical novel, and in this sense Sorrentino's Mulligan Stew, with its running commentary on novels, novelists, critics and publishers, may be viewed as a critical novel. A critical novel, however, has a striking feature which it does not share with the other sorts of novels mentioned above in that a critical novel is itself a novel, and a member of the class of objects on which it is commenting. This is a structure that logicians call “self-reference” and the phenomenon of self-reference has provided a central theme in twentieth century logic and philosophy.
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- Copyright © 1982 Fédération Internationale des Sociétés de Philosophie / International Federation of Philosophical Societies (FISP)
References
1 Throughout this discussion I am assuming what logicians call the "law of excluded middle," i.e., that every declarative sentence is true or false; there are two reasons for proceeding in this way. The first is that this principle was accepted in the discussions of self-reference that I am concerned with. The second is that although it may seem possible to avoid the paradoxical result by rejecting this law and thus refusing to move from the claim that a sentence is not true to the claim that it is false, or from the claim that a sentence is not false to the claim that it is true, there is a "strengthened liar paradox" that can be constructed for this case as well. Cf. Susan Haack, Philosophy of Logics (Cambridge, Cambridge Univ. Press, 1978), p. 140.
2 No evaluative sense should be attached to the use of "lower" and "higher" in this context. Rather, the idea is that higher levels are built on lower levels much as the higher stories of a building are built on the lower stories.
3 Haack, op. cit., p. 139.
4 See Frederick B. Fitch, "Self-Reference in Philosophy," Mind 65, 1946, pp. 64-73. Harold I. Brown, "Need There Be a Problem of Induction?" Canadian Journal of Philosophy 8, 1978, pp. 521-532.
5 For excellent detailed discussions of Gödel's extremely complex proof see Ernest Nagel and James R. Newman, Gödel's Proof (New York: New York Univ. Press, 1958), and Douglas R. Hofstadter, Gödel, Escher, Bach (New York: Basic Books, 1979). For those who wish to tackle the original paper see Kurt Gödel, On Formally Undecidable Propositions (New York: Basic Books, 1962).
6 Hofstadter, op. cit., p. 10.
7 Ibid.
8 Ibid., p. 11. References to Escher drawings are to reproductions in Gödel, Escher, Bach, although they are available in many other places, e.g., The Graphic Work of M. C. Escher (New York: Ballantine Books, 1971).
9 Hofstadter, op. cit., p. 12.
10 Ibid., p. 690.
11 Ibid., p. 709.
12 Miguel de Cervantes Saavedra, Don Quixote, trans. Walter Starkie (New York: Signet Books, 1964), part II, ch. 59.
13 Ibid, part II, ch. 72.
14 John Barth, The Floating Opera (New York: Avon Books, 1956), ch. 17.
15 Raymond Queneau, The Flight of Icarus, trans. Barbara Wright (New York: New Directions, 1973).
16 Gilbert Sorrentino, Mulligan Stew (New York: Grove Press, 1979 London: Marion Boyars Publishers Ltd., 1980), p. 25.
17 Ibid., p. 241.
18 Ibid., p. 153.
19 Ibid., p. 154.
20 Ibid., p. 152.
21 Ibid., p. 242.
22 Ibid., p. 4.
23 Ibid., p. 153.
24 Ibid., p. 27.
25 Ibid., pp. 409-414.
26 Ibid., p. 400.
27 Ibid., p. 272. The masturbation incident occurs in Sorrentino's own novel Imaginative Qualities of Actual Things.
28 I wish to thank William Tolhurst and Gregory Galica for a number of helpful comments on an earlier draft of this essay.