Paulos, John Allen. Mathematics and Humor. Chicago: The University of Chicago Press, 1980.
1 Mathematics and Humor 1
2 Axioms, Levels, and Iteration 19
3 Self-Reference and Paradox 41
4 Humor, Grammar, and Philosophy 57
5 A Catastrophe Theory Model of Jokes and Humor 75
6 Odds and the End 101
52: donʼt eliminate paradox?
98: Northrop Frye
102: Chomsky & Piaget
105: ethnic / outsiders
Frye, Northrop. 1958. The structure of comedy. In Eight great comedies, ed. S. Barnett. New York: New American Library.
(Read 25 August 2022)
Boutot, Alain. “Catastrophe Theory and Its Critics,” Synthese, vol. 96, no. 2, August 1993), pp. 167-200.
Catastrophe theory - Wikipedia, the free encyclopedia
John Allen Paulos (Paulos web site)
Attardo, Salvatore. “Humor and Irony in Interaction: From Mode Adoption to Failure of Detection,” in Say Not to Say: New Perspectives on Miscommunication, edited by Luigi Anolli, Rita Ciceri, and Giuseppe Riva (Amsterdam: IOS Press, 2002), pp. 159-179.
Section III - Communicate to Pretend: Irony and Humor
6. ʽ“You’re a Real Genius!”: Irony as a Miscommunication Design,ʼ by L. Anolli, M.G. Infantino and R. Ciceri, pp. 135-157;
8. “The Risks and Rewards of Ironic Communication,” by R. W. Gibbs and H.L. Colston, pp. 181-194.
Salvatore Attardo - Wikipedia, the free encyclopedia
Garmendia, Joana. Irony (Cambridge: Cambridge University Press, 2018), Chapter 7: Sarcasm and Humour, pp. 126 - 146.
Gibbs, Raymond W., Jr.; Bryant, Gregory A.; Colston, Herbert L. “Where is the Humor in Verbal Irony?” Humor, vol. 27, no. 4, 2014, pp. 575–595.
Piskorska, Agnieszka. “A Relevance-Theoretic Perspective on Humorous Irony and Its Failure,” Humor, vol. 27, no. 4, 2014, pp. 661–685.
Tkalac, Slavko. “The Types of Incongruity and Paulosʼs Model,” Zbornik radova, vol. 24, no. 1, 2000, pp. 83-91.
Query: The structure of humorous or ironic specimens can be modelled logically, but formal logic itself cannot be ironic, can it? I would think the chain of inference must be unequivocal, even for Godel's Theorem or paraconsistent logic. (Re the stronger claims of paraconsistency—Graham Priests dialetheism—I have my doubts). Any formalism that generates a range of truth values must still do this consistently, or am I wrong? Even considering paradoxes and self-reference, is it not impossible, from inside of logic itself, for logic to operate ironically? Would not catastrophe theory be unequivocal in its application, or to put it less ambiguously, unequivocal in any given construct even when modeling ambiguous specimens and alternative interpretations?
It seems that natural language (and also nonlinguistic semiotic gestures, media, and nonverbal communication) constitutes something richer than the formal apparatus of logical calculi, in that we can express polysemy, self-reference, irony, meta-cognitive deliberation, and outright nonsense without restraint. And even discussing the philosophy and interpretation of formal systems must be done extraformally, so it seems, or no logicians or mathematicians would ever have argued with one another (e.g. the controversy over Cantor's bombshell on transfinites) or developed alternative philosophical conceptions.
Now it seems to me thst irony is weaker and a more general category than humor, as a punchline is not required, and irony shares the characteristic of the many-layered nature of linguistic communication (symbolism, polysemy, poetry). All of this can be graphed to unpack an expression, but it need not be done using catastrophe theory.
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and Dialectical Consistency
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