A dilemma (Greek: δίλημμα "double proposition") is a problem offering two possibilities, neither of which is unambiguously acceptable or preferable. The possibilities are termed the horns of the dilemma, a clichéd usage, but distinguishing the dilemma from other kinds of predicament as a matter of usage.
The term dilemma is attributed by Gabriel Nuchelmans to Lorenzo Valla in the 15th century, in later versions of his logic text traditionally called Dialectica. Valla claimed that it was the appropriate Latin equivalent of the Greek dilemmaton. Nuchelmans argued that his probable source was a logic text of c.1433 of George of Trebizond. He also concluded that Valla had reintroduced to the Latin West a type of argument that had fallen into disuse.
Valla's neologism did not immediately take hold, preference being given to the established Latin term complexio, used by Cicero, with conversio applied to the upsetting of dilemmatic reasoning. With the support of Juan Luis Vives, however, dilemma was widely applied by the end of the 16th century.
In the form "you must accept either A, or B" — here A and B are propositions each leading to some further conclusion — and applied incorrectly, the dilemma constitutes a false dichotomy, that is, a fallacy. Traditional usage distinguished the dilemma as a "horned syllogism" from the sophism that attracted the Latin name cornutus. The original use of the word horns in English has been attributed to Nicholas Udall in his 1548 book Paraphrases, translating from the Latin term cornuta interrogatio.
The dilemma is sometimes used as a rhetorical device. Its isolation as textbook material has been attributed to Hermogenes of Tarsus in his work On Invention. C. S. Peirce gave a definition of dilemmatic argument as any argument relying on excluded middle.
In propositional logic, dilemma is applied to a group of rules of inference, which are in themselves valid rather than fallacious. They each have three premises, and include the constructive dilemma and destructive dilemma. Such arguments can be refuted by showing that the disjunctive premise — the "horns of the dilemma" — does not in fact hold, because it presents a false dichotomy. You are asked to accept "A or B", but counter by showing that is not all. Successfully undermining that premise is called "escaping through the horns of the dilemma".
Dilemmatic reasoning has been attributed to Melissus of Samos, a Presocratic philosopher whose works survive in fragmentary form, making the origins of the technique in philosophy imponderable. It was established with Diodorus Cronus (died c. 284 BCE). The paradoxes of Zeno of Elea were reported by Aristotle in dilemma form, but that may have been to conform with what Plato said about Zeno's style.
Moral and ethical dilemmas
In cases where two moral principles appear to be inconsistent, an actor has a dilemma in terms of which principle to follow. This kind of moral case study is attributed to Cicero, in book III of his De Officiis. In the Christian tradition of casuistry, an approach to abstract ranking of principles introduced by Bartolomé de Medina in the 16th century became tainted with the accusation of laxism, as did casuistry itself. Another approach, with legal roots, is to lay emphasis on particular features present in a given case: in other words, the exact framing of the dilemma.
- Garner, Bryan (2009). Garner's Modern American Usage. Oxford University Press. ISBN 9780199888771.
- Nuchelmans, Gabriel (1991). Dilemmatic arguments : towards a history of their logic and rhetoric. North-Holland. p. 89. ISBN 0-444-85730-3.
- Nuchelmans, Gabriel (1991). Dilemmatic arguments : towards a history of their logic and rhetoric. North-Holland. p. 94. ISBN 0-444-85730-3.
- Nuchelmans, Gabriel (1991). Dilemmatic arguments : towards a history of their logic and rhetoric. North-Holland. pp. 102–6. ISBN 0-444-85730-3.
- Hamilton, Sir William (1863). The Logic of Sir William Hamilton, Bart. Moore, Wilstach & Baldwin.
- Erasmus, Desiderius (2003). Paraphrase on Luke 11-24. University of Toronto Press. ISBN 9780802036537.
- Lucia Calboli Montefusco, Rhetorical use of dilemmatic arguments, Rhetorica: A Journal of the History of Rhetoric Vol. 28, No. 4 (Autumn 2010), pp. 363–383, at p. 364. Published by: University of California Press on behalf of the International Society for the History of Rhetoric. DOI: 10.1525/rh.2010.28.4.363 JSTOR 10.1525/rh.2010.28.4.363
- Ghosh, Sujata; Prasad, Sanjiva (2016). Logic and Its Applications: 7th Indian Conference, ICLA 2017, Kanpur, India, January 5-7, 2017, Proceedings. Springer. p. 177 note 5. ISBN 9783662540695.
- Church, Alonzo (1996). Introduction to Mathematical Logic. Princeton University Press. ISBN 0691029067.
- Govier, Trudy (2009). A Practical Study of Argument. Cengage Learning. ISBN 0495603406.
- Harriman, Benjamin (2018). Melissus and Eleatic Monism. Cambridge University Press. p. 44. ISBN 9781108416337.
- Sedley, David (2018). "Diodorus Cronus". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.
- Palmer, John (2017). "Zeno of Elea". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.
- Jonsen, Albert R.; Toulmin, Stephen Edelston (1988). The Abuse of Casuistry: A History of Moral Reasoning. University of California Press. p. 75. ISBN 9780520060630.
- Peters, Francis E. (2003). The words and will of God. Princeton University Press. p. 154. ISBN 0691114617.
- Jonsen, Albert R.; Toulmin, Stephen Edelston (1988). The Abuse of Casuistry: A History of Moral Reasoning. University of California Press. p. 54. ISBN 9780520060630.
- Media related to Dilemmas at Wikimedia Commons