Dilemma

A dilemma (from Ancient Greek δίλημμα (dílēmma) '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.^[1]

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Let's say Mr. Blue, and Ms. Red have each been arrested for some minor crime. The police think they committed a more serious crime but they don't have enough evidence to convict them. They need a confession. They take them and put them in separate rooms so they can't talk, and play a little game. To try to force a confession the police give them each a choice. Admit your partner committed the crime, and you will go free. We'll pardon you for the minor crime but your partner will have to spend 3 years in prison. If you stay silent and your partner lets us know that you were the one who really did it then you're going to have to go away for 3 years. They know that the police don't have any evidence and if they both stay silent then they will only go to prison for 1 year each for the minor crime. If they both betray each other then they'll both go to prison for 2 years each. OK, each partner can do 1 of 2 things. Stay Silent, or Betray. Staying silent would be cooperating and betraying would be defecting. If they both stay silent, they each spend a year in prison. If one betrays and the other stays silent, then the betrayer goes free and the silent spends 3 years in prison. If they both betray then it's 2 years each. So what are they going to do? Well they should cooperate. That's the best option for the group, if we add the total number of years in prison. But let's take it from Red's perspective. If she thinks blue is going to stay silent, then she should betray so she can go free. Going free is better than a year in prison. If she thinks he's going to betray her then she should definitely betray, 2 years in jail is better than 3 and being made a fool of. Blue is in the exact same situation and will think the exact same thing, he should betray if she stays silent and he should betray if she betrays. They should have both cooperated, but from an individual stand point they noticed they could always gain by defecting. If they have no control over what the other person is going to do. So they'll both defect to try to better their own situation. But come away not only hurting the group, but themselves. Individually they're worse off than if they both cooperated. This situation is pretty made up, but it has some real world analogues. A common example is with marketing . Let's say 2 cigarette companies, Red Strikes, and Smooth blue, are deciding how much money they should spend on advertising. Since the product they each make is identical to one another, advertising has a huge impact on sales. For simplicity let's say their choices are: to advertise a bunch, or not advertise at all. And there's just 100 people in this society and they all smoke. If both don't advertise, then just by random chance picking cigarette boxes, 50 people buy Red Strikes and 50 people buy Smooth blue. At $2 a pack they each make $100. Let's say advertising costs $30. If one person advertises and the other does not, then 80 people will buy the cigarettes from the ads and 20 people buy the other ones. The advertiser makes $160 minus $30 for ads, and comes away with $130. The non advertiser didn't spend money, but only made $40. If they both advertise, again half will buy Red Strikes, and half will buy Smooth blue. But since they both spent $30 on advertising, they only come away with only $70 each. Same deal, both people cooperating and not advertising is the most preferable situation, but both company can see that advertising will always make them more money. But unlike the prisoner's in jail, these companies can talk and try to influence each other. From here Blue would be better off if Red didn't advertise. Red wouldn't go for that because that would be worse for them. Blue could try to convince Red that they would both not advertise, the only other situation where they're both better off. But without any real obligation to each other, there's nothing that's stopping them from trying to advertise to gain more of the market anyway. If you think your opponent's going to not advertise, you're better off advertising. Although we're still making assumptions to make this situation work too. With this model we're assuming they only play once. The game changes when the players have a chance to build a relationship and work together to get more gains over time, or punish each other by not cooperating. Also to make the model work we have to make up rules for the players. Assume they're basically computer programs with predictable actions. These guys are creepier than they were in my head. They were supposed to be cute. For the prisoner's dilemma and other similar models, we're assuming they are Rational Agents. A rational agent is a hypothetical person that will always pick the option that they predict will work out best for them. They're not really thinking about the gains of someone else. Seems selfish but it something that real people will generally do too. People always want what's best for themselves and we don't like to made a fool of. But if you put real people in the prisoner's dilemma, people don't always defect like the model predicts. In one study, 40 people playing prisoner's dilemma games, through a computer, without ever meeting or talking, only playing each opponent once, these are one off games, using a payoff matrix that looks like this, cooperated an averaged 22% of the time. These people never cooperated. These are people always cooperated. These guys cooperated on half of their games and everyone else is in between. This is a lot of cooperation coming from a model that predicts no cooperation. The largest group did act like rational agents, but most people tried to cooperate at least once. It's because there's more to real people. We are social creatures and even in a one off scenario with no guarantees and obligations and no chance to build a relationship, we're still thinking about how the group might decide. We're actually thinking from the perspective of the group, and making an optimistic decision. Cooperating an average of 20% of the time might not seem very optimistic, but remember this is with absolutely no communication or obligations. Anyways, that's not really the point. Using the rational agent is still useful. The model is just trying to point out the dilemma of certain specific situation where people actually hurting themselves when counter-intuitively, they're only thinking about themselves... and that's why we're modelling using the cold robotic sociopaths.

Terminology

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.^[2] He also concluded that Valla had reintroduced to the Latin West a type of argument that had fallen into disuse.^[3]

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.^[4]

A dilemma is often phrased as "you must accept either A, or B", where A and B are propositions each leading to some further conclusion. In the case where this is true, it can be called a "dichotomy", but when it is not true, the dilemma constitutes a false dichotomy, which is a logical fallacy. Traditional usage distinguished the dilemma as a "horned syllogism" from the sophism that attracted the Latin name cornutus.^[5] 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.^[6]

Dilemmatic arguments

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.^[7] C. S. Peirce gave a definition of dilemmatic argument as any argument relying on excluded middle.^[8]

In logic

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.^[9] 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".^[10]

In philosophy

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.^[11] It was established with Diodorus Cronus (died c. 284 BCE).^[12] 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.^[13]

Moral dilemmas along with ethical dilemmas

In cases where two moral principles appear to be inconsistent, an actor confronts 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.^[14] 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.^[15] 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.^[16]

In law

In law, Valentin Jeutner has argued that the term "legal dilemma" could be used as a term-of-art, to describe a situation where a legal subject is confronted with two or more legal norms that the legal subject cannot simultaneously comply with.^[17]

Examples include contradictory contracts where one clause directly negates another clause, or conflicts between fundamental (e.g. constitutional) legal norms. Leibniz's 1666 doctoral dissertation De casibus perplexis (Perplexing Cases) is an early study of contradictory legal conditions.^[18] In domestic law, it has been argued that the German Constitutional Court confronted a legal dilemma when determining, in connection with proceedings relating to the German Aviation Security Act, whether a government official could intentionally kill innocent civilians by shooting down a hijacked airplane that would otherwise have crashed into a football stadium, killing tens of thousands.^[19]

In international law, it has been suggested that the International Court of Justice confronted a legal dilemma in its 1996 Nuclear Weapons Advisory Opinion. It was faced with the question whether, in an extreme circumstance of self-defence, it is a state's right to self-defence or international law's general prohibition of nuclear weapons that should take priority.^[20]

References

^ Garner, Bryan (2009). Garner’s Modern American Usage. Oxford University Press. p. 257. 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. p. 185.
^ Erasmus, Desiderius (2003). Paraphrase on Luke 11-24. University of Toronto Press. p. 158. 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 978-0495603405.
^ 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.
^ Birkenkötter, Hannah, Valentin Jeutner: Irresolvable Norm Conflicts in International Law: The Concept of a Legal Dilemma, 28 (2017) European Journal of International Law 1415-1428.
^ Leibniz, Gottfried Wilhelm, "Inaugural Dissertation on Perplexing Cases in the Law" in Alberto Artosi, Bernardo Pieri, and Giovanni Sartor (eds.), Leibniz: Logico-Philosophical Puzzles in the Law (Springer 2013).
^ Jeutner, Valentin (2017), Irresolvable Norm Conflicts in International Law: The Concept of a Legal Dilemma, Oxford University Press, p. 15, 72. See also Michael Bohlander, ‘Of Shipwrecked Sailors, Unborn Children, Conjoined Twins and Hijacked Airplanes—Taking Human Life and the Defence of Necessity’ (2006) 70 The Journal of Criminal Law 147.
^ Jeutner, Valentin (2017), Irresolvable Norm Conflicts in International Law: The Concept of a Legal Dilemma, Oxford University Press, p. 10-11.