A dilemma (Greek δίλημμα "double proposition") is a problem offering at least two solutions or possibilities, of which none are practically acceptable. One in this position has been traditionally described as "being on the horns of a dilemma", neither horn being comfortable, "between Scylla and Charybdis"; or "being between a rock and a hard place", since both objects or metaphorical choices are rough.
The dilemma is sometimes used as a rhetorical device, in the form "you must accept either A, or B"; here A and B would be propositions each leading to some further conclusion. Applied in this way, it may be a fallacy, a false dichotomy.
In formal logic, the definition of a dilemma differs markedly from everyday usage. Two options are still present, but choosing between them is immaterial because they both imply the same conclusion. Symbolically expressed thus:
Which can be translated informally as "one (or both) of A or B is known to be true, but they both imply C, so regardless of the truth values of A and B we can conclude C."
Horned dilemmas can present more than two choices. The number of choices of Horned dilemmas can be used in their alternative names, such as twopronged (twohorned) or dilemma proper , or threepronged (threehorned) or trilemma, and so on.
Constructive dilemmas
Destructive dilemmas
DILEMMA (Gr. & Xj jsa, a double proposition, from 81 and Xaµ(3avav), a term used technically in logic, and popularly in common parlance and rhetoric. (I) The latter use has no exact definition, but in general it describes a situation wherein from either of two (or more) possible alternatives an unsatisfactory conclusion results. The alternatives are called the "horns" of the dilemma. Thus a nation which has to choose between bankruptcy and the repudiation of its debts is on the horns of a dilemma. (2) In logic there is considerable divergence of opinion as to the best definition. Whately defined it as "a conditional syllogism with two or more antecedents in the major and a disjunctive minor." Aulus Gellius gives an example as follows:  "Women are either fair or ugly; if you marry a fair woman, she will attract other men; if an ugly woman she will not please you; therefore marriage is absurd." From either alternative, an unpleasant result follows. Four kinds of dilemma are admitted:  (a) Simple Constructive: If A, then C; if B, then C, but either B or A; therefore C. (b) Simple Destructive: If A is true, B is true; if A is true, C is true; B and C are not both true; therefore A is not true. (c) Complex Constructive: If A, then B; if C, then D; but either A or C; therefore either B or D. (d) Complex Destructive: If A is true, B is true; if C is true, D is true; but B and D are not both true; hence A and C are not both true. The soundness of the dilemmatic argument in general depends on the alternative possibilities. Unless the alternatives produced exhaust the possibilities of the case, the conclusion is invalid. The logical form of the argument makes it especially valuable in public speaking, before uncritical audiences. It is, in fact, important rather as a rhetorcial subtlety than as a serious argu ment.
Dilemmist is also a term used to translate Vaibhashikas, the name of a Buddhist school of philosophy.
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Categories: DIGDIS  Rhetoric  Philosophy
Dilemma n. (genitive Dilemmas, plural Dilemmas or Dilemmata)
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Cladus: Eukaryota
Supergroup: Unikonta
Cladus: Opisthokonta
Regnum: Animalia
Subregnum: Eumetazoa
Cladus: Bilateria
Cladus: Nephrozoa
Cladus: Protostomia
Cladus: Spiralia
Cladus: Lophotrochozoa
Phylum: Mollusca
Classis: Bivalvia
Subclassis: Anomalosdesmata
Ordo: Septibranchia
Superfamilia: Poromyoidea
Familia: Poromyidae
Genus: Dilemma
Species: D. frumarkernorum 
D. inexpectatum 
D. japonicum  D. spectralis
Dilemma Leal, 2008
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A dilemma (Greek δίλημμα "double proposition") is a problem with at least two solutions or possibilities. None of the solutions are practically acceptable; one in this position has been traditionally described as being impaled on the horns of a dilemma, neither horn being comfortable.
The dilemma is sometimes used as a rhetorical device, in the form "you must accept either A, or B"; here A and B would be propositions each leading to some further conclusion. Applied in this way, it may be a fallacy, a false dichotomy.
In formal logic, the definition of a dilemma differs markedly from everyday usage. Two options are still present, but choosing between them is immaterial because they both imply the same conclusion. Symbolically expressed thus:
$A\; \backslash vee\; B,\; A\; \backslash Rightarrow\; C,\; B\; \backslash Rightarrow\; C\; \backslash vdash\; C$
This can be translated informally as "one (or both) of A or B is known to be true, but they both imply C, so regardless of the truth values of A and B we can conclude C."
Horned dilemmas can present more than two choices. The number of choices of Horned dilemmas can be used in their alternative names, such as twopronged (twohorned) or dilemma proper , or threepronged (threehorned) or trilemma, and so on.
Constructive dilemmas
Destructive dilemmas
In Zen and the Art of Motorcycle Maintenance, Robert Pirsig outlines possible responses to a dilemma. The classical responses are to either choose one of the two horns and refute the other or alternatively to refute both horns by showing that there are additional choices. Pirsig then mentions three illogical or rhetorical responses. One can "throw sand in the bull's eyes" by, for example, questioning the competence of the questioner. One can "sing the bull to sleep" by, for example, stating that the answer to the question is beyond one's own humble powers and asking the questioner for help. Finally one can "refuse to enter the arena" by, for example, stating that the question is unanswerable.
