Polylemma

A polylemma is - based on the dilemma - a situation in which you can choose between more than two options, none of which is clearly preferable because all are equally (or similarly) bad or good.

logic

In classical logic , a polylemma can be represented as the syllogistic conclusion of the second figure if the major clause consists of hypothetical-disjunctive (neither-nor-) terms and the premise has the same number of negative terms:

Upper sentence: .. Premise: .. Conclusion: ${\displaystyle A\rightarrow B_{1}\lor }$ ${\displaystyle \lor B_{n}}$
${\displaystyle \lnot B_{1}\land }$ ${\displaystyle \land \lnot B_{n}}$
${\displaystyle \lnot A}$

The "polylemma" of father, son and a donkey

The following story is passed down from Hodscha Nasreddin : Hodscha goes to a cattle market with his son to buy a donkey. After buying a donkey after a long search, they make their way home. At first, both Hodja and his son walk next to the donkey until an oncoming hiker laughs at them and asks: "You have a donkey, but why is nobody riding it?" After a brief thought, the son sits on the donkey, and so they continue on their way home until the next hiker meets them and says to the son: “Young man, you should be ashamed of yourself. You have young legs and ride the donkey while your father has to run! ” So the father sits on the donkey and the son walks on foot. Now they meet another hiker who says to the father: "You should be ashamed of yourself, you are riding the donkey with your strong legs while the tender boy has to walk!" - So both of them sit on the donkey and sit down so on the way home until they meet another hiker who insults them: “You should be ashamed! You both sit lazily on the donkey and the poor animal has to carry the heavy load of both of you the whole way! ” Thereupon father and son decide to tie the donkey to a pole and now carry the donkey home. When they arrive there quite late and completely exhausted, the father's wife says: “You are maybe two fools! Why don't you let the donkey run to its new stable yourself? "

This humorous narrative, which has been handed down in different versions , is a typical polylemma, since father and son have to choose between the following five options, none of which - taking into account all possible objections - are clearly preferable:

• 1st possibility: Nobody rides the donkey
• 2nd possibility: the son rides the donkey
• 3rd possibility: The father rides the donkey
• 4th possibility: The father and the son ride the donkey together
• 5th possibility: The father and the son carry the donkey

Result: Each of these two named individuals has to decide what they would do themselves in this or a similar situation.