Paradoxes

Question 1

Barbershop paradox

Answer 1

Barbershop paradox: The supposition that, ‘if one of two simultaneous assumptions leads to a contradiction, the other assumption is also disproved’ leads to paradoxical consequences. Not to be confused with the Barber paradox.

Question 2

What the Tortoise Said to Achilles

Answer 2

What the Tortoise Said to Achilles: If a presumption needs to be made that a specific result can be deduced from premises, then the result can never be deduced. An inference rule, which is valid (or not), cannot be a premise, which is true (or false), otherwise one has an infinite regress. Also known as Carroll’s paradox and is not to be confused with the “Achilles and the tortoise” paradox by Zeno of Elea.

Question 3

Catch-22

Answer 3

Catch-22: A situation in which someone is in need of something that can only be had by not being in need of it. A soldier who wants to be declared insane to avoid combat is deemed not insane for that very reason and will therefore not be declared insane.

Question 4

Drinker paradox

Answer 4

Drinker paradox: In any pub there is a customer such that if that customer is drinking, everybody in the pub is drinking.

Question 5

Paradox of free choice

Answer 5

Paradox of free choice: Disjunction introduction poses a problem for modal inferences, permitting arbitrary modal statements to be inferred.