# Favorite logical paradox?

**Posted by:**PetersSmith

I was going to include automatic descriptions, but I included the plain ones so that more people could understand what they entail.

Vote

21 Total Votes

1

### Card paradox

"The next statement is true. The previous statement is false." A variant of the liar paradox that does not use self-reference.1 comment

2

### Sorites paradox

(also known as the paradox of the heap): If you remove a single grain of sand from a heap, you still have a heap. Keep removing single grains, and the heap will disappear. Can a single grain of sand make the difference between heap and non-heap?1 comment

4

### Lottery paradox

If there is one winning ticket in a large lottery. It is reasonable to believe of a particular lottery ticket that it is not the winning ticket, since the probability that it is the winner is so very small, but it is not reasonable to believe that n... o lottery ticket will win more0 comments

5

### Catch-22

A situation in which someone is in need of something that can only be had by not being in need of it.1 comment

6

### Unexpected hanging paradox

The day of the hanging will be a surprise, so it cannot happen at all, so it will be a surprise.0 comments

7

### Barber paradox

A barber (who is a man) shaves all and only those men who do not shave themselves. Does he shave himself?1 comment

8

### Berry paradox

The phrase "the first number not nameable in under ten words" appears to name it in nine words.0 comments

9

### Crocodile dilemma

If a crocodile steals a child and promises its return if the father can correctly guess exactly what the crocodile will do, how should the crocodile respond in the case that the father correctly guesses that the child will not be returned?1 comment

10

### Paradox of the Court

A law student agrees to pay his teacher after winning his first case. The teacher then sues the student (who has not yet won a case) for payment.0 comments

11

### Russell's paradox

Does the set of all those sets that do not contain themselves contain itself?1 comment

13

### Liar paradox

"This sentence is false." This is the canonical self-referential paradox. Also "Is the answer to this question no?", and "I'm lying."1 comment

15

### I don't understand.

If something exists that nothing can know exists, then does it exist?0 comments

16

### Opposite Day

"It is opposite day today." Therefore it is not opposite day, but if you say it is a normal day it would be considered a normal day.0 comments

17

### Kleene–Rosser paradox

In mathematics, the Kleene–Rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of Curry's combinatory logic introduced in 1930, and Church's original lambda calculus, introduced in ... 1932–1933, both originally intended as systems of formal logic. The paradox was exhibited by Stephen Kleene and J. B. Rosser in 1935 more0 comments

18

### Petronius' paradox

"Moderation in all things, including moderation" (unsourced quotation sometimes attributed to Petronius).0 comments

19

### Ship of Theseus

(a.K.A. George Washington's axe or Grandfather's old axe or Trigger's Broom in the UK): It seems like you can replace any component of a ship, and it is still the same ship. So you can replace them all, one at a time, and it is still the same ship. ... However, you can then take all the original pieces, and assemble them into a ship. That, too, is the same ship you began with more0 comments

20

### Grelling–Nelson paradox

Is the word "heterological", meaning "not applicable to itself", a heterological word?0 comments

21

### Exception paradox

"If there is an exception to every rule, then every rule must have at least one exception; the exception to this one being that it has no exception." "There's always an exception to the rule, except to the exception of the rule—which is, in of itsel... f, an accepted exception of the rule." "In a world with no rules, there should be at least one rule - a rule against rules. more0 comments

23

### Quine's paradox

"'Yields a falsehood when appended to its own quotation' yields a falsehood when appended to its own quotation." Shows that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals.0 comments

24

### Unsignifiability paradox

"There are some things which are unsignifiable: but they become signifiable by calling them unsignifiable."0 comments

25

### Hypergame

A finite game is a game which always ends after a finite number of moves. The hypergame is a game where the first move is that player 1 names a finite game, and then player 2 makes the first move. If the hypergame is a finite game, then when playing... the hypergame player 1 can name the hypergame as the game to be played, and then player 2 can name the hypergame, etc., ad infinitum. But if the hypergame is not a finite game, then there is a series of moves that never ends more0 comments

26

### Unnameability paradox

"There are some things which are unnameable: but they become nameable by calling them unnameable."0 comments

27

### Bhartrhari's paradox

Hans and Radhika Herzbergers (1981) argue that the Indian grammarian-philosopher Bhartrhari (late fifth century CE) held a thesis which the authors call the Unnameability Thesis (the thesis that there are some things which are unnameable), and that ... Bhartrhari was well aware that it leads to a problematic situation which they call 'Bhartrhari's paradox' more0 comments

28

### Drinker paradox

The drinker paradox is a theorem of classical predicate logic, usually stated in natural language as: There is someone in the pub such that, if he is drinking, everyone in the pub is drinking. The actual theorem is where D is an arbitrary predicate ... and P is an arbitrary set. The paradox was popularised by the mathematical logician Raymond Smullyan, who called it the "drinking principle" in his 1978 book What Is the Name of this Book more0 comments

30

### 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.0 comments

31

### What the Tortoise Said to Achilles

"What the Tortoise Said to Achilles", written by Lewis Carroll in 1895 for the philosophical journal Mind, is a brief dialogue which problematises the foundations of logic. The title alludes to one of Zeno's paradoxes of motion, in which Achilles co... uld never overtake the tortoise in a race. In Carroll's dialogue, the tortoise challenges Achilles to use the force of logic to make him accept the conclusion of a simple deductive argument. Ultimately, Achilles fails, because the clever tortoise leads him into an infinite regression more0 comments

32

### Raven paradox

The raven paradox, also known as Hempel's paradox or Hempel's ravens, is a paradox arising from the question of what constitutes evidence for a statement. Observing objects that are neither black nor ravens may formally increase the likelihood that ... all ravens are black – even though, intuitively, these observations are unrelated.This problem was proposed by the logician Carl Gustav Hempel in the 1940s to illustrate a contradiction between inductive logic and intuition. A related issue is the problem of induction and the gap between inductive and deductive reasoning more0 comments

33

### Ross's paradox

Disjunction introduction poses a problem for imperative inference by seemingly permitting arbitrary imperatives to be inferred.0 comments

34

### Yablo's paradox

An ordered infinite sequence of sentences, each of which says that all following sentences are false. Uses neither self-reference nor circular reference.0 comments

35

### Richard's paradox

We appear to be able to use simple English to define a decimal expansion in a way that is self-contradictory.0 comments

Great list, but too much options and not worth the effort.

Forbidden words JSJUNG. You should learn to respect the effort PetersSmith puts into these "too" good polls.

@Mathgeekjoe True, I think she is the only one on this site that puts effort into their polls (⌐■_■)