What is a paradox?

A paradox is a sentence that seems to be true, but actually makes no logical sense.

Types of paradox

Here are 2 types of paradox:

1) Self-reference: a sentence that refers to itself, but the reference seems to make the sentence illogical (or make no sense)

2) A vicious circle: a sentence, or collection of sentences, that seems to go in a circle that will never end.

Examples of Self-reference

– This sentence is false.

(the sentence says it is false, but must be true if it is going to be false. It therefore makes no sense.)

– A barber only shaves people who do not shave themselves, so does he shave himself?

(if the barber shaves himself, he should not shave himself because he only shaves people who do not shave themselves; if he doesn’t shave himself he should shave himself, because he doesn’t shave himself)

– ‘I know that I know nothing.’

(if the person knows this, then he/she can’t know nothing; if he/she knows nothing, then he/she shouldn’t know this)

– Spies do not look like spies

(a spy must look like a spy, because he/she is a spy; this sentence therefore seems to make no sense)

– This is madness, but it has method in it

(madness has no method, so something with method cannot be madness)

Examples of vicious circles

– The following sentence is true. The previous sentence is false.

(these two sentences go around in a circle: the first sentence is true, so the second sentence is true; but the second sentence says the first sentence is false, so the second sentence is not true, so it is false etc.)

– ‘Everything I say is a lie.’

(if everything I say is a lie, then this sentence is a lie, so not everything I say is a lie, meaning this sentence may be true etc.)

– ‘What happens to Pinocchio’s nose when he says ‘My nose will grow now’?

(Pinocchio’s nose grows when he lies. So if he says his nose will grow and it doesn’t, he is lying, so his nose will grow; if he says his nose will grow and it does, then he isn’t lying, so his nose shouldn’t grow etc.)

– ‘Pursuing happiness will make you miserable. Pursuing other things will give you happiness. If I want to be happy, what should I pursue?

(pursuing other things to be happy is actually pursuing happiness, and therefore will make you miserable)

– Only crazy people would fly these missions. And these missions are no place for crazy people. If you know the missions are crazy, then you are not crazy and you should be flying these missions.

(used in the novel ‘Catch 22’ as Yossarian tries to think of ways to get out of an insane war)

Other Paradoxes

The half-paradox

This is not a real paradox, but can look like one if people do not think clearly.

– A father and son are driving. The car crashes and the father dies. The boy is taken to hospital, where the doctor says ‘I can’t operate on this boy. This is my son.’

(if people think the doctor is a man, then it looks like it makes no sense; however, if they think that the doctor is a woman there is no problem).

– A man is celebrating his 5th birthday, but is now 21.

(the answer is in knowing the man was born on February 29th, so only has a birthday every 4 years)

Thought Experiments

Some people have thought up interesting situations to make paradoxes.

– A man makes a time-travelling machine. He goes back in time and kills his grandfather before his mother and father are born. What happens to the time-traveller?

– Which came first: the chicken or the egg?

– You can never go from one place to another, because first you must go half way. After that you must go half way again. Then another half way. And so on.

Using Paradoxes

Paradoxes can be used in writing to make the reader think.
They do not need to have an answer (as in a half-paradox): the idea is purely to make the reader examine the words and look for an answer.
They are often used to make writing seem more interesting (and the reader to enjoy feeling clever spotting the paradox)