If I say: “I always lie” – am I then lying, or not? If the sentence “I always lie” is true, then it should not be true, because I always lie. If the sentence is not true, this would translate into “I never lie”, But in this case I lied to you, and we again have a contradiction. This is an example of a paradox. A paradox is a statement which contradicts itself. In this episode I’d like to show you a few other examples of paradoxes. Just for the fun of it.

Once there was a crocodile, which stole a child. The mother talked to the crocodile and the crocodile said that it will return the child to the mother if she answers to a question correctly. If the answer is wrong, then the crocodile would eat the child. The mother agreed. The crocodile now asked the question: “What am I going to do next?”. What should the mother answer? If she says: “You are not going to eat my child.”, then the crocodile would respond: “Wrong answer, I would have eaten the child, and now I’m really going to eat it because your answer was wrong”. What’s going to happen if the mother answered: “You are going to eat my child.”. The question is now: Should the crocodile now eat the child or not? If the answer is correct, then the crocodile promised to return the child. But this would make the answer wrong again. If the crocodile really intended to eat the child, he has to return it, but at the same time can’t do that because then the answer would be wrong again.

If this one was a little difficult to understand, here is a simpler one. It’s called the Omnipotence Paradox: Assuming that God is all-powerful, is He able to create a rock which is so heavy that He can not even lift it himself? I leave it up to you to reason out this one, and I think I don’t need to mention that the paradox is theological nonsense, but this is a different issue.

And this one is a classic: “I know that I know nothing.” This is also a contradiction in itself. The person does know something, namely that he/she knows nothing.

Russell’s paradox is also quite famous: In a village there is a barber (a hairdresser). The barber shaves everyone who does not shave himself. If I don’t have a razor at home (in this case I don’t shave myself), then the barber will take care of it and shave my beard. The question is now: Who shaves the barber? The barber is not allowed to shave himself because he only shaves those people who do not shave themselves! But then, if he does not shave himself, then he must do so, because he shaves all those who do not shave themselves. So you see, we have another contradictory, paradoxical situation.

For those of you, who read George Orwell’s novel 1984, “War is peace.”, “Freedom is slavery.”, “Ignorance is strength.”. These too are self-contradictory, paradoxical statements, which, in this case, are used for propaganda purposes.

There is also a quite famous song from Simon & Garfunkel called “Sounds of Silence”. How do the sounds of silence sound like?

The paradoxes that I like most are the real-world paradoxes, however. A simple one: You forgot your key in your apartment and locked yourself out. But you need the key in order to open the door and to get to the key.

Another one: in some countries you need to have a fixed residential address in order to be able to work. Now, if you are homeless because you don’t have any money and need a job, you can’t get a job because you don’t have an address. In other words, you need a home to get a job, and you need a job in order to earn the money to pay for a home. Again, you have a cat biting its own tail – a paradoxical situation.

How wonderful that we have met with a paradox. Now we have some hope of making progress.
Niels Bohr

Way of Knowing: Logics/Reason