Suppose someone said to you
What I am now saying is a lie.
Is what they said true or false? If what they said was true, then they are telling a lie so it is false; on the other hand, if it is false then it isn’t a lie and so must be true!
This paradox known as the Paradox of the Liar is usually attributed to Epimenides – although it was actually devised by Eubilides. Epimenides, who was a Cretan, was supposed to have said
All Cretans are liars.
The problem is: Is he telling the truth or not. It seems that if the sentence is true, then it is false. But if it is false, then it is true.
A tempting way out is to suppose that the problem is to do with the notion of self-reference, that Epimenides was referring to himself when he said ‘All Cretans are liars’. After all, one favourite version of the paradox is
This sentence is false
and a clearer case of self-reference couldn’t be given, as the ‘this’ of the sentence refers to the sentence itself.
Such a solution would, however, be premature. Consider the following pair of sentences
The following sentence is true.
The preceding sentence is false.
Neither of these sentences refers to itself, and yet the same paradox is generated: if the first sentence is true then it is false – but if it is false then it is true. So the problem can’t be about self-reference.
Perhaps by now you may be thinking that the problem is that such utterances as Epimenides’ and the other versions given above are not true or false but meaningless, that they may, on the surface, appear to make sense but really have no more meaning than the nonsense verse of Lewis Carroll. This solution may also be attractive but consider the following case. You are walking down the street and you find a card on the pavement which says
The sentence on the other side of this card is true.
When you turn over the card, the other side reads
The sentence on the other side of this card is false.
The problem is that if the first sentence was meaningless then how did you know that you should turn over the card and read the other side…
Also, the appeal to meaningless does not avoid a further version of the same paradox, often called the Strengthened Liar, which comes about from considering the following sentence:
This sentence is either false or meaningless.
Is this sentence true? If it is, then it is either false or meaningless – both options leading to the conclusion that the sentence is not true, for if the sentence is meaningless then it cannot be true. Is it false? If it is, then it is neither false nor meaningless – so it is both true and meaningful.