The classical ‘liar’ paradox is the statement by someone who always tells lies—a 'liar':
‘I am lying’.
If the 'liar' does always tell lies, then what he is saying is the truth, which means he does not always tell lies.
So the person 'always tells lies' and 'doesn't always tells lies'—a paradox.
‘I am lying’.
If the 'liar' does always tell lies, then what he is saying is the truth, which means he does not always tell lies.
So the person 'always tells lies' and 'doesn't always tells lies'—a paradox.
The following statement (in a book devoted to modern philosophy1*) is presented as an example of the ‘liar’ paradox:
‘Nietzsche ... argued that there are no truths, only interpretations. But you need only ask yourself whether what Nietzsche says is true, to realise how paradoxical it is. (If it is true, then it is false! — an instance of the so-called ‘liar’ paradox.)’
The author criticises Nietzsche with the question: ‘Is the statement true or false?’ If Nietzsche was here today he might reply: ‘I have just stated that there are no truths. When you ask whether my statement is true (or not), you are claiming that there are such things as ‘truths’. Hardly an argument or a proof; it is the equivalent of a 6 year old stamping their foot and crying: ‘Not so!’’
Scruton’s criticism might have been a ‘throw-away’ comment to arouse the interest of his readers, but it is indicative of the pervasive misunderstanding of language, words and grammatical constructions in discussions of logic and in the world in general.
A similar analysis is seen in Kant’s criticism of Descarte’s phrase ‘Cogito ergo sum’ (I think therefore I am). Descartes proposed it as proof of his own existence. But Kant commented, that by stating ‘Cogito’ (I think) Descartes is already acknowledging that he exists. So what is being said is: ‘I am and I think, therefore I am’ — a nonsense.
Consider the sentence: ‘The liar paradox is the statement of a liar that they are lying.’ By calling the person a ‘liar’, we are already claiming that they (always) tell lies and would be incapable of making the statement ‘I am lying’. So the whole scenario is entirely hypothetical and logically impossible to start with.
1. Scruton, Roger, 1997 (1994), Modern Philosophy, Arrow Books, London. pp.5-6 Back