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 Paradoxes
The
first in Francis Moorcroft's series looking at some the classic
philosophical paradoxes.
No.
1 The Paradox of the Liar
Francis Moorcroft
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...
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The
paradoxes series will be updated at the beginning of August 2001
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