Susan asked:

The question I have before me, from a philosophy course is: What is the truth-value of the following
statement?

This statement is false.

My instructor thinks we might have fun with this, that it is like a riddle. I don't think this is funny.
Could you help me?

============

The question is funny-peculiar rather than funny-haha. There are philosophical jokes, but this isn't
one of them. Like all good philosophical paradoxes, it exposes our lack of understanding of a
concept. I do, however, agree with your instructor that it is a question you can have a lot of fun with.

One doesn't need to study philosophy to realize that truth is a problem. In 'This statement is false', the
problem turns up in a completely unexpected place. The worry posed by this childishly simple
paradox has nothing to do with the limits of human knowledge, or the relation between facts and
values, or the nature of scientific laws, all questions which cast doubt on our ability to define truth. Yet
the doubts it raises are no less potent.

'This statement is false' can't be true and it can't be false. If it's true, then it's false, if it's false then it's
true. Either way, you end up contradicting yourself. But it can't be neither true nor false, because that
implies contradiction too.

So the task is to find some principled reason why one is not permitted to raise the question whether a
statement like 'This statement is false' is true. Suppose we said that a statement was not allowed to
refer to itself. That won't do. You can make the statement, 'This statement is in English' which is true,
or 'This statement is in French' which is false.

What about, 'This statement is true'? No contradiction there. Yet there is definitely something funny
going on. 'This statement is in English' reports a fact. whereas 'This statement is true' doesn't report a
fact. Should we say then that a statement can be true only if it reports a fact? That's no good,
because we want to say that examples of the laws of logic, like 'If it's raining then it's raining' are true
even though they don't report facts.

Still, there is a strong suspicion that the principle we are looking for to rule out the question whether
'This statement is false' is true is also going to rule out the question whether 'This statement is true' is
true. And so it goes on. Whatever principle we come up with, it has to be an essential part of a
definition of truth, not tacked on as an afterthought.

The logician Alfred Tarski, in his famous paper on the 'Definition of truth in Formalized Languages',
thought he had found an acceptable solution, but his complicated theory of an infinite hierarchy of
'meta-languages', each one of which is allowed to refer to statements made in the language below,
remains a matter of debate today.

Geoffrey Klempner