A harmful and all too common idea is that it is impossible to know anything — that facts do not exist. The popularity of this claim, and the fact that anyone could possibly believe it, is quite astonishing given that the claim is both self-refuting and preposterous on its face. For if we apply the claim “there are no facts” to itself, then it must be true that the claim itself is not true either, and the claim therefore refutes itself. Adding to the claim that there are no facts except for the fact that there are no facts other than this one fact is no better, because, according to this claim, it must then also be the case — it must be a fact — that, say, 2+2=4 is not a fact. So the problem with this expanded claim is that accepting it forces us to admit that there is an infinite number of facts, because we can make an infinite number of claims about the world, and it must be true according to this expanded claim that none of these other claims are facts, which of course contradicts the claim itself. So, as closer examination reveals, this second claim is also incoherent and self-refuting, and therefore it cannot be true either.
Once we have accepted the validity of logic, the claim that there are no truths, or only a limited number of truths, is bound to fail, as reason itself compels us to admit that there is an infinite number of facts, and if we do not accept the validity of logic and reason, then why even try to make an argument in the first place?
Nothing keeps us from answering the biggest questions in life and agreeing upon their answers more effectively than the attitude of relativism, which is why it is so important to expose this attitude for the obvious self-contradiction it is, and to go beyond it.
 A similar logical demolition of pragmatism of the kind that Richard Rorty and Jürgen Habermas defend can be found in Sam Harris' The End of Faith, pp. 179-181 and pp. 279-283.