Postmodernists believe that there is no such thing as Truth, which is different from the notion that there is no such thing as truth. I am not sure that any serious philosopher would argue against the existence of empirical truth.
Can you dumb that down a little.
They don't deny that there is a material world beyond their senses. They deny that the mere fact they can sense it gives them any sort of privileged vantage-point to interpret the meaning of that world.
Essentially yes. In fact the system holds a dichotomy between "fact" and "truth." A fact is something that happens. It can be described no other way; it
is reality (of course some postmodernists I'm sure even deconstruct the notion of phenomenon as discrete, observable facts [that is to say, they deny even empirical truth]).
Truth on the other hand, as they have it, is based off of facts but can only essentially approximate it. A truth can be a normative category or a scientific law (religion and science are more dependent upon each other than we might think).
The basis of Western truth, for example, is causality, and the attempt to understand nature through it. Of course we could have never proceeded with this without the innate faith in causality born in the Catholic tradition around the year 1000. God's exists in all "forces" of the universe and thus the universe acts in accord to causality. Simultaneously thus we see the roots for both Calvinist predestination
and Darwin's natural selection.
Alas, no system is perfect, and that is why we have to introduce complete alien metaphysics into our science, such as Heisenberg's Uncertainty Principle or the 2nd Law of Thermodynamics, neither of which are in any way related to causality.