I don't think of this as an attack of Postmodernism as much as analytic philosophy in general. You cannot construct a proof of a philosophical statement by referencing chunks of math and physics. Analytic philosophy is science for those who do not understand science and better left to the field of science. The real philosophy is moral and ethical philosophy, because everyone uses it to decide on every conscious prescriptive actions they undertake, yet they cannot be derived from science and are arbitrarily agreed on by societies. Pure science is purely descriptive and observational, it does not provide a proof for correct future action. Individuals often reference science as post-facto justification for their actions, for example I would reference my knowledge of natural selection as justification for pursuing a job, whereas the Nazis also used natural selection as justification for undertaking the Holocaust. Moral and ethical philosophy are the most important area of philosphy, it is a discussion that guides every action we take yet one with no completely "correct" answers.
I was trained in analytic philosophy, and I'm not convinced you know what analytic philosophy is. Postmodernism isn't analytic philosophy--it's close to the exact opposite. In fact, analytic philosophy originated as a response to continental philosophy, the intellectual cesspool of Hegel and friends from which postmodernism is spawned.
Some analytic philosophers you may have heard of include: Bertrand Russell, Karl Popper, Ludwig Wittgenstein, G.E. Moore, R.M. Hare, A.J. Ayer, Saul Kripke, David Lewis, Edmund Gettier, John Rawls, Robert Nozick, and Nick Bostrom. Many of these philosophers discussed morality and justice a great deal. Others discussed the logical underpinnings of science and mathematics--Popper in particular is highly esteemed by many scientists I've known, and Russell needs no introduction.
EDIT: There are of course many great analytic philosophers I forgot, but I found it worth editing this post to include W.V.O. Quine, in honor of whom we write programs which print their own source code.
If you reread the original link you'll see the main source of Dawkin's frustration comes from the misappropriation and misuse of mathematical logic and scientific fact with disregard for the preserving precise meaning.
This is a large problem not just in Postmodernism but in many areas of modern analytic philosophy as well, especially Philosophy of Mind.
It's not a universal view, but there's a decent number of scholars on both sides of the Atlantic who see Derrida and the later Wittgenstein as actually getting at pretty similar ideas. Both are fundamentally concerned with the indeterminacy of language, language as a kind of game, etc.
Let's be clear, though. Heidegger was an existentialist (in the continental tradition). He was dense, but understandable. Postmodernism is just gibberish.
