If post-modernism is anything, I suppose the fundamental idea is a kind of self-defeating premise that there is no such thing as objective truth.
Postmodernism isn't really anything beyond a label that gets applied to ideas that challenge the modernist project--it's not a single cohesive school of thought at all. I don't think you need commit yourself to the idea that there's no such thing as objective truth in order to be called a postmodernist. I don't even see someone like Foucault as necessarily rejecting the
existence of truth--he might be just critiquing the idea that we can get at it in an impartial way. I don't know; I don't have the patience to read him.
When people reject postmodernism out of hand, it reads to me like dogmatism--it implies that the modernist project is necessarily beyond reproach. That's a weird stance to take, and one that's fundamentally at odds with the aims of modernism, where dogma is meant to be anathema.
I think that this was the main target for Sokal, when critics of scientific objectivity tried to argue that science is no better at understanding the world than, say, critical theory. Julia Kristeva, for example, I believe that said E=MC2 was a sexed equation.
I think that was Luce Irigaray, not that I can tell you the difference. But yeah, "fashionable nonsense" pretty much covers it.
I think Sokal's point was perfectly well-made with his hoax, so I support it. However, these days, if you are trying to find someone arguing that there is objective scientific truth, and then there are some other, different important truths that may not actually be true, but are still true in an important sense, then who would be the poster child for this? Jordan Peterson of course. Nobody writes more like the right-wing reactionary idea of a post-modernist than he does. He blathers long and hard about Jung and Nietzsche and creates these incredible intellectual towers of ********, and the right-wingers, the reactionaries can't get enough of his total and utter drivel.
I think so too, but I don't think Sokal ever claimed to have demolished postmodernism, because he obviously didn't. We do probably owe him a debt for putting some of the obscurantists in a corner.
As for Peterson, you don't need to look further than his account of truth, which is half-baked nonsense. And yes, he looks awfully like postmodernist when attempting to elucidate it. But for that guy, everything is culture war, hence the weirdo conspiracy theories about "postmodern neo-Marxists" trying to undermine western civilization.
Of course, Neil deGrasse Tyson also has a completely boneheaded account of truth, and he's supposed to be one of the good guys.