Twenty years on, one lesson of Sokal’s hoax is that many educators are uneducable. Another is that although wonderful sendups have been written about academia...it now might be beyond satire.
Not to put too fine a point on it, I'd say: the most important lesson is that a mishmash of stupid theories has taken over many of the humanities and some of the social sciences. As usual, the culture (only) seems to absorb the worst ideas produced by the humanities, and the aforementioned mishmash has, sadly, influenced middlebrow culture. Members of the chattering class tend to have humanities backgrounds, and like to seem familiar with what's fashionable in the academy, and so they tend to speak the mishmash. Worse, the bad theory is bound up inextricably with extremist left-wing identity politics. Worst of all, that theory is bound up with a catastrophically bad theory of reasoning. That theory is the kind of theory you might expect to be favored by interpretive, non-empirical disciplines: it basically holds that you grab whatever conclusion strikes your fancy, and then you free associate, riffing on trendy ideas, until you can pretend that you've offered an argument for the conclusion you wanted all along. And (see above) these conclusions are almost always of a kind favored by far-left identity politics.
People have long thought that the humanities are full of shit. But, for the last thirty years of so, the humanities have
been full of shit--or largely full of it, anyway. And unsurprisingly, it's affected our public discussions and decisions. The thing about all this is that it doesn't just yield one or two bad conclusions. When you have adopted a defective method of reasoning, the error spreads far and wide, permeating almost everything you think. And that's a very bad thing indeed.