Is Sokal & Bricmont's lambasting of Post-Modern Intellectuals proof of the vacuity of Post-Modernism?
Does this offer us a hope at proving that some schools of Philosophy can be proven to be pure Sophistry?
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Much of philosophy is true but vacuous: dualism vs monism, various theories of mind, etc. They are interesting, but ultimately don't have real bearing on life. Proving something does not prove a workable way of addressing the world does not make it untrue or sophistical. Nor does it mean that older solutions might not in some way be better than ones that are more correct.
It would be difficult if not impossible to live your life thinking of everything in a way that takes relativity and quantum dynamics seriously at every moment. But they are real.
In my interpretation, the problem we seem to be having with postmodernism is in wishing it had more significance and guiding value than it really can provide. We marry it to other objections to modernism and logical positivism and claim it vindicates or supports them them.
But it did not provide those, other forms of sophistry did. We mix up together the effects of having too much information in our culture for people to digest, the war between science and religion that we created and all of the sophistical dancing it has spun into our worldview, our own conflicting history of Christian morality promulgated through extremely anti-Christian execution, and postmodernist awareness of social reality. And we pretend this holds together as a piece and that it proceeds primarily from its latest contributor.
At the same time in terms of really providing a better solution for the problems it addresses, one needs to do so by taking it seriously, if only as an adversary. I cannot speak directly to Sokal & Bridgemont, but most of those who object to it fail to do so.
If you want to criticize postmodernism from any point other than from inside itself, you are not going to manage this by looking at its effects, only its causes. You need to provide the kind of solution for realistically describing our own process of definition and reasoning that Wittgenstein and Quine finally gave up on.
We have no problem identifying and addressing sophistry, throughout the history of philosophy. This is why we name that subject after the given group of people against whom our leading lights of ancient philosophy stood in the west, the professional sophists. Had they not won, we would not idolize them.
"Lambasting" is not a proof. English editors obviously have been unwilling to translate French rebukes to S&B's rhetoric. The case is open and one should hear both sides, even if one of them speaks mostly a foreign language.
Yves Jeanneret, L’affaire Sokal ou la querelle des impostures (Paris, PUF, 1998, 274 p.) is abook length "lambasting" of Sokal & Bricmont written soon after their bestseller. For a few quotes there's a good review. Also Baudouin Jurdant edited Impostures scientifiques, Les malentendus de l'Affaire Sokal (Paris: La Découverte, 1998).
Sorry, this is not a proof and so there si no hope.