While this seems silly to philosophically-uninitiated me: is there a version of Grothendieck universes for this sort of thing, or even some kind of restricted quantification?
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Right… So, historically, the French stuff mostly comes from working out implications of Nietzsche and Heidegger.
The other major thread of meta-rational thinking starts from the failure of logical positivism, and Wittgenstein’s analysis of that in his _Philosophical Investigations_.
From a STEM pov it’s easier to follow the Wittgenstein thread, because logical positivism was trying to use cutting-edge methods to prove Science Is True, and subsequent work is more informed about STEM than the French thread.
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