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Potemkin wrote

Hmm... I originally thought not, but then more thoughts followed. Haha.

If the statement "classical logic is to paraconsistent logic" is synonymous with the statement "analytic logic is to dialectical logic," then I think we have problems in formulation before we even begin. My understanding is that it is controversial, even among dialecticians, to suggest a dialectical logic separate from, or in violation of, formal logic.That being said, theorists like Murray Bookchin have suggested or implied that a dialectical logic was separate from the analytic. I guess also I'm wondering if we mean the broader "formal logic" of which "classical logic" is a part, or if we can juxtapose a "dialectical logic" to a "classical logic" without violating the larger "formal logic?"

That being said, I think there is a substantive sense in which we can see parallels between the breakdown in the relation between classical and quantum physics with that of the difference between analytic and dialectic modes of investigation. If things like Schrodinger's cat are explanations of quantum mechanical processes, this can obviously be seen as parallel to a dialectical method of inquiry. And definitely there is a dialectical approach to science that can be pursued (and has been, see particularly Levins & Lewontin's The Dialectical Biologist, for instance).

So on the other hand, yes, there are definite parallels between the "logic" (I use this here in a general, informal sense) of dialectic and quantum physics. And I think we can see parallels in the classical senses of logic and physics. Without looking it up, I would imagine both of these "classical" concepts came about in the West at around the same time, perhaps from the same "logic" or ideology.

In conclusion, I'm not sure. Haha. This particular area isn't my expertise, so this could all be incorrect, but I think I understand what you're asking. And I think, dialectically, there are substantive senses in which we can say it is a valid analogy, and substantive senses in which we might not. Maybe we should just put it in Schrodinger's box, with his cat, and all will be satisfied. Until it's opened.