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A somewhat recent article coming out of the University of Toronto and the Institute for Theoretical Physics in Zurich claims "no":

Constructivist epistemology posits that all truths are knowable. One might ask to what extent constructivism is compatible with naturalized epistemology and knowledge obtained from inference-making using successful scientific theories. If quantum theory correctly describes the structure of the physical world, and if quantum theoretic inferences about which measurement outcomes will be observed with unit probability count as knowledge, we demonstrate that constructivism cannot be upheld. Our derivation is compatible with both intuitionistic and quantum propositional logic. This result is implied by the Frauchiger-Renner theorem, though it is of independent importance as well.

The introduction reads:

There are many different perspectives available in contemporary epistemology, and it is not obvious which primitive epistemological commitments are mutually compatible. In this paper, we compare two epistemological perspectives—constructivism and naturalism—and show them to be mutually inconsistent in Section 2 by appealing to the epistemic content of quantum theory on the naturalistic view. We then discuss the significance of this result and show it blocks the derivation of Fitch’s paradox within the naturalistic (quantum) epistemic setting in Section 3.

(So I will note that I found this essay while researching Fitch's knowability result.) The thematism of constructivism that Fraser, et. al. offer is:

... the constructivist position may generalize to a hypothesis about the relation between truth, knowledge, and knowability simpliciter. It is this general constructivist epistemology that we here bring under scrutiny.

I can follow the article's technical side fairly well, but the conclusion strikes me as too surprising to be acceptable without some sort of qualifications. I've seen how Fitch's result is applied to (moderate) anti-realism, among other things, and this perception comprises one of the few times in my logic/set-theory studies that I've been able to follow technical notation without my mind's eyes glazing over in horror. But so even so, intuitively, how could constructivism be countered so drastically by appeal to naturalized epistemology? Is Fraser, et. al.'s characterization of constructivism fair in the first place? Again, the essay was published only some few months ago, so I assume responses to it are still much forthcoming. How have constructivists responded to it, if at all, yet?

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