  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.
