Epistemic Horizons: This Sentence is $\frac{1}{\sqrt{2}}(|True\rangle + |False\rangle)$ (2007.14909v2)

Abstract: In [Found. Phys. 48.12 (2018): 1669], the notion of 'epistemic horizon' was introduced as an explanation for many of the puzzling features of quantum mechanics. There, it was shown that Lawvere's theorem, which forms the categorical backdrop to phenomena such as G\"odelian incompleteness, Turing undecidability, Russell's paradox and others, applied to a measurement context, yields bounds on the maximum knowledge that can be obtained about a system, which produces many paradigmatically quantum phenomena. We give a brief presentation of the framework, and then demonstrate how it naturally yields Bell inequality violations. We then study the argument due to Einstein, Podolsky, and Rosen, and show how the counterfactual inference needed to conclude the incompleteness of the quantum formalism is barred by the epistemic horizon. Similarly, the paradoxes due to Hardy and Frauchiger-Renner are discussed, and found to turn on an inconsistent combination of information from incompatible contexts.