  What if the paradoxical nature of quantum theory could find its source in
some undecidability analog to that of G\"odel's incompleteness theorem ? This
essay aims at arguing for such G\"odelian hunch via two case studies. Firstly,
using a narrative based on the Newcomb problem, the theological motivational
origin of quantum contextuality is introduced in order to show how this result
might be related to a Liar-like undecidability. A topological generalization of
contextuality by Abramsky et al. in which the logical structure of quantum
contextuality is compared with "Liar cycles" is also presented. Secondly, the
measurement problem is analyzed as emerging from a logical error. A personal
analysis of the related Wigner's friend thought experiment and and a recent
paradox by Frauchiger and Renner is presented, by introducing the notion of
"meta-contextuality" as a Liar-like feature underlying the neo-Copenhagen
interpretations of quantum theory. Finally, this quantum G\"odelian hunch opens
a discussion of the paradoxical nature of quantum physics and the emergence of
time itself from self-contradiction.
