  In-principle restrictions on the amount of information that can be gathered
about a system have been proposed as a foundational principle in several recent
reconstructions of the formalism of quantum mechanics. However, it seems
unclear precisely why one should be thus restricted. We investigate the notion
of paradoxical self-reference as a possible origin of such epistemic horizons
by means of a fixed-point theorem in Cartesian closed categories due to F. W.
Lawvere that illuminates and unifies the different perspectives on
self-reference.
