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 Lawvere that illuminates and unifies the different perspectives on self-reference.

It is shown that it is impossible for an observer to distinguish all present states of a system in which he or she is contained, irrespective of whether this system is a classical or a quantum mechanical one and irrespective of whether the time evolution is deterministic or stochastic. As a corollary, this implies that it is impossible for an observer to measure the EPR-correlations between himself or herself and an outside system. Implications of the main result are discussed for (...) how we have to conceive of universally valid theories. (shrink)

General results about restrictions on measurements from inside are applied to quantum mechanics. They imply subjective decoherence: For an apparatus it is not possible to determine whether the joint system consisting of itself and the observed system is in a statistical state with or without interference terms; it is possible that the apparatus systematically mistakes the real pure state of the joint system for the decohered state. We discuss the relevance of subjective decoherence for quantum measurements and for the problem (...) of Wigner's friend. (shrink)