  Specker's principle, the condition that pairwise orthogonal propositions must
be jointly orthogonal, has been much investigated recently within the programme
of finding physical principles to characterise quantum mechanics. It largely
appears, however, to lack a transparent justification. In this paper, I provide
a derivation of Specker's principle from three assumptions (made suitably
precise): the existence of maximal entanglement, the existence of non-maximal
measurements, and no-signalling. I discuss these three assumptions and describe
canonical examples of non-Specker sets of propositions satisfying any two of
them. These examples display analogies with various approaches in the
interpretation of quantum mechanics, notably ones based on retrocausation. I
also discuss connections with the work of Popescu and Rohrlich. The core of the
proof (and the main example violating no-signalling) is illustrated by a
variant of Specker's tale of the seer of Nineveh, with which I open the paper.

Quantum Physics