We revisit an example of stronger-than-quantum correlations that was discovered by Ernst Specker in 1960. It is found to provide a narrative thread that weaves together a large number of foundational topics: proofs of the impossibility of measurement-noncontextual and outcome-deterministic ontological models of quantum theory (the Kochen-Specker theorem), in particular the recent state-specific pentagram proof of Klyachko; proofs of the impossibility of Bell-local models of quantum theory (Bell's theorem), especially the proofs by Mermin and Hardy and extensions thereof; proofs of the impossibility of a preparation-noncontextual ontological model of quantum theory; and the demonstration that there are triples of positive operator valued measures (POVMs) that can be measured jointly pairwise but not triplewise. Along the way, several novel results are presented, including: a generalization of half of a theorem by Fine connecting the existence of a joint distribution over outcomes of counterfactual measurements to the existence of a measurement-noncontextual and outcome-deterministic ontological model; a generalization of Klyachko's proof of the Kochen-Specker theorem from pentagrams to a family of star polygons; a proof of the Kochen-Specker theorem in the style of Hardy's proof of Bell's theorem, i.e., one that makes use of the failure of the transitivity of implication for counterfactual statements; a categorization of contextual and Bell-nonlocal correlations in terms of frustrated networks; a derivation of a new inequality testing preparation noncontextuality; and finally, some novel results on the joint measurability of POVMs and the question of whether these can be modeled noncontextually. Specker's parable also provides a novel type of foil to quantum theory, prompting the question of why the particular sort of complementarity embodied therein does not arise in a quantum world.