Blackburn’s dilemma (as commonly understood) is that in explaining truths of the form ‘Necessarily-P’ we have to appeal either to a necessary truth, in which case we don’t seem to make the right kind of progress, or to a contingent truth, in which case we seem to undermine the necessity we were meant to be explaining. This paper advances two claims. First, it is argued that the dilemma is wider in scope than usually supposed. The standard assumption (evident also in Blackburn’s original paper (1993)) is that the dilemma applies to explanations of truths of the form ‘Necessarily-P’. I argue that the real problem identified by Blackburn doesn’t just apply to explanations of truths of this form, but to explanations of necessary truths in general (e.g. truths of logic, mathematics, etc.). In the course of this argument it also transpires that the real problem on the necessity horn is rather different—and rather less susceptible to obvious objections—than it is usually taken to be. It concerns the antinaturalistic core of necessity. Second, it is argued that there is an escape from the antinaturalistic core on the contingency horn. In the footsteps of Wright (1985), the claim is that the contingency horn is tenable for those who believe that the necessary truth in question is analytic, i.e. follows from its meaning.