 Third, one could reject either the Truth Constraint or the Definability Constraint. The trouble is that if one rejects the Truth Constraint then on this view (assuming the Ω Conjecture) Π2 truth in set theory is reducible in the sense of Turing reducibility to truth in H(δ0) (or, assuming the Strong Ω Conjecture, H(c+)). And if one rejects the Definability Constraint then on this view (assuming the Ω Conjecture) Π2 truth in set theory is reducible in the sense of definability to truth in H(δ0) (or, assuming the Strong Ω Conjecture, H(c+)). On either view, the reduction is in tension with the acceptance of non-pluralism regarding the background theory ZFC + “There is a proper class of Woodin cardinals”. 