 Many philosophers are willing to concede that zombies are conceivable in some sense (e.g. Hill 1997; Hill and McLaughlin 1999; Loar 1999; Yablo 1999). However, that sense is sometimes quite broad. For example, a claim that ‘there are no substantive a priori ties between the concept of pain and the concept of C-fiber stimulation’ has been backed up by the point that ‘it is in principle possible to master either of these concepts fully without having mastered the other’ (Hill 1997, 76). By that standard, though, it would be conceivable that the ratio of a circle’s circumference to its diameter is a rational number, when it isn’t. If conceivability in that sense entailed possibility, it would be both possible and impossible for the ratio to be rational; which would make such conceivability useless for the purposes of the conceivability argument. So understood, premiss (1) of the argument would be easy to swallow; but (2) would have to be rejected. Evidently, the lower the threshold for conceivability, the easier it is to accept (1) — but the harder it is to accept (2). So the kind of conceivability invoked in premisses (1) and (2) needs to be strongly constrained. A common and useful definition, which will be followed here, is: cannot be known a priori to be false; so A is conceivable if and only if not-A cannot be ruled out a priori. (For sophistication of these and related ideas see Chalmers 1999, 477; 2002; 2007; 2010; 5.1 below.) 