  It would be wrong to equate what X-standards sanction with what X-practitioners believe (for X = science or mathematics or more generally). For one thing, X-practitioners may not have given a particular question any thought. For another, X-practitioners might all be mistaken. Moreover, X-practitioners might self-consciously maintain the opposite of or at any rate something distinct from what X-standards sanction. For instance, a scientist may believe p, perhaps on the basis of a ‘gut feeling’ or on account of some overriding religious convictions or for whatever non-scientific reason, whilst still recognising that scientific standards support not-p. Or a mathematician may believe that the number 7 has mystical properties but not believe it qua mathematician. A tighter connection between practitioners and standards, then, might be this: what X-standards sanction is what X-practitioners are disposed to correctly believe qua X-practitioners. (This is not intended as a reductive analysis.)