Charles Taliaferro, Evidenca and Faith: Philosophy and Religion Since the Seventeeth Century, Cambridge UP, 2005, p.350, under the heading “Contra Positivism”:
The Cartesian possibility—that our sensory data corresponds to a deceptive pattern of electrochemical signals, and not to some functional engagement with the world we think we perceive—surely limits the confidence we may responsibly feel in our physics or metaphysics. However, a practical epistemology doesn’t demand logical certainty. We may proceed with intellectual confidence, and some degree of moral assurance, if we possess warrant sufficient for our beliefs. This principle would make epistemology a relative system, as sufficiency is relative both to the claim in question and the evidence for that claim. Well, a relative epistemology needn't be thought a useless epistemology! The incompleteness theorem did not paralyze either mathematics or computer science; there is no reason we cannot make use of a verificationist epistemology in such circumstances that are not weakened by this foundational limitation.
Ayer, Schlick, and the others wanted to rule out what is untestable, partly because they were opposed to radical skepticism. […] For the positivists, the demon hypotheses (or brain in vat scenarios) are to be rejected for they are not verifiable. […] To insist on verifiability as a requirement for meaning seems to rule out meaningful narratives of how one might be systematically and irrevocably deceived.Emphasis mine. The word “insist” in the last sentence above is too strong. That “comprehensive Cartesian skepticism advances (at least initially) the possibility that one’s sensory experiences may all be systematically mistaken” (ibid.) entails a limitation, not the ruin, of verificationist positivism. The more charitable interpretation of the verifiability requirement is as a methodological, rather than an (ideological?) act of insistence.
The Cartesian possibility—that our sensory data corresponds to a deceptive pattern of electrochemical signals, and not to some functional engagement with the world we think we perceive—surely limits the confidence we may responsibly feel in our physics or metaphysics. However, a practical epistemology doesn’t demand logical certainty. We may proceed with intellectual confidence, and some degree of moral assurance, if we possess warrant sufficient for our beliefs. This principle would make epistemology a relative system, as sufficiency is relative both to the claim in question and the evidence for that claim. Well, a relative epistemology needn't be thought a useless epistemology! The incompleteness theorem did not paralyze either mathematics or computer science; there is no reason we cannot make use of a verificationist epistemology in such circumstances that are not weakened by this foundational limitation.