Logical versus epistemic possibility

It seems to me that the following is axiomatic: For any person S and public-world proposition p that S accepts, S lacks infallible warrant for accepting p unless the relevant warrant is incompatible with (precludes) the falsity of p. Accordingly, my justification for subscribing to the proposition that there is now an olive on the kitchen floor fails to be infallible (is fallible) so long as there is at least one possible world at which I have precisely the degree of warrant which I actually possess for accepting that proposition, but it is false that there is now an olive on the kitchen floor. So long as there is at least one such possible world, it is epistemically possible for me to be mistaken in subscribing to this proposition.

However, it is Blaauw's contention that infallibilism is best construed as a thesis about logical possibilities of error rather than (just) epistemic possibilities of error (350). And he maintains that, as a consequence of my emphasis on the latter rather than the former, my argument is less effective than it might otherwise be. It would seem, however, that there is something very odd about the notion that infallibilist epistemology should be regarded as precluding the logical (or conceptual) possibility of error. Consider: any logically contingent proposition – and, of course, public-world propositions tend to be logically contingent – which is true is such that its negation is logically possible. Accordingly, assuming it to be actually true that there is now an olive on the kitchen floor, it is clearly logically possible for that proposition to be false: there is at least one merely (or non-actual) possible world at which this proposition is false. Accordingly, it is logically possible that there fails to be an olive on the kitchen floor now.

But why is this – by itself – epistemically interesting, i.e. why take it to have significance for the issue between fallibilism and infallibilism? Clearly, the logical contingency of the relevant proposition hardly implies (by itself) that the degree of justification which I actually have for accepting it fails to preclude its actually being false, i.e. hardly implies that the degree of justification which I actually have for maintaining that there is now an olive on the kitchen floor does not require that the undeniable logical possibility of its being false does not in fact obtain. And, of course, this is radically distinct from the patently unacceptable notion that I can have a degree of warrant in this regard which implies that its negation is logically impossible. No amount of evidence for the truth of a logically contingent proposition could conceivably establish that.

Brains in a vat?

Having noted this, however, it can readily be seen that classical supernaturalism gives profound indication of precluding even the logical possibility of our being brains-in-vats: a popular notion these days – arguably our ‘scientific’ update of the malicious demon hypothesis – to which Blaauw makes brief reference (351–353). For it seems central to traditional theism that God constitutes a necessary being: that ‘God exists’ expresses a true proposition at all possible worlds. A fortiori, classical supernaturalism can properly be taken to imply that that there is no possible world which includes the existence of natural objects but fails to include the existence of God (who constitutes the creator-and-conserver of all natural objects at every possible world which includes their existence). Hence, traditional theism, by virtue of God's impeccable veracity, can properly be regarded as patently incompatible with our existing as brains-in-vats (what could be more maliciously deceptive than such a circumstance?). Accordingly, since any proposition that is incompatible with a logically necessary truth is logically impossible, classical supernaturalism gives profound indication of precluding the existence of possible worlds at which we exist as brains-in-vats.

Divorcing theism from infallibilism

The very heart of Blaauw's counter-argument becomes explicit in the final section of his paper, i.e. ‘Divorcing theism from infallibilism’. The key passage is as follows (italics mine):

Why contend, however, that we are required to have infallible knowledge of the truth of theism in order for theism to imply that, by virtue of God's impeccable veracity, there can be (many) public-world propositions such that our perceptual warrant for subscribing to them would be infallible? Whether theism actually implies that – and what I attempted to establish is that we are eminently entitled to maintain that it does – is entirely independent of whether theism is known infallibly to be true or, indeed (unless ‘knowing that p’ and ‘knowing infallibly that p’ constitutes a distinction without a difference) known to be true at all. Compare: Berkeley's metaphysic implies that there is no thing as material substance, but that Berkeley's metaphysic implies this hardly requires our knowing that his idealistic metaphysic is true. Accordingly, that we cannot (if we cannot) have an infallible grasp of the truth of theism is not an acceptable justification for maintaining that theism does not imply the falsity of the doctrine of public-world fallibilism.

Thus, as Blaauw has rightly contended in e-mail correspondence of 12 May 2006 (all subsequent citations from Blaauw are from this source), our disagreement rides heavily on the internalism–externalism debate within contemporary epistemology. After asking how the notion of ‘eliminating a possibility’ is to be interpreted, he goes on to say: ‘If it is interpreted internalistically, I don't think that theism implies infallibilism … we would need to know that the BIV [brains-in-vats] possibilities are logically impossible, which would require us to know that theism is true.’ Blaauw then makes clear his strong preference for internalism in this regard. For he maintains that an externalist analysis of what it is to ‘eliminate a possibility’ is just too weak, i.e. ‘it does not really solve the sceptical problem because all can now say is: if theism is true, we have infallible knowledge’. But if infallible knowledge thus reduces to knowledge that is merely ‘conditional’, it is hard, claims Blaauw, to see ‘why we would even be interested in having it’.

My brief response here is this: as normally construed, an internalist conception of justification – the view that, for any proposition p and person S, S is justified in accepting p only if S can grasp or articulate the relevant justification – seems to me to be deeply flawed. For if internalism is true, S's justification for accepting p can be adequate only if S knows or is justified in believing that the relevant justification for accepting p is adequate. How, then, can internalism fail to imply a vicious regress? Further, and for reasons not unrelated to the foregoing, internalism strongly suggests that Kp requires KKp, i.e. that no one can know that p without knowing that she knows that p. This, however, entails (since belief is an uncontroversially necessary condition for knowledge) that it is impossible to believe that one fails to know that p and be mistaken. Accordingly, given the assumption that Kp requires KKp, the belief that one knows nothing would fully suffice for the truth of that belief. Are these not compelling reasons for rejecting internalism?