Apologies for the delay. Vlastimil: Thanks for the reference. I'll have to check it out. Julian and Jonathan : I think you've got some interesting questions about the notion of infallible justification. I see the concern that, modulo its definition, infallible justification may turn out to be a weak or even trivial form of justification. To address Julian's concern directly, I don't think defining infallible justification in terms of the warrant W for a proposition P entailing P and precluding -P implies that P is a necessary truth or that all justified propositions are necessary, infallibly justified propositions. One can think of infallible justification along the following lines: W entails P iff given W the objective probability of P is 1. Now certainly some propositions have the potential to be infallibly justified in this sense yet not be necessary truths. Conceivably (for argument's sake)  the proposition that Winston Churchill sneezed 3 times on January 7, 1941 might have an objective probability of 1 which is yielded by evidence. But this is certainly not a necessary truth. In fact if we take almost any contingent proposition P we might conceive of the possibility that evidence infallibly justifies it or gives it a probability of 1 (at least if we think infallible justification is possible). The question is whether we can sensibly apply this definition of infallibility to a priori propositions. I don't see why not. I don't think any a priori propositions are infallibly justified in this sense but I don't see that it's a meaningless or insignificant question to ask whether an a priori proposition can be warranted to a degree that gives it an objective probability of 1. Perhaps, then, using entailment as the crucial notion in spelling out infallibility is not the right way to go (i.e. it's misleading at the very least).