Another issue arising from ej’s new comments here:
Let e be evidence you possess, and let p be a proposition you’ve never considered but which is entailed by e. Under what conditions is p propositionally justified for you?
A couple of egregiously bad answers:
1. The Profligate Position: always and everywhere. PP is too broad since justified false mathematical and logical beliefs are possible, and if you are doxastically justified in believing ~p, you can’t also be propositionally justified in believing p. (Note on terminology: doxastic justification involves justification for actual belief; propositional justification involves justification for a proposition, whether or not the person in question believes that proposition.)
Moreover, we have 3-lb. brains; there are some mathematical truths beyond our powers to conceive, and our theory of justification ought to be sensitive to the difference between such wetware and the wetware of beings capable of logical and mathematical omniscience.
2. The Miserly Position: never and nowhere. MP is too narrow since we often have propositional justification for things we don’t believe and have never considered, such as that I’m taller than a midget, though not as much taller as Plantinga. (OK, I believe it now but I didn’t believe it before constructing the example and hadn’t considered it either; but it was propositionally justified for me.)
[I’m going to edit this to put the rest of the entry below the fold so as to clean up the main page of the blog (contributors, when you create an entry, you can do the same by clicking on the “more” button).]
Some more less-obviously bad answers:
3. Propositional justification obtains for those propositions which are such that were you to add the belief in question, it would be doxastically justified. I’ve argued against this view in several places, most recently in APQ, content here. The basic problem is that believing itself can both create and destroy evidence for its content.
4. You can’t have propositional justification except for propositions that you could consider or which you are capable of considering. Not a complete approach, since not every proposition entailed by your evidence and which you can consider but don’t is one justified for you. But there is a deeper problem. My post on Shope’s demon shows, at a minimum, that the first one is false, since the demon can collapse entirely the distinction between this position and the Miserly Position by collapsing the distinction between what you haven’t considered and what you can’t consider. But what of the capability suggestion? Is there a way to understand capabilities so that even if it is impossible for you to consider p because of Shope’s demon, you still have the capability or power to do so? I think we are tempted to answer in the affirmative here, but the view is troubling. We can’t say, “in worlds where Shope’s demon isn’t around, you can consider p,” since by hypothesis, there are no such worlds. And we can’t say, “were it not for Shope’s demon, you could consider p.” There are lots of other potential blockers of your considering p besides this specific one. Moreover we can’t say, “were no interferers present, you could consider p,” since such a proposal is no advance unless we can say what an interferer is without trivializing the counterfactual in question. E.g., suppose your pet is a millipede. If all interfering factors were eliminated, your millipede could consider Fermat’s last theorem. Or again, remove all interfering factors and you’d be omniscient. I don’t know how to understand the notion of interference here to avoid these reductios of the view.
Going general won’t help either, as in: for nomologically possible biological organisms just like you, some can consider the proposition in question. This isn’t a necessary truth, since Shope’s demon could go after all such organisms, repeating as mantra, “It’s not all about you.”
So here’s what we know. With regard to all the propositions entailed by your evidence and which you haven’t considered and don’t presently believe, some are justified for you and some are not. The egregiously bad approaches deny this data. Among the approaches that don’t deny the data is one that begins to sort things with reference to what you have the power to conceive.
Maybe if we follow C.B. Martin by being realists about dispositions and powers we can avoid Shope’s demon. We can say the following. You must have the power to conceive the proposition in question in order to have propositional justification for it. When you cite Shope’s demon as a counter to this claim, you fail to undermine it. All Shope’s demon can do is put a logical barrier in front of your displaying this power; the demon can only make it such that it is logically impossible for you to display the power you have. Being realists about powers, rather than reductionists who think we have to be able to give some conditional analysis of powers, makes our position immune from Shope’s demon. (For those interested in the realism question, see the literature on finkish dispositions by Martin; David Lewis has responded trying to save the reductionist position, and I’ve argued against the rescue mission in PPR, content here, followed by others trying to rescue Lewis’s conditional approach, including work by our own Lars Gundersen in his Synthese 2002 piece.)
Even assuming realism about dispositions and powers, we get only a partial answer, since not everything you have the power to conceive and which is entailed by your evidence do you have propositional justification for. (Think of set theoretic paradoxes for Frege’s comprehension axiom, for example.) Perhaps its a start, however; it at least rules out some propositions from being justified for you even though they are entailed by your evidence.