In this post, I want to show how we to derive FactivityJ from FactivityE:
FactivityJ: If you justifiably believe p, p is true.
FactivityE: If p is a justifying reason of yours, p is true.
The derivation requires three assumptions about doxastic justification:
Proper Basis: If you justifiably believe p, you have some justifying reason for this belief and your belief is based on it.
Same Basis: If you justifiably believe p on the basis of some reason, q, any of your epistemic counterparts that justifiably believes p on the basis of some reason will believe it on the basis of q.
J-Closure: If you justifiably believe p, you have sufficient justification to believe at least one of p’s obvious logical consequences and could come justifiably believe this proposition if you form this belief by means of competent deduction.
These assumptions are reasonably uncontroversial, but I can offer a brief word in support of each of them.
According to Proper Basis, whatever you justifiably believe you have a justifying reason to believe and this reason is the reason for which you believe what you do. If Proper Basis were false, it would be possible to (i) justifiably believe something without having any reason whatever to believe it or (ii) to justifiably believe something you need good reasons to believe without believing for good reasons. On its face, (i) seems rather implausible since it seems contradictory to say that although Agnes has no reason to believe the market will recover, she justifiably believes that it will or to say that there is no justification for Agnes’ belief that the there will be an uptick in consumer confidence, but she nevertheless justifiably believes there will be. Once (i) is rejected, it is hard to how to defend (ii). Consider these remarks from Pollock and Cruz:
One could have a good reason at one’s disposal but never make the connection. Suppose, for instance, that you are giving a mathematical proof. At a certain point you get stuck. You want to derive a particular intermediate conclusion, but you cannot see how to do it. In despair, you just write it down and think to youself, “That’s got to be true.” In fact, the conclusion follows from two earlier lines by modus ponens, but you have overlooked that. Surely, you are not justified in believing the conclusion, despite the fact that you have impeccable reasons for it at your disposal. What is lacking is that you do not believe the conclusion on the basis of those reasons.
It makes little sense to say that you cannot justifiably accept the proof’s conclusion without justifiably believing the premises of the proof if belief in those premises plays no role in convincing you of the proof’s conclusion. If you have the premises before you but they do not move you to accept the conclusion, how could you be better off epistemically for having them?
Agnes thinks the conservatives will do badly in the upcoming elections. The reason she thinks this is that she thinks that they overreached in the recent budget negotiations. According to Same Basis, Agnes’ epistemic counterparts will believe what Agnes believes for the same reasons that Agnes does if their beliefs are based on any reasons at all. If Agnes’ reason for believing that the conservatives will do poorly in the upcoming elections is not that the liberal base is energized, her epistemic counterparts will not believe the conservatives will do poorly in the upcoming elections for the reason that the liberal base is energized. If some subject is Agnes’ epistemic counterpart, they are in the same non-factive mental states as Agnes for their entire lives and the causal relations between their mental states are the same as the causal relations between Agnes’ mental states. On standard accounts of the basing relation, causal relations among your mental states determine which reasons move you to believe or to act. If we hold these relations fixed, the reasons for which epistemic counterparts believe what they do will not vary, provided that these subjects believe what they do for reasons.
Notice that J-Closure is far weaker than standard formulations of closure principles. Maybe you cannot justifiably believe that the animal in the cage is not a cleverly disguised mule even if you justifiably believe that it is a zebra. Maybe you can justifiably believe you have hands without being in any position to justifiably judge that you are not a handless BIV. Even if you thought that cases such as these constituted counterexamples to unrestricted closure principles for justification, remember that J-Closure is restricted. J-Closure only requires that for any proposition you justifiably believe you have sufficient justification to believe one of that proposition’s obvious logical consequences. Can you justifiably believe you have hands without having sufficient justification to believe the disjunctive proposition that you either have hands or you do not? Not if you have a modicum of logical ability.
With these assumptions in place, I can now show that it is impossible to justifiably believe false propositions concerning contingent matters of fact. Let’s start with the case of non-inferential justification. Suppose your belief concerning p is justified non-inferentially. According to Proper Basis, you have some justifying reason for this belief and your belief is based on this reason. If your belief is based on p itself, FactivityE tells us that p must be true. Thus, there are no non-inferentially justified, false beliefs.
Suppose your belief about p is inferentially justified. According to Proper Basis, you have some justifying reason for that belief, q, where q is the basis on which you believe p. According to FactivityE, q is true. If we suppose q entails p, p must be true as well. Thus, there are no inferentially justified, false beliefs based on entailing evidence. What about cases of inferentially justified beliefs based on non-entailing evidence? If we suppose you justifiably believe p on the basis of q where q does not entail p, the argument just offered does not apply. No matter. According to J-Closure, if you justifiably believe p you could justifiably believe some obvious logical consequence of p. Let’s suppose that you do justifiably believe p and suppose further that r is an obvious logical consequence of p. You competently deduce r from p and all through modal space your epistemic counterparts follow your lead. In some possible world one of your counterparts justifiably concludes that r is the case on the basis of p. According to Proper Basis, p is one of your counterpart’s justifying reasons. According to FactivityE, your counterpart is in a p-world. If you justifiably believe r, Proper Basis implies that you have a justifying reason. According to Same Basis, your justifying reason is what your counterpart’s justifying reason is, so your justifying reason for believing r has to be p. According to FactivityE, you are in a p-world. Our argument is complete. You cannot justifiably believe any false propositions concerning any contingent matter of fact regardless of whether your belief is non-inferentially justified, justified by entailing evidence, or justified by non-entailing evidence.