Let S be a set of beliefs and experiences that is the evidence on which we are going to apply defeasible reasoning. Then suppose we have propositions p1…pn with the following properties:
1. S |~ p1 (p1 is a defeasible consequence of S).
2. S U p1 |~ p2 (p2 is a defeasible consequence of the union of S and p1).
n. S U p1…pn-1 |~ pn.
Question: what does it take for this sequence of belief revisions matching this sequence to result in the belief that pn to be rational or justified?
First answer, Williamson’s: it requires that, by step n in the process, one knows S U p1…pn-1. We’ve discussed this view before here, but it’s not very plausible.
Second answer, the empiricist view: where S is one’s basic empirical evidence–sensory experience, perhaps–pn is justifiedly believed just in case it is justified relative to S. Again, not very plausible, since sometimes our coming to believe something legitimately makes it part of our evidence.
Third answer, Chisholm’s: not in his written work that I can detect, but in conversation, he said something like the following. Where S is some initial set of appearance states, justification for pn requires a sequence of rational addings of p1…pn-1. If that occurs, however, the set S is no longer the set of appearance states that characterize the person in question. Instead, one will have added a number of other appearance states, including being appeared to p1-ly, being appeared to p2-ly, etc. (For those who insist on syntax making a property the appropriate value in the adverbial characterization, we could employ lambda conversion on p1 … pn.) Of course, this is not enough for justification for Chisholm, but let’s hold fixed satisfying the other constraints. The important point is that the class of evidence will not be exhausted by S U p1…pn for Chisholm.
Fourth answer, the defeasibilist’s: pn is justified if each of p1…pn is added without thereby undermining any of the information in S or any of the pi’s. The probabilist will say: but pn might be improbable given S U p1…pn.
There are lots of issues here, one important one being whether the logic of defeasible consequence can come apart from probability in this way (I think Jim Hawthorne’s posts argue they can’t, but I may be misunderstanding here.) Another one is why probability should be assumed to have the kind of power over justification that the objection assumes. Perhaps known probability does, but then the class of evidence would no longer be S U p1…pn.
The question that interests me the most, however, is whether the Chisholm position helps. That is, if we assume that the probabilist objection to the defeasibilist position is telling, does the problem disappear if we adopt Chisholm’s view?