Right, so, one think that is left open by both definitions is the kind of interpretation given to the function P. Is that suppose to be interpreted as a (rational) credence function? If so, the Positive Relevance account would say that e is evidence that h when one is rational in having a bigger credence in h when one has e as evidence than when one does not have e as evidence. For some, though, it would seem that in our case the agent that already knows b and e1 wouldn’t be rational in having a bigger credence that Bill will win the lottery if she learns e2.
But I think we can try to solve the problem without having to deal with the interpretation of the probability issue. One way to go, for the defender of the Positive Relevance account, would be to say that the counterexample assumes a universal quantification over the conditionalizing sentence that was not intended—one would be interpreting Positive Relevance as saying:
(For every background b) e is evidence that h iff P(h|e&b) > P(h|b)
But such interpretation, the defender of Positive Relevance could say, is wrong, and it is wrong just because of the kinds of examples as the one presented in the post. So, in order for e2 to be evidence that h, e2 does not need to increase the probability of h conditional on every conceivable background b. Specifically, it doesn’t need to increase the probability of h conditional on b when b contains e1, for example. But how would the definition look like without such quantification. Well, I don’t quite know sufficiently about it yet (this is new to me), but I think that maybe the following would do:
(For every tautology b) e is evidence that h iff P(h|e&b) > P(h|b)
The new definition does not require e to increase h’s probability conditional on every possible background. How does that sound?
But that these are the truth conditions for evidential support relations does not mean that only tautologies can be evidence, nor that only sets of tautologies can be one’s background. If you prefer, this is supposed to be a ‘test’ for checking if particular bits of information are evidence for something else. So I agree that backgrounds in minds is one of the things we got to be interested in, as long as we want to say something about rationality. I just don’t think that the usefulness of the test (the new truth-conditions) is killed. =]
Right, so, one think that is left open by both definitions is the kind of interpretation given to the function P. Is that suppose to be interpreted as a (rational) credence function? If so, the Positive Relevance account would say that e is evidence that h when one is rational in having a bigger credence in h when one has e as evidence than when one does not have e as evidence. For some, though, it would seem that in our case the agent that already knows b and e1 wouldn’t be rational in having a bigger credence that Bill will win the lottery if she learns e2.
But I think we can try to solve the problem without having to deal with the interpretation of the probability issue. One way to go, for the defender of the Positive Relevance account, would be to say that the counterexample assumes a universal quantification over the conditionalizing sentence that was not intended—one would be interpreting Positive Relevance as saying:
(For every background b) e is evidence that h iff P(h|e&b) > P(h|b)
But such interpretation, the defender of Positive Relevance could say, is wrong, and it is wrong just because of the kinds of examples as the one presented in the post. So, in order for e2 to be evidence that h, e2 does not need to increase the probability of h conditional on every conceivable background b. Specifically, it doesn’t need to increase the probability of h conditional on b when b contains e1, for example. But how would the definition look like without such quantification. Well, I don’t quite know sufficiently about it yet (this is new to me), but I think that maybe the following would do:
(For every tautology b) e is evidence that h iff P(h|e&b) > P(h|b)
The new definition does not require e to increase h’s probability conditional on every possible background. How does that sound?
It’s not clear to me why exactly you want the definition of evidence to not rely on the particular background of the mind where the P resides.
If you limit b to tautologies, you kill its usefulness. “This is a fair lottery in which one ticket drawn at random will win” isn’t a tautology.
But that these are the truth conditions for evidential support relations does not mean that only tautologies can be evidence, nor that only sets of tautologies can be one’s background. If you prefer, this is supposed to be a ‘test’ for checking if particular bits of information are evidence for something else. So I agree that backgrounds in minds is one of the things we got to be interested in, as long as we want to say something about rationality. I just don’t think that the usefulness of the test (the new truth-conditions) is killed. =]