Yes, we agree on that. There is an example that copes with the structure you just mentioned. Suppose that
h: I will get rid of the flu
e1: I took Fluminex
e2: I took Fluminalva
b: Fluminex and Fluminalva cancel each other's effect against flu
Now suppose that both, Fluminex and Fluminalva, are effective against flu. Given this setting, P(h|b&e1)>P(h|b) and P(h|b&e2)>P(h|b), but P(h|b&e1&e2)<P(h|b). If the use of background b is bothering you, just embed the information about the canceling of effects in each of the pieces of evidence e1 and e2.
I see further problems with the Positive Relevance account, like the one that lies in saying that the fact that a swimmer is swimming is evidence that she will drown - just because swimming increases the probability of drowning. I see more hope for a combination of these two accounts, but one in which quantification over the background b is very important. We shouldn't require that in order for e to be evidence that h it has to increase the probability of h conditional in any background b.
So, he claims that it is just a necessary condition - not a sufficient one. I didn't reach the point where he offers the further conditions that, together with high probability, are supposed to be sufficient for evidential support.
p.s: still, you earned a point for the comment =|
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. =]
All right, I see. I agree that order is not determinant for evidential support relations.
It seems to me that the relevant sentence is not meaningful, or false.
Actually, Achinstein's claim is that the first one does not need to be satisfied - the probability of h does not need to be increased by e in order for e to be evidence that h. He gives up the first condition because of the counterexamples.
Thanks. I would say that what we have in front of us are clear cases where someone have evidence for something else. In the example given, we have in front of us that both, e1 and e2 (together with the assumption that the NYT and WP are reliable) are evidence for g. So, presumably, there is an agreement between people offering the truth conditions for 'e is evidence that h' about the range of cases where there is evidence - while the is no agreement between people answering the question about the sound of the three, because the don't agree on the range of cases where sound occurs. Otherwise, there would be no counterexamples such as the one that Achinstein tried to offer. If I offer some set of truth-conditions for Fa, and one of the data that I use to explain what it is for something to be F is the range of cases where F is applied, then if you present to me a case where F applies but it is not satisfied by the truth-conditions I offered, I will think that there is something wrong with that truth-conditions.
Trying to flesh out truth-conditions for a certain type of sentence is not the same thing as giving a definition. I'm not saying you're completely wrong on this, I just really think that this is not merely verbal dispute. About what would I expect to accomplish by finding out the best set of truth-conditions for 'e is evidence that h', I would say that a certain concept that is used in the law, natural science and philosophy has now clear boundaries, and if some charlatan offers an argument in a public space for some conclusion of his interest, I can argue with him that he has no evidence for his claims.
Thanks for the reference to the fortitudinence concept - I didn't know it yet.
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:
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:
The new definition does not require e to increase h's probability conditional on every possible background. How does that sound?
This is not a case where we have two definitions talking about two sorts of things (like sound waves versus perception of sound waves). This is a case where we have two rival mathematical definitions to account for the relation of evidential support. You seem to think that the answer to questions about disputes over distinct definitions is in that post you are referring to. I read the post, and I didn't find the answer to the question I'm interested in answering - which is not even that of deciding between two rival definitions.
Yeah, one of the problems of the example is that it seems to take for granted that both, the NYT and WP are 100% reliable.
Me neither - but I am not thinking that it is a good idea to divorce h from b.
Just a technical point: P(x) = P(x|b)P(b) + P(x|~b)P(~b)