I would like to share a doubt with you. Peter Achinstein, in his The Book of Evidence considers two probabilistic views about the conditions that must be satisfied in order for e to be evidence that h. The first one says that e is evidence that h when e increases...
I present here two puzzles of rationality you LessWrongers may think is worth to deal with. Maybe the first one looks more amenable to a simple solution, while the second one has called attention of a number of contemporary epistemologists (Cargile, Feldman, Harman), and does not look that simple when...
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... (read more)
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... (read more)
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... (read more)
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.
I would like to share a doubt with you. Peter Achinstein, in his The Book of Evidence considers two probabilistic views about the conditions that must be satisfied in order for e to be evidence that h. The first one says that e is evidence that h when e increases the probability of h when added to some background information b:
(Increase in Probability) e is evidence that h iff P(h|e&b) > P(h|b).
The second one says that e is evidence that h when the probability of h conditional on e is higher than some threshold k:
(High Probability) e is evidence that h iff P(h|e) > k.
A plausible way of interpreting the second definition is by saying that k = 1/2. When one takes k to have such fixed value, it turns out that P(h|e) > k has the same truth-conditions as P(h|e) > P(~h|e) - at least if we are assuming that P is a function obeying Kolmogorov's axioms of... (read 381 more words →)
I present here two puzzles of rationality you LessWrongers may think is worth to deal with. Maybe the first one looks more amenable to a simple solution, while the second one has called attention of a number of contemporary epistemologists (Cargile, Feldman, Harman), and does not look that simple when it comes to a solution. So, let's go to the puzzles!
Puzzle 1
At t1 I justifiably believe theorem T is true, on the basis of a complex argument I just validly reasoned from the also justified premises P1, P2 and P3.
So, in t1 I reason from premises:
(R1) P1, P2 ,P3
To the known conclusion:
(T) T is true
At t2, Ms. Math, a well known authority
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)