Fitelson proposes the following principle: "If E constitutes conclusive evidence for H1, but E constitutes less than conclusive evidence for H2 (where it is assumed that E, H1 and H2 are all contingent), then E favors H1 over H2."
The principle is false. You witness Jones being shot and after approaching you observe that he is dead. Let E be this evidence. Let H1 be the hypothesis that Jones is dead. Let H2 be the hypothesis that Jones has been killed. Then E is conclusive evidence for H1 and less than conclusive evidence for H2. (That you observed that Jones is dead entails H1. But on one reading of "Jones being shot", E is compatible with the hypothesis that Jones was already dead when he was shot—we can say "He was shot after he died." And on any reading, E is compatible with Jones having died of some other cause, coincidentally.) But it is wrong to say that E favors the hypothesis that Jones is dead over the hypothesis that Jones was killed.
I like your counterexample, but Fitelson might have a straightforward way out of it. He might accept your example and claim it merely shows that entailment does not establish conclusiveness. Even though E entails H1 this does not mean that E is conclusive evidence for H1. Conclusive evidence, for Fitelson, seems to involve validity. Despite H1 logically following from E it is not the case that the truth of E guarantees the truth of H1; whereas, in the case Fitelson uses in the paper, drawing a spade from a fair (i.e., standard, well-shuffled) deck guarantees the truth of the claim that the card is black. This guaranteeing of truth is what makes the evidence conclusive. It being true that you observed Jones being shot and observed that Jones is dead does not guarantee the truth that Jones is dead. This is because what you observed is compatible with the hypothesis that Jones’ body is in severe shock and merely showing signs of death. Even though you observed no pulse and breathing, it is logically possible that the paramedics will have no trouble resuscitating Jones.
ReplyDeleteThat I saw that he is dead guarantees that he is dead. If he isn't dead, I didn't see him dead--I seemed to have seen him dead.
ReplyDeleteRight, but the context for the discussion is subjective (Bayesian) confirmation. Your subjective evidence might favor, but it does not guarantee. Your comment seems to bring in an objective dimension not in the case such that Jones is in fact (beyond a shadow of a doubt) dead. But, it’s not your observation of Jones being shot and him being dead doing the work. It’s the additional fact doing the guaranteeing, namely, that he is in fact (objectively) dead. Otherwise, as you said, you merely seemed to see…
ReplyDeleteThe same point could be made about Fitelson's example. If you insist on taking the evidence in my case to be the apparent observation of death, then for consistency you need to take in Fitelson's case the evidence to be the apparent presence of a spade. And then your criticism applies just as much to his case.
ReplyDeleteI’m not sure your counterexample is analogous to Fitelson’s example and thereby warrants equal treatment in the name of consistency. This was my original intuition--that something was not quite the same with your counterexample when compared to his example. Now I think I can say what that difference is. Your counterexample builds perception into the evidence, as seeing Jones getting shot and being dead is the evidence. In Fitelson’s example, though perception is required to see that the card is a spade, the evidence is not the observation of the spade, the evidence is ‘by definition’: “Let E (def) the card is a spade, H1 (def) the card is the ace of spades, and H2 (def) the card is black” (p. 6). There is no observation in the evidence to make apparent. It’s a definitional matter in Fitelson’s example. Tweaking the evidence is his case would be tweaking the definition, not making only apparent the agent’s perception of the evidence.
ReplyDeleteIn my case the evidence is by definition seeing that the guy is dead, not just seeming to see that the guy is dead.
ReplyDeleteBy the way, my theorems about the measure of confirmation (another recent post, and a paper I am finishing) sort of agree with Fitelson. More precisely, I agree that if E is conclusive evidence for H1 but inconclusive evidence for H2, then E confirms H1 more than it confirms H2. But I disagree that under those circumstances it confirms H1 over H2. In other words, I want to drive a wedge between "confirms more than" and "confirms over".
ReplyDeleteYour last comment raises some interesting issues. Is it possible for E to be conclusive evidence for H1 even though the probability of H1 given E is less than 1? If I bought 9,999 of the tickets in a 10,000 ticket fair lottery and I won the lottery is the fact that I bought 9,999 tickets conclusive evidence that I won? It does not seem like conclusive evidence that I won. Further, if conclusiveness is not associated with a probability of 1, then you get into threshold questions. How high is high enough to guarantee truth? In addition, what if E is conclusive evidence for H1 but slightly less conclusive evidence for H2? Does E really confirm H1 more than it confirms H2?
ReplyDeleteIf the probability of H1 given E must be 1 to conclusively establish H1, and E is conclusive evidence for H1, then it seems redundant (uninformative) to claim that “E confirms H1 more than it confirms H2.” All the latter tells us is that H2 is not also established conclusively by E. If the hypotheses are truly independent (interesting), then all that needs to be said is that E conclusively establishes H1. As such, E will confirm any alternative, independent hypothesis (like H2) to a lesser degree.
If, on the other hand, conclusiveness can be established with a probability less than 1, then this runs into the issue of veridicality that is less than conclusive. This is another way of questioning your counterexample while granting you veridical perception.
I look forward to looking at your paper when it’s finished.
I am afraid I still don't see the point you're making. P(he died | I saw that he died)=1. So we have conclusiveness both by the probability=1 criterion and by the entailment criterion.
ReplyDeleteMy point was that observation can be less than conclusive (much less than 1) as evidence for the proposition that it entails, so mere entailment does not equal conclusiveness. It requires this extra ‘guaranteeing of truth’ criterion, which the fallibility of perception works against. But, I’ll grant you the point in your case. This allows me to move on.
ReplyDeleteNow I’m not sure I see the force of your counterexample. You introduce an additional hypothesis (H3). According to H3 Jones was shot after he died. Let’s say he had a heart attack right before he was shot. You claim E’s compatibility with H3 makes it wrong to say E ‘favors’ H1 over H2. I’m not sure how your reversal of the order of causation between what you thought you saw [shot > dead] versus the causation in H3 [dead > shot] makes it wrong to claim E ‘favors’ H1 over H2. Either way, Jones is dead so Pr(E|H1) = 1. If Jones was shot after he died this only seems to lessen the degree to which E supports the hypothesis that Jones was killed (H2). Perhaps this makes Pr(E|H2) = .6 instead of .8, or something. I still get E favoring H1 over H2 because the probability is still certain that Jones is dead.