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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)
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:
- (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?
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.
So, I'll kind of second the observation in the comment above. It seems to me that, from the fact that reading the same story in the Washington Post does not make your epistemic situation better, it does not seem to follow that the Post story is not evidence that Bill win the lottery. That is: from the fact that a certain piece of evidence is swamped by another piece of evidence in a certain situation, it does not follow that the former is not evidence. We can see that it is evidence just following your steps: we conceive another situation where I didn't read the Times story but I read the Post story - and it is evidence that Bill win the lottery in this situation.
I agree that it seems just wrong to grant that strong evidence and weak evidence is determined by the access we have to evidence in order of time. But from the fact that one does not gain more justification to believe h by learning e it does not follow that e is evidence that h, all things considered.
Thanks. Your first question is showing a case where the evidential support of e1 is swamped by the evidential support of g, right? It seems that, if I have g as evidence, e1 doesn't change my epistemic situation as regards the proposition that Bill will win the lottery. So if we answer that e1 is not evidence that h in this case, we are assuming that if one piece of evidence is swamped by another, it is not evidence anymore. I wouldn't go that way (would you?), because in a situation where I didn't see Bill buying the tickets, I still would have e2 as evidence. About the question over not knowing the exact number of tickets bought by Bill, I don't know what to say besides this: seems to be a case where Jeffrey conditionalization is wellcome, given the 'uncertain' character of evidence.
Yes I did - but thanks for the tip anyway.
Thanks Vaniver. Doesn't your example shows something unsatisfactory about the High Probability interpretation also? Given that P(A or ~A|My socks are white)>1/2, that my socks are white would also count as evidence that A or ~A. Your point seems to suggest that there must be something having to do with content in common between the evidence and the hypothesis.
Thanks, that's interesting. The exercise of thinking how people would act to gather evidence having in mind the two probabilistic definitions gives food for thought. Specifically, I'm thinking that, if we were to tell people: "Look for evidence in favor of h and, remember, evidence is that which ...", where we substitute '...' by the relevant definition of evidence, they would gather evidence in a different way from the way we naturally look for evidence for some hypotheses. The agents to whom that advice was given would have a reflexive access to their own definition of evidence, and they would gather only what is in the scope of that definition. People being given the first definition of evidence could balk when looking for evidence that Obama will be involved in an airplane accident: if they find out that Obama will be in an airplane today, they find out evidence that Obama will be involved in an airplane accident. Now given that these people would have the advice we gave them in mind, they could start questioning themselves if they didn't receive silly advice.
I agree that some philosophical searches for analyses of concepts turn out generating endless, fruitless, sequences of counterexamples and new definitions. However, it is not the case that, always, when we are trying to find out the truth conditions for something, we are engaged in such kind of unproductive thinking. As long as we care about what it is for something to be evidence for something else (we may care about this because we want to understand what gives support to scientific theories, etc), it seems legitimate for us to look for satisfactory truth conditions for 'e is evidence that h'. Trying to make the boundaries of our concepts clear is also part of the project of optimizing our rationality.
So, I would like to thank you guys for the hints and critical comments here - you are helping me a lot! I'll read what you recommended in order to investigate the epistemological properties of the degree-of-belief version of bayesianism. For now, I'm just full of doubts: "does bayesianism really stand as a normative theory of rational doxastic attitudes?"; "what is the relation between degrees of belief and evidential support?", "is it correct to say that people reason in accordance to probability principles when they reason correctly?", "is the idea of defeating evidence an ilusion?", and still others. =]
I can't believe people apply Baye's theorem when confronted to counter-evidence. What evidence do we have to believe that Bayesian probability theories describe the way we reason inductively?
we are not justified in assigning probability 1 to the belief that 'A=A' or to the belief that 'p -> p'? Why not?
OK, got it, thank you. I have two doubts. (i) Why a belief with degree 1 is not affected by new information which is counter-evidence to that belief? Does it mean every belief with degree 1 I have now will never be lost/defeated/changed? (ii) The difference between what you call traditional epistemology and Bayesianism involves lots of things. I think one of them is their objectives - the traditional epistemologist and the Bayesian in general have different goals. The first one is interested in posing the correct norms of reasoning and other sources of beliefs (perception, memory, etc). The second one maybe is more interested in modelling rational structures for a variety of purposes. That being the case, the puzzles I brought maybe are not of interest for Bayesians - but that does not mean Bayesianism solve the question of what is the correct thing to do in such cases. Thanks for the link (I already know Harman's approach, which is heavily criticized by Conee and others).
I didn't downvote! And I am not shooting the messenger, as I am also sure it is not and argument about Gettier problems. I am sorry if the post offended you - maybe it is better not to mix different views of something.
Well, puzzle 2 is a puzzle with a case of knowledge: I know (T). Changing to probabilities does not solve the problem, only changes it!
Thank you, Zed. You are right: I didn't specified the meaning of 'misleading evidence'. It means evidence to believe something that is false (whether or not the cognitive agent receiving such evidence knows it is misleading). Now, maybe it I'm missing something, but I don't see any silliness in thinking of terms of "belief A defeats belief B". On the basis of having an experiential evidence, I believe there is a tree in front of me. But then, I discover I'm drugged with LCD (a friend of mine put it in my coffee previously, unknown to me). This new piece of information defeats the justification I had for believing there is a tree in front of me - my evidence does not support this belief anymore. There is a good material on defeasible reasoning and justification in John Pollock's website: http://oscarhome.soc-sci.arizona.edu/ftp/publications.html#reasoning
Thank you! Well, you didn't answered to the puzzle. The puzzles are not showing that my reasoning is broken because I have evidence to believe T and ~T. The puzzles are asking what is the rational thing to do in such a case - what is the right choice from the epitemological point of view. So, when you answer in puzzle 1 that believing (~T) is the rational thing to do, you must explain why that is so. The same applies to puzzle 2. I don't think that degrees of beliefs, expressed as probabilities, can solve the problem. Whether my belief is rational or not doesn't seem to depend on the degree of my belief. There are cases in which the degree of my belief that P is very low and, yet, I am rational in believing that P. There are cases where I infer a proposition from a long argument, have no counter-evidence to any premise or to the support relation between premises and conclusion but, yet, have a low degree of confidence in the conclusion. Degrees of belief is a psychological matter, or at least so it appear to me. Nevertheless, even accepting the degree-of-belief model of doxastic rational changes, I can conceive the puzzle as one where all the relevant beliefs - (R1), (T), (AME), etc, - have degree 1. Can you explain what is the rational thing to do in each case, and why?
Good afternoon, morning or night! I'm a graduate student in Epistemology. My research is about epistemic rationality, logic and AI. I'm actually investigating about the general pattern of epistemic norms and about their nature - if these norms must be actually accessed by the cognitive agent to do their job or not; if these norms in fact optimize the epistemic goal of having true beliefs and avoiding false ones, or rather if these norms just appear to do so; and still other questions. I was navigating through the web and looking for web-based softwares to calculate probabilites, so that I found LW, and guess what! I started to read it and couldn't stop - each link sounds exciting and interesting (bias, probability, belief, bayesianism...). So, I happily made an account, and I'm eager to discuss with you guys! Hope I can contribute to LW some way. We (me and my research partners) have a blog (https://fsopho.wordpress.com) on epistemology and reasoning. We're all together in the search for knowledge, fighting bias and requiring evidence! see ya =]