I have a take on the role of probabilistic arguments that might be of help here. Look, when it comes to the resurrection of Jesus, a person's decision to accept or not accept the Resurrection is likely to be a combination of the evidence specific to the Resurrection, and a prior assessment of how likely the background beliefs that are behind belief in the resurrection are to be true. We know that people who are thinking about the Resurrection are bound to differ about whether the claim that Jesus rose from the dead is antecedently plausible. There's going to be people who find the fact that something would have to be explained as a divine miracle grounds for giving it as close to a probability of zero as you can get. There are some people who are already committed to some form of supernaturalism, and who are not going to be deterred by the fact that the explanation involves the miraculous. So, how can we carry on the discussion? One way of doing it is to ask merely whether the evidence in more like what we should expect if the Resurrection happened, or whether it's more like what we should expect if it didn't. In other words, is there anything in the reports coming out of the first-century church that is more like what you should expect if Jesus was raised than if Jesus was not raised. If the answer to that question is yes, then the evidence confirms the resurrection, but it might still be rejected by reasonable people on the grounds that a Resurrection would commit you to the existence of God, or other features of Christianity that you consider to be improbable. Fine, but you can at least say, in response to the evidence, that the evidence directly bearing on the resurrection of Jesus is easier to explain if the Resurrection occurred than if it didn't. In other words, we can isolate one particular piece of evidence from the total evidence we have that bears on the issue and ask whether this piece of evidence supports the Christian claim that Jesus was resurrected or not.
Similarly, we can ask, concerning the fact of pain and suffering, how it impacts the credibility of theism. It could turn out that yes, pain and suffering adversely affects the credibility of theism, but it does not show that anyone who believes in the existence of God is just being delusional.
I understand that some people do Bayesian probability theory to get a correct final conclusion based upon agreed-upon methods for ascertaining probabilities. That's legitimate, but we also might like to isolate the impact of a piece of evidence on the overall plausibility of theism and Christianity. I find Bayes' theorem to be a helpful tool in doing that, even though I do not expect an agreed-upon conclusion concerning the Resurrection after we are done. To me, it's not a misuse of Bayes' theorem, just a different use.
Showing posts with label Bayesianism. Show all posts
Showing posts with label Bayesianism. Show all posts
Pride Goeth
Here's what Carrier says about his chapter of The Christian Delusion.
Two of The Christian Delusion's fifteen chapters are mine. The first is Why the Resurrection Is Unbelievable, which is the most definitive refutation of warranted belief in the resurrection I have ever composed. It's a deliberate tour de force, such that I doubt I'll ever have to write another. It even takes down recent attempts to use Bayes' Theorem to argue for the resurrection, and it contextualizes everything so there just isn't any rational basis left for claiming the resurrection is historically proven.
In the next paragraph he refers to both of his contributions as tours de force.
When you talk like that, you had better be able to take out the McGrews. In my brainwashed opinion, that's a chess game he has no chance of winning.
Two of The Christian Delusion's fifteen chapters are mine. The first is Why the Resurrection Is Unbelievable, which is the most definitive refutation of warranted belief in the resurrection I have ever composed. It's a deliberate tour de force, such that I doubt I'll ever have to write another. It even takes down recent attempts to use Bayes' Theorem to argue for the resurrection, and it contextualizes everything so there just isn't any rational basis left for claiming the resurrection is historically proven.
In the next paragraph he refers to both of his contributions as tours de force.
When you talk like that, you had better be able to take out the McGrews. In my brainwashed opinion, that's a chess game he has no chance of winning.
Two Sides of the Bayesian Analysis of the Resurrection
I see two major issues with respect to the Bayesian analysis of Resurrection history. One has to do with the left side of the theorem. Is there some way of showing that everyone ought to go into the discussion with such a low prior for any miracle that we can virtually guarantee that nothing coming out of the ancient world will be sufficient evidence.
The usual approach to getting that result is via some form of frequentism. There have been 96,100,000,000 persons who have ever lived, there has only been a very few resurrection reports that have so much as surface credibility, so therefore the one in 96.1 billion, and therefore resurrection has to lose even to the swoon theory. But these lead-footed methods don't work for various reasons that have been pointed out quite often. Earman is, I think, the guy you have to get around if you think you can prove something like this about the prior for miracles.
If you say "Extraordinary claims require extraordinary evidence," (which invariably implies evidence that you're never going to be able to get out of the ancient world), then you have to figure out how do define extraordinary in this context. Does it mean historically unique? In that case you have Indian Prince worries, and there's even a problem believing media reports that Obama won the election. If you think it means contrary to the laws of nature, then why do you presume that every event has a natural cause? Doesn't that beg the question from the beginning? Whether a miracle-working God exists is part of what's at issue here. The skeptic needs an account of extraordinariness that doesn't beg the question and pins an unmanageable prior on all miracle claims for everyone.
The other issue looks at the right side of the theorem, and asks if the evidence surrounding the resurrection is more like what we should expect if the miracle happened or more like what we should expect if it didn't happen. My approach on this is to say that prior probabilities on the matter are certainly going to vary, and that nevertheless we can see if the evidence confirms the miracle story of disconfirms it. Unless you have an argument that shows that no one should have a manageable prior for miracles, you can and should ask this question.
Now notice that I have nowhere said that there is some definite conclusion that everyone will come to, that it is 94% likely that the Resurrection happened based on historical evidence. I am interested in whether the case for the Resurrection confirms it, even if many unbelievers fail to find such evidence "extraordinary" enough.
The usual approach to getting that result is via some form of frequentism. There have been 96,100,000,000 persons who have ever lived, there has only been a very few resurrection reports that have so much as surface credibility, so therefore the one in 96.1 billion, and therefore resurrection has to lose even to the swoon theory. But these lead-footed methods don't work for various reasons that have been pointed out quite often. Earman is, I think, the guy you have to get around if you think you can prove something like this about the prior for miracles.
If you say "Extraordinary claims require extraordinary evidence," (which invariably implies evidence that you're never going to be able to get out of the ancient world), then you have to figure out how do define extraordinary in this context. Does it mean historically unique? In that case you have Indian Prince worries, and there's even a problem believing media reports that Obama won the election. If you think it means contrary to the laws of nature, then why do you presume that every event has a natural cause? Doesn't that beg the question from the beginning? Whether a miracle-working God exists is part of what's at issue here. The skeptic needs an account of extraordinariness that doesn't beg the question and pins an unmanageable prior on all miracle claims for everyone.
The other issue looks at the right side of the theorem, and asks if the evidence surrounding the resurrection is more like what we should expect if the miracle happened or more like what we should expect if it didn't happen. My approach on this is to say that prior probabilities on the matter are certainly going to vary, and that nevertheless we can see if the evidence confirms the miracle story of disconfirms it. Unless you have an argument that shows that no one should have a manageable prior for miracles, you can and should ask this question.
Now notice that I have nowhere said that there is some definite conclusion that everyone will come to, that it is 94% likely that the Resurrection happened based on historical evidence. I am interested in whether the case for the Resurrection confirms it, even if many unbelievers fail to find such evidence "extraordinary" enough.
Lydia McGrew rebuts Richard Carrier.
I understand that the current atheist meme on this, which shows a rather striking lack of understanding of probability, is to say that if one does not argue for a particular prior probability for some proposition, one literally can say nothing meaningful about the confirmation provided by evidence beyond the statement that there is some confirmation or other.
This is flatly false, as both the second of the quotations above from the paper and my rather detailed explanation to Luke M. show.
This is flatly false, as both the second of the quotations above from the paper and my rather detailed explanation to Luke M. show.
Richard Carrier on Bayes' Theorem
I don't know if Tim McGrew is going to call this crappy. But he has told me he has numerous objections to it.
Care and Feeding of Prior Probabilities
Roffle wrote: I would agree that someone who comes to a conversation with a lot of unfounded assumptions (uninformed priors) will form different conclusions based on the evidence at hand, but that doesn't mean that that person's opinion should carry any weight.
If you want to convince others that your conclusion is rational, you need to justify your assumptions (priors). If you can't, and instead hide behind a smokescreen of subjectivity about priors while at the same time pretending to be rational, then don't be surprised when you receive as much condemnation as you do.
VR: When I say I am a pluralist about priors what I mean is that I don't think it's necessary to show that everyone ought to have the same priors I do. But that doesn't mean the priors are uninformed. They are affected, in my case at least, on the positive side by natural-theological argumentation, and on the negative side by the problem of evil. There are differences of opinion about these arguments. Whether I think the universe exists contingently and this needs something to cause its existence, or whether I think it can exist on its own, is going to affect my prior for miracles. Whether the universe was designed by someone for intelligent life, or whether intelligent life arise with no design would be another factor. Whether our power to reason requires a mentalistic universe, or whether it can be the by-product of a purely material and fully evolved brain is another issue. Whether the world as we know it with the evil it contains is compatible with a perfectly good creator would be another factor. Lewis's whole book, Miracles: A Preliminary Study, offers an explanation as to why he thinks the miracle claims of Christianity should not be considered overwhelming improbable prior to investigation.
If you think the whole case for God apart from arguments for miracles is nonsense, and the case against God overwhelming, then no case for the Resurrection will ever be good enough. But some of us don't concur with the antecedent of this conditional.
If you want to convince others that your conclusion is rational, you need to justify your assumptions (priors). If you can't, and instead hide behind a smokescreen of subjectivity about priors while at the same time pretending to be rational, then don't be surprised when you receive as much condemnation as you do.
VR: When I say I am a pluralist about priors what I mean is that I don't think it's necessary to show that everyone ought to have the same priors I do. But that doesn't mean the priors are uninformed. They are affected, in my case at least, on the positive side by natural-theological argumentation, and on the negative side by the problem of evil. There are differences of opinion about these arguments. Whether I think the universe exists contingently and this needs something to cause its existence, or whether I think it can exist on its own, is going to affect my prior for miracles. Whether the universe was designed by someone for intelligent life, or whether intelligent life arise with no design would be another factor. Whether our power to reason requires a mentalistic universe, or whether it can be the by-product of a purely material and fully evolved brain is another issue. Whether the world as we know it with the evil it contains is compatible with a perfectly good creator would be another factor. Lewis's whole book, Miracles: A Preliminary Study, offers an explanation as to why he thinks the miracle claims of Christianity should not be considered overwhelming improbable prior to investigation.
If you think the whole case for God apart from arguments for miracles is nonsense, and the case against God overwhelming, then no case for the Resurrection will ever be good enough. But some of us don't concur with the antecedent of this conditional.
Rational Reflection and Prior Probability
John: I have never denied that upbringing has any influence. I suppose my upbringing might have provided a set of initial priors. But when I consider the question of the Resurrection of Christ today, I have to consider all the waterboarding, as Bob would say, all the critical reflection that has taken place since that time. I became a philosophy major because if there were reasons to reject Christianity, I wanted to hear them sooner rather than later. During my time as a philosophy major, where I encountered Hume's essay on miracles for the first time, and wrote two papers on it. During my time in seminary, I not only encounter more skepticism about the Bible than I had ever encountered before, but also got to know Keith Parsons when we lived in the same house. My career graduate student was in highly secularized philosophy departments, where I was part of a Christian minority. There was one known believer in the 18-man University of Illinois philosophy faculty. I spent did my dissertation work under a teacher who grilled my arguments incessantly, and while he didn't officially state his own views on religion, certain did not come across as a believer.
Add to that the style of questioning that I consistently engaged in. Coming from the logic-dominated world of chess I was highly resistant to any appeal to blind faith. I've always had trouble with doctrines like biblical inerrancy and papal infallibility.
So I've got a lot feeding into my priors besides my upbringing. Do you deny that?
So, by the time I get to 2010, and I start reflecting on the question of the Resurrection, there is a lot of learning and questioning that has gone on since my upbringing occurred, so if someone says "Well, your priors just come from your upbringing," what that seems to me to be doing is to just ignore or denigrate all the questioning and learning I might have done since. When you imply that none of the thinking and learning I did over a 39-year period has anything to do with why I believe what I believe, that's what makes me irate. If that isn't what you're saying, then you need to be clearer.
Many people come to beliefs which differ sharply from the way they were raised. Bob Prokop and I had a friend, Joe Sheffer, who had no religious upbringing, converted to Protestant Christianity in college, and later joined the Catholic Church. So much for the overwhelming power of upbringing. If upbringing is so powerful, what happened to you?
It would be easy to pick on non-rational factors from your personal story and explain your nonbelief in terms of those things. Your Christian opponents have done it many times. And you don't like it, since it ignores your actual arguments.
There are many reasons that I could give for why I have priors that leave me open to the possibility of a miraculous explanation for the founding of Christianity. One that I have devoted considerable energy to is Lewis's argument from reason. If the physical is causally closed, then of course there can't be any miracles, but I maintain the if the physical is causally closed, then no scientist, mathematician, or philosopher has ever performed a rational inference. I have never seen you deal with that argument in any serious way, but it is very relevant. To give a full account of why I believe what I do would take at least a whole new book, and maybe I will write it.
If we critically reflect on our beliefs, if we consider the views of our opponents, if we take the raft of beliefs that we started with and add planks that are shown to be needed by the evidence and discard those that are shown to be faulty by the evidence, we have done all we can do to discover the truth. I'm not a Cartesian foundationalist. That doesn't mean that bias can't hide from us. Just saying "follow science" doesn't help us much. These questions are not purely scientific questions, nor can they be. Sure, science gives us information that is relevant to these matters, and that has to be considered. But does science really help to answer the question as to whether or not the universe exists contingently, and therefore must depend on something else for its existence? Well may be it does--it seems to be telling us these days that the universe began to exist. But I'm afraid metaphysics, and metaphysical questions (questions that go beyond physics) will be with us always.
Add to that the style of questioning that I consistently engaged in. Coming from the logic-dominated world of chess I was highly resistant to any appeal to blind faith. I've always had trouble with doctrines like biblical inerrancy and papal infallibility.
So I've got a lot feeding into my priors besides my upbringing. Do you deny that?
So, by the time I get to 2010, and I start reflecting on the question of the Resurrection, there is a lot of learning and questioning that has gone on since my upbringing occurred, so if someone says "Well, your priors just come from your upbringing," what that seems to me to be doing is to just ignore or denigrate all the questioning and learning I might have done since. When you imply that none of the thinking and learning I did over a 39-year period has anything to do with why I believe what I believe, that's what makes me irate. If that isn't what you're saying, then you need to be clearer.
Many people come to beliefs which differ sharply from the way they were raised. Bob Prokop and I had a friend, Joe Sheffer, who had no religious upbringing, converted to Protestant Christianity in college, and later joined the Catholic Church. So much for the overwhelming power of upbringing. If upbringing is so powerful, what happened to you?
It would be easy to pick on non-rational factors from your personal story and explain your nonbelief in terms of those things. Your Christian opponents have done it many times. And you don't like it, since it ignores your actual arguments.
There are many reasons that I could give for why I have priors that leave me open to the possibility of a miraculous explanation for the founding of Christianity. One that I have devoted considerable energy to is Lewis's argument from reason. If the physical is causally closed, then of course there can't be any miracles, but I maintain the if the physical is causally closed, then no scientist, mathematician, or philosopher has ever performed a rational inference. I have never seen you deal with that argument in any serious way, but it is very relevant. To give a full account of why I believe what I do would take at least a whole new book, and maybe I will write it.
If we critically reflect on our beliefs, if we consider the views of our opponents, if we take the raft of beliefs that we started with and add planks that are shown to be needed by the evidence and discard those that are shown to be faulty by the evidence, we have done all we can do to discover the truth. I'm not a Cartesian foundationalist. That doesn't mean that bias can't hide from us. Just saying "follow science" doesn't help us much. These questions are not purely scientific questions, nor can they be. Sure, science gives us information that is relevant to these matters, and that has to be considered. But does science really help to answer the question as to whether or not the universe exists contingently, and therefore must depend on something else for its existence? Well may be it does--it seems to be telling us these days that the universe began to exist. But I'm afraid metaphysics, and metaphysical questions (questions that go beyond physics) will be with us always.
Pluralism about Antecedent Probabilities and Miracles
Reading Earman, I think I prefer to set the whole personalist-anti-personalist debate aside by introducing the idea of pluralism about prior probabilities. If you start talking like a personalist people start getting the idea that you are just starting from wherever your personal biases have taken you, while for most of us who have reflected about religion and the philosophy of religion, our prior for miracle claims is going to be fed into by such things as the credibility of theism, the moral credibility of Jesus and Christianity, our sense of whether Christians are right about what humans most profoundly need, etc. Indeed, another part of it would be whether the miracles attributed to Jesus are ones that appropriate fit with the concept of God. All of this stuff is tough to quantify, and as a result you have to just deal with the fact that people will be looking at evidence for and against Christian miracles informed by very different perspectives. Even though Hume didn't prove that we should look at the evidence essentially epistemically closed to the miraculous, his opponents have not proved that everyone has to come to this discussion with priors that will allow them to be genuinely open-minded about being persuaded to accept these miracle reports. So what I like to do is to "bracket" the left side of the equals sign in Bayes' theorem, on the assumption that of course people with lots of different priors are going to be looking at this, and just concentrate on the right side of the equals sign. Is there anything in the evidence that ought to surprise a skeptic who is paying attention? If there is, and it makes sense from a Christian standpoint, then I figure I've got something that will pull the skeptic in the direction of Christianity, even though his priors may be such that it won't come anywhere near to convincing him that Christianity is true.
Abusing Bayes: A Reply to Rebel1 from the Secular Outpost
Rebel1 wrote: @Victor Reppert: You completely missed the point, once again. YOU DON'T HAVE THE RIGHT TO USE THE WORD "BAYESIAN". It's a term that has a clear meaning in Mathematics, and it is clearly not the one you imagine. Is that clear enough, now that I've used ALL CAPS??? Bayes' Theorem REQUIRES quantifiable prior probabilities to have any meaning, especially when those probabilities are likely to be low. And miracles are not miracles if they are not highly improbable.
The very point made by many of your critics remain. If miracles exist, then they will be resistant to any sort of probabilistic analysis. You cannot steal the language of Mathematics to give your personal, unvalidated beliefs the credibility attached to that field. You are not even a philosopher, because I expect from philosophers a little rigour in their use of language.
What you are, is a hack, no better than Deepak Chopra when he uses the word Quantum to give his pablum a "sciency" air.
So stop using the word "Bayesian", and we might be able to have a conversation. Use the word, and all you'll get from people who actually know what the word means is ridicule.
VR: You might want to read John Earman's (University of Pittsburgh philosopher of science and an atheist, and Keith's former teacher) book "Hume's Abject Failure" before you accuse me of not knowing what the word Bayesian means. (He references one of my papers in his book). Or you might try convincing my philosophy of science teacher at the University of Illinois, Patrick Maher (author of books like Betting On Theories), who worked with me on Bayesian theory while I was getting my doctorate, and explain to him that I don't know anything about Bayesianism. If Jordan Howard Sobel were still alive, you might want to ask him also, since he read two of my papers, and found them reasonable efforts, even though he differed with my conclusions and is the leading defender of the Bayesianized version of Hume's argument against miracles. Or, you can ask Keith. NONE of these people believe in miracles, but all of them thought I made some reasonable points in my two papers, one which appears on Internet Infidels, and the other of which came out in International Journal for Philosophy of Religion in 1989.
You might also want to read up on the Personalist school of Bayesian prior probabilities, a school that has many adherents. You might want to read Colin Howson and Peter Urbach's Scientific Inference: A Bayesian Approach, before you dismiss personalism as hogwash.
You might also try examining my arguments in my Infidels paper on miracles against frequentism before you make charges like this.
You also might want to think twice about the fact that you completely misrepresented my position before you blast me into the outer darkness for a complete misunderstanding of Bayesianism. In short, you might want to do your homework.
The fact that Bayesian inference is used with certain conventions within your scientific enterprise doesn't mean that you can dismiss the work of many other people who use that same methodology in different contexts, with different ground rules. To me, Bayesian personalism isn't a way of claiming a kind of mathematical precision for beliefs about, say, the resurrection which I know to be impossible. It is an attempt on my part to think from the standpoint of a model which allows a plurality of antecedent probabilities to start with, but nevetheless leaves people open to the consideration of evidence for and against religious beliefs. It's the best model I know of to do this job.
I could be thoroughly misguided, but I think I can appeal to the authority of some people who know a lot more about Bayesianism than I do to show that I do know what Bayesianism is.
The very point made by many of your critics remain. If miracles exist, then they will be resistant to any sort of probabilistic analysis. You cannot steal the language of Mathematics to give your personal, unvalidated beliefs the credibility attached to that field. You are not even a philosopher, because I expect from philosophers a little rigour in their use of language.
What you are, is a hack, no better than Deepak Chopra when he uses the word Quantum to give his pablum a "sciency" air.
So stop using the word "Bayesian", and we might be able to have a conversation. Use the word, and all you'll get from people who actually know what the word means is ridicule.
VR: You might want to read John Earman's (University of Pittsburgh philosopher of science and an atheist, and Keith's former teacher) book "Hume's Abject Failure" before you accuse me of not knowing what the word Bayesian means. (He references one of my papers in his book). Or you might try convincing my philosophy of science teacher at the University of Illinois, Patrick Maher (author of books like Betting On Theories), who worked with me on Bayesian theory while I was getting my doctorate, and explain to him that I don't know anything about Bayesianism. If Jordan Howard Sobel were still alive, you might want to ask him also, since he read two of my papers, and found them reasonable efforts, even though he differed with my conclusions and is the leading defender of the Bayesianized version of Hume's argument against miracles. Or, you can ask Keith. NONE of these people believe in miracles, but all of them thought I made some reasonable points in my two papers, one which appears on Internet Infidels, and the other of which came out in International Journal for Philosophy of Religion in 1989.
You might also want to read up on the Personalist school of Bayesian prior probabilities, a school that has many adherents. You might want to read Colin Howson and Peter Urbach's Scientific Inference: A Bayesian Approach, before you dismiss personalism as hogwash.
You might also try examining my arguments in my Infidels paper on miracles against frequentism before you make charges like this.
You also might want to think twice about the fact that you completely misrepresented my position before you blast me into the outer darkness for a complete misunderstanding of Bayesianism. In short, you might want to do your homework.
The fact that Bayesian inference is used with certain conventions within your scientific enterprise doesn't mean that you can dismiss the work of many other people who use that same methodology in different contexts, with different ground rules. To me, Bayesian personalism isn't a way of claiming a kind of mathematical precision for beliefs about, say, the resurrection which I know to be impossible. It is an attempt on my part to think from the standpoint of a model which allows a plurality of antecedent probabilities to start with, but nevetheless leaves people open to the consideration of evidence for and against religious beliefs. It's the best model I know of to do this job.
I could be thoroughly misguided, but I think I can appeal to the authority of some people who know a lot more about Bayesianism than I do to show that I do know what Bayesianism is.
ECREE and Antecedent Probabilities
There is a sense in which I agree with the ECREE thesis, it is just that I don't believe that there is any objective way of proving that one set of antecedent probabilities is rational and another is not. So what is "extraordinary" is just what your antecendent probabilities tell you is improbable.
I think that as you pull at the story of the founding of Christianity, as you play out the various scenarios all the way through, you end up thinking that none of the scenarios for what might have really happened fit the facts very well. They run into factual brick walls of one kind or another. The Christian story, IF you can get over the initial antecedent improbability of the miraculous, makes more sense of it that any other story does. I think there is no logical proof that a miracle cannot happen, since it is possible that God exists, and God is omnipotent. Further, I think that this miracle is one that God would have a fairly understandable reason to perform. So, given my prior probabilities, the evidence lifts the case for the resurrection at least over 90%. But I can't prove the someone else that they shouldn't have priors so low for the Resurrection that it never gets above 10 for them. Both can be rational, and that's just life in the big city. (I also don't think salvation is a matter of passing a theology test). If you don't believe in the Resurrection, then I think there are a bunch of inconvenient facts out there that are hard to make sense of. But I think every philosophy has to deal with inconvenient facts.
Keith Parsons would probably call this Bayesian Balkanization.
I think that as you pull at the story of the founding of Christianity, as you play out the various scenarios all the way through, you end up thinking that none of the scenarios for what might have really happened fit the facts very well. They run into factual brick walls of one kind or another. The Christian story, IF you can get over the initial antecedent improbability of the miraculous, makes more sense of it that any other story does. I think there is no logical proof that a miracle cannot happen, since it is possible that God exists, and God is omnipotent. Further, I think that this miracle is one that God would have a fairly understandable reason to perform. So, given my prior probabilities, the evidence lifts the case for the resurrection at least over 90%. But I can't prove the someone else that they shouldn't have priors so low for the Resurrection that it never gets above 10 for them. Both can be rational, and that's just life in the big city. (I also don't think salvation is a matter of passing a theology test). If you don't believe in the Resurrection, then I think there are a bunch of inconvenient facts out there that are hard to make sense of. But I think every philosophy has to deal with inconvenient facts.
Keith Parsons would probably call this Bayesian Balkanization.
Reply to David Parker on Bayesianism and Trajectory of Science Arguments
David Parker has noticed my commitment to a subjectivist Bayesian model of belief acceptance. I should add what Monty Python said about Camelot: "It's only a model!" However, I don't see a better one. I believe in openness to evidence, but I don't believe in neutral perspectives. I believe in rationality, but I don't believe in artificial standards of rationality. And I certainly don't believe that people should claim to have achieved objectivity when they really are far from that lofty goal.
Parker wonders if my commitment to a Bayesian model of evidence commits me to the idea that all evidence is physical evidence, and hence will have to support physicalism by definition. I don't see why. Why these constraints? With Richard Swinburne, I see no good reason to suppose that there can't be evidence for theistic hypotheses. If I physically observe someone alive on Thursday, dead on Friday, and alive again on Sunday, that is prima facie evidence for the claim that that person was resurrected supernaturally from the dead. It is what I should expect if there was a resurrection, and what is very puzzling on the assumption that there was no resurrection. Now, I might, on further investigation, decide that indeed there was no resurrection, but the idea that I must rule a supernatural resurrection out from the outset strikes me as absurd. Or, to use my favorite example from atheist philosopher Keith Parsons, if the galaxies in the Virgo Cluster were to spell out the words "Turn or Burn! This means you, Parsons," then I suspect we have evidence that strongly confirms the claim that a deity exists who is threatening my atheist philosopher friend with eternal perdition.
I am unpersuaded of "trajectory of science" arguments which suggest that as we investigate further we will find greater and greater support for reductionism. Two aspects of the materialistic vision of the world as it has been historically understood are the following:
1) The universe had no beginning, and has always existed.
2) The universe is deterministic, and as we do science we will come closer and closer to finding determining causes for everything.
Now, thanks to the development of the Big Bang theory in the first instance, and quantum mechanics in the second instance, confidence in both of these theses has eroded in comparison to what might have been thought in the early days of the 20th Century.
Now, of course, naturalists have revised their conception of what is naturalistically acceptable to accommodate a universe with a temporal beginning, and a universe with quantum level indeterminism. But the point is that science frustrated the expectations of what at the time were the expected results of the naturalistic thrust of science, as it was understood at that time. This gives me some serious doubts about the idea that we can predict that the future of science will confirm physicalism, as we now understand it.
With respect to the analysis of mind, I see a lot of bravado about reductive analyses but no real hard evidence that reductions are going to be successful. In fact, given the fact that "the material" or "the natural" has to be defined in terms of the absence of the mental, it looks to me as if reduction of the mental to the physical is logically impossible, and that the more we study things scientifically the more evident this will become.
Parker wonders if my commitment to a Bayesian model of evidence commits me to the idea that all evidence is physical evidence, and hence will have to support physicalism by definition. I don't see why. Why these constraints? With Richard Swinburne, I see no good reason to suppose that there can't be evidence for theistic hypotheses. If I physically observe someone alive on Thursday, dead on Friday, and alive again on Sunday, that is prima facie evidence for the claim that that person was resurrected supernaturally from the dead. It is what I should expect if there was a resurrection, and what is very puzzling on the assumption that there was no resurrection. Now, I might, on further investigation, decide that indeed there was no resurrection, but the idea that I must rule a supernatural resurrection out from the outset strikes me as absurd. Or, to use my favorite example from atheist philosopher Keith Parsons, if the galaxies in the Virgo Cluster were to spell out the words "Turn or Burn! This means you, Parsons," then I suspect we have evidence that strongly confirms the claim that a deity exists who is threatening my atheist philosopher friend with eternal perdition.
I am unpersuaded of "trajectory of science" arguments which suggest that as we investigate further we will find greater and greater support for reductionism. Two aspects of the materialistic vision of the world as it has been historically understood are the following:
1) The universe had no beginning, and has always existed.
2) The universe is deterministic, and as we do science we will come closer and closer to finding determining causes for everything.
Now, thanks to the development of the Big Bang theory in the first instance, and quantum mechanics in the second instance, confidence in both of these theses has eroded in comparison to what might have been thought in the early days of the 20th Century.
Now, of course, naturalists have revised their conception of what is naturalistically acceptable to accommodate a universe with a temporal beginning, and a universe with quantum level indeterminism. But the point is that science frustrated the expectations of what at the time were the expected results of the naturalistic thrust of science, as it was understood at that time. This gives me some serious doubts about the idea that we can predict that the future of science will confirm physicalism, as we now understand it.
With respect to the analysis of mind, I see a lot of bravado about reductive analyses but no real hard evidence that reductions are going to be successful. In fact, given the fact that "the material" or "the natural" has to be defined in terms of the absence of the mental, it looks to me as if reduction of the mental to the physical is logically impossible, and that the more we study things scientifically the more evident this will become.
Reply to Mark Frank on abusing probability theory
Mark Frank: You are quite right about abusing Bayes' theorem. Bayes also says we have to take into account the a priori probability of a natural or supernatural explanation. You have only considered the likelihood side of the equation. This is the famous gremlins in the attic paradox. Given gremlins in the attic it is very likely that they caused a noise. But that doesn't mean that Gremlins in the attic are a likely explanation of a noise in the attic.
Quite correct. However, we don't have any good way of measuring what the "prior" side of Bayes' theorem ought to be, and I presume that it can differ amongst reasonable people. That was the whole point of the anti-frequentism argument that I gave a few posts ago. I don't think there's a good way to go back into one's belief system and discount everything that is the product of a non-truth-conducive belief-producing mechanism, a la the Outsider Test. This is partly because it is not transparent to any of us why we think as we do.
Quite correct. However, we don't have any good way of measuring what the "prior" side of Bayes' theorem ought to be, and I presume that it can differ amongst reasonable people. That was the whole point of the anti-frequentism argument that I gave a few posts ago. I don't think there's a good way to go back into one's belief system and discount everything that is the product of a non-truth-conducive belief-producing mechanism, a la the Outsider Test. This is partly because it is not transparent to any of us why we think as we do.
The Case Against Frequentism
From my Infidels paper on miracles.
IV. Probability and its Empirical Foundations
According to Hume, probabilistic beliefs concerning the intentions of a supernatural being are inadmissible in reasonings concerning matters of fact because these beliefs fail to be grounded in experience. This insistence has been enunciated by Bayesian theorists, and it is the frequency theory. But the frequency theory has fallen on hard times, and most Bayesian theorists do not accept it, largely because of difficulties related to the problem of the single case.The problem is this. Frequencies give us information as to how often event-types have occurred in the past. But we often want to know the probability of particular events: this coin-toss, this horse-race, this piece of testimony to the miraculous, etc. If we are to accept Hume's conclusion that testimony to the miraculous ought never to be accepted, we need to show more than just that rejecting testimony to miracles in general is a good idea because false miracle claims outnumber true ones. Many Christians are skeptical of miracle claims put forward by televangelists, but nonetheless believe that the evidence in support of the resurrection of Jesus, and perhaps in support of some modern miracles, is sufficient to overthrow our ordinary presumption against accepting miracle reports.
Frequentists have attempted to assess the prior probability of individual purported events by assimiliating them some class of events. Thus, we assess the probability of a particular coin-toss as 1/2 in virtue of its membership in the class of coin-tosses. But the question is which class the relevant reference class is. The claimed resurrection of Jesus falls into many classes: into the class of miracles, into the class of events reported in Scripture, the class of events reported by Peter, the class of events believed by millions to have occurred, into the class of events basic to the belief-system of a religion, etc. Of course it is what is at issue between orthodox Christians and their opponents whether the class of miracles in the life of Jesus is empty or relatively large.
Wesley Salmon attempts to solve this problem by defining the conception of an epistemically homogeneous reference class. A class is homogenous just in case so far as we know it cannot be subdivided in a statistically relevant way. Thus, according to Salmon, if Jackson hits .322 overall but hits .294 on Wednesdays, the Wednesday statistic is not to be treated as relevant unless we know something about Wednesday that makes a difference as to how well Jackson will bat. Thus, according to Salmon, the relevant reference class is the largest homogeneous reference class; we should try to get a sample as large as we can without overlooking a statistically relevant factor.[13]
There are two difficulties with this method as an attempt to satisfy Hume's strong empiricist requirements for properly grounded probability judgments. First, questions of statisical relevance cannot be fully adjucated by appeal to frequencies. Second, the very heuristic of selecting the largest homogeneous reference class cannot be read off experience.
On the first point, consider the situation of a baseball manager who must choose between allowing Wallace to bat or letting Avery pinch-hit for him. Wallace has an overall batting average of .272, while Avery's is .262. But the pitcher is left-handed, and while Wallace bats .242 against left-handed pitching, Avery bats .302. Nevertheless, the pitcher is Williams, and while Avery is 2-for-10 against Williams, Wallace is 4-for-11. Have these batters faced Williams too few times for this last statistic to count? And can this be straightforwardly determined from experience? What is needed is a judgment call about the relevance of this statistical information, and this judgment cannot simply be read straightforwardly from frequencies. The frequentist's epistemology for probabilistic beliefs, insofar as it is an attempt to conform to empiricist/foundationalist constraints, seems impossible to complete.
On the second point, is the heuristic of selecting the smallest homogeneous reference class justified simply by an appeal to experience? Admittedly it makes a certain amount of common sense. But this attempt to go from a statistical "is" to an epistemological "ought" seems to suffer from with the same (or worse) difficulties that getting "ought" from "is" suffers from in ethics, and here again Hume's empiricist/foundationalist assumptions impose an impossible burden on probability theory.
The frequency theory seems clearly to be the theory of priors that Hume would have adopted had he been involved in the contemporary Bayesian debate on prior probabilities. But even this theory fails to adjudicate the issue concerning miracles in Hume's favor or in favor of the defenders of miracles, because it lacks the resources within itself to select the appropriate reference class. This inability to provide determinate answers to questions of probability is what makes this theory inadequate for resolving the question of miracles. Therefore Hume cannot justify his claim that it is never rational to believe testimony to any miracle on the grounds that miracles are less frequent in experience than false miracle reports.[14]
13] Salmon, The Foundations of Scientific Inference (Pittsburgh: University of Pittsburgh Press, 1967), pp. 90-93.
[14] These objections were suggested to me by in conversation by Patrick Maher.
On Bayesian subjectivism
JWL: Vic, if your "priors" are truly "priors" then they need to be there "prior."
So here you are wondering whether Christian theism is true. You were probably raised to believe in this Christian culture but now as the adult you have become you want to examine the case for yourself.
So when doing so what are your "priors" at that point? That is, what do you know and when? When do you place which "priors" into your bag of "priors"?
Name them in order to the best of your ability. And tell me how you arrived at them without using any subsequent ones.
VR: But the whole subjectivist theory of Bayesianism says that we best arrive at the truth if we conditionalize on the priors we have, since an arbitrary shift in priors won't be helpful in getting to the truth. If our priors are bad priors, then the evidence should move us off those priors to a more adequate belief system.
Bayesian subjectivism is a strongly anti-foundationalist theory of knowledge. I suppose it's a version of coherentism.
So here you are wondering whether Christian theism is true. You were probably raised to believe in this Christian culture but now as the adult you have become you want to examine the case for yourself.
So when doing so what are your "priors" at that point? That is, what do you know and when? When do you place which "priors" into your bag of "priors"?
Name them in order to the best of your ability. And tell me how you arrived at them without using any subsequent ones.
VR: But the whole subjectivist theory of Bayesianism says that we best arrive at the truth if we conditionalize on the priors we have, since an arbitrary shift in priors won't be helpful in getting to the truth. If our priors are bad priors, then the evidence should move us off those priors to a more adequate belief system.
Bayesian subjectivism is a strongly anti-foundationalist theory of knowledge. I suppose it's a version of coherentism.
My Bayesian paper on Hume on Miracles
A redated post.
My first published paper, "Miracles and the Case for Theism" replied to Mackie's treatment of miracles in The Miracle of Theism. I discovered a formal error in Mackie's analysis, which violates the Mackie Revelance Principle. The paper came out in February 1989 International Journal for Philosophy of Religion. And, of course, a follow-up treatment of miracles is on Internet Infidels. Someone who wants to defend Mackie's or Hume's position might want to start by rebutting me in those papers.
My first published paper, "Miracles and the Case for Theism" replied to Mackie's treatment of miracles in The Miracle of Theism. I discovered a formal error in Mackie's analysis, which violates the Mackie Revelance Principle. The paper came out in February 1989 International Journal for Philosophy of Religion. And, of course, a follow-up treatment of miracles is on Internet Infidels. Someone who wants to defend Mackie's or Hume's position might want to start by rebutting me in those papers.
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