A drop in the sea

What are the odds that Jesus rose or Moses parted the waves? Even with the best witnesses, vanishingly small

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Charlton Heston as Moses in The Ten Commandments. Photo by J R Eyerman/Time Life Pictures/Getty

Charlton Heston as Moses in The Ten Commandments. Photo by J R Eyerman/Time Life Pictures/Getty

Lawrence Shapiro is a professor in philosophy at the University of Wisconsin, Madison. His latest book is Embodied Cognition (2011).

Do you believe in miracles? You shouldn’t — not in the strict sense of ‘miracles’, anyway. If you’re just using the word as a kind of hyperbole, that’s fine: believe away. People sometimes refer to the ‘miracle of birth’, but they don’t mean that a supernatural agent was involved. They just mean that birth is wonderful and momentous. In other contexts, calling an event a miracle draws attention to its unlikely good fortune. In 1980, the United States Olympic hockey team defeated the Soviet team in a medal round. The USSR had won the gold medal in this sport at every Olympic Games bar one since 1956, so no one expected the US to prevail. Americans now refer to this game as the ‘Miracle on Ice’, and some of them might well believe that God assisted their players. Nevertheless, most who describe that victory at Lake Placid, New York as a miracle mean simply that it came as a huge, and very nice, surprise. I doubt many in the USSR referred to their loss as a miracle, though they will have been just as surprised as viewers in the US.

This is not the kind of miracle that interests me. My sights are set on those alleged occurrences that depend on the activities of supernatural forces. When Moses parted the Red Sea, or Jesus raised Lazarus from the dead, or Aaron turned his staff into a serpent, one might be inclined to think that something outside of nature was at work. Each of these events appears inconsistent with how we know nature to operate. Had it run its normal course, the Red Sea would never have parted, Lazarus would have remained dead, and Aaron’s staff would never have eaten the Pharaoh’s serpents.

Miracles, as I think of them, will tend to be improbable. This is not to say that they must be improbable ‘by definition’, just as bachelors, ‘by definition’, must be unmarried. On the contrary, the improbability of miracles functions only as evidence for their supernatural origin. If you look up and see unrelenting grey skies, this might persuade you that you’re in London. Similarly, if you see something unlike anything you’ve ever seen before, this might suggest that the natural order has broken down: that a supernatural presence has intervened, disrupting the normal course of things.

What is the natural order? Think about how we develop our ideas for how nature is ‘supposed’ to work. We observe, for example, that metal expands when heated. The more observations we make, the better confirmed this generalisation appears to be. The better confirmed the generalisation, the stronger our conviction that we have hit upon a deep and broad fact about nature: that all metals (and not just the ones we have observed) expand when heated. Similarly, our belief in the finality of death rests upon countless observations of living organisms (including human beings) dying and staying dead. The best evidence for the generalisations by which our sciences describe nature is frequency. The more one observes a pattern recurring again and again, the more reason one has to believe that the pattern is natural — that it is, in fact, how the world works.

The flip side to this is that when a well-confirmed generalisation fails — when that piece of metal refuses to expand, or when that dead body leaps from the grave and dances a jig — we must give up the idea that nature operates as we thought. Alternatively, when our generalisation has been confirmed as thoroughly as the notion that dead organisms remain dead, we might choose to regard the apparent violation of the natural order as the consequence of something outside nature. A non-natural force has acted to suspend the natural way of things, seeing to it that a dead organism gets a second chance at life.

Does rarity really indicate miraculousness? Suppose for a moment that Moses parting the Red Sea was not such an uncommon event. Perhaps he parted the Red Sea every day and twice on Sundays. Maybe not just Moses, but his friends Shlomo, Herb, and Esther also took turns parting the Red Sea. I think if people were parting the Red Sea frequently, we would begin to suspect that nothing unnatural was going on. We might suppose that the Red Sea has unusual tides and that Moses and his friends just figured out the schedule. On the other hand, we might come to think that Moses & Co had secretly installed a drain at the bottom of the sea. The more frequent the partings, the more inclined we’d be to regard them as a feature of nature, or a trick with a perfectly natural explanation. It’s because, to our knowledge, the sea never parts on command that we find a supernatural explanation tempting when it does.

Finally, my thesis: no one has ever been justified in believing in miracles in the strict sense.

Before we get into the defence, let me make a clarification. On the several occasions when I have presented my thesis to various groups, the first response I typically receive is this: ‘So you don’t think there have been any miracles?’ This is the wrong response: my thesis takes no stand on whether there have been miracles. My concern is only with the question of justification. We are not presently, nor has anyone ever been, justified in believing in miracles.

To grasp the distinction I’m drawing, consider the question of whether life exists on Mars. Many people believe that it might, most probably in microbial form. Certainly, we can all agree that life either exists on Mars or it does not (there can be no middle ground). However, we currently lack sufficient evidence to justify a belief in life on Mars. Some day we might acquire such evidence. Perhaps methane will be discovered on the planet’s surface, raising the probability that microbes exist. Perhaps other bits of evidence will emerge as well. At some point, the accumulating data might grow so compelling that we would be justified in believing that life does indeed exist on Mars. Likewise, we can all agree that miracles such as Jesus rising from the dead either did, or did not, occur. My claim is that, to date, evidence for such an event — and any other event that is regarded as a miracle — is too weak to justify anyone’s belief in it as fact.

I claim no great originality for my argument. I’m borrowing from the great Scottish philosopher David Hume, particularly Section 10 of his magnificent Enquiry Concerning Human Understanding (1748). If there is any novelty in my presentation, it owes to the marriage of Hume’s ideas with a famous theorem in probability theory proposed by the Reverend Thomas Bayes in ‘An Essay towards solving a Problem in the Doctrine of Chances’ (1763). The technical details, fortunately, can be put to the side for our purposes.

The argument begins with an assumption that is very favourable to those who believe in miracles. Let's say that the witnesses of miracles are very reliable — far more reliable than ordinary witnesses. This is not to say that miracle witnesses are infallible. If they were, then of course we could trust their reports and there would be nothing more to discuss. But witnesses, we know, are never perfect. Things aren’t always as they seem, our eyes on occasion mislead us, and sometimes we see what we want to see. When a courtroom drama hinges on a witness who turns out to have identified the wrong person, no one doubts that such misidentifications are possible.

Even so, for the sake of argument, let’s suppose that witnesses to miracles almost never err. Of all the reports they make in the course of their lifetime — hundreds, thousands, even 100,000 — they make only one mistake. Should we believe someone who claims to have witnessed a miracle if his or her testimony has a chance of only one in 100,000 of being wrong?

If Jesus did rise from the dead, he’s in a very select group

Now I want to consider a slightly different question, albeit one that will have lessons for how we should answer the question above. Suppose you visit your doctor for a routine check-up. After testing a sample of blood, the doctor grimaces. ‘I have bad news for you,’ he says. Bad indeed. You’ve tested positive for a very lethal form of cancer. Your chance of surviving the next three years is practically zero. A treatment exists, but it carries significant costs (blindness, incontinence, all your hair falling out). Furthermore, your doctor says, the test is very good. In every 1,000 tests, it gives only one false positive – that is, a diagnosis of cancer to someone who doesn’t have the disease. Also, 0.001 per cent of the time it goes wrong the other way, giving a negative result to someone who really does have the disease. Do you opt for the treatment?

The correct answer is this: before deciding, you need a piece of information that the doctor did not provide. Without information about the base rate of the disease – its frequency in the population at large – any facts about the reliability of test are completely useless.

To demonstrate this, let’s first suppose that the cancer is not terribly uncommon. Perhaps it affects 0.001 per cent of the population. This means that, for every 1,000 people in the population, one person will have the disease. We also know that the test goes wrong 0.001 per cent of the time. That is, it errs one time in 1,000, and it errs in two ways. If we select 1,000 people at random from a larger population, one person in this group who is actually healthy is likely to test positive for cancer. However, the chances are that this group also contains one sick person, because the base rate of the disease, as we’ve said, is one in 1,000. Yet, because the test fails to detect cancer only one time in 1,000, chances are very good (999/1,000) that the test will correctly identify the sick person in the group. This means that, having tested 1,000 people, our test ends up ‘diagnosing’ two of them with cancer, when in fact only one of them has it. Given the base rate of the disease and the sensitivity of the test, if you’ve tested positive, the chance that you are actually sick is only 50 per cent.

An obvious but interesting conclusion follows. If we hold the accuracy of the test constant but decrease the base rate of the disease, the trustworthiness of the test result diminishes accordingly. For instance, let’s now suppose that the base rate of the disease is one in 10,000. That extra zero means that, having tested positive, the odds of genuine sickness slip down to 10 to one. With its one-in-1,000 error rate, the test will identify 10 people as having the disease when they do not, and one as having the disease when he or she does. Making the disease rarer still, so that it affects only one in, say, 1 million people, puts the chances of illness at a vanishing 1,000 to one. So, this test of ours turns out to be no good at all when the disease for which it tests is rare.

The practical lesson is this: knowledge of the rate at which a test errs tells you nothing by itself about whether the test results should be trusted. You need also to consider whether the thing for which you are being tested occurs frequently or seldom. If the disease is rare and you test positive, you should look for another explanation for your result than actual illness. Given a test that errs one time in a 1,000 and a disease that is present in only one person in a million, there is a better explanation. Evidently, the test is sensitive to factors other than disease. Something in your blood, perhaps, triggered the positive outcome. This possibility is far more likely than that the disease was responsible for the positive result. Indeed, it’s 1,000 times more likely.

Still another point concerns the issue of justification that I raised earlier. Because a positive test result in the conditions I have described is far more likely to be wrong than right, the result fails to justify the belief that you have the disease. Even if you do have the disease, and even if the test correctly diagnoses you as having the disease, you should not believe this on the basis of the test alone. Forget about the test result. It’s as good as worthless as far as justification goes.

Let’s see how these ruminations about tests and base rates and justification bear on the issue of miracles. Many people believe that Jesus rose from the dead (indeed, there are about two billion Christians on Earth, and if only half believe that Jesus rose from the dead, that’s still an awfully big number). If such a resurrection really took place, we can grant that this would have been an extraordinarily rare kind of event. Of course, other stories of the dead returning to life appear in mythology and fairy tales, but these stories are presumably not based on fact. This means that, if Jesus did rise from the dead, he’s in a very select group (he allegedly raised several people himself). If we were to conceive of rising from the dead as a kind of disease, we’d say that the ‘base rate’ for rising from the dead appears to be small indeed: one in several billion, at best, I should think.

Now we must ask about the reliability of the test that tells us that Jesus rose from the dead. On what basis do we form a judgment that Jesus was resurrected? Although the gospel accounts of the resurrection are surprisingly inconsistent given the magnitude of what they describe, we might grant that one or two witnesses to the resurrection were present. These witnesses are, in effect, our ‘test’ for the resurrection of Jesus. Just as we can ask about the probability of a disease given a positive test result, we can ask about the probability of Jesus’s resurrection given that a person claims to have witnessed it. I’ve already allowed that witnesses to miracles are super-reliable. This, of course, is very generous on my part. There’s really no reason to think that miracle-observers should be any more reliable than normal human beings.

I don't deny that miracles have occurred, just that the available evidence fails to justify a belief that they have occurred

Be that as it may, if Jesus’s resurrection is the ‘disease’ and the witness report is the ‘test’, we can now do the algebra to decide whether to believe in the resurrection. The base rate for the resurrection is (let’s say) one in 1 billion. The witnesses go wrong only one time in 100,000. One billion divided by 100,000 is 10,000. So, even granting the existence of extraordinary witnesses, the chance that they were right about the resurrection is only one in 10,000; hardly the basis for a justified belief.

As with the diagnostic test, the question to ask is whether there is a better explanation for the existence of these witness statements than the actual resurrection, which, as we’ve already said, is vastly improbable. What might account for such reports? Who knows, but I imagine any of the following is more likely than the supposition that Jesus actually rose from the dead: perhaps no witnesses were present and the story of the resurrection simply grew, as fantastic stories often do, from embellished retellings of Jesus’s life; or the witnesses reported a hallucination of Jesus that others then took to be a true report of Jesus in corporeal form; or maybe the witnesses were mendacious and eager to start a cult that might challenge Roman authority. How likely are any of these alternative accounts of why the witnesses, if present at all, said what they did? No idea, to be honest, but I’m quite sure that any of them are more probable than a dead person returning to life.

No one is justified in believing in Jesus’s resurrection. The numbers simply don’t justify the conclusion. But the resurrection is just one miracle. If we suppose that all miracles are similarly rare, then, by parity of reasoning, belief in any one of them is similarly unjustified. As noted earlier, my conclusion doesn’t deny that miracles have occurred or might occur, just that the available evidence fails to justify a belief that they have occurred. So, if you wish to continue to believe in miracles, you must do so knowing that the evidence is not on your side.

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Comments

  • https://www.youtube.com/watch?v=0ar-y810wS8 Phaerisee

    With faith no explanation is needed, without faith no explanation is possible.

    • mgsk

      Blah blah blah

    • Aravis Tarkheena

      So, on what basis do you have faith in X, rather than faith in Y?

    • labreuer

      It seems difficult to imagine that this is what was meant when Jesus asked his followers to love God with their minds among other things. God is basically the worst being to follow unthinkingly. As in, I'm pretty sure it's not possible. See Deut 5 and specifically, the response of the Israelites to God's booming and bumping and burning: yo God, we only want to follow you by proxy—you know, somebody who won't demand as much from us. Someone who will basically let us think what we think and get on with our lives.

  • Ben Curthoys

    When explaining the base rate fallacy to people, I normally use a more political example: a terrorist detecting machine. If you have an invasive, unpleasant, inconvenient, expensive machine that tests for terrorists - with remarkable efficiency, a false positive/negative rate of only 1 in 1000, and you put one in an airport, say, Heathrow, that feels like a major step towards improving security. But there were 70,000,000 passengers going through Heathrow last year, and as far as I know no actual hijackings. Even if apprehended attempted terrorists were being carted off to secret prisons at a rate of 70/year - more than one per week! - Baye's theorem means that the result of your machine should basically be ignored. Even if it tells you someone's a terrorist, there's a 99.9% chance they aren't.

    Your argument would mean that someone should never believe someone a terrorist intent on blowing up a plane, no matter what the machine says.

    • http://www.aeonmagazine.com/ Ed Lake

      The difference is, with the terrorists, you can definitely come up with a base rate that isn't nil. With miracles, anything over nil has to be considered a high estimate of the real base rate. And so, while for terrorists, the lottery paradox (https://en.wikipedia.org/wiki/Lottery_paradox) arises (there's got to a winner, right?) there may or may not be real miracles, and it doesn't seem irrational to decide against each individal candidate miracle, reach the end of the list, and conclude that none of them were real after all.

    • http://www.aeonmagazine.com/ Ed Lake

      Or a slightly different reply - it seems right that you should never *just* take the machine's word for it that someone is a terrorist. The value that the machine provides is in identifying good candidates for further investigation. Likewise testimony of miracles, except that further investigation seems impossible.

  • Flotsam Files

    The flaw in this article is how miracles and the supernatural are defined here. The author assumes that the belief in alleged historical miracles requires improbable "supernatural" events.

    That's not how I view miracles. Suppose that the Israelites escaped Egypt because Moses figured out the tide tables of the Red Sea and knew they could cross at low tide. Does this make the story any less miraculous? Not really. You could argue, who made Moses intelligent enough to figure out the tide tables and devise this plan? It can only be God. What prevented Egyptian spies from discovering the plan and foiling it? It's a miracle from God. How were the Israelites all able to reach the Red Sea at the right time and cross without delay? It's because they had God's protection. I realize this is not really the miracle described in the strict sense, but the point is, it makes no difference. If God exists then God is nature and nothing is supernatural. Or everything is supernatural, take your pick. The tide tables and the ideas of people all come from God.

    If you believe this, then it actually doesn't matter whether you think Moses understood the tide tables, or if he parted the Red Sea by magic. All are works of God and amount to the same thing. You can believe either one. The real miracle is God guiding the Israelites out of Egypt, by whatever means. It could be that the Israelite who first told this story didn't know about Moses' trick with the tide tables and really thought the sea parted by magic. But for that guy the miracle was that he reached the Promised Land

  • blsDisqus

    This means that, if Jesus did rise from the dead, he’s in a very select group...

    And this is exactly what Christians claim. So no real news here, I think.

    In any case: isn't abiogenesis also thought to be "highly improbable"?

    • Hugh Slaman

      Not only that, there is not even a single eyewitness to abiogenesis. It is just speculation being treated as fact, while at the same time improbable events which do have some limited evidence in their favor are dismissed.
      Good point!

  • Trimegistus

    This article is the most massive case of utterly missing the point I've ever seen. Of course miracles are unlikely. That's what makes them miraculous! They are matters of faith, not statistics. The whole POINT of religious belief is that one believes -- on faith, not because of evidence -- some extremely improbable things.

    I'm an atheist and I understand this: saying that miracles probably didn't happen because they're so unlikely is simply irrelevant to the belief of the faithful. You're not disproving anything. The faithful know miracles are unlikely. That's why they believe they're miraculous.

    Frankly, I think Team Unbeliever needs to learn a lot more about religion and the beliefs of the faithful. Too often I see simplistic, ham-handed, or outright foolish attempts to "debunk" religion. Guys, the Church has had two thousand years to think this stuff through! Their theologians and logicians were the ones who laid much of the framework for modern scientific thought. You're not going to prove anything with some back-of-the-envelope calculations.

    • Robert Rucker

      If you think Shapiro is "saying that miracles probably didn't happen because they're so unlikely," you need to reread the article.

      • Flotsam Files

        Shapiro is saying no one is justified in believing in miracles based on the evidence, but the point is that no one needs supporting evidence to justify their belief in miracles. That is the whole point of miracles.

        • Robert Rucker

          No, the whole point of miracles is to convince nonbelievers that some person or artifact is divine or in touch with the divine.

          True believers don't need supporting evidence to justify THEIR OWN beliefs in miracles, but they DO try to use supporting evidence to justify OTHERS in believing in miracles.

          • Flotsam Files

            That might be true, but true believers don't desire to make supporting evidence a watertight case. The ultimate goal is that the convert will make a leap of faith and become a true believer themselves, thus abandoning the need for evidence. Supporting evidence is just a crutch which it is hoped will become unneccessary.

          • Larry Shapiro

            Dear FF, please see my response to Trimegistus. Many very smart, very well educated, scholars have spent good portions of their lives defending the idea that belief in miracles is justified. It may be, as you say, that true believers don't think watertight evidence is necessary for belief. But that still leaves the project of evaluating whatever evidence they do take seriously.

          • Richard McCargar

            To say nothing of the fact that people are losing their faith at an increasing pace, and they do so for many reasons, including arguments, such as you've made here.

          • Kathleen M. Ritter

            The whole point of miracles is to convince nonbelievers that some person or artifact is divine or in touch with the divine? That's just not true. It might be a happy by-product, but as a practical matter miracles tend to expose the believers to ridicule and persecution. I don't pretend to know what the "whole point of miracles" is -- I don't know how you can be so certain.

    • Flotsam Files

      Absolutely. I mean let's take a totally ridiculous example like someone believes that the Virgin Mary appears on a piece of toast. We can assemble any amount of proof to say it's highly improbable that the Virgin Mary would appear on toast, that it's unjustifiable to have such a belief. But if someone testifies to such a miracle and it's their sincere interpretation of their beliefs, evidence is not an issue.

      • Richard McCargar

        Yet every year, people who used to believe, no longer do. And they lose their belief for a variety of reasons.

        • Flotsam Files

          That's true, good point.

    • Larry Shapiro

      On the one hand, you claim that the point of religious belief is that one believes on faith. On the other hand, you note that theologians have been thinking things through for 2000 years. Why so much thought if the point or religious belief is faith? More seriously, I do agree with you that many religious folk think that requests for evidence for their beliefs is misplaced. However, there's a long tradition in natural theology going as far back (at least) to Aquinas that seeks to ground claims about god in reason. There's also a stack of books on my desk by Christian apologists (historians, philosophers, theologians) that nearly reaches the ceiling. Every one of these books includes detailed defenses of the claim that belief in miracles is justified. So, if I've utterly missed the point, I'm in very good company.

      • Flotsam Files

        But I wonder if there are any theologists who would argue that belief in miracles is justified based on the reasoning that they are highly probable as a pattern in nature? I doubt that theologists would consider probability as a factor when seeking rational justification for miracles, because of the place of miracles in religious belief, that is that they are by definition, exceptional unique events.

      • Flotsam Files

        All right, looking it up on Wikipedia I see that your argument follows Hume who asserted that miracles could never be proved and therefore could not be the foundation of religious belief. Whereas Aquinas argued miracles were events done by God which nature could never do, outside the natural order of things. Which is pretty much what we have here. Interesting.

    • lottasplainin

      I remember in logic class that "miracles are impossible because they violate the laws of nature" was the example the textbook used of "begging the question." Beyond that, however, as a mathematician, I do not understand any proposition beginning "what are the odds that..." applied to a non-repeatable event, which relates directly to the issue of why we feel it useful to make a distinction between "natural" and "supernatural" in the first place. Seems like an "artificial" distinction.

    • David Marshall

      Frankly, I think YOU need to learn a lot more about Christianity and why Christians believe. This is the most common, and least justifiable, myth in the atheist arsenal. Knowledgeable Christians have been combatting this "blind faith" meme for centuries (I have published contrary evidence in several places myself), but our critics never seem to learn.

      Shapiro's argument has more genuine problems than that.

  • Gyrus

    Maybe I missed some subtleties by reading just the intro and the final paragraphs. But isn't this entirely pointless? It's like taking the choir into a sound-proofed room, sticking a "CHOIR ONLY - ANYONE ELSE WILL BE SHOT" sign on the door, and then preaching to them. By definition, anyone who believes in this sort of thing will be immune to this mode of argument. In any case, the position taken here is merely the flip-side of "belief" - both are uninterestingly literalist.

    • Larry Shapiro

      Hi Gyrus, I address this point in several posts above. Far from being immune to this type of argument, many Christian apologists take it quite seriously and have responded to versions of it at length. Many Christians regard their belief in miracles to be quite rational and grounded in sound reasoning and evidence.

      • Gyrus

        I thought of "intelligent design" as I wrote, aware of that segment of Christianity that think rationality is a friend - but I erred on the side of emphasis to make a point. I guess it might be good if someone is doing your job, for the minuscule number of Christians whose supposed rationality actually is rational, i.e. amenable to reasoned argument, and thus susceptible to an analysis that will tear it down. But I suspect there's a very firm irrational faith propping up most of these Christians, and taking the bait of their supposed rationality just adds to the skewing of the debate away from what's sidelined by both fundamentalist religion and science - the reality of metaphor.

    • TJ

      That's false. Some people who initially believe in miracles have been talked out of it on account of Humean style arguments. There is nothing in the concept of religious belief, or even religious faith, according to many, that says it is immune to revision in principle.

  • Brian P.

    I'm self-embarassed I just posted here.

  • Flotsam Files

    I think the real mistaken idea here is that miracles can be thought of as a general phenomena of nature that can be analyzed based on their probability, like rare diseases. Of course even in the case of diseases, extremely rare cases may occur from time to time. That's what makes them rare. Doctors occasionally encounter patients with completely unique conditions that have never been seen before. Such cases are, of course, exceedingly improbable, but they do happen.

    The whole premise of miracles is that miracles themselves constitute such exceptional events. The testimony of miracles is itself evidence that probability is not a valid basis for measuring reality because, a divine intention exists that can make some specific, exceedingly improbable event, a reality.

    • Richard McCargar

      How can you be certain that "Doctors occasionally encounter patients with completely unique conditions that have never been seen before?"

      • Flotsam Files

        I would think discovery of amazing new conditions is simply a part of the progress of medical science. Forty years ago no one suspected the AIDS virus existed, but then it appeared. Mad cow disease was not revealed until fairly recently. When these conditions first appeared in patients, they were unique mysteries, until they were researched and understood.

  • James Savage

    The piece suffers from a basic reasoning error. Prof. Shapiro is making two different arguments and conflating them. He argues, in his piece, for the proposition, that one should not believe any specific account of a miracle. That, for instance, I cannot have a justified belief in the report that "Person X rose from the dead" because of Bayes' law. Barring my issues explored below after the break, this argument is fine. He takes this, however, to be that I cannot have a justified belief that "Miracles occur." That is incorrect, and Shapiro has not argued that claim with any force.

    To see why, note that he is essentially committing the lottery fallacy (ironic, since it is usually committed by those, for instance, who argue for a designed universe). To use his numbers, say, the chance of any individual winning the lottery is 1 in 5 million (base rate), and our witness retains the reliability ascribed to him. The witness then reports "person X won the lottery." On Prof. Shapiro's logic, I am not justified in believing the report of the witness. This may well be correct. But the error is then claiming that I am not justified in believing "Of all such witness reports, at least one is true." Clearly, I am well justified in believing the latter because *someone* must have won the lottery [formally, the prior of "the lottery had a winner" is 1].

    To make this more concrete, again, think about the disease example. I am not justified in believing, on the basis of a given positive test result, that an individual has the disease. But it does not follow, at all, that I am not justified in believing that the disease exists! This is what Shapiro argues. This is a horribly serious error in reasoning. Just because a particular positive test does not justify belief [due to its overwhelming likelihood of falsity], so too does such likelihood not justify the non-belief in *at least one* correct [non-false] positive test existing. My belief in disease is not equivalent to my belief that a given person has the disease.

    To bring this application back here - we need only see that: while rising from the dead may have an extremely low rate, and a single report is unjustified, all so-called miraculous events put together may not be subject to the same base rate. I am arguing, in short, that the relevant proposition is "At least some miracles occur". The base rate for that is different than for "This particular miracle occurred." Prof. Shapiro has a long way to go to show that "belief in miracles" is unjustified. Just as I might not be justified in believing that a particular individual won the lottery, I would be equally well unjustified in failing to believe that someone won the lottery. The belief in miracles is the belief of the latter variety, whereas the belief in the parting of the Red Sea by Moses is of the former.

    To repeat myself, a belief in miracles is not equivalent to a belief that a given miracle occurred. Professor Shapiro's entire argument applies only to the latter and has no bearing on the former, as even his own preferred disease example quite easily and clearly demonstrates. This should be the end of it.

    -----------

    As a side note, there is another and more subtle error with Prof. Shapiro's argument, and such arguments relying on base-rates generally (at least when applied to the real world). This is that the choice of category affects the base rate.

    The base rate fallacy may be well defined in the standard lab setting of a Kahneman and Tversky where there is only one possible base rate, but the reason the base-rate fallacy is not that useful in settings such as this is intimately tied to Simpson's Paradox: the base rate, and our conclusions on the basis of the base rate, are deeply related to the group or category that we consider to be the base. I will explain the category sensitivity briefly below, and then briefly discuss the relationship to Simpson - though it should be immediately apparent. I will also lastly note the error in suggesting base rate neglect from a single judgment.

    For example, though the prior probability of a human rising from the dead is say 1 in 3 billion, the prior probability of "the son of God" rising from the dead may be 1 in 2. If the witness reports the latter, we may well be justified in believing the report. (There are, admittedly a number of other questions that precede that second report - "what is the prior of someone being the son of God?" as well as others "in the report that the witness making - that she saw the son of God rise from the dead - does she assume the first part of the report from the second observation?" [though note well, in the latter case, the witness would be a good Bayesian, so long as the prior of seeing "someone - human or otherwise" rise from the dead is not so low, and the question is rather "given that someone rose from the dead, is this someone a human or the son of God?"]).

    To relate this to Simpson's Paradox, let us again return to the disease example. If we know that cancer affects 1 out of 1000 people, that is a base rate. But if we know that cancer affects 1 out of 500 men, and 0 women - we still have the same "base rate" for the entire population, but now we have different conclusions on how justified our belief are when applied to a given individual. Either way, we can extend this even further until we see that each piece of information may just have one base rate, but this doesn't tie back to the original fallacy.

    The base-rate fallacy is only proper (in Kahneman and Tversky's argument at least) when it compares relative odds ratios from modifying a given base rate. We can't conclude on the basis of a single probability judgment that someone is neglecting base rates (except in the extreme cases of 0 and 1, or such related boundaries). We can only tell that they are neglecting base-rates when they do not update odds ratios to match the change in base-rates: we need to compare TWO probability judgments to know they are in error. This is the argument in Kahneman/Tversky's famous lawyers/engineers example - and it is correct (that is, KT do not err in this argument). But the extension of this argument to one single judgment is not correct.

    In short, Shapiro's argument is riddled with misunderstanding and error.

    • Flotsam Files

      Excellent. Thank you.

    • Robert Rucker

      The problem with your lottery example is that it is not true for all lotteries that someone must win.The problem with your disease example is that, typically, the test is not our only reason for believing that the disease exists. However, the testimony of alleged witnesses is the ONLY putative evidence for claims of the miraculous.

      • James Savage

        Oh I understand that (trust me - I'm not arguing that miracles have a prior of 1) - but Shapiro is the one who commits the reasoning error because whether or not miracles have a low prior as a class, he does not present that argument.

        I am not saying that Shapiro's conclusion is incorrect, in other words. I am saying that his conclusion does not follow from his premises. This is what argument invalidity means.

        So if I said, "the sky is blue therefore unjustified killing is wrong" - you would be open to critique my argument without yourself having to defend unjustified killing. I am doing the same thing here. I am not saying that belief in miracles is justified; I am saying that Shapiro's argument doesn't work.

      • http://www.aeonmagazine.com/ Ed Lake

        Agreed; the base rate for miracles has to be deemed *at best* non-zero, so the lottery paradox doesn't arise. At the end, you don't have to look at all the candidates and pick a winner. Likewise, the point about reference classes seems to me to be somewhat disingenuous. If you already believe that Jesus is the Son of God, you would tend to put him in a different category to ordinary people and the calculations would come out differently. But since the miracles are commonly used as evidence for his divinity, it seems illegitimate to simultaneously use his divinity as evidence for his miracles.

        • James Savage

          As noted already, I'm not arguing about the truth of the conclusion. I'm arguing about the validity of the conclusion.

          As to the reference class argument - I noted your exact problem: I said that the person could simultaneously be concluding divinity from miracles and then using divinity as evidence for miracles. I also said the prior of divinity is something to consider. So my reference class argument is far from disingenuous - I made both of these issues apparent as soon as I introduced the argument and made no attempt to hide or mislead on these complications. That doesn't change the logical structure of the claim.

          • http://www.aeonmagazine.com/ Ed Lake

            So, absent separate evidence of divinity, you accept that the appropriate prior is the one for humans rising from the dead?

          • James Savage

            Sure, of course I accept that that is the appropriate prior for assessing whether or not Jesus of Nazareth rose from the dead. Like I said, Shapiro's argument that we are unjustified on the sole basis of witness reports, even from highly reliable witnesses, in believing that Jesus rose from the dead is perfectly valid. There is nothing majorly wrong with that argument.

            My issue, to repeat, is that this is NOT the conclusion Shapiro purports to reach. He does not merely conclude "Thus, believing that Jesus resurrected is unjustified." He concludes instead "Thus, believing in miracles is unjustified." Surely you see the difference?

          • http://www.aeonmagazine.com/ Ed Lake

            I see the difference, but here's why I'm not sure it's a problem for Shapiro. The lottery paradox arises because there has to be a winner. It is rational to believe of each individual ticket that it is not the winner, but the aggregate of these beliefs (ie that no ticket is the winner) is known to be false, hence the paradox. In the case of miracles, the base rate is either a very low frequency or it is nil. Given the highest feasible positive estimate of the base rate, it is still not rational to believe in any given miracle. But what happens when you aggregate those beliefs? Should you still expect a winner, consistent with your charitable original estimate of the base rate? Or should you remember that a perfectly credible real value for the base rate is zero, and decide that in this situation the aggregate of your beliefs is fine as it is?

          • James Savage

            You're arguing that it's not a problem for Shapiro's conclusion. You're arguing that "Believing in miracles is unjustified" - this is fine. But you're not arguing that the *way* Shapiro gets there is correct. I'm not saying I disagree with Shapiro on his ultimate judgment. I'm demonstrating the invalidity of his argument by showing that it depends on the specific base rate of miracles, not on the connection to Bayes/posterior evidence, etc.

            Let me explore the deeper issue with your claim. If the base rate is zero - then no finite amount of evidence can ever change your posterior (I'll set aside the mathematical issues of infinite evidence with a degenerate prior). That is, you have ruled out the possibility of justified belief in miracles from the start. That is a perfectly fine position to take, but that cannot then be the basis for arguing that justified belief in miracles is impossible. You would then need to argue WHY the prior should be zero. You're almost making a definitional claim at that point ("there can be no married bachelors") if the prior is actually a hard zero.

            Either way, if the prior is extremely small, that is what is doing all the work in the argument. You've simply buried the debate.

            This is why: If I have a sufficiently large prior, I am indeed justified in believing in miracles even with witness reports to the contrary! If I have a sufficiently small prior, even with reliable-witness reports confirming miracles, I am still unjustified in believing in them.

            So the real question is: what prior am I justified in believing? Almost by the very nature of the question, Bayes can be of no help to us at all. In the lab setting, we "know" (again, punting a bit on the epistemological questions) that there are 30 engineers and 70 lawyers, so we are justified *only* in that single value for a prior. In the real world, the source or origin of priors is nearly everything. One can only make the claim "given this range of priors, this evidence does not justify this posterior belief." That is distinct from saying "this posterior belief is not justified for any prior." So Shapiro needs a more compelling and fleshed out argument for what the prior of "miracles" is and why.

            Otherwise, he is simply stating the obvious and trivial - that in essence: if the prior is lower than the reliability of the witness making the report, our justified belief following the report does not change, because the prior constitutes the bulk of the total evidence we have about the hypothesis.

            Of course, that last issue raises a more important question. For a non-zero prior (even 1 in 10 billion, say, of rising), and with error of testimony small (say 1 in 100,000 as he does), if all testimony were consistent on that point of rising from the dead (set aside the issue of inconsistency in other details - this is a hypothetical argument), and if error in testimony were uncorrelated, then even 3 individuals reporting that they observed the event would in fact justify our belief.

            This is a more serious challenge to the argument, because many so-called "miracles" have more than one witness. As the number of witnesses grows large, for even small priors, we gain justification.

          • http://www.aeonmagazine.com/ Ed Lake

            You're right that with more witnesses, the posterior probability rises dramatically. But the reason for the low prior for miracles is addressed in the first section of the essay. Extreme rarity is assumed because without it, miracles seem much less miraculous. The plausible supposition is that even the most ardent believer in miracles would accept, and indeed prefer, a very low base rate. And that's all you need to get the argument up and running.

          • James Savage

            Ah but this isn't so. But even a low base rate is to concede belief in miracles, and merely to deny that some particular event IS a miracle. Let me demonstrate, again by analogy to disease.

            The most ardent believer in ebola (e.g., every rational scientist on earth) believes it has a low base rate- that something like 1 in 100 million people have ever had it. This low base rate provides reason to claim, with any evidence consistent with ebola but of a lower power than that prior rate, "Don't believe that ebola is the explanation for this particular patient's symptoms on the basis of that evidence" but it does emphatically NOT provide evidence for the claim "Don't believe that ebola"

            All scientists/Bayesians/etc would correctly hold both "I believe ebola" and "I do not believe that ebola explains this case, on that basis of that evidence alone." The latter statement turns on the base rate; the former does not. Your URL's lede is "Don't believe in miracles" - again, the Bayesian argument simply cannot establish that proposition.

            To "get the argument up and running" regarding a *specific* event being a miracle, all I need is a low base rate, but that is not all I need to get the argument up and running regarding the existence of miracles. Because even if miracles are extremely rare, if I am an ardent believer in them, Shapiro has not convinced me to abandon that belief that *miracles are real.* He can simply argue "because miracles are so rare, they are likely not the explanation for some event* - that's all a base-rate argument can do. It cannot establish "there are no miracles" nor can it establish "a non-zero prior on miracles in unjustified". This is what the claim "don't believe in miracles" means. For that, you need an entirely different set of arguments (about what evidence is consistent with or against the presence of any non-naturalistic or non-materialistic phenomena in the universe, for instance). So again, Shapiro has not argued that claim.

            Again, ebola has an exceptionally low base rate: you would not use that to conclude that "ebola is not real" or "don't believe in ebola" but instead you would simply use that to conclude that "this particular report of ebola, even from a reliable witness, is likely not correct." Indeed, you get a non-zero base rate *because* you believe in ebola. Shapiro has confused the two arguments. Explaining why "ebola should be rare, if ever observed" which is what Shapiro does at the start of the argument (as you note) does not help.

          • James Savage

            More tersely, the confusion is between the base rates on the propositions "this event is a miracle" which is perhaps vanishingly small, and "there are miracles" - you and Rucker have argued that the latter has an extremely small prior, but this is the entire point in question. A small prior on the latter would, obviously, place an upper bound on the prior of the former (by logical conjunction), but appealing to the small prior of the former in evaluating evidence does no work on moving the posterior of the latter. This is Shapiro's error.

            If you wanted to actually argue "don't believe in miracles" - you COULD try a Bayesian argument, where you say that "The prior on the belief 'there are miracles' is p." If p is 1, we can't do anything, but for anything else, even epsilon less, let's proceed. "This evidence is inconsistent with the claim 'there are miracles' and it is more informative evidence than the prior" Now finally, "Thus after considering both your prior, and this evidence, the posterior on 'there are miracles' is q < t, where t is the threshold for justified belief, and thus, you are unjustified in believing 'there are miracles'"

            That is an argument that would accomplish what Shapiro purports to do. Unfortunately for him, he does not do that. Neither he, nor you, nor Rucker, provide the crucial second step of evidence: you engage in no Bayesian reasoning as a result. You simply assert that p is low, and hence that q must be less than t. You don't provide the E that allows me to update p to q. Even if p is less than t, you don't tell me if q is less than t. This is the shortcoming.

          • http://www.aeonmagazine.com/ Ed Lake

            You say: '"a non-zero prior on miracles in unjustified"... This is what the claim "don't believe in miracles" means'. But that's false, isn't it? One's prior for the reality of miracles could get quite a long way from zero without one having to believe in miracles. Say my confidence in miracles is 0.2. Do I believe in them in that case? Obviously not.

            There are some other interesting claims that are also not equivalent to "the appropriate prior for miracles is zero". For instance, there is the assertion that there are no reports of miracles that you should believe. This is consistent with a non-zero prior. If, for each individual report of a miracle, you should disbelieve it, and there is no decisive reason for supposing that there must be a miracle *somewhere* in the aggregate of all such reports obtained to date (as there is in the lottery case), then you shouldn't believe (that there have been any) miracles (... yet?).

            Finally, the word "prior" doesn't appear in the essay, and base rates are not priors: they are observed frequencies, or guesses at what the observed frequency might be; they don't measure degrees of belief (what could "the frequency of the existence of miracles" possibly be?). It is of course possible to use Bayes's theorem without committing to the whole apparatus of subjectivist Bayesian epistemology, and the article avoids subjectivist language, so I suggest that subjectivist interpretations are also to be avoided.

          • James Savage

            Sure, yes, you're correct that the sentence exceprted is false, and I didn't really argue from it anyway. I should have edited that out, because I backed off from it later - which is evident when I outlined what an appropriate Bayesian argument against miracles would look like. It doesn't rely on a non-zero prior, and it still concludes in "thus, belief is miracles in unjustified." So that sentence is indeed false, but it doesn't matter for my point.

            The fundamental confusion (which too does not involve "prior", but does involve base rates) is outlined in my ebola example. Unavoidably, there will be a circularity. You note that the base rate is an "observed frequency" or guess at such a frequency, and it's not subjectivist. In some limited sense that's true, but life is not so convenient. How can we know that we've observed a genuine case of ebola, from which to add to our base rate? On your logic, no new cases of ebola can be observed, because in each such instance, we should disbelieve it. That's the problem. In order to know "for each report of a miracle, we should disbelieve it" relies on a base rate, but you cannot provide grounds for that base rate without rejecting new "observed instances" on the very basis that the base rate is low.

            The very determination of what counts as an "observed miracle" to add to the count to determine the observed frequency from which we form a base rate *does* ultimately collapse to subjectivism. Your attempt at avoiding a subjectivist interpretation is noble, but will still punt the question down another layer. It doesn't help. If base rates are observed frequencies, any non-zero base rate corresponds to at least one observed miracle. Even if it's a just a guess, and the claim is that there haven't been any miracles yet, that's not proper disbelief, if I think the "true" base rate is non-zero. The question of whether belief in miracles is justified more or less has to follow the form of the argument I outlined above. The reason is simple: any uncontrovertibly observed instance of a miracle would be sufficient to settle the question: belief is justified and non-belief is unjustified. Lack of observed instances (at least non-controversial ones) means we are forced to be subjective. A "guess at the observed frequency" IS a prior, it's not a base rate. The moment you go there, you've abandoned your attempt to prevent the collapse to subjectivism.

            The argument also doesn't help because it relies on "there is no decisive reason to believe that there must be a miracle *somewhere*" to contrast the lottery case. There are two problems - first, were there a *decisive* reason ipso facto we'd be done, so surely even something less than a decisive reason will suffice. I demonstrated this in showing that even when the p on existence of miracles is quite low, one can construct a Bayesian argument showing that such belief is unjustified. This is not what is done here, and the introduction of your premise here is overkill and itself circular because we are searching precisely for what "decisive reasons" might be. Second, this is where the joint probability question is important. Your fallacy is treating each report as 0. You say, effectively "since report 1 is likely to be false, and report 2 is likely to be false, and report 3 is likely to be false, all the reports are likely to false" but you ignored my point that you need to consider the *joint* probability. While there is no good reason to believe report 1 or report 2 or report 3, given that we observe ALL of report 1 and 2 and 3, we may now have reason to believe *all* of them, though considered alone, we believe *none* of them. So you've ignored the joint probability issue, which more or less tells us, a single report and the base rate isn't enough context to evaluate. We also need the context of the base rate of false reports and the number of such reports that we are indeed observing.

          • James Savage

            To be short, again: if the observed frequency is non-zero, you are unjustified in not believing in miracles. If the observed frequency is zero, there's more to be argued. That observed frequency, either way, cannot provide the grounds for rejecting future instances, on the basis that the past observed frequency is so low! There's a lot more to say here, but switching to "observed frequency" doesn't save the argument.

            The reason it does work (mostly, at least) for non-subjectivist Bayesian inference is because, for instance, in the classic example of the taxi color - the taxi is one that was *already* observed and comes from a known reference class. The "true" observed frequency is known, and is used to evaluate an observation from that group. Here you are reason about the so-far observed frequency to filter future observations. That is the use of a base rate AS a prior, even though the two things are not *intrinsically* the same. Anyway, you can't escape the circularity of this form of argument.

            And finally, the lottery fallacy stands, because the fallacy lies in the fact that the *reasoning* "because each claim of X is unlikely to be true, thre are no true claims of X" is not reliable. In philosophical logic, this is what argument invalidity means. That the premises do not provide warrant for the conclusion. The lottery example *demonstrates* WHY the premises do not provide warrant for the conclusion. They render all instances of the argument fallacious because they are invalid. This does not mean that all conclusions of such arguments are false. It does mean that, without more, the conclusion does not follow from the premises. You are adding the premise that "there is no definitive reason to believe that there must be a miracle somewhere" - but this needs justification. If I believe in the "necessity of God" (in the metaphysical sense), then you simply have produced the lottery paradox.

            Reference class definition is also everything. We've avoided this argument, but it more or less is literally everything.

          • http://www.aeonmagazine.com/ Ed Lake

            Well, to the extent that we've argued to the no-man's land between frequentist and subjectivist probability, I think we should call it a night. Wine has been taken and I suspect my replies will deteriorate from it from here in any case. But I have enjoyed this discussion, and you have given me several points to think about. Who are you, if you don't mind my asking?

          • James Savage

            Hi Ed - agreed. I realized we were going there quickly. I'm actually sympathetic to Shapiro's view (despite what my writing may suggest) and a huge fan of the magazine: it has become a regular part of my reading diet.

            As for me, I'm a doctoral student pursuing joint degrees in law and economics, not concentrating in philosophy unfortunately; but my interest in this area [even narrowly, justified belief] is especially important to the intersections of behavioral and normative dimensions of those two fields. I'll probably comment around here more regularly, and at some point, may give you a name, though I prefer it private on my postings for now :-)

            I had too much writers block on some other essays and as such took to writing lengthy responses here! Thanks for engaging with me and apologies for extending this argument at such length.

          • http://www.aeonmagazine.com/ Ed Lake

            No apologies necessary; it was a stimulating conversation. Good luck with the PhD. I look forward to seeing you around here more often.

          • Larry Shapiro

            A stimulating conversation to follow too! I learned a lot from your exchanges. Thanks for putting so much thought into my essay.

          • James Savage

            Just a short follow-on: I had not realized until just now that you're primarily a philosopher of mind and psychology - a field that was my first philosophical love. I studied the subject nearly some 5 years ago wth Frank Jackson [who was absolutely wonderful], and will surely give a shot to some of your recent writing on the topic!

      • James Savage

        As a further follow-on, the testimony of alleged witnesses need not be our only evidence for believing claims of the miraculous, at least not unless we equivocate on what testimony means.

        To relate to the disease example (as this is easiest), presumably you think we observe physical symptoms (such as death, blindness, rashes, etc. - because you can't mean biological titers, since those are the test) as our "other evidence" - but then, who observes this evidence? We do! Precisely, it is the "testimony of witnesses" [here, the diseased themselves and others around the diseased who witness their death, and so on] that they are diseased that is our other evidence. Is it not?

        Likewise, miracles may have other markers. I find this to be completely junk science, but you can google and find "chariot wheels found in red sea!" as physical evidence that the claimed event occurred. (Still, of course, evidence only has value in so far as "witnesses" [even if they are modern day ones like us] observe it, but either way...)

    • Larry Shapiro

      HI James, thanks for the helpful comments. As Ed Lake also noted, the lottery fallacy analogy breaks down for a crucial reason. The fallacy in that case involves inferring from the low probability that some particular x will win to a low probability that any x will win. Given that some x must win, the inference is not valid. But it's here that the difference arises. It's not true that a miracle must have occurred. And, while I agree that the probability that some miracle occurred is higher than the probability that miracle x occurred, this needn't be a high probability. Certainly not one high enough to justify belief that miracles have occurred.

      • James Savage

        Prof. Shapiro, surely you can't stand by this reply. As I explained, I'm aware of the breakdown in the analogy to the lottery case. I'm not claiming that one is justified in believe that miracles have occurred. I'm claiming that your argument cannot make the case against it, because your argument takes uses poor reasoning. Your argument is deductively invalid, and the lottery example, and the less-fanciful ebola example, demonstrate convincingly why.

        To be more concrete, there is no connection, logically, between the premises "the low probability that some particular x will win" to the conclusion "a low probability that any x will win." It does not matter that you and I might agree that there is, in this particular case, "a low probability that any x will win" (that there is a low probability that some miracle has occurred). That happy coincidence (that the conclusion of your argument comes out true anyway) does not save your argument from invalidity; this is my point. The premises you devote your time to establishing - that there is a low probabiltiy that any particular x (say, rising from the dead) was a miracle, even with highly reliable witnesses - are time wasted because they do not provide an argument for why one ought not believe in miracles. I outlined, above, what such an argument could look like, but this isn't it. I'm truly sorry.

        As I point out also, quite easily in my ebola example, if we are using a base rate - any non-zero base rate, however small, even if we think it's 1 in 3 billion - since a base rate, unlike a prior, correspond to an "observed frequency" - is to admit that you believe in miracles. You think that miracles are rare events (that the "true" rate of resurrection is only 1 in 3 billion) but because the true rate is non-zero, that is precisely belief. Believing that miracles are rare does not constitute non-belief in them; all it does is provide reason, by the Bayesian argument, to believe that *some particular event* is not likely best explained by a miracle. But it does not that there is no belief in miracles. See the ebola argument above - it is exactly parallel in structure- it illustrates an apparently fundamental confusion of yours. You yourself liken resurrection to a disease, and fail to recognize that a low base rate for a disease is *not* non-existence of the disease, simply rarity. As I said, all rational scientific minds would correctly hold both "I believe ebola" and "I do not believe that ebola explains this case, on that basis of this evidence alone." Your argument outlines a case for the latter, not the former - this is the problem.

        Finally, there's the issue of reference classes that's been glossed over: arguably, most of the evangelical/ardent Christian-types to whom this essay is directed reject the argument out of hand because it's a different reference class; either miracles exist from necessity, for one, or Jesus isn't subject to this low base rate, for two.

        And also, to be fair, the multiplicity of historical observers, should we grant the existence of such multiple accounts, poses a serious problem (mechanically/mathematically) for your attempt to apply Bayes. As noted, three indepedent witnesses of your given reliability (1 in 100k), jointly reporting an event, even with a base rate of 1 in 10 billion, would tip the scales in favor of that event.

        There's much much more to my responses above than simply "lottery fallacy" - I genuinely think it's a confusion as to what needs to be established and what is being established. I almost prefer not to use the example of miracles, but ebola instead, because it showcases all of the logical features necessary to see why your article falls short. Thank you for posting though; much appreciated to have the author join the conversation.

        • Rodger Dodger

          Of course he can stand by this reply. You read the article. You know his reasoning isn't the best.

        • Matt

          I'm going to address this in as neutral a fashion as possible, because I avoid religious arguments for obvious reasons. For these reasons I will be referring to the original article being a mathematical proof as a counter to religious belief (even if it wasn't intended as such) as 'Shapiro's Folly'. In your first post you wrote:

          'To make this more concrete, again, think about the disease example. I am not justified in believing, on the basis of a given positive test result, that an individual has the disease. But it does not follow, at all, that I am not justified in believing that the disease exists! This is what Shapiro argues. This is a horribly serious error in reasoning. Just because a particular positive test does not justify belief [due to its overwhelming likelihood of falsity], so too does such likelihood not justify the non-belief in *at least one* correct [non-false] positive test existing. My belief in disease is not equivalent to my belief that a given person has the disease.'

          Disease as used as an analogue for miracles, while mathematically sound, doesn't work because disease is a fact of life we see every day. If we were to reduce the likelihood of disease to that of miracles, would you believe in them? If you have lived healthy your entire life, never seen anyone fall ill, never heard of anyone becoming ill, would you believe that someone 2000 years ago got sick, wasn't able to get out of bed for three days, and then became better? We could also re-write this argument to say all disease were fatal no matter what was done, but one person who lived long before you were born survived.

          Shapiro's Folly states that miracles might exist but there is no justifiable reason to believe in them. I have a feeling that if he had titled his article, 'Don't believe in the Chupacabra' we would be having a very different discussion.

  • http://www.obliqueideas.com Michael Hopkins

    It started out better than it ended. I have tried explaining to people who believe faith heals, etc., that God intervenes in our health very consistently. Christianity teaches that God's intervention in the world to sustain it is constant and something we can rely on. As you point out, by definition, we can't rely on something that happens often enough to be a 'thing' yet not often enough that we don't notice it. Good job pointing that out.

    Everything else was quite illogical. Your numbers are not impressive at all, because Jesus Christ is by definition the only person like himself. We are asked by some *exceptionally* reliable observers and recorders, for the time, to believe that one person is different than all the other people. Naturally, the denominator is going to be larger as the rest of us are different. What are the odds such a person would exist at all? That is what you are asking.

    The answer is that those odds are much higher than one divided by the number of people who have ever existed. That is because a lot of writing and documentation about Jesus exists. This alone makes him different than nearly every other human. As for Moses and other unusual people, if Jesus is who he says he is, then they become highly likely to exist as recorded. The existence of Moses is consistent with existence of Jesus. So, the assumptions behind the numbers are off by several orders of magnitude and make your conclusion similarly incorrect. Does that make you want to reconsider your conclusion that personal belief regardless of the numbers is okay?

    • Plato’s Beard

      I don't think you can claim that a person who is supposed to have actually existed has some property by definition.

      Part of the issue is whether Jesus was one of a kind. You can't help yourself to this alleged property when criticizing an argument for the claim that he did not have that property.

      And while Jesus is perhaps one of a kind in the sense that he's been written abut more than any other person who has every existed, this isn't obviously relevant to the issue of whether he actually rose from the dead. His being widely written about can be explained by his being (incorrectly) thought to have risen from the dead.

      • http://www.obliqueideas.com Michael Hopkins

        Yes, but the claim that he did not have that property is based on his being a normal human and being asked to fit on the normal distribution curve, when he actually is supposed to be something else which should have its own curve. It is absurd logic and the absurdity can be exposed by carrying it further. Why not calculate the odds of a piece of wood becoming a cross? Why not calculate the odds of a liter of water spontaneously becoming a liter of wine? Why not multiply all these by each other to arrive at a completely incalculable number? The logic of this article is that such a figure would mean something, but it doesn't.

        Put another way, you must be willing to ask yourself questions like: what are the odds that a vastly superior being visiting earth could die and come back to life again? What are the odds such a being exists? What are the odds such a being, if it existed, would visit earth?

        Quickly you will realize it makes more sense to examine the matter directly and draw conclusions from what can be observed and deduced from the observations of others.

        Also, explaining documentation of an event away as being a result of that event only being thought to occur makes less sense than that event occurring, all else equal. All else is not equal, but the odds are nothing like the silly numbers in this article.

  • Doug Doakes

    Of course, Moses did not part the Red Sea. Of course, Jesus didn't arise from the dead. Of course, the moon is not made of cheese.

  • Barbara Piper

    Prof. Shapiro: how does your argument differ from Larry Blackman's gloss on Hume on miracles?

    • Larry Shapiro

      Hi Barbara, I haven't seen LB's gloss but will be sure to check it out -- thanks. As I mentioned in the article, I've merely provided a "souped-up" Hume, so I wouldn't be surprised if LB and I are of a single mind here.

      • Barbara Piper

        Larry Lee Blackman "The Logical Impossibility of Miracles in Hume" International Journal for Philosophy of Religion. 9(3):179-187. 1978

        You may have tracked this down already, but if not I recommend it based on my reading of it years ago...

  • bubenhaft

    Sorry, but I stopped reading when I encountered a grade-school math error. A disease that "affects 0.001 per cent of the population" will strike one in 100,000, not one in 1,000. Decimal point--small but important!

    • bubenhaft’s mistake

      That is an irrational response. Just b/c an error occurs in a paper does not mean that the paper's thesis is false or unsupported. You need to ask whether the error undermines the thesis or argument for the thesis.

      in this case, the correction only strengthens his argument!

  • deegeejay

    Don't worry - you don't have to believe in them for them to happen.

  • MyKitchenandI

    If a test is right 99 percent of the time, then I'm not going to assume that I was that one in 1000 times it was wrong. I don't think the rate of occurrence in the General Population has any bearing on whether the test was right in any given individual's case. Saying the test is right 999 times out of 1000 tests means that only one of the tests will be wrong, and that rate will hold true regardless of what the rate is in the general population.

  • http://www.facebook.com/people/Boon-Tee-Tan/1068880297 Boon Tee Tan

    The word "miracle" could carry different meaning for different people. Its definition has been stretched to mean something strange for an observer at the particular instant or a very unusual event that has never occurred or been observed before.

    Try not to believe in "miracles" (especially those that cannot be replicated) unless there are strong and substantive evidences.

    (btt1943)

  • HowardBrazee

    By definition something that is supernatural, is not natural. If magic was part of our natural world, it would be science. If Zeus really hurled thunderbolts from the top of Mount Olympus, it would be part of our natural world that we could observe, measure, and analyze. As long as he was part of our natural world. But there's no amount of statistics to show whether his supernatural self is more likely than Odin's.

  • John

    You math is off, 0.001% is 1 in 100,000, not 1 in 1000 as you say.

    • John

      Your*

    • Reply

      Relevance?

  • Rodger Dodger

    It is kind of weird and sad to watch an author wade into the online comment section to argue. You had 2800 words to make a point. If you didn't do a good enough job with 2800 words to make your points maybe you should just step back and let others discuss it for awhile.

    • Gyrus

      I don't really like this piece, but I always appreciate the author joining the discussion. Otherwise, they're just someone preaching from on high then buggering off. Discussion's part of the writing process. Outside poetry and fiction, there's always something more to absorb outside the writing itself and its delivery.

      • Rodger Dodger

        It reminds me of this gallery opening I went to where the artist went around "correcting" people's take on his work. It just looks awkward and petty when the author jumps in to further argue the points he already tried to make.

        • Gyrus

          When I said "outside poetry and fiction", I was taking in the "art" side of writing - so obviously the artist you saw "correcting" people's interpretation falls outside my appreciation of people engaging with their audience. He sounds like a twat, agreed. Non-fiction, especially philosophy is completely different. I don't have time to read all the discussion here, and I totally accept that Shapiro may have engaged in a less than interesting way. But you can't go from there to a categorical condemnation of philosophers engaging with discussion of their work.

  • mtv

    "Perhaps it affects 0.001 per cent of the population. This means that, for every 1,000 people in the population, one person will have the disease." No, it doesn't mean that. One percent is one in a hundred. Therefore 0.001 percent is one in 100,000.

    • MTV Sucks

      Ok. And? Do you want to do anything with this point?

  • Gary Kerridge

    This article is correct in one sense.... and incorrect in
    another. As a PhD in philosophy of social science the author is making claims
    about beliefs based on a positivist epistemology (we can know reality through
    the reliability of repeated empirical observation) and a naive realist ontology
    (an independent objective rule-like reality). Professor Shapiro is obviously
    correct when he argues that statistical probability as a basis for inferring
    the truth is not possible. His example of the fact that medical tests are
    unreliable statistically and thus cannot be a basis for inferring an objectively
    correct interpretation of the data generated by the test is entirely correct.
    However, what this implies is that all reasoning about the validity of
    empirical data (qualified by statistical probability of the LIKELIHOOD of its occurrence)
    is also incorrect. This view is shared by many historians and philosophers of
    social science.

    However, the conclusion of the article is fundamentally
    flawed since it argues that if we cannot reliably ascertain whether or not an
    event historically occurred in the empirical domain, then we must reject the
    notion that miracles can occur. This is because the author has committed the epistemic
    fallacy common to naive realism (Bhaskar). That is he concludes what must be
    the case from what has been observed (a potentially unreliable account of Jesus’
    resurrection). As such if the account was unreliable and there are no empirical
    grounds (based on probability) that Jesus’ rose from the dead then Jesus could
    not have risen from the dead and therefore there is no rational objective and
    independent basis for knowing objectively that miracles can occur. Importantly
    here, the difference is between objectively knowing and interpretively
    understanding.

    All knowledge is mediated by hermeneutics. That is we
    interpret data to make sense of it. By itself, data is meaningless since to
    make sense of it we must postulate why the pattern of data (the event) occurred
    – are we really naive enough to think it was only because of A? To achieve this
    involves retroductive reasoning (working back from an event and asking what
    must be possible for this to have occurred). For example, it is very much like
    the idea of the Higgs particle in Physics. To explain everything in a grand
    theory requires the presence of a hypothetical particle. This then leads
    physicists to search for the elusive particle. It is a belief that the particle
    exists since it must be so to explain what has been observed. In terms of this
    article, when we are faced with a phenomenon that cannot be explained by existing
    theory, we must retroduct back and ask what must exist for the event (resurrection)
    to be explained. This would lead to a number of possible explanations. 1) Jesus
    was human and didn’t really die but appeared dead and thus never really rose from
    the dead, 2) that Jesus did actually die but for a number of socio-political
    reasons it was claimed he did not, 3) Jesus was not actually human and thus did
    not die in the way we think of death and thus rose again, 4) Someone suffered a
    hallucination, but Jesus definitely died. What we see from these possible
    explanations is that there are different assumptions about the ontological
    nature of Jesus: A) he was human and thus subject to physical forces or B) he
    was not human and therefore not subject to physical forces as a human would be.
    Neither of these can be tested. Ontology is a question of assumption and belief;
    it is a philosophical problem, not a scientific one.

    If one starts from ontological foundation of A (Jesus = human)
    then it reasonable to assume that there must be a physical, human explanation
    for the event and that it did not occur. However, if someone starts from the
    ontological assumption of B (Jesus = not human), then the event may indeed be
    plausible. Thus, it is impossible to claim that miraculous events do not occur
    from the likelihood of empirical observation. The difference between a miracle
    and a freak occurrence/lie/error is one that can only be determined by ontology
    and not epistemology. Since ontology is a belief rather than truth, both
    explanations for the event are worthy and possible within their respective paradigmatic
    assumptions about the nature of reality. As a philosopher, I would argue that
    miracles occur every day... how is this possible?

    When not a lab rat sat in an experimental laboratory the
    world we live in is an open system (Bhaskar, Sayer 1992). That is we cannot have
    controls over which outcomes will occur in a real world setting. For example A &
    B may be causally connected in a laboratory (closed system), but in a real
    world setting any number of other factors (or mechanisms) could be enhancing/inhbiting
    the typical relationship between A & B that ought to occur. This leads to C
    occurring instead of B or nothing happening at all. When things like this
    happen we seek an alternative explanation. If one cannot be found we must
    either question the original belief that A & B are always causally related,
    or attribute the event to an unexplained anomaly, or quite possibly a miracle.
    For example when the knife fell on my foot in the kitchen, and I didn’t get
    cut, I could say that was a miracle or I could spend a long time (that I don’t
    have) trying to develop some theory (explanation) for why it didn’t occur. To
    be sure of it I would have to test it to see whether or not it was true and I wouldn’t
    want to keep dropping a knife on my foot! Without testing it, I would just be
    guessing and believing something that was potentially not real or correct. This
    of course is all dependent on whether or not I assume a realist physical
    ontology or whether or not I endorse a more structured and complex ontology
    that includes a metaphysical dimension. If this was the case then I may go as
    far to even attribute the event to a metaphysical causal determinant such as a
    guardian angel, or God, or just simply lady luck herself.

    Daily occurrences happen when events do not turn out as they
    ought to, particularly if we follow a law system of cause and effect. Thus,
    every time this occurs, something miraculous happens – something lacking a
    predictable explanation. On closer inspection it may not have been a miracle at
    all, but for our time constrained daily lives and the purposes of cognitive
    economy, a miracle will certainly suffice. They need not be supernatural or
    depend upon a metaphysical cosmology; miracles are simply quick and dirty theories
    about why C occurred instead of B that ‘should’ have happened. However, I for
    one believe that a little of the miraculous in our lives helps to enrich our experience
    of life, causes us to pause and marvel at the fact that we cannot and are
    unable to predict our lives and the world around us with absolute certainty. Although
    insurance premiums would go down and up accordingly if we could, a little magic
    in a rather dull and positivist society prevents a fateful determinism, in
    which those in power (Scientists) ultimately determine the nature and fabric of
    reality. Miracles are good for us – they open a narrow vision wider. I hope that
    Professor Shapiro personally experiences the joy of having something wonderful
    happen that can’t be explained – quite simply... just enjoy the odd miracle!

    P.S. If you want to look into this further I encourage you
    to read further about critical realism, Roy Bhaskar, ‘The Possibility of Naturalism’,
    but Sayer, 1992 is more accessible.

    • confettifoot

      Long comment. Worth reading.

  • Walter Adams

    The error here is the belief that what is, is dependant on your ability to perceive and catalogue it.
    What is possible or not isn't subject to your limitations of observation or definition.
    There is a God, or there isn't.
    If there is, surely you don't think He is bound by your ability to quantify Him statisticaly?

  • Kg

    Almost all widely accepted "miracles" are from a very long time ago. I think that is an important part of the discussion. No offense to Mormons but most of us believe Joseph Smith's miraculous story is utter fiction and it has many witnesses but is recent.
    If somebody you trust told you their "guru" was arrested last week, tried, convicted and put to death, we could believe that. If they then told you they rose from the dead and then ascended into the sky, we would call them a doctor.
    If fact, all widely accepted "miracle" stories would be immediately dismissed if they were told today.
    Why is that? It is important to ask ourselves why we will believe a "miracle" from 2000 years ago but would immediately dismiss the same story if told to us like it happened last week.
    It's cultural, environmental and socially acceptable to believe ancient miracles. But we then use critical thinking to dissect any recent claims, as we should.

  • Truth

    This idiot can't even get his math straight .oo1 per cent is one in 100,000 not one in a thousand

    • Disheartened

      And the correction only strengthens his argument. I suggest that the real idiot is the one who seems to dismiss an argument on the basis of an error that is irrelevant to the argument.

      I also don't know why you feel compelled to call a PhD an "idiot". It's quite easy to make a tiny error in a long essay.

      • Jackbennet

        I concur.

  • Ed G.

    Actually, stating that people are unjustified in believing in miracles must be qualified better than this. For instance, the writer concedes that witnesses believe in events that didn't occur the way they remember them quite often. Either their senses or their memories of the event are flawed. In that case are people unjustified in belieiving their own memories? But we believe in so called inaccurate stories of our own individual lives constantly. Clearly, what we know can never really be confirmed. Therefore these stories, religious or otherwise that exist within a culture are very similar to our own misrepresnted memories. However, what should be asked in justification of believing in these stories is not the probability that they events occurred the way they are remembered, but rather whether or not the belief in these events are beneficial to human existence.

  • Jeffrey Guterman PhD

    "We have met the enemy and he is us." ~ Walt Kelly

    For some people, especially scientists and philosophers, the discussion in this article speaks to the domains of epistemology and ontology; For others, especially religious persons, theology. Thus far, there does not seem to be any empirical evidence to support the view that any supernatural miracles have ever occurred during human history. This does not mean, however, that supernatural miracles have never occurred or never will occur.

    The same premise applies to the existence of a supernatural God. There does not seem to be any empirical evidence to support the view that there ever has been, is, or ever will be a supernatural God. But this does not mean that such a God has never existed, does not exist, or may not appear in the future.

    The same view could be applied to intelligent extraterrestrial life or "aliens." Despite many claims to the contrary, there has never been empirical proof of the existence of aliens. But again, aliens may have existed in the past, they may exist now, and they may exist in the future. We simply don't know. And it's okay to not know. We don't have to know the answers to all things, especially about the great mysteries of the Universe. Philip Morrison put it well when he said, "Perhaps we are alone in the universe, or perhaps that's not true. Both alternatives are mind-boggling." So, maybe there is no intelligent life elsewhere. Maybe there is. And maybe there are hundreds of thousands of intelligent civilizations in the Universe, none of which have visited us because they are either too far away or too smart to try.

    Until we are able to verify such phenomena, we can only wonder if there is or is not a God and other supernatural phenomena such as miracles. Now what?

    This raises questions that are larger than the author may have intended to raise. Despite our advanced technological stage, we remain relatively primitive in an emotional sense. It's ironic that of all the forces that threaten to destruct humanity the greatest nemesis may be our our own nature. Yet we still know so little about what it means to be human.

    Human progress has been facilitated by unique forms of cooperation that, in turn, allows the species to enhance its quality of life. Although there is debate regarding precisely why people are altruistic (the most plausible being that it works), it is clear that complex, diverse, and interrelated forms of social organizations have developed as a resulted of human cooperation. This is not to say that civilization is conflict-free. Civil disorder, illiteracy, poverty, war, and violence, although steadily declining, continue to impede our efforts to achieve global collaboration.

    The extinction of the human species is inevitable. This inexorable conclusion will likely come much sooner than later unless we learn to get along.

    - Jeffrey Guterman, Ph.D.
    http://JeffreyGuterman
    Follow on Twitter: http://twitter.com/JeffreyGuterman

  • jayson Sandborn

    ONE Modern day 2013 Miracle. But If you are skeptical Disbelieving that almost negates you from even seeing one.. believing in one.. actually it is the " sin " of Disbelief that will also keep you out of heaven. maybe you "aught" to start believing in Miracles..... God heals a woman of stage 4 cancer.. http://www.youtube.com/watch?v=X8KApDn4pm0

  • Guest

    Not sure how likely the alternatives are? You might be surprised. Watch Doug Powell run through the options: http://dougpowell.com/wp/wp-content/uploads/video-gallery/Video/11resurrection.mp4

  • confettifoot

    This is silly. By definition miracles are improbable, evidentially implausible and etc.. That's rather the point, whether or not they actually occur.

    • Question

      He's talking about whether belief in miracles is justified. Are you saying that the whole point of belief in miracles is to have an unjustified belief? If so, that's an odd claim.

  • Joe

    I don't think religious people think of miracles in this way. Their ontology includes a supernatural being that interacts with the world in lots of ways. Sometimes these ways are small day-to-day events, such as prayer, emotional support, preparing minds to read scripture, etc. Then there are really big interventions: Red Sea parting, raising from the dead, etc. "Miracle" is a word reserved for the "BIG" end of the scale, and I think it is particularly linked with the REASON or PURPOSE of the "big" event - usually to impact an audience in a way that expresses God's glory or telos. For such religious people, it could still be true that their base-rate would be pretty small (since God only does "BIG" interventions very occasionally) while the justification to believe in them (which is the main point - Hume's point - of the article) stems from a larger context of cases that includes many smaller events too.

    Maybe the author would respond that Hume's argument still shows that in these "BIG" interventions (even if true) their probability precludes religious people identifying them as miracles. But absent any alternative explanation for the Red Sea's parting, why can't they just say its the BEST EXPLANATION they have?

  • Ovadiah ben Avraham

    How would it change *your* life, if it were proven with archaeological evidence that the sea actually parted (the Torah narrative is that G-d parted the sea, not Moses), that Israel did pass through, and that the Egyptian army was destroyed by the relapse of the sea to normal conditions. I mean apodictic evidence in the Husserlian sense, such that a scientist issued a set of predictive predicative statements (based on various philological elements of ancient texts, physical culture artifacts, and paleogeographical artifacts) saying dig here, and the chariots, swords, scabbards, etc. of the Ancient Egyptian army bearing the cartouche of the Pharaoh of the Exodus were found at that location. How would it affect your thinking, in general?

  • Guest

    Well, I'll leave i here...

  • Manishtana

    How exactly is this an advance on Hume's argument? And how does it avoid the standard objections?

  • Rick Jackson

    The miracles (Christian and non-Christian) that effect our physical world in a gross way, which have described over the ages are caused by the physical interaction of spiritual forces - this has been given a name: Physical Mediumship.

    "If you wish to upset the law that all crows are black, it is enough if
    you prove that one crow is white. My white crow is Mrs. Piper.", William James, father of modern psychology

    William James is quoted as stating that phrase because he became convinced that mediumship was real. http://en.wikipedia.org/wiki/Leonora_Piper

    See The Afterlife Investigations: The Scole Experiment for a recent example & the scientist who study Physical Mediumship.

  • Granite Sentry

    "So, if you wish to continue to believe in miracles, you must do so knowing that the evidence is not on your side."

    Isn't that essentially the definition of faith anyway? We knew that already, Dr. Shapiro.

  • lolya

    believe IN MIRACLES!

  • lolya

    if u don't then u don't believe in god! D-U-H-!

  • PC

    Actually, the gospels don't record any witnesses to the resurrection. You can check: What they record is various people visiting the tomb and finding it empty. Somewhat earlier than the gospels are the letters of Paul, in which he records various post-death appearances of Jesus to his followers - but nothing about the tomb. These post-death appearances, by the way, are not of a corporeal Jesus - Paul is quite defininite that his own vision of the risen Jesus was exactly what the other witnesses had seen. For Paul, this was crucially important, as it established him as the equal of those followers. The point was that in that world visions had more authority than mere seeing - gods came in visions and dreams, but what was seen was merely of this this physical world.

    The point is, an argument for or against the reality of this particular miracle which is based on statistics misses the point - its necessary to understand the cultural world behind the reports.

  • John 4

    As John Earman has argued (in *Hume's Abject Failure*), this line of argument is seriously flawed for an important reason that I didn't noticed discussed in the comments: according to the official story, there are many different *independent* testimonies of Christ's resurrection. The dramatically changes the equation. If you take one of these unreliable medical tests a three times, and it comes up positive each time, you should be (it would be irrational not to be) concerned about your health.

    I guess there might be some good reply to Earman's objection, but I would have thought that reply would have made an appearance in the article.

  • Eric Olander

    The argument is flawed by imposing now on the past. The number of believers by written accounts was less the a dozen not a billion. Poorly designed argument to justify to end the essay with pure speculation about miracles being hallucination and such.. Is two or three gathered in name and the repeating of the story over and over to create 1 billion believers of the resurrection actually qualify as frequency?

  • Karen

    Here's an interesting reply to Shapiro's argument:

    http://1000wordphilosophy.wordpress.com/2014/03/17/can-we-believe-in-miracles/

    • Robert Rucker

      Seems to beg the question at the end.

      • Karen

        Which part begs the question? When the religious believer judges the prior probability of divine action in the world not to be vanishingly small? But isn't that just what a religious believer would do? And that a religious believer would do that isn't meant to imply that everyone else must as well. So where's the question begging?

        • Robert Rucker

          "'It needn’t follow that the prior probability of God’s raising Jesus from the dead is small. For we know of things like that, how such a thing easily might happen. It’s God, after all, who can do as he likes. . . .'"

          Well, if God can do as he likes, doesn't that pretty much mean that he can cause miracles? And isn't that just what's at issue here? That's question begging.

          • Karen

            Shapiro's claim was: If something happens rarely, its prior probability is very small.

            Don't you agree that's false? The lipstick-face case in the link I provided is a nice counterexample.

            Cases like that show:

            (1) A person can rationally take the prior probability of an event E to be high, even if an event exactly like E has never happened, so long as the person takes herself to know of events like E, to know how something like E might happen.

            And:

            (2) Religious believers take themselves to know that God exists, that he has purposes he occasionally acts on, etc.

            Nobody's claiming that religious believers really DO know that, only that they *take* themselves to know it! (So no questions are begged here.)

            But then wouldn't this follow?

            (3) It can be rational, "from the inside" at least, for a religious believer to judge the prior probability of a miracle to be high.

            But if that's right, then:

            (4) For religious believers like that, testimony of a miracle could raise the already substantial prior probability to the point where it becomes rational to believe in the miracle.

            But that's contrary to what Shapiro says. And without any question begging. Or, if you still believe this argument is question begging, please point to the premise that begs the question.

          • Robert Rucker

            Well, of course I meant the religious believer is begging the question if he presents this argument himself.

            By twisting it into third person, you have, strictly speaking, removed the question-begging, but at the cost of introducing a false premise (#1). Here's why premise #1 is false:

            You identify a mental state which you describe as "X takes herself to know Y." I take this to mean both (1) X believes Y, and (2) X believes that her belief in Y was arrived at rationally. Finally, you claim that if X takes herself to know Y, it is rational to believe that the prior probability of Y-like events is relatively high.

            But this isn't necessarily so. It's only true if the belief I've labeled (2) above is actually true. But claiming that (2) is true in this case is tantamount to claiming that belief in miracles is rational. So maybe there's still a little question-begging after all.

            The most you're going to be able to get out of this argument is: If you already believe in miracles, you have a reason to believe that your belief in miracles is rational. But that's nothing special (it's similar to the observation behind Moore's paradox), nor will it convince non-miracle-believers to believe.

          • Karen

            >>By twisting it into third person, you have, strictly speaking, removed the question-begging>>

            I'm not sure why that counts as "twisting, but I guess we agree that, when given in the third-person, this argument doesn't beg the question. And the conclusion reached by this argument contradicts Shapiro's main thesis. So I guess we can agree that Shapiro's main thesis is wrong?

            >>Well, of course I meant the religious believer is begging the question if he presents this argument himself.>>

            Even if we consider the argument given in the first-person, I can't see how any questions are begged. Can you explain why you think the first-person form of the argument begs the question? The religious believer needs only to claim that she *takes* herself to know that God exists, that he might raise people from the dead, etc. How is that question-begging? That's undeniably true, and accepted by all parties to the debate.

            >>Finally, you claim that if X takes herself to know Y, it is rational to believe that the prior probability of Y-like events is relatively high.>>

            I didn't claim that, actually. Check the tape: I claimed that if a person takes herself to know of events like E, to know how something like E might happen, then she can rationally take the prior probability of an event E to be high, even if an event exactly like E has never happened. ;-)

            >>But this isn't necessarily so. It's only true if the belief I've labeled (2) above is actually true.>>

            You didn't label any belief as "2." In fact, you mentioned two beliefs in the proposition you labeled "2." Anyway, I can't see how the claim I actually made requires that the belief in question (that there have been events like E, that events like E could easily happen) be true. Would you care to elaborate?

            >>The most you're going to be able to get out of this argument is...>>

            For all you've said, what I get out of this argument is that it can easily be rational to believe in a miracle. And that's contrary to Shapiro's (and Hume's!) main thesis here. Soooooo, that seems pretty important.

            >>nor will it convince non-miracle-believers to believe.>>

            I wasn't trying to convince non-miracle-believers to believe. I was just rebutting Shapiro's/Hume's claim that nobody can ever rationally believe in a miracle. Seems like an important result! :-)

          • Robert Rucker

            ". . . I guess we agree that, when given in the third-person, this argument doesn't beg the question."

            Like I said, that's true, strictly speaking; the argument is circular in a way that I wouldn't quite call begging the question.

            "And the conclusion reached by this argument contradicts Shapiro's main thesis."

            Only partially, and in a way that doesn't really matter (because of the circularity).

            "So I guess we can agree that Shapiro's main thesis is wrong?"

            Well, no. To prove your conclusion, your premises actually have to be true. Since it seems you're misunderstanding the problem with your premise #1, I'll give an example:

            Let's say that I believe that dogs can fly. On your view, it is rational for me to believe that the prior probability of a dog surviving a fall from a twentieth-floor balcony is high, because I take myself to know that they can fly. But that's wrong--it's NOT rational for me to assign probability this way, because the belief on which it's based (i.e., that dogs can fly) is itself irrational. The well is poisoned, so to speak, and any conclusion I draw from my irrational belief will be tainted.

            Your argument can go no further unless you provide an argument for your premise #1. If you think you can, go ahead.

          • Karen

            >>Let's say that I believe that dogs can fly. On your view, it is rational for me to believe that the prior probability of a dog surviving a fall from a twentieth-floor balcony is high, because I take myself to know that they can fly. >>

            Yes, that's what I'm saying.

            >>But that's wrong--it's NOT rational for me to assign probability this way, because the belief on which it's based (i.e., that dogs can fly) is itself irrational.>>

            So you think that if a belief B was formed irrationally, any belief B* inferred from B will also be irrational.

            I don't think that's right. Suppose someone just guesses that Hillary Clinton is in Virginia right now; that belief is formed irrationally. Now suppose this person infers from that belief that someone is in Virginia. On your view, that inference was irrational; the resulting belief is not formed rationally. I, on the other hand, think it was perfectly rational for this person to conclude that someone is in Virginia on the basis of her belief that Clinton is in Virginia. Super rational. Totally logical. It certainly follows: if Clinton is in Virginia, *someone* is in Virginia! How can you fault that inference on the grounds of rationality?

            Similarly, even if someone irrationally believes dogs can fly, it can nevertheless be rational for her to hold, on that basis, that the prior probability of a dog surviving a fall from a twentieth-floor balcony is high. That's the right view for her to hold, "from the inside," given her beliefs.

            To modify what I think was Descartes' example: it's not irrational for a crazy person who believes his head is made out of clay to wear a helmet all the time. In fact, that's exactly the rational thing for him to do, given his beliefs.

          • Robert Rucker

            ". . . it was perfectly rational for this person to conclude that someone is in
            Virginia on the basis of her belief that Clinton is in Virginia."

            When you phrase it that way, it does sound compelling. That's because the *inferential* step is indeed rational. But try it this way: "It is perfectly rational for this person to believe that someone is in Virginia."

            That sounds wrong to me. It's NOT rational believe something based on a guess, even if the belief is derived in a logically unimpeachable way from the guess. Maybe your intuition differs from mine on this point--you did mention something about something being rational "from the inside," while I would prefer to have a more objective, or at least intersubjective, concept of what is rational.

            If our intuitions do differ in this way, further conversation may not be fruitful Thanks for the discussion, though!

  • Curio

    First, James Savage has offered a remarkably thoughtful and thorough critique. Great stuff. Second, it would be remiss not to mention that the McGrews (Tim and Lydia) have written a Bayesian argument for the Resurrection, starting from a very low prior. As is so often the case, the unconvinced will remain unconvinced, but it's worth throwing it out since Shapiro uses a Bayesian framework to argue just the opposite.

    http://www.lydiamcgrew.com/Resurrectionarticlesinglefile.pdf

  • Amidmany

    I'm a Christian Theist and the only miracle I'm absolutely positive about is the Big Bang. We are here are we not?

    • Robert Rucker

      Well, Christ said that a spiritual being (God) could indeed exist as a human (Jesus himself). Assuming you haven't actually seen both God and Jesus, I'd say your beliefs look inconsistent.