To make it quite clear, I want to quote a half a paragraph from Loftus's Why I Became an Atheist (original edition) where he introduces the Outsider Test for Faith. From pp. 66-67,
The outsider test is simply a challenge to test one's own religious faith with the presumption of skepticism, as an outsider. Test your beliefs as if you were an outsider to your faith. An outsider would begin her journey as a disinterested investigator who didn't think the religious faith in question is true since there are so many different religious faiths in the world. An outsider would be someone who was only interested in which, if any, religious faith is correct and would have no intellectual affiliation with any of them at all. She would have to assume that her culturally inherited religious faith is probably false. (emphasis added, see below)This is where Loftus first lays out the OTF in Why I Became an Atheist, where he defines it (so one can see why I recommend reading his writing if they are not yet doing so). Much of the rest of the chapter this paragraph is pulled from justifies two legs upon which this can stand, while quelling some objections
- The OTF is a justified activity for any believer to engage in;
- The geographic component to the distributions of religious faiths are the predominant factor that such a disinterested investigator will have to face down, e.g. that being born in Saudi Arabia gives a better than 99% chance of being a Sunni Muslim, while being born to Christian parents in the United States gave better than a 99% chance of being a Christian (until recently, at least--lots of people are leaving religion now, after all).
The italicized text in the quote from Loftus above indicates that Loftus's main conception of the OTF at the time he wrote Why I Became an Atheist focused only on one of the three numbers: the prior probability (that the religion being tested is true). In the long post I made previously, I make the case that, indeed, by far the heaviest bit of argument to be made (and being made!) is in the consequent P(e|h,b) (which I called t for convenience there) that measures how likely it is that the evidence we see in the world matches what we would expect to see if the hypothesis that the religion under examination is true.
Here's why working only on the prior probability is a relatively weak approach. Suppose we are dealing with a serious believer who is willing to take the test. First, if this serious believer is a "faith-head," one who would estimate that the evidence-based probabilities completely in his favor (t=P(e|h,b)=1 and n=P(e|~h,b)=0), no matter what prior probability he assumes for his religion, Bayes's theorem tells him that the likelihood his religion is true is 100% (if you think about this, it makes sense trivially: this position assumes the evidence is perfectly explained by his religion). In other words, you could easily get this faith-head to concede that there are millions upon millions of other religions out there, from the outside all just as likely to be valid as the next, and yet a Bayesian analysis will return absolute certainty for him that his particular religion is correct. Thus, more has to be dented than the prior for the OTF to have any effect.
Now, suppose another case where we have a very sincere (or deluded) believer, but not one that is impervious to looking at the evidence from the outside. Imagine now instead a very serious believer who holds that there is a 99% chance the evidence we see is what we would have if his religion is true and a 1% chance that there could be any other explanation for the evidence we see, i.e. t=P(e|h,b)=0.99 and n=P(e|~h,b)=0.01. Loftus's original conception primarily has this believer assault the prior probability without looking at the weight of other evidences. Here's what the math says about this.
- If the OTF gets him to admit a still-biased 50% chance that his religion is true, a very common error among people who do not understand probabilities, then Bayes's theorem allows him to conclude that it's 99% likely that his religion is true. In other words, the OTF will have no chance of convincing him.
- If the OTF gets him to admit that there are 4 equally likely positions to take (say, Christianity, Islam, Judaism, and "other")--surprisingly common among Abrahamic believers--he will put his prior at 25% and Bayes's theorem will tell him that there is a 97% chance that his religion is true. The OTF will not convince this person.
- If the OTF gets him to admit 10 equally likely religions, for a prior of 10%, Bayes's theorem will tell him that his own is 91.7% likely to be true. The OTF will not convince this person.
- In order to achieve an outcome from Bayes's theorem of 50%, it will be incumbent upon the person to recognize and admit that there are 100 religions that are equally likely to be true. This will be a tall order since there are only 20 "major" religions in the world.
- If the person can be convinced, however, by the OTF that there are 1000 religions to consider equally, historically speaking not ridiculous, then Bayes gives back a 9% chance that the religion is true, and for 10,000 religions, Bayes returns just under a 1% chance.
The easiest point to make to help this problem:
Now, in the previous post I noted that because the naturalist position has a 100% chance of explaining nature from the outsider perspective, that this number is unlikely to be low for believers taking the OTF. This may not be accurate, though, as many sincere believers think the world would simply be chaos if any other explanation but their God were behind it. So, I'll amend that to say that serious believers will underestimate this number (n=P(e|~h,b)) perhaps quite grossly. This opens the door very widely for the OTF to have success, though.
The simple argument that will add strength is to get believers to recognize that the same process that is reducing the prior (per above) is admitting that there are other viable explanations for the evidence (the universe).
In more technical terms, reducing the estimate on the prior and raising the estimate on the value of evidence being supported by other explanations, i.e. n=P(e|~h,b), is essentially the same. It would even be possible to claim on this argument alone that the complement of the prior (e.g. 95% if the prior is 5%--that which would add to 100% with the prior) is the lowest value that n=P(e|~h,b) can take.
Consider the example above to see the impact that this change has, we can use even our super-sure, faith-head with t=P(e|h,b)=1 here (even though that's inconsistent--see next section).
- If the OTF gets him to admit "don't know," i.e. a prior of 50%, then Bayes returns only a 66% chance that his religion is true: two out of three. Whether this would be convincing or not is hard to say, but it's far from "my soul burns in hell if I'm wrong" certainty.
- If the OTF gets him to admit a prior of 25% (four religions), then Bayes tells him he's only able to be 30% sure that he is right.
- If the OTF gets a prior of 10% out of him, then he can only be 11% sure.
- If the OTF gets a prior of 1%, then he can be 1% sure.
- Likewise, within a narrow margin of error, for lower priors.
Thus, the easiest argument for the OTF to make, in addition to the recognition that the prior should be reduced, is that the possibility that other explanations are correct is essentially no less than the complement of the prior.
Consistency is the next easiest point
People like to be consistent (because not being consistent causes cognitive dissonance, which is actually uncomfortable). Thus, it should be relatively easy for the OTF to make the point that one cannot be 100% sure that their religion predicts the evidence and that there is some chance that other explanations predict the evidence. That, of course, is nonsense.
This problem isn't as obvious if the person doesn't believe that there is a 100% chance that their religion predicts the evidence, but it still shouldn't be hard for the OTF to make the next most straightforward assertion and have it taken seriously.
The probability that any particular religion predicts the evidence should be no higher than the probability that particular religion is true. In other words, the OTF should easily be able to make the case that the prior probability sets an upper boundary for t=P(e|h,b).
[EDIT (12/7/2012): A commenter (below) noted that a and t here are technically independent, and certainly that is generally true. I do not wish to mislead anyone here into thinking that they must be related to one another. The (exclusionist) religions (i.e. the big ones), however, contain within themselves the assertion that nothing else could explain the evidence, so this would add weight to the claim that the prior should serve as an upper bound since the very existence of other religions severely challenges the notion that "this is what we would see if there was indeed one true religion."]
Let's examine the effects of this assertion on the outcomes of Bayes's theorem if t=P(e|h,b)<(prior) and n=P(e|~h,b)>(1-prior):
- If the OTF can get a believer to admit a "don't know" position of 50% for the prior, then this construction tells them exactly that: 50%, i.e. "you don't know."
- (As a pointed aside: the infamous argumentum ad populum. "But so many people believe in my religion! It has to be right!" Well, let's use Christianity here, since it's the biggest religion going. We'll be generous and say that all brands of Christians are Christians, including the nominal ones that aren't even really believers at all any longer. In that case, 33% of the world's population is Christian (and if we look historically over time, this number would be smaller). This results in a argumentum ad populum prior of 33% from the OTF, if we want to concede it. Bayes's theorem, in the full analysis (admitting modification to all three relevant numbers) gives this person a 19.5% chance that their religion is true, a bit less than one in five. Probably not enough to be getting on with.)
- If the OTF can get the believer to admit 4 religions, i.e. a prior of 25%, then Bayes's theorem tells him that there is only a 10% chance his religion is true. This is likely to crack the walls of many faiths.
- If the OTF can get the believer to admit to 10 religions, Bayes's theorem tells him there's only a 1.2% chance his religion is true. This is, by definition, essentially a decimation.
- If he admits 100 religions, there is a 0.01% chance his religion is true, and if he admits 1000 religions, there is a 0.0001% chance (1 in 100,000) that his religion is true.
- This number gets small fast for more religions, say if one were to make the argument that every religion that does exist, has existed, will exist, or could exist must be considered, plus no religion at all. Bear in mind that there are over 40,000 denominations of Christianity alone here.
Again, because this is hard to overstate--the OTF can be this effective on one, and only one point of debate: how many religions do you admit exist and have a possible claim at being true? There needs be no debating evolution, no discussing whether or not Hitler was Christian or atheist, no mention of how many people died under Stalin, no comments about the origin of the universe, and no nonsense about without God whether or not there can be morals. One question is all that's needed to seriously break open religious faith: how many religions do you admit exist and have a possible claim at being true?
It cannot be denied by anyone that wishes to get into the real argument, which the OTF may have shown to be essentially unnecessary in principle (but unfortunately not in practice, in all likelihood), that the degree to which the evidence is explained by any religion, especially the Abrahamic ones, is abysmal. Indeed, I argue that it is zero (almost surely), end of story, but anything larger than billions to one will be very, very difficult to defend against the Problem of Evil (or Problem of a Silent God, more generally) alone (and hence the PoE is the "rock of atheism"). Similarly, that naturalism isn't a completely effective explanation for everything (even if all of the explanations aren't had) is going to be very difficult to defend, and thus the other consequent should be within billionths of one (I argue it really should be one, almost surely, end of story).
That is why the vast majority of the heavy indictments of religion from Richard Dawkins, Sam Harris, Christopher Hitchens, and others (including myself!) have worked so hard on these points--if the evidence is considered honestly, Bayes's theorem will show no mercy on any prior, at least anything short of 100% certainty. As Sam Harris has pointed out, though, "If someone does not value evidence, what evidence could you provide to change their mind?" (Capturing that the 100% certainty prior probability--i.e. mind completely already made up--case requires more work.) Attacking the evaluation of the evidence simply doesn't work against devout faith until something cracks it open. The OTF is something of a silver bullet because it says, simply enough, that you don't have to (though the rest of Harris's statement still makes for a real problem--they have to value logic or this is still out the window).
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