A Rigorous Formulation of “Extraordinary Claims Require Extraordinary Evidence”

I came across this rigorous formulation of the free thought mantra ‘Extraordinary claims require extraordinary evidence.’ I’ve always taken the phrase to mean something like this, but I’ve never worked out those intuitions with any precision. Thanks to Mr McIntosh — a Christian theist no less– for doing what the free thought community should have done but hasn’t: offer a formalized statement of their well-worn slogan.

To summarize, an ‘extraordinary claim’ is defined as ‘a claim with a very low intrinsic probability.’ Another way of saying this is that the prior probability of the claim being true based on our background knowledge is very low (but presumably not zero). So the evidence for this claim must be strong enough to bring the posterior probability of the claim up to .5 or better. This is indeed the strategy adopted by people like Richard Swinburne and Lydia and Timothy McGrew in their Bayesian arguments for the Resurrection of Jesus. They argue that even if the initial probability is low, this antecedent improbability can be counterbalanced by the specific evidence in this case. When one considers this evidence, the probability of the claim’s being true goes up well over .5 (I think both Swinburne and the McGrew put it at over .9).

If this is what the mantra basically means, then it is relatively uncontroversial. Theists, at least in the cases I mentioned, believe that they can meet their burden of proof here; non-theists will disagree. The non-theists will simply deny that the amount or kind of specific evidence in this case is sufficient to overcome the very low prior probability. But here is where the issue gets a bit complicated. What evidence could overcome this low intrinsic probability? As Mr McIntosh asks, ‘Would it be a lot of evidence that cumulatively confirms c (ignoring the problem of dwindling probabilities), or just one piece of evidence that highly confirms c, or possibly a combination?’ The answer here is not clear.

Another problem: theists and non-theists are unlikely to agree on what constitutes ‘background knowledge.’ Some theists say that if God exists, then we have to start with higher priors than we otherwise would. If the existence of God is one of our background beliefs, so it goes, the prior probability of the claim goes up. The claim would no longer be so extraordinary, nor would it need extraordinary evidence. Perhaps good evidence — testimonial evidence of the kind we would accept in mundane matters — would suffice. This seems to be the way William Lane Craig argues. I’ve heard him say in the context of debates that the free thought mantra is demonstrably false. I think he takes it to mean, following Hume, that the only relevant factor to consider when assessing a miracle claim is the prior intrinsic probability. However, we also have to consider our background beliefs and the posterior probability on the evidence that we have. Obviously we do have to consider those factors as McIntosh’s formulation notes.

So let’s take the issue of prior probability on our background beliefs. The legitimacy of granting a claim, like the Resurrection, a higher antecedent probability depends on the theist’s dialectical strategy. In Craig’s case, he argues for the Resurrection only after he believes he’s made a good case for the existence of God from natural theology. He then thinks it’s not overwhelmingly improbable that God would raise Jesus from the dead. Swinburne seems to argue similarly. The McGrews, however, are arguing for the existence of God from this particular miracle claim. As such, they can’t help themselves to higher priors. They assume low priors, but contend that the evidence brings the posterior probability up. They also argue that we can use this evidence to retroactively update our priors. The non-theist will remain unimpressed by this, I think. Obviously theists and non-theists in this debate disagree about the success of natural theology and the quality and/or amount of evidence we have in this particular case. There is also the problem of dwindling probabilities that Plantinga points out. Even if we assume for the sake of argument that it’s very probable, say .9, that God exists, that probability dwindles the more claims we add. Thus, the probability that God exists might be high, but the probability that he’d become incarnate is necessarily lower and the probability that he would die and rise again lower still, until we’re below .5. Both Swinburne and the McGrews have responded to Plantinga. Because of the technical nature of these replies, I can’t comment in detail. In any case, it’s a bit of a moot point. The non-theist is not going to grant the claim ‘God exists’ a probability exceeding .5. So agreeing on the background beliefs seems like a non-starter.

What about the quality or quantity of evidence in the case of the Resurrection? Again, the theist and non-theist are going to disagree about it’s strength. The theist will say that it succeeds in overcoming the antecedent improbability — and is thus ‘extraordinary’ — while the non-theist is going to deny this. So it seems we’re stuck with a stalemate. We’re left with the question of the merit of the slogan ‘extraordinary claims require extraordinary evidence.’ Provided the terms are rigorously defined, the slogan is admissible. However, I still doubt that it will be dialectically useful. It seems to me that we’re unlikely to reach consensus on what beliefs should form our background knowledge and, therefore, how to assign the priors. However, it seems to me that we have to assign low priors, even if we’re willing to concede for the sake of argument that God exists. After all, God, if he exists, is stingy with resurrections, as I think even the theist will have to admit. Therefore, on their alleged frequency alone, we should assign a low prior probability. The theist and non-theist will also disagree about whether the evidence is ‘extraordinary’ enough to overcome the low antecedent probability and raise the posterior probability above .5.

Nonetheless, a more rigorous formulation of this mantra is valuable. It helps us avoid semantic dead ends and focus on the argument in more detail. It also suggests that theists (at least evidentialist ones) and non-theists might be able to agree in principle that ‘extraordinary claims require extraordinary evidence’ even while disagreeing in practice when it comes to a particular claim like the Resurrection. However, such agreement on methodology is no small matter. Indeed, it might be the best we can hope for in theist/non-theist debate.

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One response to “A Rigorous Formulation of “Extraordinary Claims Require Extraordinary Evidence”

  1. Pingback: Bayes’ Theorem and Extraordinary Claims | dude ex machina

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