Some time ago I had a go at doing a calculation using what I thought were reasonable numbers, and the results are here. I know the numbers I used can be contested, but I'm not worried about that - but I'd be interested to know if I got the method totally wrong.

I'd love to know what the readers of your blog think about this paper. I've seen many commenters say that Bayesian analysis of religious is mere pseudo mathematics

I think people often misunderstand what Bayes's Theorem is doing in these arguments. Bayes's Theorem itself does not provide any content to the argument. It is a syntactical framework or a tool that operates with values that someone has to "plug in" to it. In this respect, it is just like deductive symbolic logic. Bayes's Theorem is just a calculating tool that churns out the results of probabilistic values that are put into it. It does not in itself assign probable values to any propositions ex nihilo.

I've seen many commenters say that Bayesian analysis of religious [claims] is mere pseudo mathematics

Hopefully, they aren't calling into question the soundness of Bayes's Theorem, which necessarily follows from Kolmogorov's axioms. This is tantamount to responding to a logically valid argument by calling into question the axioms of deductive logic. More plausibly, someone could call into question the probabilistic values that people use with Bayes's Theorem. But, then, I wouldn't call that pseudo-mathematics, it's just a difference in opinion about different probabilistic values. Most good philosophers who use Bayes's Theorem in service of arguments in philosophy of religion (e.g., Richard Swinburne) typically provide some basis for the probabilities they assign to different propositions, or they make it clear that specific numbers are merely estimates/placeholders used for illustrative purposes, or they don't use specific numbers at all (instead focus on the probabilistic equalities & inequalities that can be established with certain specified assumption). Once again, none of this is hardly worthy of the name "pseudo-mathematics." It's just a difference of opinion about the assignment of values.

I don't believe that one can establish a probability for God especially not with Bayes

I understand why some people are skeptical about some aspects of assigning probabilities to metaphysical claims, but I wonder whether this is any worse than trying to use deductive logic where the only values that can be used are True (100%) or False (0%). The improvement, as I see it, is that Bayes's Theorem allows for logical inferences that lie between 100%-0%. The mistake is to think that Bayes's theorem requires assigning precise values for each probability, when in fact a lot can be demonstrated just by looking at the relations between different ratios of relevant probabilities, illustrated with stand-in figures. The second and third pages of the article to which Victor linked show this nicely. It also gives an example where Bayes's Theorem can sidestep the problem of prior probabilities in some contexts. The dispute here, then, isn't with the reliability of Bayes's Theorem, but theoretical questions that generally apply to how we assign probabilities to any metaphysical claims.

I completely agree with everything you wrote. The usual complaint is not that's Bayes' Theorem is invalid, but rather that it has a restricted domain of applicability and cannot be used to assess religious questions. But as you said, if you think of probability just as a logic, then it's really not much different than using deductive logic to assess religious claims

## 5 comments:

Some time ago I had a go at doing a calculation using what I thought were reasonable numbers, and the results are here. I know the numbers I used can be contested, but I'm not worried about that - but I'd be interested to know if I got the method totally wrong.

I'd love to know what the readers of your blog think about this paper. I've seen many commenters say that Bayesian analysis of religious is mere pseudo mathematics

I don't believe that one can establish a probability for God especially not with Bayes

The Bayes CrazeI think people often misunderstand what Bayes's Theorem is doing in these arguments. Bayes's Theorem itself does not provide any content to the argument. It is a syntactical framework or a tool that operates with values that someone has to "plug in" to it. In this respect, it is just like deductive symbolic logic. Bayes's Theorem is just a calculating tool that churns out the results of probabilistic values that are put into it. It does not in itself assign probable values to any propositions

ex nihilo.I've seen many commenters say that Bayesian analysis of religious [claims] is mere pseudo mathematicsHopefully, they aren't calling into question the soundness of Bayes's Theorem, which necessarily follows from Kolmogorov's axioms. This is tantamount to responding to a logically valid argument by calling into question the axioms of deductive logic. More plausibly, someone could call into question the probabilistic values that people use with Bayes's Theorem. But, then, I wouldn't call that pseudo-mathematics, it's just a difference in opinion about different probabilistic values. Most good philosophers who use Bayes's Theorem in service of arguments in philosophy of religion (e.g., Richard Swinburne) typically provide some basis for the probabilities they assign to different propositions, or they make it clear that specific numbers are merely estimates/placeholders used for illustrative purposes, or they don't use specific numbers at all (instead focus on the probabilistic equalities & inequalities that can be established with certain specified assumption). Once again, none of this is hardly worthy of the name "pseudo-mathematics." It's just a difference of opinion about the assignment of values.

I don't believe that one can establish a probability for God especially not with BayesI understand why some people are skeptical about some aspects of assigning probabilities to metaphysical claims, but I wonder whether this is any worse than trying to use deductive logic where the only values that can be used are True (100%) or False (0%). The improvement, as I see it, is that Bayes's Theorem allows for logical inferences that lie between 100%-0%. The mistake is to think that Bayes's theorem requires assigning precise values for each probability, when in fact a lot can be demonstrated just by looking at the relations between different ratios of relevant probabilities, illustrated with stand-in figures. The second and third pages of the article to which Victor linked show this nicely. It also gives an example where Bayes's Theorem can sidestep the problem of prior probabilities in some contexts. The dispute here, then, isn't with the reliability of Bayes's Theorem, but theoretical questions that generally apply to how we assign probabilities to any metaphysical claims.

Johnny-Dee,

I completely agree with everything you wrote. The usual complaint is not that's Bayes' Theorem is invalid, but rather that it has a restricted domain of applicability and cannot be used to assess religious questions. But as you said, if you think of probability just as a logic, then it's really not much different than using deductive logic to assess religious claims

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