Papal Bayes?
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[Update — mistaken identity corrected…] Someone with the same name as Robert Prevost, now Pope Leo XIV, published a paper in 1985 evaluating the application of Bayes' Theorem to the question of God's existence. The paper ("Swinburne, Mackie and Bayes' Theorem" ) was published in the International journal for philosophy of religion.
Thomas Bayes (1701-1761) was a Presbyterian minister, but the theorem that bears his name was presented in a posthumously-published work on gambling, "An Essay Towards Solving a Problem in the Doctrine of Chances". The Economist once called Bayes' Theorem "the most important equation in the history of mathematics", but Rev. Prevost's paper argued that "the Bayesian method of evaluating the adequacy of theistic explanation … [falls] short both in practice and in principle".
Here's the start of his paper:
Prof. Richard Swinburne believes in the existence of God; Mr. John Mackie not. Their disagreement ends there. They share assumptions about the nature the claim that God exists and about the use of Bayes' theorem to evaluate that claim. In this essay I want to discuss some of these commonalities and to address the issue of theism as an explanation for the existence of the universe. I shall against Swinburne and Mackie's use of Bayesian confirmation theory and attempt in conclusion to sketch out a defense of theism which is explanatory but not susceptible to criticisms of the same kind.
Bayesian theorists such as Mackie and Swinburne believe that Bayes' theorem represents accurately the epistemic relations between propositions. Consequently both appeal to the theorem or at least to questions which follow from it in support of their case. I believe there are both in principle and in practice arguments against this appeal.
To make the theorem useful the values of the particular elements, such as the prior probabilities, have to be known. And, though it is typically claimed that the support relation between evidence and conclusion is necessary and a priori, there must be some means by which these values are calculated. The actual method used varies from context to context. The important and ironic thing is that unless some mode of evaluation is available, the concept of epistemic probability has little relevance.
If you lack the (equivalent of the) Pope's educational background (a B.A. in mathematics from Villanova) and want to know more about what Bayes's theorem is, I'll point you to my lecture notes from a couple of decades ago. I accept the argument that the theorem is not theologically relevant, but it's been central in many aspects of Psychology, Human Language Technology, and so on. As those lecture notes put it:
This way of thinking about things is very widely used in engineering approaches to pattern recognition.
In particular, equation (8), with theory replaced by sentence and evidence replaced by sound, has been called "the fundamental equation of speech recognition."
The Bayesian framework is also a natural one for models of the computational problems of perception.
As Helmholtz pointed out a century and a half ago, what we perceive is our "best guess" given both sensory data and our prior experience. Bayes' rule shows us how to reconstruct this concept in formal mathematical and computational terms.
Update — I should also note that the introduction to Bayes' posthumous essay, written by Richard Price, argued for its theological (or at least teleological) relevance:
"The purpose I mean is, to show what reason we have for believing that there are in the constitution of things fixt laws according to which things happen, and that, therefore, the frame of the world must be the effect of the wisdom and power of an intelligent cause; and thus to confirm the argument taken from final causes for the existence of the Deity. It will be easy to see that the converse problem solved in this essay is more directly applicable to this purpose; for it shews us, with distinctness and precision, in every case of any particular order or recurrency of events, what reason there is to think that such recurrency or order is derived from stable causes or regulations in nature, and not from any irregularities of chance."
J.W. Brewer said,
May 9, 2025 @ 11:04 am
Neither wikipedia nor as best as I can tell the last 24 hours of news coverage indicate that the new Pontiff was ever affiliated with Oriel College, Oxford, although an American doing graduate work at the Pontifical University in Rome as the future Pope was at the time (although not in philosphy) could plausibly have spent a term or two in Oxford. Are we sure it's the same Robert Prevost? One would think that Oxford's PR people would be hyping the connection if it were.
jin defang said,
May 9, 2025 @ 11:31 am
it almost certainly is the same Robert Prevost. I happened to sit next to the chairman of our math dep't at commencement earlier today, and he happily informed me that the new pope majored in math at Villanova and was interested in the nexus between math and theology.
Yves Rehbein said,
May 9, 2025 @ 11:40 am
That's such an Anglo biased thing to say. I learned Laplace Formel (WP; has not even a interwiki-link) in the frequentist tradition (xkcd: Frequentists vs. Bayesians). I see no difference whatsoever to Bayes' rule. It's the exact same thing to me. I don't want to appear ignorant; a quick check with History of Exact Sciences confirms:
"More explicitly, let us note some respects in which the main results of BAYES' paper differ from those of LAPLACE and of more modern writers:
(i) Theorem 1 above (the so-called "BAYES' Theorem") applies to discrete rather than continuous distributions (though modern BAYEsian analysis is faith-ful to BAYES original work inasmuch as it applies these results to continuous distributions). LAPLACE was apparently the first to introduce the discrete formulation (see § 3.2 below)."–(Dale, A. I. (1982). Bayes or Laplace? An examination of the origin and early applications of Bayes' theorem. Archive for History of Exact Sciences)
You hear that? The so-called "Bayes' Theorem"! Whatever.
D.O. said,
May 9, 2025 @ 12:33 pm
This is almost certainly a different Robert Prevost than the one who became Pope. The one who published on Bayes-Laplace (I am sure that Laplace, though not reaching Eulerian levels of fame, doesn't need his name to be attached to yet another result, but fine, we can do it) theorem is also published a monograph "Probability and Theistic Explanation". I cannot find any details about the author except that Amazon page for the book says that he is "at University of Texas". There is Rob Prevost who teaches at Wingate with zero biographical details. I will assign a subjective probability of 0.5 to him being the author. Acknowledgement section in the book acknowledges author's parents as "Dr and Mrs R.W. Prevost, Jr" which doesn't agree with what Prevost the Pope parents are referred as elsewhere (Louis Marius Prevost and Mildred Martínez, respectively).
Stephen Goranson said,
May 9, 2025 @ 1:13 pm
There is a difference between Robert F. Prevost and Robert W. Prevost.
Anthony said,
May 9, 2025 @ 2:38 pm
I had to read the Abbé Prévost in French Literature class.
J.W. Brewer said,
May 9, 2025 @ 3:03 pm
"Prevost" was as of the 1990 Census only the 6625th-most-common surname in the U.S. but there are a LOT of people in the U.S. and Robert is or was in certain generational cohorts a very common first name, so it is unsurprising that one (almost certainly incomplete) database I just checked lists over 200 separate individuals in the U.S., plus no doubt hundreds more in other countries, including Canada and the U.K. as well as majority-Francophone places. (For an English example who might have kin who went to Oxford, consider Sir Christopher Gerald Prevost, 6th Baronet, who is said to descend from an 18th-century Swiss immigrant.)
With a few hundred Robert Prevosts out there, having at least two who share the same unusual sounding combination of interests (such as math + theology) is probably not particularly unlikely. Someone with more skill at statistics than I have could probably work out the math of how likely/unlikely given semi-arbitrary but reasonable-sounding assumptions.
Stephen Goranson said,
May 9, 2025 @ 4:26 pm
According to the commercial site trading as Academia.edu,
"Swinburne, Mackie and Bayes' Theorem"
was posted by Robert Prevost,
"Wingate University, Religion and Philosophy, Faculty Member."
https://wingate.academia.edu/RobertPrevost
Julian said,
May 9, 2025 @ 6:08 pm
This is one of those non-intuitive probability questions, like: in a group of 30 people, what's the probability that two share the same birthday?
My mother, during her family history period, once announced with some surprise: "I never knew that my grandfather was once the premier of Victoria!" She was curious about why this had never come up in family talk in her youth.
It turned out later that in what was presumably a pretty small cohort in the Melbourne University law school in the 1880s there were two William Shiels. One went on to become premier of Victoria; the other my ancestor.
MattF said,
May 9, 2025 @ 8:07 pm
This seems to be a case of the Law of Truly Large Numbers
https://en.wikipedia.org/wiki/Law_of_truly_large_numbers
which holds that if there are a truly large enough number of independent samples, even very implausible events will occur.
ohwilleke said,
May 9, 2025 @ 8:53 pm
FWIW, the substantive argument in the article is a close cousin of the more famous probability based argument for believing in God known as Pascal's Wager, https://en.wikipedia.org/wiki/Pascal%27s_wager which has been widely criticized as logically invalid.
Philip Taylor said,
May 10, 2025 @ 3:20 am
Some errors in the introductory transcription — two examples thereof :
They share assumptions about the nature the claim that God exists -> They share assumptions about the nature of the claim that God exists
I shall against Swinburne and Mackie's use of Bayesian confirmation theory -> I shall argue against Swinburne and Mackie's use of Bayesian confirmation theory
There may be others, but those two leapt out at a first reading.
.mau. said,
May 10, 2025 @ 3:21 pm
I checked the monography written by this Robert Prevost (which, as other readers pointed out, is an expansion of the original article), and in the acknowledgements he wrote "I would like to thank especially my parents, Dr and Mrs R. W. Prevost, Jr., whose support and encouragement made this essay possible.". Since the father of Leo XIV is Louis Marius Prevost, they are definitively different persons.
Martin said,
May 11, 2025 @ 8:32 am
@Yves Rehbein: the Laplace – Formel is an elementary statement of the frequentist definition of probability. Bayes' theorem is in one sense an elementary definition of *conditional* probability but the two are certainly not the same thing.
Daphne Preston-Kendal said,
May 12, 2025 @ 3:09 am
I emailed Oriel College and they confirmed that it is a different Robert Prevost.