Is Christianity compatible with Objective Bayesian Epistemology?

Question

From Bayesian epistemology (SEP):

Bayesian Epistemology

First published Mon Jun 13, 2022

We can think of belief as an all-or-nothing affair. For example, I believe that I am alive, and I don’t believe that I am a historian of the Mongol Empire. However, often we want to make distinctions between how strongly we believe or disbelieve something. I strongly believe that I am alive, am fairly confident that I will stay alive until my next conference presentation, less confident that the presentation will go well, and strongly disbelieve that its topic will concern the rise and fall of the Mongol Empire. The idea that beliefs can come in different strengths is a central idea behind Bayesian epistemology. Such strengths are called degrees of belief, or credences. Bayesian epistemologists study norms governing degrees of beliefs, including how one’s degrees of belief ought to change in response to a varying body of evidence. Bayesian epistemology has a long history. Some of its core ideas can be identified in Bayes’ (1763) seminal paper in statistics (Earman 1992: ch. 1), with applications that are now very influential in many areas of philosophy and of science.

[...]

4.2 Objective Bayesianism

Objective Bayesians contend that, in addition to coherence, there is another epistemic virtue or ideal that needs to be codified into a norm for prior credences: freedom from bias and avoidance of overly strong opinions (Jeffreys 1939; Carnap 1945; Jaynes 1957, 1968; Rosenkrantz 1981; J. Williamson 2010). This view is often motivated by a case like this:

Example (Six-Faced Die). Suppose that there is a cubic die with six faces that look symmetric, and we are going to toss it. Suppose further that we have no other idea about this die. Now, what should our credence be that the die will come up 6?

An intuitive answer is 1/6, for it seems that we ought to distribute our credences evenly, with an equal credence, 1/6, in each of the six possible outcomes. While subjective Bayesians would only say that we may do so, objective Bayesians would make the stronger claim that we ought to do so. More generally, objective Bayesians are sympathetic to this norm:

The Principle of Indifference. A person’s credences in any two propositions should be equal if her total evidence no more supports one than the other (the evidential symmetry version), or if she has no sufficient reason to have a higher credence in one than in the other (the insufficient reason version).

Consider a person who subscribes to Objective Bayesianism. According to the principles outlined above, such a person would strive to eliminate bias and avoid overly strong opinions in their priors. They would also adhere to the principle of indifference, assigning equal credence to propositions in the absence of reasons or asymmetries in the evidence to justify favoring one over another. Within these epistemological constraints, can an Objective Bayesian epistemologist become a Christian while remaining consistent with Objective Bayesianism?

Can belief in God, miracles, angels, demons, the resurrection, souls, an afterlife, and similar doctrines be justified within the framework of Objective Bayesian Epistemology? Have any Christian authors written about this?

Answer 1

That sounds entirely antithetical to the principles of Christian faith, because the first principle is faith, which can be described in epistemological terms as a very strong "prior" meant to intentionally induce bias against contradictory evidence.

A person of faith might well describe the "objective Bayesian" system as "not believing in anything," or if they're feeling less charitable, as a form of intellectual paranoia. ("Just look at what people are reduced to when they have no firm foundation for their beliefs, and actually think seriously about the implications! With no anchor for their souls, they can't trust anything and end up having to carefully derive every bit of knowledge from first principles, never able to trust confidently in anything.")

By contrast, faith tells you that if you believe that X is true, and someone produces evidence that X is incorrect and Y is the truth instead, do not update your priors, because 1) there is moral virtue in refusing to do so and 2) the evidence being presented is probably incorrect in some way anyway.

Answer 2

Bayesian theory... The formula is "P(A|B)=P(B|A)P(A)/P(B)" (I'm not getting into that, but see here for equations and reasoning)

Well I assume the works of those who find this work from Bayes is something you already considered?

It all began in 1748, when the philosopher David Hume published An Enquiry Concerning Human Understanding, calling into question, among other things, the existence of miracles. According to Hume, the probability of people inaccurately claiming that they’d seen Jesus’ resurrection far outweighed the probability that the event had occurred in the first place. This did not sit well with the reverend.

Inspired to prove Hume wrong, Bayes tried to quantify the probability of an event. He came up with a simple fictional scenario to start: Consider a ball thrown onto a flat table behind your back. You can make a guess as to where it landed, but there’s no way to know for certain how accurate you were, at least not without looking. Then, he says, have a colleague throw another ball onto the table and tell you whether it landed to the right or left of the first ball. If it landed to the right, for example, the first ball is more likely to be on the left side of the table (such an assumption leaves more space to the ball’s right for the second ball to land). With each new ball your colleague throws, you can update your guess to better model the location of the original ball. In a similar fashion, Bayes thought, the various testimonials to Christ’s resurrection suggested the event couldn’t be discounted the way Hume asserted.

In 1767, Richard Price, Bayes’ friend, published “On the Importance of Christianity, its Evidences, and the Objections which have been made to it,” which used Bayes’ ideas to mount a challenge to Hume’s argument. “The basic probabilistic point” of Price’s article, says statistician and historian Stephen Stigler, “was that Hume underestimated the impact of there being a number of independent witnesses to a miracle, and that Bayes’ results showed how the multiplication of even fallible evidence could overwhelm the great improbability of an event and establish it as fact.”

Yale

Here is a digital commons article: The Resurrection of Christ: A Bayesian analysis of...

And here is the original piece of work including Bayes' work...

Richard Swinburne uses it to attempt to prove God...

---

As for the question, I don't believe these things are incompatible with the Christian Faith.

• eliminate bias
• avoid overly strong opinions in their priors (assumptions).
• the principle of indifference: assigning equal credence to propositions in the absence of reasons or asymmetries in the evidence to justify favoring one over another.

Within these epistemological constraints, can an Objective Bayesian epistemologist become a Christian while remaining consistent with Objective Bayesianism?

Yes. The issue seems to generally be that the same theories can be used against the position of Christianity just as effectively. (Such as by Richard Dawkins)

Can belief in God, miracles, angels, demons, the resurrection, souls, an afterlife, and similar doctrines be justified within the framework of Objective Bayesian Epistemology?

Yes, but not with razor sharp clarity that modern people like to have.

Because fundamentally some things cannot be understood. For example, the complete nature of God is unknowable and many things are determined by what God is not. If however one were to accept that sometimes the answer is "I cannot know" or "I will never know" then things work.

---

Here is an online use of the theorem to defend Christianity.

---

Also, to present more thought for you the reader.

Please be wary of claims that say things like "knowing is not faith". Knowledge and Faith are not opposites, they actually belong together.

Faith is sometimes opposed to reason, and belief to knowledge. According to Orthodoxy, faith and reason, belief and knowledge, are indeed two different things. They are two different things, however, which always belong together and which may never be opposed to each other or separated from each other. - Orthodox Church of America, The Orthodox Faith, Volume 1

Peace be with you

Answer 3

Can belief in God, miracles, angels, demons, the resurrection, souls, an afterlife, and similar doctrines be justified within the framework of Objective Bayesian Epistemology?

All those things* can be known by natural reason.
_{*except perhaps the resurrection of the body, though can know the immateriality and eternity of the human soul and the necessity of the body for humans to acquire knowledge; cf. Ed Feser, Immortal Souls, pt. 4.}

However, the supernatural, theological virtue of faith (or its assent) does not "ultimately rest on a mass of probabilities" (Pope St. Pius X, Lamentabili Sane). Commenting on the first article of the Creed, "I believe", the Catechism of the Council of Trent says:

The word believe does not here mean to think, to suppose, to be of opinion; but, as the Sacred Scriptures teach, it expresses the deepest conviction, by which the mind gives a firm and unhesitating assent to God revealing His mysterious truths. As far, therefore, as regards the use of the word here, he who firmly and without hesitation is convinced of anything is said to believe.

The knowledge derived through faith must not be considered less certain because its objects are not seen; for the divine light by which we know them, although it does not render them evident, yet suffers us not to doubt them.

In fact, "faith is more certain than science and the other intellectual virtues" (St. Thomas Aquinas, Summa Theologiæ II-II q. 4 a. 8).

And de fide dogmas have the highest degree of certainty; cf. the theological notes, a way of classifying the proximity of a theological proposition to Divine Revelation (and hence a ranking of certainty).

---

The Principle of Indifference

In moral theology, there is something similar called equiprobabilism (cf. Davis, S.J., Moral and Pastoral Theology pp. 8-10 for an overview of the different moral systems' ways of resolving practical doubt).

Also, see the various degrees of moral certitude (metaphysical, physical, and moral).

---

In philosophy, the great Thomist, German, Josef Kleutgen, S.J., discusses certainty in the Third Treatise of his Pre-Modern Philosophy Defended.

Another good book on this topic is the Catholic mathematician and philosopher James Franklin's The Science of Conjecture: Evidence and Probability Before Pascal. Catholic statistician William M. Briggs discusses Bayes passim in Uncertainty: The Soul of Modeling, Probability & Statistics.