Can Bayesianism Quantify True Belief?

The first part of Evelyn Waugh’s masterpiece Brideshead Revisited (1945) centers around the relationship between protagonist Charles Ryder and his friend Sebastian Flyte, whom he met at Oxford. Sebastian rebels against his rigid Catholic upbringing by living a life of debauchery. Charles begins the following dialogue by asking Sebastian about the faith:

“I suppose they try and make you believe an awful lot of nonsense?”
“Is it nonsense? I wish it were. It sometimes sounds terribly sensible to me.”
“But my dear Sebastian, you can’t seriously believe it all.”
“Can’t I?”
“I mean about Christmas and the star and the three kings and the ox and the ass.”
“Oh yes, I believe that. It’s a lovely idea.”
“But you can’t believe things because they’re a lovely idea.”
“But I do. That’s how I believe.”

This dialogue reveals that Sebastian is childish, which is a central theme of the novel. We may ask, however, whether his view of faith, which seems to make no use of reason, constitutes bad theology. More generally, we may ask, How should we determine what we believe? For some, it seems obvious that we ought to rely on logic and evidence and should not, in any context, accept ideas merely because they are lovely. Many philosophers, mathematicians, and other thinkers have contributed to the tradition of this evidence-based approach. Perhaps the greatest modern school of thought in this tradition is called Bayesianism, which incorporates ideas from many brilliant thinkers into a coherent system to describe how we know things. St. John Henry Newman, whom Pope Leo XIV recently named a doctor of the Church, has a different — and, I will argue, broader — epistemology, because it can incorporate the best aspects of Bayesianism as well as crucial aspects of human nature that Bayesianism misses.

It is natural to desire certainty in our beliefs. One way to obtain it is through deductive logic, in which some premises are assumed and others are proven. The classic example is:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

In this argument, the first two sentences, called postulates, are not proven but are assumed to be true. If they are, then the third sentence is certainly true. This method of reasoning has the benefit of giving mathematical surety, but it has the obvious limitation of requiring postulates that are unproven. Sometimes the postulates can be deductively proven, but these proofs require additional unproven postulates.