I was originally going to write a post on Peter Millican’s updating and revision of Hume’s maxim to be more compatible with Bayesian reasoning. But when I started writing about how Hume’s vocabulary and conceptualization of probability were pivotal to understanding him (and Millican’s assessment), I realized this could be its own post.
I’m going to end on more theological and ethical points, which I imagine many people would love to read.
Hume’s Maxim Is An Operating Procedure, Not An Equation
The fundamental problem with translating Hume into numerical terms is that Hume’s probability is factual, using our intuitions about relative quantity, such as relative weight. Though weight may have a numerical quality, we don’t need to be perfectly numerate to be able to tell when something weighs more than something else.
To use a metaphor, it’s like using your sense of touch to determine which cup of tea is hotter than the other. If one tea cup is only two degrees cooler than the other, you won’t know by sense of touch, but if one is boiling while the other is frozen, you can tell which one is hotter (preferably not by touch!).
For Hume, comparing miracle probabilities is of a similar nature. You don’t need to know the precise probability to know that one is much greater than the other. And one kind of probability is much more likely than the other. As he writes:
“A wise man, therefore, proportions his belief to the evidence. In such conclusions as are founded on an infallible experience, he expects the event with the last degree of assurance, and regards his past experience as a full proof of the future existence of that event. In other cases, he proceeds with more caution: He weighs the opposite experiments: He considers which side is supported by the greater number of experiments: To that side he inclines, with doubt and hesitation; and when at last he fixes his judgment, the evidence exceeds not what we properly call probability. All probability, then, supposes an opposition of experiments and observations, where the one side is found to overbalance the other, and to produce a degree of evidence, proportioned to the superiority. A hundred instances or experiments on one side, and fifty on another, afford a doubtful expectation of any event; though a hundred uniform experiments, with only one that is contradictory, reasonably beget a pretty strong degree of assurance. In all cases, we must balance the opposite experiments, where they are opposite, and deduct the smaller number from the greater, in order to know the exact force of the superior evidence.”
A proof is different from a probability in the sense that a probability is far more doubtful, while a proof, by definition, has no reason to be doubted. And so, for this formulation of probability, a proof will always be superior to a probability.
If you’ve read my previous posts on Hume, this may seem obvious, but there is nuance here. Because Hume is measuring relative weights against each other, with one being very clearly superior, his subsequent maxim is more of an operating procedure or heuristic to assessing two disparate, mutually exclusive probabilities than it is a precise formula.
The operating procedure is thus:
If a proof is being weighed against a (mere) mutually exclusive probability, the proof will always win.
If a law of nature is being weighed against a (mere) mutually exclusive probability, the law will also win.
You’d think that’s simple, but many non-Humean commentators make the predictable mistake of reading Hume as defining a miracle as a maximally improbable event, when in reality he defines it as an event that goes against the most probable event.
That may seem like semantics, but the nuance is important. The relative weighing of the improbability of the event is built into the Humean definition of miracle. That doesn’t mean that the definition entails that the event conclusively didn’t happen or was impossible to happen, just that it’s (by definition) extremely unlikely.1
Again, I like this web comic because it expresses the point even if you believe in miracles!
It’s Only A Maxim
All of this is to say that if you dispose of Hume’s language of proof, probability, law of nature, etc. and the relative weighing aspects of Hume’s probability, you’ve rendered his argument unrecognizable from his original intent and reasoning.
In this way, Hume’s maxim only works for making judgments weighing mutually exclusive probabilities with extreme disparities in confidence or likelihood, such as miracle testimony against laws of nature.
That is, the maxim is a maxim, not a universal law for comparing all probabilities. You shouldn’t use it to evaluate merely-improbable-yet-possible events, like lotteries.
For Hume, a lottery winner would be a probability, not a miracle. We don’t have the built-in understanding of lotteries that they near-conclusively don’t have winners. Indeed, we hear about these winners all the time, and we have evidence beyond just testimony that they occur, and the testimony is of higher quality than that of religious miracles.
Similarly, Hume would say you shouldn’t side with one probability over another just because it is marginally more probable than the other.
For example, if two sports teams are playing each other, and one has lost one game while the other has lost two games, Hume wouldn’t dismiss the two-loss team as the likely loser with no other evidence, especially not with the same confidence as he would dismiss a miracle claim.
In this way, the maxim has a particular use purpose and makes no greater claim than what it says:
“No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish.”
…But It’s Not Trivial
Some may say this reading renders Hume’s maxim trivial, but I disagree. After all, many philosophers and theologians have misunderstood this argument and maxim,2 leading them to both refute a straw man and fail to grasp the implications of the maxim and argument.
After all, how many philosophers have you read about on this substack that erroneously said Hume’s argument was circular or defined miracles out of existence or attributed principles to Hume that he would deny or misread Hume’s maxim to say that no evidence could establish a miracle?
No, I think if Hume’s maxim was trivial, you wouldn’t have an army of philosophers disagreeing with it and misreading it, and a corp of theologians changing the subject from epistemology to ontology.
It Has Radical Implications
Some believe assenting to the truth of the maxim necessarily leads to atheism or agnosticism, but I don’t think this is the case. Indeed, if you read Hume’s Dialogues Concerning Natural Religion, where Hume is in many instances more sympathetic to orthodox belief relative to deistic natural theology, you may get a different impression altogether.
The questions that arise from Hume’s maxim and argument (I’m using the terms interchangeably at this point) go something like this (non-comprehensive) list:
If we can never be confident in testimony by itself to credibly establish a miracle, and testimony for miracles is all we have supporting the supernatural foundations of religions, should we believe in religion?
Is it appropriate or rational to believe in religion for non-evidential reasons?
Is it rational to believe in religion for those non-evidential reasons when we have good evidence against specific religious claims?
I don’t have answers to these questions (or at least I'm not going to share them here), but I do think they are very interesting, and the most interesting religious thinkers I have met take them seriously and shape their faith in response to these questions.
As a brief aside, when it comes to Christianity, my Humean sensibilities are much more sympathetic to forms of Christianity that conceptualize faith as pistis in Christ, a form of loyalty and relationship, from which various obligations follow. This, in contrast to a form of faith that’s about accepting or denying propositional sentences.
This pistis faith says “I believe this evidence, not because it’s rational, but because I had (and still have) an experience or relationship with God, and from that experience/relationship, I infer the truth of these purported events.”
Obviously, these Christians take the teachings of their faith seriously, from the Bible to Liturgy to Tradition, but they understand that the answers to deeper questions are much less obvious and generalizable, and more ambiguous and personal. That’s not to say these Christians are relativistic or unorthodox, but that they embrace a faith of wisdom and reinterpretation. They’re in good company with the Apostle Paul.
Why I Will Continue Hume Posting
Now, I’m not saying you’re dumb or irrational or not a deep thinker if you conceptualize faith in this way or if you disagree with me. I just think that if you don't understand Hume's maxim/argument, you’ll go around saying silly things about the strength of the evidence for religion, and that will lead you to do other silly things like publishing an AI-written substack saying false things about philosophers.
And so, the reason I’m a stickler for the truth and nuances of Hume’s philosophy is because I don’t think most Theistic Philosophers or Christian Apologists who disparage him truly understand him. That leads to not just silly apologetics, but worse yet, misunderstandings about how nontheists and nonbelievers assess religious arguments. From those misunderstandings come harmful beliefs, norms, and practices that further leads to misunderstandings about the world.
Long story short, I believe those that misunderstanding Hume are more wrong and less nice people than they otherwise would be, and I think that’s bad. In response, I’m going to constantly correct them. I do this not because I think Hume’s argument will lead them to relinquish their faith in God, but because I hope they’ll grasp the full implications of his philosophy and become wiser for it.
At base, I don’t care if everyone agrees with me, I just hope they live a good, happy life.
And so, the Humean pedantry will continue until morale (wisdom and happiness) improves!
And that definition probably shouldn’t be controversial.
And plenty of smart, rational people commit the base rate fallacy every day.