In his shockingly neglected, A Treatise on Probability John Maynard Keynes put his finger on the difficulty people have with probability, particularly Bayes’s Theorem:
No other formula in the alchemy of logic has exerted more astonishing powers. For it has established the existence of God from the premiss of total ignorance; and it has measured with numerical precision the probability the sun will rise to-morrow.
Probability carries with it “a smack of astrology, of alchemy.” Comte, Keynes reminds us, regarded the application of the mathematical calculus of probability as “purement chimérique et, par conséquent, tout à fait vicieuse.”
That last word, dear reader, is vicious; a word which was laughed off in the mad rush towards the utopia of Quantification an era which Comte, incidentally, and despite his intentions, helped usher in. We are, at this moment, mere moments away before a number must by law be attached to every judgment of uncertainty. We are already there in all “scientific” uses of statistics where a thriving Pythagorean cult, complete with arcane initiations and occult formulae, worships the number 1 in 20.
So you won’t be surprised when I tell you there is not one, but two books which argue that a fixed, firm number may be put on the proposition God Exists. The first by Stephen Unwin is called The Probability of God: A Simple Calculation That Proves the Ultimate Truth, in which he uses Bayes’s theorem to demonstrate, with probability one minus epsilon, (the Christian) God exists.
This is countered by Proving History: Bayes’s Theorem and the Quest for the Historical Jesus by the very concerned Richard Carrier (pictured above), whose uses Bayes’s theorem to prove, with probability one minus epsilon, that the Christian God does not exist because Jesus himself never did.
There we have it: probability proving two diametrically opposite conclusions. Alchemy indeed.
Carrier of course has the harder task, and he attacks it with all the gusto of a man uncovering the secret machinations behind the Kennedy assassination. Updated [correction applied; see the comments] He defines a mythicist as one who believes the historical Jesus was a myth.
He doesn’t just deny the divine Jesus, but asserts that the man called Jesus never existed. That Jesus was entirely a creation of a first century conspiracy to create a new religion; made up whole cloth, to coin a phrase. I won’t bother to parse any of Carrier’s writing, as it is excruciatingly painful to do so. But if you are interested, here is a link to a several-thousand-word essay in which Carrier “takes apart” a minor blog post written by a historian who claims Jesus lived.
An Amazon.com reviewer of Unwin’s work, which I have read and which is mercifully brief (and in large font with small pages), asks just the right question: “can you imagine anyone arguing that the existence of evil in the world, given that God exists, is 23% as opposed to 24%, for instance?” Indeed. Too bad this kind of question is not asked in science.
The reviewer has also recognized that probability questions have an order. That is, the probability that evil exists given God does is different from the probability that God exists given evil does. This crucial distinction Unwin minds attentively. Judging by his obsessiveness over niggling detail, Carrier probably gets it right, too.
The real question is: how can probability prove a thing and its opposite simultaneously? The answer is simple: the same way logic can prove a thing and its opposite. This does not prove that logic should be lumped with pseudoscience however. You can’t blame the tool for its misuse.
All arguments of certainty and uncertainty are conditional. For example, is the proposition “Jesus was divine” true? Well, that depends on the evidence. If you say, “Given Jesus lived, died, and was resurrected as related in the Gospels” then the proposition has probability one, i.e. it is true. But if you say, “Given Jesus was a myth, created as a conspiracy to flummox the Romans and garner tithes” then the proposition has probability zero, i.e. it is false.
Given still other evidence, the probability the proposition is true may lie between these two extremes. In no case, however, is probability or logic broken. It does explain why focusing on probability is wrong, though. These authors would do themselves better service on explicating the evidence and eschewing unnecessary quantification.
Update 22 Aug 2014. Welcome Strange Notioners! See this blog next week for a criticism of Carrier’s methods. Meanwhile, look to the Classic Posts page for lots more about probability.
Thanks to Ye Olde Statistician for suggesting this topic.