No, that wouldn’t be nice; though the beauty of the scene should be all the proof of God’s existence required. Instead we examine in lazy fashion comments made by our friend Fran at his Alea Deum, in the post “On the certainty that God exists and why Bayesians should go π“. (I am a Bayesian and coincidentally I did go to pie last night; a local blueberry-raspberry creation which was heavenly.)
Fran begins with the excellent question “What is the probability that God exists?” The proposition of interest is “God exists”, and it is obvious he means the classic omnipotent, omniscient, etc. definition. From there our author sallies into his first error, a common one.
I should reply with “50%” or “p=1/2”. This is so because when Bayesians (The Objective Kind) have no information on a problem they use a plethora of principles in a Groucho style fashion to figure out a prior distribution to kick off Bayes’ Theorem machinery.
This is false in two separate ways; actually three. The proposition “Either God exists or not” is just like the proposition “Either X exists or not”. Both are tautologies, statements which are always true no matter what. Adding a tautology to any logical argument changes it not a whit; thus tautologies add no information and can’t be used to infer probabilities. Think of a die throw (we’d rather not; but let’s do it anyway). We could say, “A 6 will show or it won’t” but that is equivalent to “A 6 or a 2 will show or they won’t” and so forth; the partitioning is of no consequence, though it might seem it was.
Falsity two: if there is truly “no information on a problem” then no probability can be deduced. What is the probability the following proposition is true? “A rumfrom is a plorsteen.” You have no information. The tautology “A rumfrom is a plorsteen or it isn’t” adds nothing. Therefore no probability whatsoever can be deduced. It is in cases like these we should heed Wittgenstein and keep our traps shut.
Falsity troix: Groucho would have been funnier.
Fran next tries several attempts at putting “a prior” on the proposition “God exists.” This is unfortunate because the activity makes no sense (all those equations which follow have no life in them), though we graciously admit that thinking they might is forgivable. Subjective and “objective” Bayesians are always running around in the fashion of kids from Brooklyn with fresh cans of spray paint “putting priors” on things. Probabilities aren’t really theirs, they think, until they can be “tagged.”
All probability, like all other logical statements, can only be made conditional on certain fixed evidence, or premises. Textbook Bayesians slap priors on propositions (by whim as often as they do on evidence) because they always enter the problem too late, because they are too used to dealing with “parameters” without thinking about what these creations are and what they mean (here is an explanation). But since there is no parameter in the proposition “God exists”, it’s doubtful a Bayesian would attempt a prior.
A prior here would be some arbitrary (mathematical) probability pulled from the nether region of the mind. It would be based on nothing and take no meaning. It would be like saying the proposition Q is true (or probable) “just because” or “because I said so.” You would start and end with a prior, since if you had other relevant evidence (see below) you would have used it first. Priors float without basis or justification and do not “stick” to the proposition because they are not deduced from evidence relevant to the proposition.
If we’re really interested in the truth of “God exists” (and many aren’t), we should gather propositions which we believe true and which are probative. From these true and believed propositions we could deduce the probability of “God exists”. There would be no priors involved in any way.
Sufficient would be the five sets amassed by St Thomas Aquinas. Here they are done in video (I haven’t watched these; I Googled them as a service to my dear readers). And here is a series in words. And then see this series on the cosmological argument. And there are more besides these (other arguments, I mean).
Actually what we have are a not several arguments, but one grand one, all roads leading to the same inescapable destination. And all traveled without unnecessary mathematical baggage.
And now I won’t tell you that I’ll soon wander over to St Mary’s and from there to the shore (my swimsuit will be concealed cleverly by pants).