“All that is achieved is an assessment of the application of BT, not anything about any actual probability.” That is not a logical argument. You do have to defend a prior probability: it comes from b, background evidence. You can’t just make up any prior. It comes from evidence. And you have to do this whether you use Bayes’ Theorem or not. Because all probabilities are conditional on background evidence. You can’t ignore evidence and its effect on probability, and claim to have a valid probability.

Arguing by presupposition is illogical. That’s just a procedure of explicitly ignoring all pertinent evidence, and just “deciding” something is true. No logically valid method or epistemology can come from that procedure. It just begs the question all the way down.

We do not “presuppose” either naturalism or supernaturalism. We derive the prior probability of the one relative to the other from evidence: it is conditional on all past experience and confirmed facts. Which entails an extremely low prior for supernaturalism; because never ever in the whole of human history have we ever confirmed any supernatural explanation of anything is true, but have always instead, in millions of cases to date, discovered natural explanations fully explain every fact yet explained. It could have turned out the other way; but it didn’t. Therefore the evidence entails supernaturalism is extremely improbable. “Presupposing” the contrary, is simply to ignore vast quantities of evidence. In fact, all human evidence acquired in the whole of history.

And that’s maximally illogical.

On the matter of assuming anything supernatrual, I use this approach:

If we are going to argue about anything naturalistic, we necessarily pre-suppose the tested/verified assumption that naturalism exists.
If we are going to argue about anything supernaturalistic, we necessarily pre-suppose the UNtested/UNverified assumption that supernaturalism exists.

So for any argument about something supernatural, the argument will always fail to get off the ground. This is because there is no instance in which anything supernatural has been shown to exist. Indeed, it is my contention that it is impossible to demonstrate anything about the supernatural, by argument.

Also, since Swinburne carves the prior probability space as P(h|k)=0.01, P(h1|k)=0.0005, P(h2|k)=0.00001, P(h3|k)=(a very small number), P(d|k)=0.005, and P(n|k) = ~0.98449, once we remove n as irrelevant (because something exists, so the hypothesis that nothing would exist is 100% certain to be false), Swinburne’s priors become: P(h|k)= ~0.64, P(h1|k)= ~0.03, P(h2|k)=0.00064, P(h3|k)=(a very small number), and P(d|k)=0.32. In other words, he actually covertly assumes the prior probability for God, relative to all other substantial explanations of present observations, is 0.64. Well above 0.5. And pretty close to Unwin’s posterior probability.

Note the 2011 paper by Swinburne listed in a top comment above confirms my interpretation. There, in response to Gwiazda, Swinburne admits he has carved up the prior probability space into P(h|k)=0.01, P(h1|k)=0.0005, P(h2|k)=0.00001, P(h3|k)=(a very small number), P(d|k)=0.005; and the rest to P(n|k), the condition of nothing exists. Which entails Swinburne means P(n|k) = 1 – (0.01 + 0.0005 + 0.00001 + ~0 + 0.005) = 1 – 0.01551 = ~0.98449. But that’s impossible.

Of course, the probability that nothing exists is 0 (as here we are, something), so it cannot be 0.98449. So what Swinburne must mean is either of two things: that the prior probability that n caused everything now observed is ~0.98449; or that the prior probability that there would be nothing to observe is ~0.98449. But we already showed the latter has to be zero. Because something is observed. It therefore cannot be ~0.98449. And by the same reasoning neither can the prior probability that n caused everything now observed be ~0.98449, unless n has a nonzero chance of causing everything we observe. Which then obligates Swinburne to honestly determine what that probability is. And even if we allow n to have a nonzero chance of causing everything we observe, Swinburne has no basis for believing the prior probability of n is ~0.98449. There is no evidence supporting that frequency. And there is no formal logical demonstration from him that it would even be anything significant at all, much less ~0.98449.

These facts are easily shown by iteration:

(1) If h is “nothing caused everything” and ~h is “something caused everything”, but nothing ever comes from nothing, then even if we assume the prior for h is 0.99, then P(h|e.k) = P(h|k)P(e|h.k) / [P(h|k)P(e|h.k) + P(~h|k)P(e|~h.k)] = (.99)(0) / (0 + 0.01) = 0 / 0.01 = 0. So the updated prior for h, once we observe something, is 0. It disappears. Because it has exactly 0 probability of causing e. Meanwhile, swap h with ~h and carry out the math and you get the prior probability that in fact something caused what we observe is 1. So Swinburne cannot mean by n that “nothing caused what we observe observe.” That can never have an iterated prior higher than 0. Unless nothing has a nonzero probability of causing everything we observe. And then Swinburne needs to figure out what that probability is.

(2) If h is “there is nothing to observe” and ~h is “there is something to observe,” and k is background knowledge and e observations, then even if we assume the prior for h is 0.99, then P(h|e.k) = P(h|k)P(e|h.k) / [P(h|k)P(e|h.k) + P(~h|k)P(e|~h.k)] = (.99)(0) / (0 + 0.01) = 0 / 0.01 = 0. So the updated prior for h, once we observe something, is 0. It disappears. Meanwhile, swap h with ~h and carry out the math and you get the prior probability that there is something to observe is 1. So Swinburne cannot mean by n that “there is nothing to observe.” That can never have an iterated prior higher than 0.

By the same reasoning (once you iterate accordingly), that there is something to observe is in k. We observe countless things caused by something. And we never observe a nothing causing anything. So the prior probability that something caused everything is actually high on k, not low. Certainly not 0.98449. Unless we want to get hypothetical about what an unfettered nothing can cause, e.g. a nothing so null that no laws or principles or expectations even govern what it will do. Which actually ends up getting us a very high probability of the entire universe we observe. If there truly was nothing to limit what would happen. Which of course a nothing must be. Otherwise, if something is limiting what can happen, we have a something on our hands, not a nothing.

In Existence, Swinburne is cagey about what he assumes his initial and conclusory prior probability of God to be. He never states a prior. But what he weirdly does do, is actually fill almost all of the prior-probability space with “nothing,” i.e. that nothing would exist (the prior for God, he says, “might be very small” because “so improbable is it a priori that there should exist anything at all”), but that’s illogical. The probability that h = “nothing happened” would explain present observations has a prior probability of zero (literally, actually, zero). Unless “nothing” has a nonzero probability of causing everything; which Swinburne denies. So once we exclude the “nothing” hypothesis and only carve up the prior probability space with h(n) = “some brute fact event happened that caused presently observed evidence,” Swinburne’s claim that (h = God) has a higher prior than (~h) entails a prior above 0.5. He never demarcates different alternatives; he always simply compares God with “nontheism,” meaning the conjunction of all competing godless theories (such that all he need consider, he says, is whether “the hypothesis of theism makes it more likely that e will occur than it would be if theism were false”); which requires his prior to be at least 0.5. It is unclear if he ever realizes this, because he has illogically carved away almost all the prior probability space with the illogical “nothing” condition, and never reconsiders that error.

And even if Swinburne allows “something can come from nothing” (i.e. that it has a nonzero probability), we’d then have to calculate what that probability is (Swinburne doesn’t; and he might not like the result if he did), and even apart from that, of all the a priori options you can pick out of a hat, there is no reason “nothing started it all” would be more likely than that a spontaneously existing God started it all or any other nontheistic supernatural or natural “brute fact” scenario (of which there are many godless varieties available), except by arguing that nothing is simpler than all the others; but then so are all the godless theories that (unlike Swinburne’s God) are only slightly more than nothing. Which reverses Swinburne’s conclusion. So Swinburne’s treatment of the prior either entails an illogical and unspecified prior he never properly argues is greater than any actual alternative; or entails a 0.5 prior probability (once all logically impossible scenarios are excluded from the prior probability space).

It should also be noted that Swinburne also tries to dismiss all background evidence relating to what kinds of explanations tend to be true, with the self-contradictory argument that there are no comparands to what I call “magic and ghosts” explanations and therefore “magic and ghosts” explanations can enjoy a high prior. In the real world, the lack of comparands entails a low prior. By every definition of frequency there is. Lower, in fact, than any other type of explanation that has ever turned out to be true. Just as I argue in this article.

Thanks to a commentator:

Recommended works criticizing Swinburne on many similar points (and some attempts at reply):

Julia Braunsteiner-Berger, “Swinburne’s Argument for the Existence of God: A Critical Comment on Conceptual Issues,” Religious Studies 50 (2014): 359-78.

John Ostrowick, “Is Theism a Simple, and Hence Probable, Explanation for the Universe?” South African Journal of Philosophy 31.2 (2012): 354-68.

Jeremy Gwiazda, “Richard Swinburne, The Existence of God, and Exact Numerical Values,” Philosophia 38 (2010): 357-63.

Jeremy Gwiazda, “Richard Swinburne’s Argument to the Simplicity of God via the Infinite,” Religious Studies 45 (2009): 487-93.

Jeremy Gwiazda, “Richard Swinburne, The Existence of God, and Principle P,” Sophia 48 (2009): 393–98.

Emma Beckman, “Richard Swinburne’s Inductive Argument for the Existence of God: A Critical Analysis,” Masters Thesis, Linköpings Universitet (2008).

Don Fawkes and Tom Smythe, “Simplicity and Theology,” Religious Studies 32.2 (June 1996): 259-70.

Richard Swinburne, “How the Divine Properties Fit Together: Reply to Gwiazda,” Religious Studies 45 (2009): 495–98.

Richard Swinburne, “Gwiazda on the Bayesian Argument for God,” Philosophia 39 (2011): 393–96.

Calum Miller, “Is Theism a Simple Hypothesis? The Simplicity of Omni-Properties,” Religious Studies 52 (2016): 45-61.