My argument, in very short, is that I don't think it is necessarily the case that it is philosophically indefensible to say that the plausibility of the God hypothesis is zero, with the qualifier "almost surely."
Evidently, I have not communicated my case very well, or so I'm told, so I will try again to clarify.
First: "Almost surely" means something very precise in mathematics. It means "off a set of measure zero." Communicating clearly what "measure" means for a lay reader is a bit tricky, but in the sense I'm using it (probability/plausibility), it works out essentially, though very, very loosely, to having an infinite-to-one chance against it.
It must be noted that "one" here could be replaced with any finite value without changing matters. It also should be noted that if I compare two different sizes of infinity, the smaller size is effectively measure zero against the larger size, and, indeed, (as with the Cantor set in the interval [0,1], using Lebesgue measure, or as with the primes in the natural numbers cheating to use the natural density false-measure) measure zero can still occur by comparing two infinite sets of the same cardinality, i.e. same size. If this paragraph was confusing, I'm sorry. Math is hard.
Here are a couple of important points I've argued on this theme so far:
- Almost surely not the case is not categorical denial. Because events with probability zero, almost surely, or hypotheses with plausibility zero, almost surely, could conceivably occur, we are not engaging in categorical denial to say zero, almost surely, in this context. Categorical denial is philosophically indefensible. This is not categorical denial, and the only reason I know of standing in the way here is one that is debatable.
- I don't think there's any way to justify any nonzero plausibility for God's existence. Because we have absolutely no evidence for the existence of God, we have absolutely no justifiable reason to assign any nonzero plausibility to the hypothesis of God's existence. To summarize this briefly, I'm suggesting that since they have no evidence to go on, believers in God cannot produce anything to justify a claim of any nonzero plausibility for God's existence.
- Putting those together lands the God hypothesis in zero, almost surely, plausibility because (a) they cannot justify a nonzero plausibility; (b) categorical denial is not defensible; and (c) plausibility zero, almost surely, is what's left over.
- If some "God" exists, then, it is almost surely an abstract concept, not an entity in reality, particularly not an entity with agency that interacts with our universe in any way at all.
This is the essential core of my argument. It gets rather a lot of objection. I'll address a few of those.
"But couldn't people just turn this around and argue for God."
No. Evidence is at the center of this argument, and the burden of proof is on the believer to produce it. There is no credible evidence for an extant God that interacts with our universe in any way. None. I'm willing to concede that "incredible evidence" contributes evidence that has measure zero because it is not credible.
How would someone turn this around? There almost surely is a God because atheists can't produce evidence that there isn't one? But this is shifting the burden of proof. We have no trouble dismissing such an attempt as exactly that.
"But you can't say something has probability/plausibility zero."
Please, understand that prob/plaus. zero, almost surely, is not the same as categorical denial. It's very likely if you're arguing "but you can't..." that you might be missing this point.
If this sounds ridiculous still, I recommend the following litmus test. Replace God with "the Force" from Star Wars, or any other known fiction. Should we hesitate to say that the Force, specifically as it was conceived in Star Wars, has a nonzero probability of being a real thing in our universe? Should we hesitate to argue that the likelihood that Hogwarts School of Witchcraft and Wizardry has a nonzero probability of truly existing somewhere in the north of the UK?
If your immediate thought is "yes, we must," ask yourself why. Is it because George Lucas and J. K. Rowling wrote those ideas down? What about the ideas that other writers have written? Must all of them get a nonzero plausibility? What about ideas that writers haven't written yet? What about ideas that no writer will ever write? Must these all get nonzero plausibilities?
Here's a problem with that: if there are infinitely many conceivable fictions (and why shouldn't there be, using the numbers themselves as suggestive evidence?), then we have a problem. There are two possibilities here: either most of these fictions have zero plausibility, almost surely, or there is some mechanism by which their plausibilities diminish fast enough for the total plausibility to converge. So which is it? The vast majority of fictions have literally negligible plausibility or the vast majority of them have no plausibility off a set of measure zero? Depending on the number of conceivable fictions, this choice may not even be valid, and plausibility zero may be required.
So we have to assign nonzero plausibilities to all possible fictions, and yet we can't really. There are huge swaths of potential fictions that we simply give plausibility zero, almost surely, to without even hesitating: all of the wide, wide majority of them that will never even be thought of.
"But Bayesian reasoning says you can't assign a probability/plausibility zero."
Um, okay. Bayesian rules do assert that we cannot assign certain (zero or one) probabilities and plausibilities. It's possible that Bayesian reasoning, as conceived, has some issues with it--particularly at this point. Perhaps Bayesian reasoning doesn't apply here--to abstract hypotheses. As I repeatedly say, we can't mistake the theory for reality. Bayes's theorem is only as good as the axiomatic assumptions that it rests upon.
Also, I kind of think it could be possible. The reason Bayesian reasoning rejects assigning certain priors is because they could not be overcome by any evidence. But certain, almost surely, evidence should be able to overcome almost certain doubt (by something like L'Hospital's rule, for the math-inclined). Applying almost certain evidence against almost certain doubt produces an indeterminate form in Bayes's theorem (0/0), and if crafted carefully, this can conceivably be gotten around.
Indeed, this happens (theoretically) all the time. Every real number in the interval [0,1] has probability zero, almost surely, of being chosen in any random trial, but invariably, at lease one of those values is chosen. Once we have that (almost) certain evidence of whatever value crops up, it overcomes the almost sure doubt we had against it.
Regarding the existence of God: Show me God, and you can overcome my almost sure doubt. The same is true of the Force and Hogwarts.
A potential way to deal with this is to refuse to assign a prior and only to examine the role of evidence to see if it points uniformly one way or another. On the question of whether or not God exists, as there is no credible evidence to support it and tons of evidence refuting theological claims of all sorts, we can conclude that the evidence points us clearly in one direction: down to lower and lower plausibilities. Given that there are probably infinitely many different mechanisms (various Gods, other supernatural events, etc.) that could be proposed to account for what theologians attempt to pass off as evidence, the situation looks really, really dire for the plausibility that God exists.
"But the universe could be a simulation; we can't even know that."
So? Again, evidence: we have lots of evidence for nature existing. We have no evidence for God's existence. In the language here, I would say that God's existence has plausibility zero, almost surely, because of no evidence, and nature has plausibility one, almost surely, since we have nothing but evidence for it.
Put another way, everything we see suggests the world exists, off a set of measure-zero philosophical games, and nothing we see suggests that God exists, apart from a set of measure-zero philosophical games.
So, the same argument applies, yet again to the case I'm making and without having to change anything about it. The question ultimately comes down to epistemic gaps, which always exist. We have a very, very narrow (measure zero, almost surely, I'd argue) epistemic gap on the claim "nature exists." We have a very, very wide epistemic gap on the claim "God exists." My suggestion is merely that in the total paucity of credible evidence, that gap regarding God's existence is as wide as is philosophically defensible.
This raises an important point--the atheism versus theism argument is misleading. The question isn't really "no God" versus "God" because nature is inextricable from the discussion. The question is "nature does not require a God for its existence, operation, or explanation" versus "nature does require a God for its existence, operation, or explanation." This distinction is important.
Sure, anyone could then argue: "well, why is there nature at all, something rather than nothing?" and however philosophically interesting this question is, it doesn't really go anywhere. If it is true that nothing begets nothing, and yet we have something, the simplest conclusion to draw from this observation is that "nothing" doesn't apply to our universe. Theologians like to call the fundamental something "God," and it appears that cosmologists like to call it a "quantum field." This, other than a bad name on the part of the theologians, a term they're using to sneak across non sequiturs, doesn't really matter much. The theologians can't get to something they really want to call "God" without proving that the primordial something has agency. (Proving does not mean baldly asserting.) Good. luck. with. that.
"Either God exists or God doesn't, so this is inappropriate."
Possibly so. The argument about what it means to attempt to apply probabilistic and plausibilistic reasoning to hypotheses is not settled. Ultimately, I think that such an estimate with regard to the validity of hypotheses has to speak to our degree of certainty with which we can make the conclusion.
For example, take the Higgs boson. Either it exists or it does not, so we can't talk about the probability that it exists. Except that we can--sort of. We have amassed quite a lot of evidence matching the theory now, enough to conclude that when we say "the Higgs boson exists," we mean something. What we mean is that we are very confident that that which we mean by the term "Higgs boson" exists. To be clear, it could be that bosons do not really exist in reality, but whatever it really is that we are calling bosons clearly produces phenomena that can be explained in terms of the standard model including the term "boson." This, as it turns out, only matters a little, and in practice almost none at all.
Further, we can actually quantify how confident we are that the Higgs boson, or whatever it really is that we describe by that idea, is a real thing. We can't know for certain, but before scientists at CERN were willing to claim that it does exist, they had to be quite sure. How sure? The standard is roughly that a false identification, given statistics on the data, has a likelihood of less than one in 3,500,000.
In other words, we have a hypothesis, "the Higgs boson exists," to which we can assign a probability that tells us our degree of confidence in the given hypothesis. This sort of discussion of our level of epistemic confidence in the existence of God is somehow fundamentally invalid, though? The only reason we'd say so is because there is no credible evidence that God exists.
So, hopefully this clears it up some. Ultimately, I don't consider this argument central to what I'm doing or really all that important, even if it seems to gather a lot of attention. I will admit that I'm more than a bit annoyed that non-believers are bullied into saying things like "there's a very, very small chance, short of zero, that God exists," which opportunistic theologians and journalists pounce upon very disingenuously. After having thought about it for a long time, I'm just not convinced that it has to be "short of zero" or that any of us needs to say that anymore.