Tuesday, July 30, 2013

Re-revisiting my case that the existence of God has no plausibility

Something interesting: an argument I consider to be something of an aside from the main thrust of my thoughts and discussion on God and religion seems to be the one that works people up the most. Of course, it sounds far more contentious than it may be.

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:
  1. 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.
  2. 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.
  3. 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.
  4. 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.


  1. James, I want to teach Critical thinking skills to children age 4+

    Is there any way to simplify this to that audience !

    1. There's a lot of abstract machinery in this that might not cross the gaps to children, especially younger children. The key things to try to get across to them, I would wager, is this:

      1. Anyone could make up any kind of story, like Harry Potter, the Force from Star Wars, and every kind of myth (use whatever myths might be appropriate plus other ideas from fiction books). That's fine if you want to make up a story. We don't have to believe everything in a story exists, though. People could make up any kind of story, including ones that are not true.

      2. A lot of people like to think in terms of belief, but it is better to think in terms of "confidence." How much confidence can we have in an idea? When we have lots of confidence, we can say we believe or accept it. When we have very little confidence, we should not say we believe or accept it.

      3. Sometimes we get more reasons to have confidence in stories and explanations, and sometimes we get reasons to have less. The way we get confidence in them is by finding evidence for them. There are two main ways we get less confidence in them. First, we could get evidence that tells us we're wrong. Second, we could get no evidence when it should be expected. In both of these cases, we have less confidence in the story or explanation.

      4. If we don't use evidence as our guide, then we might believe any crazy thing. Some things are wrong, and others are wrong in a way that is dangerous to believe in, like believing that you cannot be hurt when you really can be.

  2. Given our background knowledge about the state of the world, God is the best explanation for motion in the universe; the finely tuned universe and everything in it; the existence of objective morals and duties; and consciousness. If God is the best explanation for these things then God’s existence is very likely. Since God’s existence is very likely, it can’t be the case that the plausibility of God’s existence is zero almost surely. If God is the cause of motion in the universe; the finely tuned universe and everything in it; the existence of objective morals and duties; and consciousness then God can’t possibly be an abstract object as abstract objects have no casual power.

    The Argument from First Motion:
    1. Some things are changing.
    2. Whatever is changing is being changed by something else.
    3. The prime mover can be either A) just potential, B) a mix of potential and actual, or C) just actual.
    4. The prime mover is pure actuality.
    5. Therefore the prime mover is pure actuality.

    Experience shows that contingent material objects like people, trees, cars and stars are caused to change by something else. However, this chain of contingent cause and effect can’t go back to infinity because if there is no necessarily existing agent/object that is pure actuality to actualize everything that is a mix of potential and actual then everything in the chain of causality will cease to change and exist. However, since there is change and motion in the universe there must be a prime mover that is pure actuality. Since all material objects in the universe are changing and appear to be contingent it is improbable that the prime mover is a material object. However, God is said to be a necessarily existent, immaterial mind and so is more likely to be the prime mover with pure actuality.

  3. The Kalam Cosmological Argument:
    1. Whatever begins to exist has a cause of its existence.
    2. The universe began to exist.
    3. Therefore the universe has a cause of its existence.

    The Argument from First Motion deals with a potential eternal universe, but current scientific research shows that the universe has existed for ~13.7 billion years and arose out of the big bang and so it not eternal. This means, most likely, that the universe had some sort of cause for its existence. It is very, very, very unlikely that the universe popped into existence uncaused out of nothing as nothingness has no causality. Also, it would be strange that nothingness causes something to pop into existence only once every 13.7 billion years-or-so; after all we don’t observe mountains, planets and people just popping into existence uncaused.

    Another naturalistic explanation for the origin of the universe, that the laws of nature caused the universe to come into being, is implausible because laws of nature are abstract objects that can’t, in of themselves cause anything—abstract objects are causally inert. Another implausible explanation is that subatomic particles and natural laws caused the universe to come into being. This explanation is implausible because everything we can see with our eyes has a cause of its existence, and even microscopic things like the elements didn’t exist prior to the big bang, so necessarily existent subatomic particles would fly in the face of what we know about the universe. Even natural laws seem to be contingent in that they could easily be different then they are. Positing subatomic particles and natural laws as the necessary entities that caused the universe to coming into being is also un-parsimonious as we would need to assume that there are physical objects and abstract objects that need to exist necessarily in order to be the cause of everything else.

    On the other hand, positing God as the transcendent being that exists necessarily is more plausible because an un-embodied mind has no parts that need to be formed or created and needs nothing in order to exist. Positing God is also more parsimonious as we need to assume that only one necessary being needs to exist in order to cause everything else to exist.

  4. The Teleological Argument:
    1. The fine tuning of the universe is due to either physical necessity, chance or design.
    2. It is not due to physical necessity or chance.
    3. Therefore, it is due to design.

    Observations about the universe show that the cosmological constants are exquisitely fine tuned and that if many of them were only slightly different then they are then the universe would be devoid of stars, planets and life. Oxford physicist Roger Penrose calculates that the odds of the special low entropy condition having arisen by chance alone in the absence of any constraining principles is a least as small as about one part in 10^10(123) in order for the universe to exist. It is very, very, very improbable that the fine tuning that we see in the universe arose by physical necessity or chance. Positing an agent, such as God, who designed the universe in such a way so that life could arise, is much, much, much more plausible then naturalistic alternatives.

    The Axiological Argument:
    1. If God does not exist, objective moral values and duties do not exist.
    2. Objective moral values and duties do exist.
    3. Therefore, God exists.

    Certain propositions such as, “It is wrong to murder innocent people,” “Raping and torturing little children is wrong,” and “It is good to help someone in need,” just seem to be objectively true no matter what a particular culture says. It is extremely difficult for naturalism to account for the existence of objective morals and duties, but they can be accounted for in the nature of God’s being.

    The Argument from Consciousness:
    1. Genuinely non-physical mental states exist.
    2. There is an explanation for the existence of mental states.
    3. Personal explanation is different from natural scientific explanation.
    4. The explanation for the existence of mental states is either a personal or natural scientific explanation.
    5. The explanation is not a natural scientific one.
    6. Therefore the explanation is a personal one.
    7. If the explanation is personal, then it is theistic.
    8. Therefore the explanation [for the existence of mental states] is theistic.

    If matter is all that exists in the universe then we would expect more complex arrangements of matter as time goes by, but consciousness coming out of non-consciousness is extremely unlikely. It is much more plausible to say that the consciousness that we see on earth arose from the conscious mind of God.

    As we can see from the arguments I’ve presented, God is the best explanation for motion in the universe; the finely tuned universe and everything in it; the existence of objective morals and duties; and consciousness. Naturalistic explanations for these things range from implausible to extremely implausible. Since God is the best explanation for these things it can’t be the case that God’s existence is zero almost surely. God’s existence is very likely.

    1. So many words. So little meaning. That's all you're getting. I have better things to do than deal with this stuff yet again. (Where? Hint: I wrote a book. I'm about to publish another.)

  5. Wow, you're just conceding defeat by not even making an attempt to defend your argument.

    You know, these days, just about anyone can self publish books making all kinds of claims, but it is a much more difficult thing to have to defend your claims and arguments against against a rigorous critique, of those ideas, from an intelligent person who disagrees with your position. From what I've seen of you and you're work you're either unwilling or unable to defend your claims and arguments against critique, and so your arguments and claims are worthless.

    I have hope that you will someday come back to God,but I am disappointed that you don't appear to be critically engaged with the search for him. You deny him with eyes wide shut. Take care, James, I wish you the best.

    1. Not every crank on the internet deserves a response, Keith.

    2. James A. Lindsay said: "Not every crank on the internet deserves a response, Keith."

      Translation: "It's perfectly obvious to everyone that my argument was torn to shreds, so I'm going to try to save face by coming up with lame excuses for why I'm not going to try to defend what's left of it."

      This reminds me of the BS excuses that Richard Dawkins gave for not wanting to debate William Lane Craig. The real reason why Dawkins won't debate WLC is that he and everyone else knows that Dawkins would get crushed in a head-to-head debate with Craig.