Zero probabilities

There is a subset of the supernatural being fan club whose members are enamored of improbability arguments. That is, they will calculate the probability of some feature of the universe, get a very small number, and declare that since the probability is so low under a naturalistic scenario, supernatural intervention is required.

Usually there are some blatant surface errors in such a calculation, such as assumptions no one is entitled to, or an artificially narrow set of naturalistic scenarios. But there are also deeper concerns. “Inverse problems” are notoriously nasty, and inferences to supernatural causes based on alleged improbabilities is a particularly good place to find pathologies.

Try these examples out for size:

1 (Strong version): The probability of the universe is exactly zero. If lower probabilities mean increased credibilty for a supernatural explanation, then we can conclude with certainty that God created the universe.

As a matter of fact, the probability of the exact state of our universe is (probably) zero. That is, it seems reasonable to say that there are an uncountable infinity of possible states of the universe. In that case, whatever state we occupy is trivially a zero measure set. Its probability is exactly (not approximately) equal to zero. Short of logical impossibilities, it’s hard to find a better candidate for divine causation on account of improbability.

2 (Weak version): As we increase our knowledge about the universe, we automatically decrease the probability of the universe. Therefore, as science advances, the likelihood that there is a God inevitably increases.

Our universe is constrained by the (finite) information we have about it. As we increase our information, we eliminate possible universes that do not conform to the new information from the set of possibilities. Therefore the probability of the information we have decreases as the amount of information increases.

I hope the bullshit nature of these arguments is obvious. Many supernaturalists think they can infer a supernatural cause based only on improbability of a data set, without specifying any new pattern in the data that is explained by a supernatural agent. You simply can’t do that—it’s merely a failure to recognize randomness. The pathology here is not merely in using inappropriate statistical models and so forth, though often these show up as devices to inflate alleged improbabilities. (The above arguments are independent of such concerns.) Even if you get the probabilities right, you are not entitled to infer supernatural agency. Improbability is not a excuse to get out of doing real, novel explanatory work.

But then again, I do think that a major thread through almost all intellectualized supernatural belief is a failure to appreciate randomness.

About Taner Edis

Professor of physics at Truman State University

  • http://www.blogger.com/profile/05211466026535549638 Bradley Bowen

    Very interesting.

    I think a bit more explanation of your objection would be helpful.

    "I hope the bullshit nature of these arguments is obvious. Many supernaturalists think they can infer a supernatural cause based only on improbability of a data set, without specifying any new pattern in the data that is explained by a supernatural agent."

    I don't think that theists make the argument soley on the basis of improbability. It is improbability plus the appearance of design (or something like that).

    If I get out my game of Scrabble, turn all the squares with letters on them over (letter facing down), thouroughly mix-up the squares, and randomly select several letters one at a time, laying them out in a row in the order selected, then I would be quite amazed if upon turning the squares over I saw the following sequence of letters: BRADLEYBOWENSTOPPLAYINGGAMES
    BELIVEINJESUSCHRISTANDBESAVED.

    I would be tempted to convert to Christianity. Not just because this sequence of letters is improbable, but because they are improbable AND have the appearance of being a message from God or Jesus.

    In this hypothetical scenario, would I be foolish to give serious consideration to the idea that this is a message from God or the Son of God?

  • http://www.blogger.com/profile/10778996187937943820 Taner Edis

    Bradley Bowen: "I don't think that theists make the argument soley on the basis of improbability. It is improbability plus the appearance of design."

    How you mix those two varies. Biological ID puts more emphasis on the appearance of design. Cosmological ID puts more emphasis on apparent improbability.

    I'm trying to come up with an example or two that might quickly illustrate what's wrong with trying to convert improbability alone into support for supernatural causes.

  • http://www.blogger.com/profile/09925591703967774000 Dianelos Georgoudis

    Taner Edis said: “ That is, [theists] will calculate the probability of some feature of the universe, get a very small number, and declare that since the probability is so low under a naturalistic scenario, supernatural intervention is required.

    The issue is not intervention. It’s not like, here is the universe perfectly capable of existing naturalistically and all by itself, but let’s see if there some issues in it which can only be explained by supernatural meddling, in which case some supernatural agent must exist out there.

    Rather, it’s like this: Here is the universe as we know it, or, better still, here is life as we know it (from our objective observation of a mechanical order in how apples fall to our subjective experience of the beauty of sunsets, to our sense of freedom or of morality, to our sense of rationality, to the very fact of our experience of life). So, is life as we know it more probable on naturalism or on theism? Can a naturalistic worldview better account for our life than a theistic worldview, or vice versa?

    What has lately changed, and what Taner probably refers to, is that now theists are arguing that even objective (aka scientific) facts are difficult to account for naturalistically, unless one is willing to embrace some really fantastic and credulity stressing worldviews. And sometimes not even then.

  • http://www.blogger.com/profile/05211466026535549638 Bradley Bowen

    http://www.origins.org/articles/
    swinburne_justificationtheism.html

    Consider this paragraph from “The Justification of Theism” by Richard Swinburne:

    “Each of the phenomena (things in need of explanation) which I have mentioned has formed the starting point of a philosophical argument for the existence of God, but all that philosophers have tried to do is to codify in a rigorous form the vague reasons which many ordinary men have had for believing that there is a God. These arguments seem to me to have a common pattern. Some phenomenon E, which we can all observe, is considered. It is claimed that E is puzzling, strange, not to be expected in the ordinary course of things; but that E is to be expected if there is a God; for God has the power to bring about E and He might well choose to do so. Hence the occurrence of E is reason for supposing that there is a God. E may be a large phenomenon, such as the existence of the Universe, or something a lot smaller, such as our own individual religious experiences.”
    (from section I. on “Inductive Arguments”)

    There are two elements typical of arguments for God, according to Swinburne:

    1. Some phenomenon E is puzzling, strange, not to be expected in the ordinary course of things.
    2. This phenomenon E is to be expected if there is a God.

    The first element corresponds to the idea of improbability, and the second element corresponds to the idea of that I termed “the appearance of design.”

    In my Scrabble example, the phenomenon E is the order of the letters resulting from a random selection of letters. This order is “puzzling, strange, not to be expected in the ordinary course of things”. However, as with probability estimates and calculations, what counts as “to be expected in the normal course of things” or “not to be expected…” depends on one’s assumptions or point of view.

    If I believed in the God of Christianity, I would expect God to constantly be arranging Scrabble letters and all manner of other means to communicate important messages to people, especially if there was some message that people needed to understand in order to avoid spending an eternity in suffering and misery. There would be nothing “puzzling” or “strange” or unexpected about God arranging the order of randomly selected Scrabble letters to send an urgent spiritual warning to someone.

    The message revealed in the Scrabble letters is “strange, puzzling” and “not to be expected” because I don’t believe there is a God or any other sort of supernatural being who has the power to design (so to speak) the order of randomly selected Scrabble letters in order to send a message to me.

    So, there is, on second thought, a distinction to be made between what is “to be expected” and what is “probable”. It is improbable that randomly selected letters would spell out a message that appeared to be from God, not just because it is improbable that random series of letters spell out a message, but more specifically, it is rare for apparently divine messages to be transmitted by any analogous means whatsoever. God is a rather quiet fellow.

    However, even given the rarity and the improbability of such a “message”, it is still the case that, for someone who believes in the God of Christianity, there is nothing “strange” or “puzzling” about such an event.

    What is puzzling is that such events are so rare. It is as if letters that are randomly drawn are never interfered with by God (imagine that!)in order to send dire warnings to people, or other important bits of divine wisdom.

  • http://www.blogger.com/profile/05211466026535549638 Bradley Bowen

    Dianelos said:

    "The issue is not intervention. It’s not like, here is the universe perfectly capable of existing naturalistically and all by itself, but let’s see if there some issues in it which can only be explained by supernatural meddling, in which case some supernatural agent must exist out there."

    According to Swinburne, the arguments for God based on the nature and origin of the universe have a similar logical structure to arguments for God based on miracles and other kinds of divine interventions, such as divine revelation and religious experiences.

    I understand that the creation of the universe by God would not violate laws of physics, since those laws are part of what is being created, on the theist's view. But the coming into existence of matter and energy ex nihilo would seem to be inexplicable in terms of the laws of physics (i.e. matter/energy is neither created nor destroyed), so the creation of a universe ex nihilo seems analogous to a miracle (such as levitation or resurrection of the dead).

    Can you say a bit more about why you think we need to distinguish between arguments for God based on the nature and origin of the universe and arguments for God based on miracles, religious experiences, etc.? Do you disagree with Swinburne's point about there being a similar logical structure to these arguments?

  • http://www.blogger.com/profile/05211466026535549638 Bradley Bowen

    P.S.
    It seems to me that the alleged plans and purposes of God are a critical element to both arguments about the origin and nature of the universe and to arguments dealing with miracles, such as arguments for the resurrection of Jesus.

    I think that Swinburne's argument about the resurrection of Jesus sheds light on arguments for God based on the nature and origin of the universe. So, I'm inclined to emphasize and look for analogies between these different sets of arguments about God.

  • http://www.blogger.com/profile/09925591703967774000 Dianelos Georgoudis

    Bradley:

    I agree that arguments for God based on the nature or origin of the universe have a similar logical structure to arguments of God based on miraculous events, namely:

    1. X is more probable on theism than on naturalism.
    2. X is the case.
    3. Therefore theism is more probable than naturalism.

    The problem with miracles it that it is difficult to substantiate premise #2 with X=miracles. I think an agnostic has good grounds to disbelieve in the existence of miracles for reasons such as the following:

    It’s remarkable that miracles such as described in all religious traditions stopped happening just as we had the means to record them. There are still some claims of miracles, but there is consistently no good evidence for them, and in such cases where there is (e.g. miracle cures at Lourdes) there is also a statistical explanation. In the context of Christianity the famous miracle stories in the Gospels, if true, would break the psychological coherence of the story. After all would anybody betray a Jesus who performed such miracles? Would anybody deny Him after he was caught by the Romans? These miracle stories do not work theologically either, for they diminish the value of Jesus’ sacrifice, and make a mockery of the idea that Jesus is a model for us to follow.

    So X=miracles, does not work very well. X=free will, or X=objective moral values, or X=the apparent fine-tuning of the fundamental constants, or X=the intelligibility of the universe, or X=rationality, or X=intentionality (in the sense of “aboutness”), or X=consciousness, or even X=quantum mechanical phenomena – all work much better. And observe that they are all facets of X=our experience of life, so I think that it is when one considers the whole of one’s experience of life that one gets the strongest evidence for theism and against naturalism. As far as I can see, naturalism remains a viable option for many people because from the whole of their experience of life they only consider their observation of objective phenomena (i.e. “the physical universe”) and simply refuse to consider the huge and indeed much more significant fraction of their experience which is subjective, assuming on faith that somehow the latter can be reduced to the former. It’s like a detective shoving all evidence that doesn’t fit under the rug and claiming that that evidence is irrelevant because in the future people will discover how to make it fit. What most naturalists are unaware of is that even if one only considers physical phenomena it turns out that it is very hard to describe a naturalistic reality that would give rise to them.

    Now, one can turn the table and consider arguments for naturalism of the form:

    1. Y is more probable on naturalism than on theism.
    2. Y is the case.
    3. Therefore naturalism is more probable than theism.

    Naturalists have tried Y=the success of science, but this is just a bad move because on further thought it would seem that Y is more probable on theism than on naturalism. The only viable Y seems to be Y=evil. But this famous argument from evil is being constantly eroded by theistic advances towards a successful theodicy, which would explain why, given God’s perfection, one should expect creation to contain evil. And even without a theodicy, it seems that the weight of Y=evil is less than the weight of X=consciousness, because Y is contingent on X: one needs consciousness to exist for evil to make sense.

    So it seems to me that the philosophical scales are moving very fast towards the theistic side, and I find it remarkable that so many intelligent people are still under the impression that naturalism is the intellectually credible option. Perhaps actual beliefs have more to do with custom or with fashion than with critical thought.

  • http://www.blogger.com/profile/05211466026535549638 Bradley Bowen

    Dianelos said:

    I agree that arguments for God based on the nature or origin of the universe have a similar logical structure to arguments of God based on miraculous events, namely:

    1. X is more probable on theism than on naturalism.
    2. X is the case.
    3. Therefore theism is more probable than naturalism.
    ========

    Response:

    I like your formulation in terms of what is "more probable" better than Swinburne's formulation in terms of what is "to be expected".

    I like the direct comparison of metaphysical theories (theism vs. naturalism) being built into the logical structure.

    As you no doubt realize, the conclusion must be qualified as ceteris paribus (other things being equal), because we can have bits of evidence that point in opposing directions.

    If we know that one person committed a murder, and we know that it was either the butler or the maid, then one piece of evidence might point towards the maid as the killer while another piece of evidence points to the butler.

    Let me try to refine your schema a bit:

    T: Theism is true.
    N: Naturalism is true.
    E: [place holder for a factual claim, e.g. The universe is life-friendly.]

    1. P(E/T) = x
    2. P(E/N) = y
    3. x > y
    4. E
    Therefore,
    5. P(T) > P(N) …other things being equal.

    1. The probability of E given Theism = x.
    2. The probability of E given Naturalism = y.
    3. x > y
    4. E is true.
    Therfore,
    5. The probability of Theism is greater than the probability of Naturalism, other things being equal.

    There may be an unstated assumption here as well:

    A. If theism is true, then naturalism is false.

    Of course, other things are not equal, so ultimately bits of relevant evidence need to be gathered together and weighed in some kind of overall evaluation of pros and cons.

  • http://www.blogger.com/profile/00575864305225735387 nazani

    To accept randomness would mean accepting that you are not special.

    Some people I know are even willing to accept the horrific premise that demons are attacking them, rather than accept that a chain of humdrum natural events made a tree fall on *their* house, or that *their* illness is the result of ordinary bad habits.


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