Tuesday, February 21, 2012

Presently and absolutely undetectable gods

In Strong atheism, two of the classes of definitions of god were absolutely undetectable deities and presently undetectable deities. Commenter Ben Wallis argues that these two classes of definitions render strong atheism untenable because "we cannot speak to the probabilities of deities in general." Ben argues that the definition of essentially undetectable is not, strictly speaking, meaningless, because the existence of an absolutely undetectable deity matters to a deity itself. Wallis argues that in a similar sense to the Bertrand Paradox, we cannot rigorously and unambiguously define the probability of any presently undetectable deity existing. Since we cannot rigorously definite the probability of a presently undetectable deity existing, it is unwarranted to hold any kind of probabilistic belief; weak atheism or agnosticism is presumably the preferred position.

While I don't entirely agree with him, I don't think Wallis is really that far wrong. The undetectable deities are already in the grey area of philosophical hair-splitting; the distinction between strong and weak atheism with regard to undetectable deities is similarly a matter of very fine, hair-splitting distinctions. New Atheism is primarily a political and social movement, and the only definitions that have political and social implications are the detectable, paranormal definitions (which I would assert, contra Wallis, encompasses Yahweh, Jesus and Allah). No actual believer talks about a perfectly deistic god who passively observes the world, and no one actually believes in a scaredy-cat god who's hiding behind the couch. Since the real debate is just about detectable gods (and what, precisely, we mean by "detectable"), we're not giving up any important ground to simply declare weak atheism and agnosticism regarding undetectable gods while still maintaining strong atheism regarding detectable gods.

I do, however, enjoy splitting hairs as much as the next philosopher, so I want to address Wallis' arguments directly.

Wallis argues against strong atheism with regard to to presently undetectable gods by invoking the Bertrand Paradox, which argues that it is possible to have mutually exclusive definitions of "random" that definitely give different answers to questions of probability. But one outcome of a careful examination of the "paradox" is that we can add a qualifier to the definition of randomness — the "maximum ignorance" principle — that seems to categorically disambiguate competing definitions of random: we can consider only those definitions that satisfy the maximum ignorance principle to constitute "true" randomness. If we assume this qualifier, Wallis fails to rebut my original argument.

On another view, the Bertrand Paradox doesn't change our view. If there is some ambiguity in the determination of the probability of some hidden deity existing, the range is either large or small. if the range of probabilities is large, then the definition is too weak to actually name a concept about which anyone can have any sort of belief. If the range is relatively small (e.g. between 10-9 and 10-12) then the ambiguity is irrelevant: no matter what the actual probability is, all the probabilities are low enough to warrant disbelief. Just as science does not include absolute certainty in its definition of knowledge, neither does it include absolute precision.

One might form a definition of a deity for which there was sufficient precision to be coherent and encompass a range of probabilities sufficiently high to warrant at least agnosticism, but I have not yet seen such a definition. The best attempt I've seen so far is the Fine Tuning argument, which has been decisively rebutted in a number of ways.

Wallis' objection to the absolutely or essentially undetectable deity hinges on a particular metaphysical view of ontology and epistemology. The scientific metaphysical system is epistemically prior: scientific ontology is just the narrative of what the world must be like to account for our knowledge. All apparently differing narratives that account for the exact same body of knowledge are, by definition, exactly equivalent. For example, the ontological narrative of (parts of) General Relativity can be expressed in two seemingly different ways: on one view, objects themselves become distorted in a gravitational field; on another, objects retain all their properties, but space itself is distorted in a gravitational field. Although seemingly different, physicists have (I'm reliably informed) determined that these two narratives always have the exact same epistemic consequences, and are thus saying exactly the same thing.

When a pair of statements in conjunction equivalently describe our actual knowledge, it's notable that the alternatives are not inverses of each other. P and not-Q in General Relativity above is not the simple inverse of not-P and Q. (The inverse of P and not-Q is not-P or Q.) Holding them as mutually exclusive alternative formations does not entail any contradiction. We have a different situation, however, when a statement (even a compound statement) and its inverse are epistemically equivalent. In this case, admitting the meaning of the statement entails a contradiction: To say, for example, that God exists and God does not exist are epistemically equivalent statements is to say that P equals not-P. To avoid the contradiction, we have to deny meaning to P: it is a category error to call it truth-apt.

It is not the case that one must adopt an epistemically prior metaphysical system, but neither is it the case, I think, that one cannot reasonably adopt epistemic priority. If Wallis wants to adopt an ontologically prior metaphysical system, then he might find strong atheism untenable, but if he wants to argue that my adoption of strong atheism is unreasonable, then he must either argue that it is unreasonable under epistemically prior metaphysics or he must problematize epistemically prior metaphysics.

Strong atheism, while not necessarily a required position (although I think ontological priority is a much more problematic metaphysical concept than epistemic priority), is, I believe, a tenable position.


  1. Yo Larry. Thanks for the detailed response.

    First a quick clarification: I don't think that we need to "rigorously" define probability measurements. Ordinary "in my best judgment" calls will do just fine.

    Next a more serious clarification: When I said that Yahweh was undetectable in principle, I don't mean to suggest that he is the aloof "his supreme indifference" type of deistic God. On the contrary, he is quite involved in the world, and we can detect all sorts of those effects if indeed he exists. However we will never be able to actually identify this havock-raising being as omnipotent, which is one of God's essential properties. So we might have enough evidence to conclude, say, that Jesus was a true wonder-worker who was sent by a nonphysical being who has an unusual interest in the Jewish people and raised from the dead after being executed by the Romans. And although I can't imagine how, as far as I know it's even within the realm of possibility that we might one day be able to reasonably conclude that all the miraculous events related in the Bible are absolutely true. But we could never rationally conclude that this amazing being is an omnipotent deity whose wishes always come true. So to the extent that omnipotence is an essential property of God, we cannot conclude God exists. (As for why I think omnipotence is undetectable, I have an argument outline here.)

    As for Bertrand's paradox, I think it's a nice illustration of how things can go wrong when we don't actually have a justification for our probability assignments. It is true that we don't have reason to prefer this deity over that one, but I would point out that we also don't have reason to prefer no deity at all over this or that deity. Nor does it follow from the fact that there are X possibilities that therefore each possibility carries a 1/X possibility (or infinitesimal probability, in case X is infinite). So although I don't think the principle of maximum ignorance satisfies Bertrand, that's really beside the point. It was just an illustration to underscore the fact that we don't have justification for a low probability assignment. This is not to say that it should be higher. Rather, we just cannot speak to probabilities, because we have no justification for one assignment over another.

    As for your distinction between epistemically and ontologically prior metaphysics, it seems to me that you are excluding our hypothetical deity when you speak of "our" body of knowledge. If there really does exist a being whose wishes always come true (and who is, perhaps for this very reason, essentially undetectable), then presumably at least the deity knows that he exists and that his wishes are coming true. So the narrative (if you can call it that) seems meaningful in the sense you demand, i.e. it is required to account for the deity's knowledge of the narrative. So if that's what you mean by "epistemically prior," then even an undetectable deity satisfies your requirements.


  2. One addition...

    I confess I'm not really clear on what you mean by "epistemically prior," so if my response to that point was off the mark, that's why. It occurred to me that by "our" body of knowledge you might just mean our own personal, individual body of knowledge. I didn't address this in my last comment because it seemed unlikely at the time you meant such a thing, but now I'm not so sure. But if this is the case, then I wonder what you think of propositions like "p is prime," where p is a number so astronomically large that we could never hope to actually determine if it is prime. Are such statements meaningful in the sense you have in mind? Also, what about statements like, "scientists will discover a cure for the common cold after my lifetime." The truth or falsity of this statement in principle cannot ever be part of my personal body of knowledge, but it certainly seems meaningful.



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