Does “Omnipotence” Defeat Itself?
Don’t call it a comeback, call it a comprehensive understanding of the implications of Bayes’ theorem which have added to my seemingly endless list of reasons people should reject the Biblical god. Okay, the name still needs some work but it has been some time since I last explicitly addressed arguments for god. I was sparked out of this pseudo-retirement by the Tom Campbell-Ricketts post on the Bayesian reasoning underlying Occam’s razor which I tried to simplify somewhat yesterday.
The case made by Campbell-Ricketts’ is complex but can be summarized as the observation that increasing the number of free parameters in a theory decreases the prior probability it is correct. Given that the prior probability of each of these parameters is less than 1 (that is less than 100%), then those theories which have models with an infinite amount of parameters, like unfalsifiable claims, combine to have a prior probability of 0 (remember you would be multiplying the prior probabilities of each parameter together, not adding them). And naturally if the prior probability of a theory is 0, the posterior probability, which is the degree of personally warranted belief after seeing the evidence, would also be 0. This clearly eliminates theories which can fit all possible evidence but Campbell-Ricketts was explicitly making the case this also applies to theories of omnipotent beings. He said of omnipotent beings:
…there is nothing that God can’t do if it wants to. That means infinitely many dimensions in the parameter sample space, and therefore infinitely low prior probability at all points.
Though usually not thought of in the same category as unfalsifiable claims, an omnipotent being fits very well into this category of theories which would have infinitely many adjustable parameters. A being which could produce all possible sequences of events would be compatible with any conceivable observation and therefore would have an infinitely low prior probability. A believer may reply “So what a being can’t be omnipotent only? I am not postulating a being that is omnipotent only but rather is omnipotent, omniscient, omnibenevolent, etc.” This is a relevant criticism but for two reasons it doesn’t rescue omnipotence. Firstly, this is merely a redefinition as omnipotence by itself meant “the ability to do anything” but in the need to escape clear self-defeat omnipotence now becomes “the ability to do anything that doesn’t conflict with one’s other properties.” By that definition every sentient being is omnipotent, they can all do anything that doesn’t conflict with their other properties.
At this point a believer may very well concede that their proposed god is restricted in some ways and is not, strictly speaking, omnipotent but they’ll protest “that doesn’t mean a near-omnipotent being with these other traits doesn’t exist.” However, this is where the second problem arises, as Campbell-Ricketts notes:
Every prayer supposedly answered or not answered, every person saved from tragedy or not saved, every event attributed to God’s will represents another degree of freedom. That’s still a tremendous number of degrees of freedom, and while it may be finite, it’s still many orders of magnitude greater than the numbers of free parameters that most specialists would claim to be sufficient for a complete theory of the universe.
In other words, by moving from truly omnipotent to near-omnipotent believers have only moved from as implausible as demonstrably possible to nearly as implausible as demonstrably possible. The amount of evidence needed not to demonstrate such a claim, but merely move it into being remotely plausible would be of such a vast quantity that it’s essentially impossible.
Ultimately, this seems to demonstrate the trait of omnipotence is self-defeating. It’s not logically impossible, as I find omniscience to be, but as a model for a proposed being it’s either certainly unbelievable or mere notches above certainly unbelievable. Simply, compared to theories of the reality which are consistent with what we observe, theories which postulate omnipotent beings will lose every time.
