Thursday, September 27, 2012

Bayes’ Theorem and the LCA

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Bayes’ Theorem and the LCA
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A while back the Maverick Atheism blog wrote a rebuttal to the Leibnizian Cosmological Argument (LCA), that was in part a rebuttal to my own series on the Leibnizian cosmological argument (though it was also largely a rebuttal to Christian philosopher William Lane Craig, whose form of the LCA I borrowed).

A Brief Recap

For those who aren’t familiar with Bayes’ theorem, I recommend reading this quick introduction to Bayes’ theorem. To recap my series on the LCA a bit, here’s one of the versions I used (one I labeled LCA 1A):
  1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or an external cause.
  2. The universe exists.
  3. If the universe does have an explanation for its existence, that explanation is God.
  4. Therefore, the universe has an explanation of its existence (from 1 and 2).
  5. Therefore, the explanation for the existence of the universe is God (from 3 and 4).
Premise 1 then is a version of the principle of sufficient reason. Another version of the LCA, one I labeled LCA 3, goes like this, where the contingent universe is the totality of all contingent things:
  1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or an external cause.
  2. The contingent universe exists.
  3. If the contingent universe has an explanation for its existence, that explanation is God.
  4. Therefore, the contingent universe has an explanation of its existence (from 1 and 2).
  5. Therefore, the explanation of the contingent universe is God (from 3 and 4).
I argued that the contingent universe could have failed to exist, and I also argued that the external cause of the universe would have to be an eternal, transcendent, metaphysically necessary, personal entity. Here’s how it worked: The external cause of the contingent universe could not itself be contingent (since then we wouldn’t have an explanation for the contingent universe) and so must be necessary. What is necessary is also eternal, since at no time and in no circumstances can metaphysically necessary entities fail to exist. Since the physical universe itself is contingent, the external cause would have to be nonphysical, and there are only two candidates in the metaphysical literature for nonphysical entities: abstract objects (like numbers) and unembodied minds (like God). But abstract objects can’t cause anything, so the only known viable explanation would be a nonphysical mind. We thus wind up with an eternal, transcendent, metaphysically necessary, personal entity that is the external cause of the universe. I also argued for a more modest conclusion: that the only known viable explanation for the contingent universe is eternal, transcendent, metaphysically necessary personal entity as the external cause of the universe—and that of course sounds suspiciously like theism, enough to make atheism rather implausible if we knew such an entity exists. Hence this toned down version:
  1. Everything that exists has an explanation of its existence, either in the necessity of its own nature or an external cause.
  2. The contingent universe exists.
  3. If the contingent universe has an explanation for its existence, that explanation is is an eternal, transcendent, metaphysically necessary, personal entity.
  4. Therefore, the contingent universe has an explanation of its existence (from 1 and 2).
  5. Therefore, the explanation of the contingent universe is an eternal, transcendent, metaphysically necessary, personal entity (from 3 and 4).
God is classically a metaphysically necessary being (i.e. he exists in all possible worlds) and the external cause of the physical universe. But if God is metaphysically necessary, his existence would also explain why there is something rather than nothing.

Maverick Atheism’s Rebuttal

Maverick Atheism attacked the first premise and argued that perhaps the universe does not have an explanation for its existence. The position he put forward:
So we can accept that ceteris paribus a worldview that explains e.g. why there is something rather than nothing is better than one that doesn’t, but given the plausibility of physical reality existing eternally without an external cause, the degree of evidential support this provides is rather small.
There is an element of plausibility in this; most of us can at least envisage the physical universe existing eternally with no external cause. But now consider the following scenario, borrowing largely from my first article on the Leibnizian cosmological argument.
Suppose we humans learned of an eternally existing monument at the center of the universe that says, “I, the Lord thy God, am the sustainer of the universe and have sustained it throughout all eternity” (if questions of different languages bother you, imagine further that it displays this message through a kind of mechanical telepathy such that anybody who looks at the monument sees the message in her own language).
Most of us can at least envisage the monument existing eternally and without an external cause for its existence. Still, somehow the monument existing eternally with no explanation for its existence sounds rather implausible here. Why?

One factor is the likelihood of there being a monument like this in the absence of a sufficient reason for its existence (like some intelligent entity being the external cause of the monument’s existence), and intuitively that likelihood is low. Where H is the hypothesis (of there being a sufficient reason) and E is the evidence (the monument’s existence), we might say that Pr(E|¬H) is very low. If you’ll recall my quick introduction to Bayes’ theorem, you’ll know that a low Pr(E|¬H) is a factor in making Pr(H|E) high.

Is the likelihood of there being something rather than nothing extremely low in the absence of a sufficient reason, an improbability akin to the hypothetical monument existing without a sufficient reason? Maybe not. Still, the question, “Why is there something rather than nothing?” is interesting precisely because (in the absence of a sufficient reason) it seems like it could have been the case that there existed nothing rather than something. Something very similar holds with the contingent universe, since the contingent universe is the totality of contingent things and thus “no contingent thing exists” is no less a real possibility than “nothing at all exists.” Similarly, “no physical thing exists” is no less a real possibility than “nothing at all exists.” In this article, I’ll examine the insights Bayes’ theorem has on this possibility of there being nothing rather than something.

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