Bayes’ theorem and the Moral Argument

Maverick Christian put up a post on Bayes’ theorem and the moral argument for God. This is not the first time Bayes’ theorem has been used to argue for religious belief, but I’d like to use this example to illustrate a generic problem with such attempts to use Bayes’ theorem.

To define some terms, propositional evidence is evidence that consists of one or more propositions; e.g. I believe evolution, in part, on the basis of certain similarities in Earth organisms, and Maverick Christian believes “objective morality exists” is evidence for theism. For want of a better nomenclature, let’s call a piece of propositional evidence veridically evidential if and only if (1) the proposition is true; (2) the claim it is evidence for is also true. Thus, where M symbolizes “objective morality exists” and G symbolizes “God exists,” the probability that objective morality is veridically evidential for theism is Pr(M & G), since it is the probability that both M and G are true. That probability can be calculated like so:

Pr(M & G) = Pr(M) × Pr(G|M)

The generic problem in using Bayes’ theorem to argue for religious belief is that we are seldom 100% certain of the evidence, and the evidential use of propositional evidence will depend on the probability of the proposition(s) being used as evidence. Suppose, as Maverick Christian suggests for his hypothetical agnostic, that Pr(G|M) = 0.8. What if the agnostic gives “objective morality exists” a probability of only 60%, making Pr(M) = 0.6? Then the probability that objective morality is veridically evidential for theism is only 48%, and by my lights the agnostic should remain agnostic even with the “evidence” of objective morality.

Rebutting the Leibnizian Cosmological Argument for God Part 2

This is part 2 in my attack on the Leibnizian cosmological argument.

1. Rebutting the Leibnizian Cosmological Argument for God Part 1
2. Rebutting the Leibnizian Cosmological Argument for God Part 2

Recap

To recap what we’ve got so far, the Leibnizian cosmological argument (LCA) I’ve been attacking is this one popularized by Christian apologist William Lane Craig:

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 is a version of the principle of sufficient reason (PSR). Call the above version LCA 1A. Another variant on the LCA (which we’ll call LCA 1B):

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 a transcendent personal cause.
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 a transcendent personal cause (from 3 and 4).

LCA 1B is identical to LCA 1A with premise 3 modified to be a more modest claim. I’ve argued that attacking premise 3 doesn’t work out so well if the goal is to prevent evidential support for theism. My position is that the better alternative for the atheist is to believe that the universe exists contingently, eternally without an external cause, thereby rejecting premise 1. Maverick Christian has a number of arguments to support premise 1, and in this article I’ll argue that they fail to be convincing.

Other Variants

Maverick Christian’s series on the LCA has a few other versions. Here’s LCA 2:

1. There is an explanation for why there is something rather than nothing.
2. If there is an explanation for why something exists, that explanation is God.
3. Therefore, the explanation for why something exists rather than nothing is God (from 1 and 2).

And here’s LCA 3:

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 external cause of the contingent universe is God (from 3 and 4).

The “contingent universe” is understood as the totality of all contingent things. The strength of LCA 3 is that it can be used to argue that the external cause of the universe is a metaphysically necessary and eternal entity. How? If we’re looking for an external cause of contingent reality, the external cause can’t be contingent because then it would be a part of the contingent universe we are supposed to be explaining in the first place. As Maverick Christian argues:

But if no contingent thing can explain the existence of the contingent universe, the only hope left is to appeal to a necessarily existing entity. But then the explanation for the universe’s existence is also eternal, since at no time and in no circumstances can necessarily existing entities fail to exist. So we have an eternal, transcendent, metaphysically necessary, personal entity that is the external cause of the contingent universe. This sounds even more like God.

LCA 1B argues that the external cause is transcendent and personal, but LCA 3 argues that not only is the external cause transcendent and personal, it is also eternal and metaphysically necessary, thereby giving us an eternal, transcendent, metaphysically necessary, personal entity as the external cause of the universe. The weakness of this LCA is also premise 1.

A very similar thing holds with LCA 2. I think it’s very likely that if atheism is true, everything is contingent, so that the contingent universe comprises all of reality. If as I say the contingent universe has no explanation of its existence (it is instead eternal and uncaused) premise 1 of LCA 2 is false. Denying premise 2 of LCA 2, while perhaps tempting, should be resisted, for reasons similar to those discussed in my previous entry on the LCA. The best known explanation for the contingent universe (and indeed the only known viable one) is an entity that is eternal, transcendent, metaphysically necessary, and personal. This entity would also be the best known explanation for why there is something rather than nothing. Why? We can posit the entity existing by the necessity of its own nature (roughly, it exists because it cannot fail to exist) thereby explaining why there is something rather than nothing, while this eternal, transcendent, metaphysically necessary, personal entity also explains why the contingent universe exists and why the physical universe exists. Conceding that both the universe and “Why is there something rather than nothing” have an explanation and that the best known explanation is such a God-like entity is conceding far too much to theism than is warranted. Denying that there is an explanation is far more preferable, and the PSR is what I’ll turn to next.

The Principle of Sufficient Reason

Theists offer a number of arguments for thinking that the PSR holds true, or at least holds true with respect to the universe. For the sake of having an easily verifiable source, I’ll quote from Maverick Christian’s series on the LCA.

The Nature of Rational Inquiry

One point made in favor of the PSR is that it’s the nature of rational inquiry to look for explanations of things. From the article:

It’s the nature of rational inquiry to look for explanations for why things exist. We seek explanations for the existence of humans, of planets, of stars, and of galaxies. Avoiding all that and saying, “It all just exists inexplicably” would cripple science. And if we are rational to accept that there are explanations for the existence of planets, stars, and galaxies, why not also accept that there is an explanation for the existence of the physical universe?

A good question. If we said that there was an explanation for the existence of planets, stars, and galaxies, it would be arbitrary to exempt the universe without good reason. But there’s a criterion that all planets, stars, and galaxies meet that the universe doesn’t: they begin to exist. Consider this weakened form of the PSR (what we can call W-PSR):

(W-PSR)

Anything that begins to exist has an explanation for its existence.

This weakened form of the principle of sufficient reason also fits in with common sense. Imagine for example you find a statue of the great atheist philosopher Bertrand Russell in your room and you ask me how it got there. If I say the statue popped into being in your room uncaused and for no reason, you would rightly disbelieve me; my proposed hypothesis would be a bit too much like magic. Similarly, if I say that stars, planets, and galaxies simply appeared for no reason at all (and thus that the explanations offered by astrophysics are wrong), you should resist that view in favor of there being an explanation. In cases where the things-to-be-explained begin to exist, it’s quite sensible to ask for explanations for why they exist, because the alternatives (them coming into being uncaused for no reason) are implausible. In contrast, if I propose that the physical universe exists eternally with no external cause, there doesn’t seem to be anything implausible about that alternative, and it’s unclear why the nature of rational inquiry should say otherwise.

If the theist wants to insist that the physical universe has a transcendent personal cause behind it instead of the universe being eternal and uncaused, it seems something more is required than the assumption that everything has an explanation for why it exists, even eternal things. So we can exempt the universe from automatically requiring an explanation for a non-arbitrary reason: things that begin to exist require an explanation, but physical reality (so many atheists believe) is eternal and didn’t begin to exist. At any rate, the alternative hypothesis of the universe existing eternally without an external cause is at least plausible and requires more than bare assumption of its falsity to believe that it is in fact false.

The Translucent Ball

The second argument I’ll address is the illustration of the translucent ball, popularized by (among others) William Lane Craig.

Here I’ll borrow a bit from philosopher Richard Taylor’s illustration of finding a translucent ball in the woods. “How did it get there?” you ask. I reply, “There is no explanation for it being in the woods; the ball just exists inexplicably.” My response seems less plausible than the idea that there is some explanation for the ball’s existence. What if we enlarged the ball to the size of a car? Same problem: some explanation seems to be needed. How about a city? Same problem. A planet? Same problem. A galaxy? Same problem; increasing the size does nothing to remove the need for an explanation.

True enough, increasing the size of the translucent ball does nothing to remove the need for an explanation (let us also assume arguendo that all translucent balls are contingent). Size doesn’t matter, but what does matter is whether the translucent ball existed eternally. It is quite conceivable that there are possible worlds where a translucent orb has existed for all eternity without an external cause. If we had no evidence that the translucent ball began to exist, it would seem at least premature to simply assume it had an external cause. Of course, if we had evidence that the eternal translucent ball had an external cause that would be a different matter, but we would need evidence that eternally existing ball had an external cause rather than just assuming it had one.

The Shoe On the Other Foot

So far then, we don’t really have a good reason for thinking the PSR holds with respect to the universe, but there is one other interesting point worth considering. Maverick Christian says that

suppose some contingent thing X meets the following conditions:

1. X is eternal but contingent (it could have failed to exist).
2. There is an explanation for why X exists.
3. It is the only explanation of X’s existence that is a live option.
4. There is no reason to believe that this explanation for X’s existence is false.

I think that if we know that all four conditions are met for thing X, then we should accept that explanation for X if we have no good reason not to. In considering these conditions it might also help to envisage the shoe being on the other foot. Suppose we had an explanation for the physical universe’s existence that was devastating to theism and the explanation met conditions 1 through 4 (it explains why the universe exists, there is no other viable explanation etc.). I have a hard time believing that atheists wouldn’t use this devastating-to-theism explanation as evidence against theism. Moreover, it seems they would be right to do so if their explanation for why the universe exists rather than not is the only viable explanation, there is no evidence against the explanation etc.

I’ll grant that atheists having an explanation for the existence of the universe fitting the above description (devastating to theism, no other viable explanation etc.) would result in correctly concluding that the explanation has at least some evidential force against theism. Typically we accept a theory explaining something (when there is no better explanation) as evidence for a theory, e.g. the big bang theory explaining the cosmic microwave background radiation. But there’s a weakness to exploit here that I think is all too often overlooked with theistic arguments. One way an argument can fail to be convincing is if it provides no rational support for its conclusion, but we should not make the mistake of thinking that’s the only way an argument can fail to be convincing. Another way is if the argument provided nonzero but nonetheless too little support for its conclusion. 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 high plausibility of physical reality existing eternally without an external cause, the degree of evidential support this provides is quite small. This, I submit, is the real weakness of the LCA and the real reason atheists should embrace for thinking the Leibnizian Cosmological Argument to be not a particularly good argument. The alternative hypothesis that the universe exists eternally and uncaused is conceivable and too plausible to ignore, with only very weak grounds for thinking it does in fact have an external cause.

Rebutting the Leibnizian Cosmological Argument for God Part 1

This is part 1 in my attack on the Leibnizian cosmological argument.

1. Rebutting the Leibnizian Cosmological Argument for God Part 1
2. Rebutting the Leibnizian Cosmological Argument for God Part 2

The Argument

In this article I’ll rebut the Leibnizian cosmological argument (LCA) for the existence of God. There are many forms of the LCA, but for starters I’ll refer to this one as used by one popularized by Christian apologist William Lane Craig. I’ll also taking a bit from Maverick Christian’s blog article on the Leibnizian cosmological argument which (among other things) tries to present more defensible versions of the LCA.

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).

The principle of sufficient reason (PSR) says that everything (of a certain class) has a reason/explanation. The PSR comes in many forms, but the version this version of the LCA uses is premise 1. Premise 1 is also the weakest part of the argument, and the one I’ll attack in my series on the LCA. My alternate hypothesis is this: the universe exists eternally, with no explanation and no external cause of its existence. Still, let’s briefly discuss the other premises.

Premise 2

Pretty obviously true; no sensible atheist would deny this. By “the universe” the LCA means all of physical reality. The universe clearly exists.

Premise 3

In another version of the LCA (and in my opinion a more defensible one), Maverick Christian has “If the universe does have an explanation for its existence, that explanation is a transcendent personal cause,” and let’s call that the “weak premise 3” and let “If the universe does have an explanation for its existence, that explanation is God” be the “strong premise 3.” The weakened version of premise 3 is just in case the atheist insists on not having God as an explanation. Some terminology intro:

What does it mean to exist by the necessity of its own nature? A thing’s existence being metaphysically necessary means it is impossible for it to not exist (whereas contingent things both could exist and could have failed to exist, e.g. my own existence is contingent) and thus metaphysically necessary things exist in all possible worlds (where a possible world is a complete description of the way reality is or could have been like; thus “all bachelors are unmarried” is true in all possible worlds whereas there are possible worlds with different physical laws than ours, hence science’s need for empirical investigation). Some philosophers and mathematicians think that abstract objects like numbers exist necessarily.

Some consider “it is not the case that torturing infants just for fun is morally right” is a metaphysically necessary truth. Why can’t the universe’s existence be necessary? To quote from the blog:

There doesn’t appear to be any physical part of physical reality that is metaphysically necessary (e.g. stars and planets are contingent and indeed at one point they failed to exist; there are also no molecules that couldn’t fail to exist) and with that in mind consider the following argument from subtraction. Is a universe with only a thousand physical things possible? It seems so. How about a hundred? Sure. How about ten? How about five, four, three, two, and one? How about none? It seems like there is some possible world where no physical reality at all exists. (Notably, if nothing existed at all, this would fit in with the PSR since if literally nothing exists then there isn’t anything to explain.)

Maverick Christian argues further for the non-necessary nature of the universe’s existence, but I think this is enough to render the necessary existence of physical objects implausible. Why think “If the universe does have an explanation for its existence, that explanation is a transcendent personal cause” is true? To quote:

If we go the explanatory route of some external cause of the universe, an external cause of all physical reality would have to be nonphysical, and there are only two sorts of things we know of that could fit requirement: abstract objects (like numbers) and unembodied minds (e.g. God, if he exists). But abstract objects can’t cause anything. So the only viable candidate for a nonphysical cause seems to be a personal cause.

Not only am I prepared to grant that the weak premise three is probably true, I’ll even endorse the strong version. Why? Premise 3 is most charitably understood as a material conditional. In philosophy and logic, a material conditional takes the form of “If p, then q” and it is equivalent to “It is not the case that p is true and q is false.” Thus what determines the truth of a material conditional is the truth of p and q as follows:

p	q		If p, then q
T	T		T
T	F		F
F	T		T
F	F		T

In the second line of the table where p is true (T), and q is false (F), the material conditional is false; otherwise the material conditional is true. This might sound odd, but a true material conditional is often good enough for deductive arguments like this, because when p is true, then q is true as well (since q can’t be false when p is true). Notice also from the table above that whenever p is false, the “If p, then q” material conditional is true. So by believing p is false one is accepting the material conditional, and thus when “If the universe has an explanation of its existence, that explanation is God” is a material conditional, by believing “the universe has an explanation of its existence” to be false (I’ll argue the universe has no explanation, that it is eternal and uncaused), I would be accepting premise (3) as true. Another way to look at it is this: I think it’s very likely that if atheism is true, the universe has no explanation of its existence (if atheism is true, it seems most likely that the universe is eternal and uncaused), but “If atheism is true, then the universe has no explanation of its existence” is logically equivalent to “If the universe has an explanation of its existence, then God exists” which is pretty close to the neighborhood of the strong premise 3.

So we can reject the argument’s conclusion by denying the universe has an explanation of its existence (a strategy I’ll defend more later) and while that means we must accept premise 3 as true, that’s hardly a fatal problem for atheism. So let this be a lesson: just because an argument is unsound, doesn’t mean that every premise is false. I propose that the universe has no explanation of its existence; it’s not metaphysically necessary, but neither does it have any external cause. This entails accepting the third premise, but we still avoid the conclusion.

But can’t an atheist believe the universe has an explanation? An atheist could, but at his peril. The universe does not plausibly exist necessarily, and an external cause of all physical reality will have to be something nonphysical. Once you go there (a nonphysical entity/force causing the physical universe to exist) by my lights you’ve already admitted some kind of supernatural force creating the universe, whether it be a deity or something else entirely. This would be conceding far too much to the theist than is warranted.

What’s worse, the only nonphysical entities in the metaphysical literature are unembodied minds and abstract objects (like numbers), but abstract objects can’t cause anything, leaving a transcendent (nonphysical) personal cause as the only known viable explanation. Yes, one could say maybe there’s a better explanation nobody’s ever thought of, but conceding that the universe has an explanation of its existence and that the best known explanation is a transcendent personal cause is again conceding far too much than is warranted (not to mention, as Maverick Christian points out in his LCA article, bare possibility of a better unknown alternative isn’t enough to reject an explanation; we wouldn’t reject the big bang theory because maybe there’s a better theory nobody’s ever thought of). Indeed, that the universe has an explanation of its existence and that the best known explanation is a transcendent personal cause—and that a transcendent personal cause is the only known viable explanation—would unavoidably constitute at least some degree of evidential support for a creator deity. So if the goal is to prevent the LCA from being evidence for theism, conceding an external cause of the physical universe is a terrible way to go. The atheist should avoid this if there is a better atheistic alternative, and I think there is.

What we’ve got so far

Some ill-advised moves for the atheist are:

1. Saying that the universe’s existence is metaphysically necessary.
2. Conceding that the physical universe has an external cause of its existence.

The first option is implausible, and the second grants too much evidential merit to theism that we don’t need to give it. Theists offer a number of arguments for their claim that the universe has an explanation of its existence, and I’ll argue that the arguments fail to present a convincing case for the third premise in my next entry, Rebutting the Leibnizian Cosmological Argument for God Part 2.

Why William Lane Craig Wins Debates

Fort those who don’t know, Dr. William Lane Craig is a renowned Christian apologist and fairly well known philosopher of religion (among philosophers of religion at least). Dr. Craig has gained notoriety in the world of internet atheism for his debates with atheists and almost always winning those debates. So why does he win them?

Craig wins because his opponents present an inadequate case for atheism. Yes, there are some exceptions, but consider the debates between various atheists and Craig, e.g. the William Lane Craig versus Christopher Hitchens debate (it starts at around 13 minutes; and while it is an admittedly extreme example of an atheist presenting an inferior intellectual case for atheism, it illustrates the point well especially since Hitchens was such a huge influence in the New Atheist movement). Some will credit Dr. Craig’s large proportion of debate victories to some vaguely described debating skills, but the truth is that Craig usually wins because atheists fail to do atheism the intellectual justice it deserves. Indeed it happens so often I’m surprised more atheists don’t see this. And while there are exceptions, all too often I’ve seen internet atheists do a poor job arguing for atheism (there are abundant examples on YouTube). Hence this blog: I want to do my part to show how formidable an opponent atheism is to theistic belief, e.g. my blog entry introducing the argument from evil.