Thursday, September 13, 2012

Rationalism Precludes Theism

I just had a long Facebook discussion about what it would take for a rationalist to believe in god.  I raised the question because the better we know exactly what sort of evidence would be required for rational theism, the more justified we are in not being theists.  It turned out to be very difficult to imagine what evidence would suffice.  In the end, I was able to prove that there are no conditions under which it would be rational to believe in god.  This surprised me, so I thought I’d share my argument.

I'll start with bunnies. One person said they’d believe in god given fossil evidence of Cambrian rabbits.  That seemed pretty weak to me at first, but I thought I should at least think it through.  I'm imagining that tomorrow morning I wake up to coffee and NPR, and find that the main story of the day is a claim that archeologists uncovered fossils from the Cambrian. My first thought is, "Simple mistake. Someone misrepresented information, got confused, fabricated evidence, etc." I do some research. It probably is a simple mistake. But suppose it isn't. Next, I think, "Earthquake anomaly." That seems pretty likely. More research. Along these lines, I entertain increasingly unlikely hypotheses (in careful order). "God did it" is nowhere near the beginning of the list. Part of that is because I'm not sure what it means, but I'll get back to that. I'd be getting near the neighborhood of god territory about the time I started hypothesizing that Earth is an alien science fair project and the rabbit fossil is left over from a test run that got a little messy and wasn't cleaned up all the way. That would indeed involve an intelligent creator of the human race, but it's quite a long way from, say, omnipotence, omniscience, omnipresence, and omnibenevolence.

The first problem with imagining sufficient evidence for belief in god is this: There are a whole lot of things we could mean when we say "god exists".  Not all of them are equally likely. Nor does one kind of evidence justify belief in all of them. "God" is fuzzy. Much like bunnies. It's semantically ambiguous and vague.  So if we want to know what it would take to reasonably believe in god, we’re going to have to figure out what it would take to reasonably believe in a pretty diverse range of entities individually.

That's one of the most frustrating things about talking with theists; they're quick to tell you what they don't mean once they've determined you're arguing for a god in whom they don't believe either, but they usually aren't so quick to pin down what they really do mean. When you try to reason with a theist, therefore, it’s a good idea to ask them explicitly what they mean by god even before you tell them that he doesn’t exist.  With many you get the impression that they themselves don't know that they mean. You'll talk with them for a long while, thinking you're getting somewhere, and then when you bring them to a conclusion they don't like but can't avoid, they say, "Well sure, but that's not what I mean by 'god'. What if god is really x?"

Legend has it that Paul Spade was once teaching a seminar on the philosophy of theology when someone pulled one of these. Another student gave an exasperated sigh, turned to the first student, and remarked, "Look, what if god is a garage in New Jersey?"

This succinctly expresses a rationalist’s frustrations with fuzzy notions of god, but let’s see what happens when we take the question seriously.  If god is a garage in New Jersey, convincing me of his existence is a fairly simple matter. I already have an awful lot of good reasons to think that there are garages in New Jersey, so showing me a picture of the particular one you're talking about would be plenty.  But this form of theism is neither interesting nor useful.  I really hope conceptions of god never get so boring as to be confined to garages in New Jersey.

So now let’s look at the somewhat more serious kinds of gods who are merely responsible for purposefully creating humans.  In light of the many observations about the universe we've so far made and systematically evaluated through science, it is tremendously unlikely that the human race was intelligently created.  Finding rabbit fossils would indeed be evidence for intelligent creation, because the probability of intelligent creation would be slightly higher after throwing large chunks of our model of biology into doubt.  But it's horribly weak evidence, especially relative to its strength for alternative hypotheses that are far more in line with the vast majority of what we've so far observed. It would be utterly irrational to believe even in the very weak meanings of god on the basis of Cambrian rabbits.  (Obviously, this isn’t evidence at all for garage-gods, since garages are equally likely to exist whether or not there were rabbits in the Cambrian.)

If god is simply any conscious thing that purposefully created the human race, then here is an example of what would convince me. A very long-lived alien could land on Earth, show us the blueprints, and explain how it did it and why. Well, that wouldn't quite be enough, because the alien could be lying. (I mean, come on, you're a brilliant alien who's run into an extremely credulous species that likes to worship even evil gods. Honesty, or godhood? I could see lying.) But if we took those blueprints, showed that they account for all pre-existing observations, and made some predictions based on them whose truth would be in direct contradiction with our current model, then we could test those predictions and the right results would convince me that we were in fact created intelligently by this alien. Which, by that definition, would mean I'd become a theist.

But for meanings of god that are bigger than this (for instance, a being that is omnipotent), I run into the following problem. It is much, much more likely that there exists a being who is capable of causing me to experience whatever it chooses, regardless of what's actually going on outside of my head, than it is that there's a being who really does possess such properties as omnipotence and omniscience. Why?  Because of conjunction. 

For any events x and y, the odds of x happening cannot be greater than the odds of x and y happening.  To figure out the base probability that x and y both happen, you multiply the odds of x by the odds of y.  Odds are expressed as percentages or fractions, so you’re multiplying something less than one by something less than one, which makes the product even smaller than either factor. 

It would take a definite, finite amount of power and/or knowledge to appear infinitely powerful or knowledgeable.  There’s a certain set of things you’d have to know or be able to do in order, say, to run a computer simulation of a lifetime’s worth of human experience.  There is probably a very large number of things you’d have to do, and many of them may be awfully improbable, but because the set isn’t infinite, the probability isn’t infinitesimal (provided the set is well founded—that is, no item on the list requires that you be able to do all the things on the list).

A being with those powers could cause me to experience what I would ordinarily take to be evidence of extraordinary things. There is a certain degree of extraordinaryness beyond which it becomes less likely that the thing I’m experiencing is actually happening than that someone is purposefully monkeying with my subjectivity. For instance, perhaps I am actually a program running on the hard drive of some human’s computer from the future.  Perhaps the future human is amused by the game of creating consciousnesses solely for the purpose of messing with them. That would have to be sort of an evil person, but I must admit it's exactly my kind of evil.
But is a creature with the power to create such a simulation rightly called a god? If so, then any experience (or group of experiences) beyond the subjectivity-monkeying threshold would make me a theist. But this god is infinitely less powerful than an omnipotent god, so again, that's a long way from the god most theists seem to believe in.  They want a god who can do anything.

I'd planned to claim next that only an a priori proof for any god less likely than the monkeying version would do, but it now occurs to me that even that would be insufficient  With a slight modification, the monkeying-god becomes Plato's evil demon.  

Plato described a demon whose only purpose in life is to make us miscount the number of sides on a triangle.  It could be that there are not actually three sides to a triangle, provided that every time we try to count the sides of a triangle, we make a mistake.  This problem is bigger than triangles.  If the monkeying god can control every aspect of my subjectivity by changing lines of computer code, he could cause me to reason incorrectly about even an apparently iron-clad mathematical proof.  And this, too, would be much more likely than anything even close to the god(s) of the theists.

Note, by the way, that even the first version of the monkeying god isn't necessary for experiences of direct revelation. If an experience could possibly be caused by a malfunctioning (or strangely functioning) human brain, it's not sufficient evidence for theism. Simple hallucination happens all the time. I came up with the monkeying god to account for experience that couldn't be pathological. Here's an example of the kind of experience I'm talking about (adapted from a splendid scene by Eliezer Yudkowsky in Harry Potter and theMethods of Rationality).

You hand a very large list of prime numbers to a friend and tell him to select two four digit prime numbers (without telling you what they are) and write down their product. He returns a paper on which is written "16285467". You walk outside directly afterward, grab a shovel, pick a random chunk of ground, and start digging. Five feet down, you hit a rock. Upon examining the rock, you find that it contains fossilized crinoid stems on the surface (and may or may not contain a rabbit in the middle, presumably from the Paleozoic this time). On one side, the crinoid stems are configured to write out "2213". On the other side, the crinoid stems say "7359".  Actually imagine that this has happened, and imagine how you would react.  “I must be hallucinating” probably wouldn’t satisfy you, for you lack the ability to factor eight digit numbers in your head.

Now, this isn't a perfect example, because it wouldn't be impossible to hallucinate this of your own accord. But it would indeed be incredibly unlikely (literally), far more so than anything people experience when they claim to communicate directly with god.  I'm not sure whether it would be more likely that an external agent is messing with your mind than that you happened to hallucinate it accidentally.  Or that you're actually that damn good at prime factorization.  Or that you multiplied every set of pairs of four digit numbers with one member less than half of 16285467 without noticeably aging and then promptly forgot about it.  But if it happened several times in a row, or many similar things happened, at some point the pathology position becomes untenable and it's time for the monkeying god hypothesis to step in.

Therefore, it's never rational to believe in an Allah or New-Testament-style god, because whatever your reason for suspecting that god is responsible, it’s more likely one of the less powerful versions of a god is the cause.  

I'd originally intended to figure out exactly what it would take to convince me of the existence of something like the Catholic god, but it appears this really is a special case.  Even if god does exist, there simply are no conditions under which it's rational to believe in him (unless you're willing to give the name god to something more like a garage in New Jersey).

1 comment:

Anonymous said...

Suppose you ask God to perform a random ten actions - like "move the stars in the sky", "flip Britain along the north-south axis", and "factor a 100 digit prime number" - and He does.

After a certain number of these, it's more plausible that God has complete power (omnipotence) than that by coincidence you just happen to have chosen the few areas He has power over.

So the argument that "since we can only put God through a finite number of tests, we can never prove He's omnipotent" is true on the "proof" level but fails on the probabilistic level.

The same might be true even if we grant God can affect your subjective experience. Any being that, for example, can teleport you to China and then simulate your life in China for a year in high-fidelity, show you an elegant proof of an unproven mathematical theorem (even if it has to fudge your mental processes to make you believe it) and show you breathtakingly beautiful art beyond what you could have conceived possible has just satisfied three independent tests for being really impressive (if only in mental manipulation).

Past a certain level, believing it is all-around impressive is simpler than believing it is impressive in only the ways it has shown you, and so you at least have high probability evidence for God or for something that you should probably call God since no conceivable test could possibly differentiate it from God (including the test of it being able to send you to Hell if you don't call it God).