General Theism (Part 5): Disproving God?

Before we dive into a couple of the strongest arguments against God’s existence, let’s lay some groundwork; in particular, how can one argue for a negative (“God does not exist”)? What would evidence against God look like?

I’ll discuss here the basics of Bayesian statistics, but I’d encourage anyone interested in mathematics or good argumentation to look into it further themselves. Essentially, when comparing two hypotheses P and Q to see which of them we ought to believe, we should consider the implications of P and the implications of Q and compare them to our observations. If a particular circumstance (let’s name it E) is more probable given P than it is given Q, then E is evidence for P (i.e. upon discovering E, we should be more confident of P and less confident of Q, though we may still believe Q on the basis of other evidence).

Let’s consider a simple example to get our heads fully around the concept. Suppose that you think there’s a 90% chance your friend is out of town. Based on prior experience, you know that there’s an 80% chance his lights will be on if he’s home but only a 5% chance that his lights will be on if he’s out of town. If you then drive by his house and discover that his lights are on, you need to adjust your confidence that he’s actually out of town – intuitively, we can see that this will decrease our confidence that he’s out of town because the lights being on is more expected if he’s in town than if he’s out of town. Bayes’ Theorem actually lets us produce numbers – you should now think that there’s only a 36% chance that your friend is out of town (and therefore a 64% chance that he’s home). So in this case, the evidence of the lights being on was strong enough to change your mind – whereas it was previously more likely that your friend was gone (90/10), it’s now more likely that he’s home (64/36).

So in seeking to provide evidence against the existence of God, the operative question will be “what aspects of reality are unexpected on theism but expected on atheism?” Circumstances with larger gaps in “expectedness” get weightier consideration – if something is 50% likely on atheism and 49% likely on theism, that’s probably not gonna change anyone’s mind unless they were already perfectly on the fence. 30% to .001%, on the other hand, will carry a lot of force.

We can also use our new understanding of evidence to quickly deal with a really bad objection to God’s existence along the lines of “we can’t directly observe Him.” Now since we can’t directly observe something that doesn’t exist, this observation is extremely expected on atheism. But since God is by definition immaterial and transcendent, we wouldn’t be able to directly observe Him on theism either! So this observation has practically no expectedness gap – it’s utterly mundane and expected for both the theist and atheist and hence doesn’t count as evidence for either.

Just as for theism, though, the abundance of bad atheistic arguments doesn’t imply that there aren’t also good ones. In our next two posts we’ll examine the problems of evil and divine hiddenness; our task will be to assess how big the “expectedness gap” is, and in particular whether it’s large enough to overwhelm the positive arguments we’ve presented.