Theism vs Atheism

An Argument from Probability

In #Unbelievable Project

On a recent Unbelievable podcast there is a discussion between Calum Miller and James Croft on the topic "is our universe more likely on atheism or theism?", where Calum introduces probabilistic arguments throughout. Although James does a good job of pressing Calum's arguments in weak points, and framing the argument in a more coherent way, I think there is much more to be said about the weaknesses of this particular argument, and the framing of these problems in terms of probability. There is a danger in this sort of thing of using mathemtics to give the veneer of authenticity to an argument that is riddled with random guesses, ill-defined concepts, and unsupported premises. Let's start with some quotes from the episode, so we can see where this is going.

The Argument

Calum - "I think one useful way of thinking about is is to consider what evidence is in general. When we think about evidence for a theory, in this case the theory is that God exists - we want to explain some features of the world, we look for things (observations) which are surprising if the theory isn't true but which aren't that surprising if the theory is true."{.tq}

Calum then goes on to do an analogy with fingerprints on a murder weapon. And then points out the observation that he believes is evidence for God. {.theist}

Calum - "There are a number of arguments that work this way. But one of the partiular pieces of evidence that I want to discuss today is that the world exhibits a real kind of regularity and there are basic laws, science works, that we can understand the world. For all we know, the universe could have been chaotic, might not have been any laws at all, we might not have been able to do science - it might have been complete chaos. "{.tq}

Here he's describing the form of the argument, as it might apply to the sun rising.{.theist}

Calum - "Even more basic things that we use scientific reasoning for, but do not always strike us as scientific truth. For example, 'the sun will rise tomorrow'. Most of us believe that. This is a common-sense inference from our observations. On atheism to expect that regularity, for the sun could just fail to rise tomorrow, but on theism we can expect that kind of regularity because God set it in place. [...] That's just one example, and you'd need a lot more for the full argument."{.tq}

He finishes by describing how moral responsibility hinges on this regularity, because I need to know the likely effect of my actions on others in order to make moral decisions and be responsible for them. If things were chaotic, if my actions had random effects, then moral responsibility could not work.{.theist}

The problem with the math - posteriors vs likelihoods

The first problem that struck me was that, from a math point of view, he is simply doing a likelihood ratio:

\begin{eqnarray} \frac{P({\rm data}|{\rm theism})}{P({\rm data}|{\rm atheism})} \end{eqnarray}

and saying that this is greater than one, and thus theism is more likely. That is just the wrong question to ask. What we really want to look at, even keeping the same structure, is the ratio of the posterior probabilities, or

\begin{eqnarray} \frac{P({\rm theism}|{\rm data})}{P({\rm atheism}|{\rm data})} \end{eqnarray}

which is related to the likelihood ratio through Bayes' theorem:

\begin{eqnarray} \frac{P({\rm theism}|{\rm data})}{P({\rm atheism}|{\rm data})} &=& \frac{P({\rm data}|{\rm theism})}{P({\rm data}|{\rm atheism})} \times \frac{P({\rm theism})}{P({\rm atheism})} \end{eqnarray}

where we factor in the prior probabilities. Already, we have an issue, because the prior probability for the universe with an extra agent should be smaller than one without such an agent. If you factor in the an agent with many specific properties, then this is smaller still. By omitting this part, you could argue for anything. For example,

\begin{eqnarray} \frac{P({\rm data}|{\rm fairies})}{P({\rm data}|{\rm no-fairies})}>1 \end{eqnarray}

or the regularity of the universe is much more likely given fairies than no-fairies, so that is evidence for the fairies. Even if true, it is clearly an uninteresting and unuseful claim.

The problem with the premise regarding theism

The next problem that struck me was that it seemed that Calum was trying to sneak in many more details into his theism than his argument would warrant. He needs to define what he means by theism to state that it is more likely to result in a regular universe. For example, a number of counter examples can be made:

  • Under the Greek pantheon, it is more likely that things would be chaotic, at the will of capricious deities
  • Gods or divine beings, such as Cthulhu, revel in chaos and thus would make it less likely to result in a regular universe

So when Calum says "theism", what he seems to mean is the existence of "order-making Gods", but then his argument is circular: a regular universe is more likely under a regular-universe-making God hypothesis than not.

The problem with the premise regarding atheism

Further, Calum never supports (and James reiterates this many times) that it is unlikely to have an ordered universe under atheism. "For all we know, the universe could be chaotic", Calum says. However, that needs to be demonstrated, not asserted, or it is an argument from ignorance in disguise. It is possible, and in fact cosmology seems to be pointing more in this direction, that the universe could not be any other way - that the regularity is the result of the production of any universe, and further that the production of universes is the only stable solution. The notion of philosophical "nothing" may be physically unstable and thus unlikely to ever exist.

Concluding thoughts

I find Calum's introduction of morality to the argument adds nothing, and only serves as a red herring. Without some regularity in the universe, even thought itself would be impossible . We couldn't even have the idea of a "being", or an animal, or life without regularity. Thus, our mere existence requires regularity - but one that need not be imposed from the outside, with a God. Introducing the notion of a generic theism causes more problems to the argument than it solves, because it includes Zeus and Cthulhu. Circularity results when restricting the relevant theism to exclude these possibilities. Even if Calum solved this, the basic set-up of the problem is answering the wrong question, and is at best an uninteresting and useless result.

There is more to this episode, which I'll address later, but these objections are enough to derail the entire argument Calum makes.