Maths versus Philosophy: Picking teleological arguments apart
Christians often point to teleological arguments as evidence of God’s existence, based on what they perceive as signs of design and purpose in the universe. In essence, they see the chances of the universe being able to sustain intelligent life as so small that there must be design, and therefore a designer, underlying it. And there’s some truth in that – as far as we can tell, the precise conditions and physical laws of the universe do need to be in an extremely precise range. So the odds are massively in favour of a designer, right?
Well, not necessarily – this is an example of the Prosecutor’s Fallacy, as it attempts to draw a conclusion based on the calculated odds of a particular event occurring, not the conditional odds given the known facts. So what’s the difference? With apologies for gratuitous maths, I’ll try to explain with a simple example.
Let’s say you’ve just been screened for a fatal disease, and you’ve been told that the error rate of the screening is 1 in 100. (In reality, there are usually different probabilities for false positives and false negatives, but for the sake of the example, let’s say this error rate applies in either direction.) So given that, if get a letter saying that your screening test indicated that you have the disease, you’d probably start dusting off your will. That’s a reasonable reaction, but it may be premature.
What you don’t know – but is vital to interpreting your test result – is what the odds are of anyone actually having this disease. I expect you’re saying to yourself, “What difference does it make? I know that the test’s right 99 times out of 100, and that’s all that matters.” And you’d be half right. The rate of error is very important to understanding the result, but it isn’t enough on its own.
Let’s say that you were screened because you’re part of a high-risk group with a 1 in 10 chance of having the disease. I’ll attempt to deal in whole numbers, rather than probabilities, in the hope that it’ll make things easier to understand. Remember, the test will give the wrong outcome for 1 in 100 people, so over the course of a million screenings you’d expect roughly these numbers:
In this situation, we know that the screening came out positive, so you’re one of 108,000 in that situation. 99,000 of those will prove to have the disease, meaning that there’s an 11 in 12 chance (91.67%) that you have it. OK, you’re saying, it’s not the 99% I instinctively came up with, but that small improvement in the odds doesn’t exactly offer much comfort. Fair enough. But what if this is routine screening of the general population, and only 1 in 10,000 will actually have the disease?
Now the chance of having the disease is only 99 in 10,098, which equates to 1 in 102, or just less than 1%. Despite a positive result in your screening, you would actually be overwhelmingly more likely not to have the disease – counterintuitive, but true nonetheless, and something that is often taken into account when deciding whether to run screening programmes. So the same error rate can mean very different things: as the basic odds of having a disease lengthen, so do the odds of anyone who tests positive actually having it.
This is directly applicable to the teleological argument: We believe we can calculate the odds of a suitable universe occurring by chance, but that’s only half the story. If we want to know the odds that it occurred by chance, given that we know we live in a suitable universe, we also need to know the relative probabilities of a designer/creator existing or not existing. As that’s the very question teleological arguments are meant to answer, it’s not very useful in drawing a conclusion.
Even if the odds of the universe coming about by chance are vanishingly small, it doesn’t tell us anything about the existence or otherwise of God. We have no way of putting any kind of range on metaphysical questions like God’s existence, so that probability may be much, much smaller than the chance probability of an inhabitable universe, or it may even be zero. Conversely, it may be quite high – the point is that we need to know in order to make sense of the parameters we can actually calculate.
So after all that, we’re back to square one.