Since I had my debate with Luke Barnes, I have received quite a few questions about different objections to fine tuning, and easily the most common one is the ‘but God could do anything’ objection. The idea is like this. God could have made a world in which there was ‘corse-tuning’. In such a world, the laws of physics are such that if you varied the values of things like gravity, the entropy of the early universe, the mass of the electron, etc, you would still have circumstances in which life as we know it could survive. Why think that if God existed then we should expect to find fine tuning? Surely, fine tuning is evidence against God? I take it this is the ‘God could do anything’ objection.
“Suppose that you’re captured by an alien race whose intentions are unclear, and they make you play Russian roulette. Then suppose that you win, and survive the game. If you are convinced by the fine-tuning argument, then you might be tempted to conclude that your captors wanted you to live.
But imagine that you discover the revolver had five of six chambers loaded, and you just happened to pull the trigger on the one empty chamber. The discovery of this second fact doesn’t confirm the benevolence of your captors. It disconfirms it. The most rational conclusion is that your captors were hostile, but you got lucky.
Similarly, the fine-tuning argument rests on an interesting discovery of physical cosmology that the odds were strongly stacked against life. But if God exists, then the odds didn’t have to be stacked this way. These bad odds could themselves be taken as evidence against the existence of God.”
This is an interesting argument. I think it is a good argument. However, I think it is not the slam-dunk that some people seem to think it is. It shows that in some sense, the existence of God is very very unlikely. However, it really poses no objection to the fine tuning argument as such.
In this post, I want to explain why this is the case.
- Doing the maths
Part of explaining the power, and limits, of this argument requires doing a bit of maths. Firstly, we need to set out the terms involved. The idea of fine tuning is that if we vary the physical parameters of the universe by a tiny amount, then the universe becomes hostile to life as we know it. Roger Penrose expresses the odds against this happening as less than one part in ten to the power ten to the power one hundred and twenty three, or:
That is a stupidly small number!
Let’s call this fact F (for Fine tuning). Let’s call the fact that the universe is hospitable to life L, and let’s call the hypothesis that God exists G. Not all cosmologists accept the fine tuning of the universe, but a lot of them do (in some sense or another at least). Regardless of whether it is true, we can agree that if it were true, then the chances of life existing, as it were by chance, are low in the following sense, and using Penrose’s numbers:
- P(L | F) = 1 /
(The probability that the universe would be life-permitting, given fine tuning, is stupidly low)
Let’s also say that, because God is good, and because life is good, God favours universes that are life-permitting, in the following sense:
2. P(L | G) > P(~L | G)
(The probability that the universe would be life-permitting given that God exists is higher than the probability that the universe would not be life-permitting given that God exists)
However, if you believe in both God and fine tuning (as people like Robin Collins or Luke Barnes do), then you believe in something only a tiny bit more likely than that the universe is life permitting by pure chance. This is what the ‘God can do anything’ objection’s most interesting implication. Here is how it works.
Firstly, let’s add in the fact of fine tuning into the conditional hypothesis in 2:
3. P(L | G & F) > P(~L | G & F)
The idea is that the proponents of fine tuning who are also theists believe both G and F to be true. F is part of their background knowledge, as it were, so we can add it in to the right side of each conditional probability. The fact of life is more likely on God and fine tuning, than no life is on God and fine tuning. Now, we can use the conditional probability formula (see it here) to express P(L | G & F) differently. The formula says:
P(A | B) = P(A & B) / P(B)
In our case, A = L and B = G & F. If we plug them in, we get:
4. P(L|G & F) = P(L & G | F) / P(G | F)
(The probability that the universe is life permitting, given God and fine tuning, equals the probability that the universe is life permitting and God exists, given fine tuning, divided by the probability that God exists given fine tuning)
We can do exactly the same thing for the other side of 3 (which just uses ~L instead of L):
5. P(~L|G & F) = P(~L & G | F) / P(G | F)
3 says (effectively) that 4 > 5, so we can restate 3 as:
6. P(L & G | F) / P(G | F) > P(~L & G | F) / P(G | F)
Each side of 6 has the same denominator, namely P( G | F). So we can eliminate that as follows:
7. P(L & G | F) > P(~L & G | F)
All we have done so far is basic algebra, and we have an inequality which says that the probability that the universe would be life permitting and that God exists, given fine tuning, is greater than that the universe would not be life permitting and that God exists, given fine tuning. This enables us to make a rather nice move here (which is where all this maths starts to become interesting). The probability that God exists given fine tuning, P(G | F) is equal to P(L & G | F) + P(~L & G | F). This is because L and ~L constitute all the possibilities for L that there are, so if we consider both of them in there, then it means we can basically just remove them from the equation. So,
8. P(G | F) = P(L & G | F) + P(~L & G | F)
And we can get P(L & G | F) + P(~L & G | F) (i.e. the right side of 8) by simply adding P(L & G | F) to each side of 7, as follows:
9. P(L & G | F) + P(L & G | F) > P(L & G | F) + P(~L & G | F)
So the right side of 8 just is the right side of 9 (which is why they are both orange). 8 says that P(G | F) equals P(L & G | F) + P(~L & G | F), and 9 says that this is less than P(L & G | F) + P(L & G | F). Because of 8, we can substitute P(G | F) for P(L & G | F) + P(~L & G | F) in 9:
9′. P(L & G | F) + P(L & G | F) > P(G | F)
We can simplify P(L & G | F) + P(L & G | F) into 2 x P(L & G | F). What this shows is that the left side of 8 is less than 2 x P(L & G | F), i.e.:
10. 2 x P(L & G | F) > P(G | F)
It is obvious that P(L & G | F) cannot be more than P(L | F) (the probability of two propositions on a hypothesis cannot be more than the probability of one of them on that same hypothesis); so P(L & G | F) ≤ P(L | F). So, because of 10, we can say that P(G | F) must be less than 2 x P(L | F). We know from Penrose what P(L | F) was; it was the stupidly small number . So we can say that the probability that God exists given fine tuning is no more than twice the probability of life given fine tuning:
11. P(G | F) ≤ 2 x
This is the mathematically rigorous way of saying that fine tuning makes the existence of God very very unlikely.
2. What does this mean?
What this shows is that if you think that a) fine tuning makes life happening by chance as unlikely as , and b) you think that God would favour life permitting universes, then you should also think that c) the probability that God exists is no better than twice 1 / . We have effectively put an upper limit on the conditional probability of God existing given fine tuning, and that limit is twice that of life existing by chance given fine tuning (which is the number fine tuning advocates are always keen to stress is so stupidly low).
Even if we think of the very top of this limit, we can see that it is not much help. Two times 1 / is not as small as one times 1 / (obviously), but because 1 / is such a stupidly low number, the upper limit is also stupidly low. 2 x stupidly low is still stupidly low. In that case, we might think, fine tuning is pretty good evidence against God. This, it seems to me, is the strength of the ‘God could do anything’ objection. It makes the probability that God exists look stupidly low.
3. The ‘God could do anything’ objection and the fine tuning argument
Yet, how does this result fit into the fine tuning argument? What impact does it have? Recall, that fine tuning argument goes like this (where N is naturalism):
- P(L | N & F) << 1
- ~(P(L | G & F) << 1)
- Therefore, L is evidence of G over N.
Using our numbers, we can restate the the first two premises as follows:
- P(L | N & F) = 1 /
- P(L | G & F) ≤ 2 x (1 / )
We don’t know that the second probability is actually twice the first, but it could be for all we have found out. So long as it is more than the probability in the first, then we can use the likelihood principle and infer the conclusion still. So we have not cut off the argument as such.
Even given all the maths we did above, we have not established that premise 2 is false. All we did was limit how much more likely than premise 1 it could be (it is at most twice as likely). But another way of saying this is that the second premise could be twice as likely as the first, which still enables us to infer the conclusion. And this is where the weakness of the ‘God could do anything’ objection is plain to see. Even if we grant it, we really have no good objection to the fine tuning argument. It isn’t itself a reason to doubt either premise or the inference to the conclusion.
What the fine tuning argument shows is not that God exists. It is not even really just supposed to be evidence that God exists. It is evidence that supports the hypothesis that God exists over the hypothesis that naturalism is true. It is about comparing two hypotheses together and picking the one with the higher probability. This conclusion is very weak, and this means that it is very hard to argue against. Even if fine tuning is evidence that makes the existence of God very unlikely, this is not a rebuttal to the fine tuning argument because it gives us no reason to suppose that life is more likely on naturalism. We need to remember that we are comparing two hypotheses here. Indeed, the upper bound is higher than on theism, so if anything it gives us some very limited reason to think that the fine tuning argument is actually correct, and no reason to doubt it.
Luke Barnes very helpfully sent me a copy of the unpublished paper ‘A probability problem in the fine tuning argument’ by Hans Halvorson, where I got the basic outline of the maths involved in this argument. I’m also indebted to HughJidiette for helping me get my head around the maths.