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## Fine-Tuning and the Sharp-Shooter Fallacy

(This is a repurposed Facebook comment.)

The Fine-Tuning Argument (FLA) is accused of committing the Texas sharpshooter fallacy. Sam the shooter wants to hit a bullseye, but isn’t having much luck. They can barely hit the side of a barn. Having sprayed bullets at the barn all day, they devise a plan: pick an arbitrary bullet hole, paint a bullseye around it, ignore the rest of the bullet holes, and announce themselves to be a sharpshooter.

The moral of this story can be stated in a few ways. Don’t ignore data. Keep in mind the number of failed attempts when you go looking for (and set a criterion for) successful attempts. You can avoid these problems if you specify your hypothesis before you collect your data. Drawing conclusions from a sub-sample is dangerous – if you must, try to choose a random sub-sample.

### A Bayesian Sharpshooter

Let’s put the tale of Sam in Bayesian terms, and then see if it applies to the FTA. Suppose,

• $S$ = Sam is a sharpshooter
• $\bar{S}$ = Sam is not a sharpshooter.
• $T$ = Sam said “I’m going to hit that painted bullseye with this shot”, and then he did.
• $P$ = Sam shot at a wall, and then painted a bullseye around his shot.
• $B$ = background information about guns and bullets and such.

In both cases $T$ and $P$, we observe a bullet at the centre of a bullseye. The difference between the cases is as follows. Sharpshooters are much more likely to hit a given target than non-sharpshooters, thus:

$p(T|S B) \gg p(T|\bar{S} B)$

Thus, from Bayes,

$p(S|T B) / p(\bar{S}|T B) \gg p(S|B) / p(\bar{S}|B)$

Thus $T$ is evidence for $S$ over $\bar{S}$.

By contrast, anyone – sharpshooter or not – can hit a wall, and then paint a target around a shot, thus:

$p(P|S B) = p(P|\bar{S} B)$

Thus,

$p(S|P B) / p(\bar{S}|P B) = p(S|B) / p(\bar{S}|B)$

I.e. $P$ is not evidence for $S$ over $\bar{S}$.

### Applying to FTA

The FTA goes something like this:

• $L$ = this universe is life-permitting.
• $T$ = theism
• $N$ = naturalism
• $B$ = background information about the laws of nature and the constants.

In any Bayesian calculation/argument, we can use any true proposition as evidence. $L$ is true, so we cannot claim that focussing on $L$ is arbitrary at this stage. As the case above shows, it is not wrong to calculate using $P$; it’s just a waste of time because the probabilities don’t change.

The claim of the FTA is that,

1. $p(L|T B) \gg p(L|N B)$

Thus $L$ is evidence for $T$ over $N$.

The accusation of “Sharpshooter Fallacy” against the FLA is that 1 is false. Instead,

2. $p(L|T B) = p(L|N B)$

So, which is true, 1 or 2?

The Texas Sharpshooter accusation is that the FTA draws an arbitrary target around life. But this simply assumes that the objection is valid, without providing any reason to think so. If 1 is true, then the focus on life is not arbitrary. The reason it is not arbitrary is that the existence of a life-permitting universe is very improbable on naturalism, and not comparably improbable on theism. Our hypotheses ($T$ and $N$) produce very different likelihoods for $L$, which makes $L$ extremely relevant. Focussing on life is not arbitrary – it’s exactly what the Bayesian is supposed to do. The order in which we learned about or postulated $L$, $T$, and $N$ is irrelevant to the Bayesian framework, so that’s not evidence that it’s arbitrary to focus on life. The objection amounts to denying 1, but provides no reason to do so.

A positive argument for 1 might be summarised as follows. Naturalism is non-informative – as I have discussed in detail here. Thus, we can treat a naturalistic universe, for Bayesian purposes, as being random – not in the sense of being stochastic, but in the sense of producing probabilities that are at the mercy of the size of the set of possibilities. The fine-tuning of the universe for life shows that $p(L|NB)$ is extraordinarily small: a randomly-chosen universe is extraordinarily unlikely to have the right conditions for life. By contrast, physical life-forms have moral value, and so a life-permitting universe is not extraordinarily unlikely on theism. (It is no part of 1 that a life-permitting universe is likely on theism. This is not a step in the argument.) Thus, 1 is true and the objection fails.

The fallacy might apply if a multiverse exists, because the other dead universes would be the analogue of all the missed shots on the barn wall. We aren’t ignoring them intentionally – we just can’t see them. This objection is then a rephrasing of the multiverse objection. The possibility, or even truth, of the multiverse hypothesis is not enough: an argument from the multiverse to the truth of 2 would need to be made.