(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,
= Sam is a sharpshooter
= Sam is not a sharpshooter.
= Sam said “I’m going to hit that painted bullseye with this shot”, and then he did.
= Sam shot at a wall, and then painted a bullseye around his shot.
= background information about guns and bullets and such.
In both cases
Thus, from Bayes,
Thus
By contrast, anyone – sharpshooter or not – can hit a wall, and then paint a target around a shot, thus:
Thus,
I.e.
Applying to FTA
The FTA goes something like this:
= this universe is life-permitting.
= naturalism
In any Bayesian calculation/argument, we can use any true proposition as evidence.
The claim of the FTA is that,
1.
Thus
The accusation of “Sharpshooter Fallacy” against the FLA is that 1 is false. Instead,
2.
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 (
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 
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.
Letters to Nature 
Thank you for answering my question so clearly.
I’m a humanities teacher, not a physicist, and so I need the clarity you provide.
I apologize for the length these comments and some of it is still fuzzy in my head.
“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.”
Would not that depend on having a good handle on the probability distributions for the laws of physics and their constants in all possible Universes ?
Also, if N includes the possibility of generating Universes galore with different laws of physics and different constants maybe p(L|NB) is not ‘low enough’. Maybe god has a really hard time making L permitting Universes and thus p(L/TB) <P(L/NB) or p(L/NB) slightly less than (L/NB) etc:
“By contrast, physical life-forms have moral value, and so a life-permitting universe is not extraordinarily unlikely on theism.”
I wonder how someone can know the likelihoods of what their deity would do.
Also, suppose we are in ancient Greece, and we observe lightning. They tell us lighting is very likely under their religion because one of their gods would want to see a world with lightning in it. How does that sound ?
One more thing. Even if p(L|T B) >> p(L|N B) how do we go from that to
p(T/LB) > p(N|LB) ? Don’t you need to invoke yet more probability distributions ? Perhaps the prior P(T/B) is vanishingly low, zero, undefined.
D. Apple: as I understand it from previous posts here (I’m just a layman), the natural range of the constants is mathematical e.g. in all modelled universes if constant x’s value is more than a certain value or less than a certain value then it becomes irrational or generates unworkable infinities etc. Therefore the range of possible values for constants when modelling universes are always the same.
@Stephen Law – thanks for the response. I think Luke has used the known physics of OUR Universe, maybe adjusted the number of dimensions, adjusted gravity, adjusted nuclear forces etc: changed constants, and shown life has low chance to emerge, (maybe Luke can verify that – have not read his book yet – on my to do list). I think that is what he means on N. But what if N is much broader than that ? What if N can have completely different laws, laws not at all related to the laws in or Universe. Is that allowed under Multiverse theories ? String Theories ? If so, then P(L/NB) may be higher than the P(L/NB) that I think Luke has in mind. I think this undercuts Theist Fine Tune arguments.
It’s not just Luke. All fine-tuning modelling – there are many scientific papers – is based on this universe’s physics. It’s the only example of a universe that we have.
It’s not clear that the laws of physics are anything other than the regularities that we observe; therefore the constants and the ‘laws of physics’ are essentially the same thing. The constants define the physics. So by asking what happens to the universe if we change the constants we are by definition changing the laws of physics.
Speculating that other possible universes could have completely different constants and laws, which behave in wildly different ways to those we observe in this universe seems to me to be both incoherent and merely rhetorical. I remember one stock objection against fine-tuning used to be, to put it bluntly, “extremophiles”: that even in cold & hostile universes containing only hydrogen there might be fabulous and unlikely creatures made of hydrogen and, er, higgs bosons and virtual particles, and therefore to claim that some universes couldn’t support the complexity necessary to support life was just a failure of imagination. But that kind of speculation, invoking an infinity of possibilities in order to relativise everything and portray we know about this universe as arbitrary and parochial, is way too imaginative. It’s science fiction, not science.
For example, is it possible to alter anything more profound and fundamental about a universe than the number of dimensions of space or time? Yet still in the models we see the same thing: short lived or stillborn universes or a monotonous uniformity and lack of complexity.
I’m not quite understanding, why supposed to be T evidence for S over ~S, when p(T|S B) » p(T|~S B) is supposed to be the case.
Let’s that two fair common dice has been thrown and the following hypothesis H1 and H2 and evidence E:
H1: The sum of the two shown numbers from the two thrown dice is 3.
H2 = ~H1: The sum of the two shown numbers from the two thrown dice is not 3.
E: One dice shows the number “1” and the other dice does not show the number “1” after they both have been thrown.
We’ve got the following sample space
Ω = {(1,1); (1,2); (1,3); (1,4); (1,5); (1,6);
(2,1); (2,2); (2,3); (2,4); (2,5); (2,6);
(3,1); (3,2); (3,3); (3,4); (3,5); (3,6);
(4,1); (4,2); (4,3); (4,4); (4,5); (4,6);
(5,1); (5,2); (5,3); (5,4); (5,5); (5,6);
(6,1); (6,2); (6,3); (6,4); (6,5); (6,6)}
(with each result being equally likely – equal distribution)
and the following sub sets for hypothesis
H1 = {(1,2); (2,1)},
the following sub set for hypothesis
H2 = Ω\H1 = {(1,1); (1,3); (1,4); (1,5); (1,6);
(2,2); (2,3); (2,4); (2,5); (2,6);
(3,1); (3,2); (3,3); (3,4); (3,5); (3,6);
(4,1); (4,2); (4,3); (4,4); (4,5); (4,6);
(5,1); (5,2); (5,3); (5,4); (5,5); (5,6);
(6,1); (6,2); (6,3); (6,4); (6,5); (6,6)}
and the following sub set for evidence
E = {(1,2); (1,3); (1,4); (1,5); (1,6);
(2,1); (3,1); (4,1); (5,1); (6,1)}.
Also we’ve got the following sets:
H1∩E = H1 = {(1,2); (2,1)},
H2∩E = E\H1 = {(1,3); (1,4); (1,5); (1,6); (3,1); (4,1); (5,1); (6,1)},
H1∩H2 = {}.
So we’ve got then the following probabilities:
p(E|H1) = |H1∩E|/|H1| = 2/2 = 1 = 100%,
p(E|H2) = |H2∩E|/|H2| = 8/34 = 4/17 ≈ 23.53%,
p(H1|E) = |H1∩E|/|E| = 2/10 = 1/5 = 20%,
p(H2|E) = |H2∩E|/|E| = 8/10 = 4/5 = 80%,
p(H1) = |H1|/|Ω| = 2/36 = 1/18 ≈ 5.56%,
p(H2) = |H2|/|Ω| = 34/36 = 17/18 ≈ 94.44%
with the following relations:
[100% = p(E|H1)] » [p(E|H2) ≈ 23.53%],
p(H1|E)/p(H2|E) = 1/5/(4/5) = 1/4 = 0.25,
p(H1)/p(H2) = 1/18/(17/18) = 1/17 ≈ 0.0588,
and therefore with the following relation:
1 » [0.25 = p(H1|E)/p(H2|E)] » [p(H1)/p(H2) ≈ 0.0588].
Sure, finding E the prior probabilities are boosted in favor for hypothesis H1 over H2. But despite that and considering the resulting posterior probabilities for both hypothesis I would still consider evidence E favoring hypothesis H2 over H1.
To state other wise is to commit some form of a prosecutor’s fallacy – not in the sense of stating the conditional probability for evidence E give hypothesis H being the same as the conditional probability for hypothesis H give evidence E, but in the sense of those two conditional probabilities being similar to each other, when they are actually not.
This goes for the given example and analogy with the sharpshooter and this goes also for the relevant discussion about the FTA.
To conclude only from the supposed and suggested fact of p(L|T B) » p(L|N B), that this universe being Life permitting is evidence for Theism over Naturalism, is some form of a prosecutor’s fallacy. This line if reasoning is not really convincing at all.