Fine-Tuning a Return to Sweet Probability

In A Return to Sweet Probability, I argued that the resurrection does not increase the likelihood of William Lane Craig's god, largely because the credibility that you give reports of the resurrection depends very heavily on your predisposition to believe that his god (or some very similar god) exists.

I want to do something similar with the fine-tuning argument.  I'll be using a variant of it implied by my old buddy, Luke Barnes (also referring to this earlier comment):

Let

o = intelligent observers exist

f = a finely tuned universe exists

b = background information.

NID = a non-terrestrial intelligent designer exists.

…

I can admit that “p(finely tuned universe | observers exist) = 1” and still conclude that

p(NID | f.o.b) >> p(~NID | f.o.b)

Now this argument between Richard Carrier and Luke Barnes was about Bayesian probability, so we know that:

P(NID | f & o & b) = P(NID & f & o & b) / P(f & o & b)

Holding f and o together (for reasons which should become apparent shortly) this eventually becomes:

If you want to see the working for this, look at A Return to Sweet Probability.

Now we need to define our terms.  I think it’s reasonably clear what the term o means, the intelligent observers in question are us.  By “intelligent”, we are not implying that the universe in question must be crammed with Albert Einsteins.  We merely need to be intelligent enough to observe the universe and note that the universe contains observers who are intelligent enough to observe their own existence.  Tick.

The term f is a little more contentious.  I’m going to use the definition that Carrier uses (see Part Deux), in part because it’s something that Barnes appears to have consistently overlooked:

If fine tuning is necessary for life, and there is no God, then necessarily life will only ever exist in correlation with fine-tuning. This is because all universes without fine tuning (sic) will thus by definition not contain life.

Note that this does not say anything about the hypothetical case in which there is a god.  A god may choose to fine tune the universe for life, or it may choose to magically create and sustain life even in universes which are not at all tuned for life, or it may choose to create a universe in which the range in which life is possible is very wide indeed.  Carrier appears to be conceding a point to apologists (such as Barnes) for the sake of the argument.  The fine-tuning argument will only work in a universe which is apparently fine-tuned for life, if there are observers in a hypothetical universe which is not fine-tuned for life then the fine-tuning argument fails (and, hypothetically, the pseudo-scientific, apologetic denizens of that universe will deploy the “non-fine-tuning argument” for whatever god they have imagined into existence).

So, in the instances in which there are observers, the universe will either be fine-tuned (either naturally or as the result of the intervention of a god) or non-fine-tuned (as the result of the invention of a god).  There is the possibility that some universes will be fine-tuned for life but, for some reason, life doesn’t manifest.  I don’t think we are particularly interested in those universes but in any event, those universes won’t have observers.  I think we can get around this scenario by strengthening the concept of fine-tuning – if a universe is sufficiently fine-tuned for intelligent life, then there will be, at some point, intelligent life.  Any tuned universe which doesn’t manifest intelligent life simply isn’t sufficiently tuned to consider it fine-tuned.  It certainly could be excluded from the set of universes that our universe fits into (also known as the reference class – that is: what is it about our universe that is pertinent to our consideration in this instance?  It would appear to be the fact that it contains not only life, but also intelligent observers).

So fine-tuning is defined as the sort of fine-tuning in our universe, that may or may not have been due to the intervention of a god, and resulted in intelligent life, life that was intelligent enough to observe that the universe is sufficiently fine-tuned to produce intelligent observers.

This is an extremely long and convoluted way to say what Carrier had been saying, P(o|f)=1 and, therefore, P(f&o)=P(f).  Or, in other words, once you have fine-tuning (as defined) you necessarily get observers, so the probability of fine-tuning and observers resolves down to the probability of fine-tuning.  This allows us to change all the (f&o) terms to f:

Perhaps you might want to weaken the definition of fine-tuning, but I don’t think that apologists want to.  If they do, I think they merely weaken their fine-tuning argument as a consequence but that can be an argument for another day if any apologist wishes to take that route.

We know that NID is the “non-terrestrial intelligent designer”.  I’m not as coy as some others, so I am just going to call this the god of people like William Lane Craig, Plantinga and (almost certainly) Barnes (but certainly many of Barnes’ adoring fans).  For the sake of the argument, let’s change NID to R as in “cReator” or “Representing god” or “what the apologists are Really arguing for”.

Fine-tuning (f) is, of course, the evidence in this argument, so let’s call it E.  If you are reluctant to roll o into f per the argument above, we could instead say that E=(f&o).

Then there’s our background, b (which we will capitalise and call B).  Background is a little vague in its definition.  What exactly constitutes background?  Fortunately, we can rely on Barnes again, who has written a piece on precisely this topic.

Background is everything we know, with the exception of the evidence that we are currently looking at, so in this case everything we know with the exception of fine-tuning (and thus observers).  However, this in effect resolves down to everything we know that is relevant.  I suspect that we have to be very careful about doing this step manually – because that which is relevant might not be immediately obvious and eliminating relevant data will skew the result.

I think we have enough to be getting on with.  We’ve renamed NID, b and f (or (f&o)) to R, B and E, respectively, so we have:

For anyone who has read A Return to Sweet Probability recently, this equation should be familiar.  On the right hand side of this equation we have four terms to consider:

P(E|R&B) – this is asking us: Given the hypothesis that there is a cReator, and our background information (everything we know, bar fine-tuning), what is the likelihood of our evidence (fine-tuning)?

P(R|B) – this is asking us: Given our background information (everything we know, bar fine-tuning), what is the likelihood of there being a cReator?

P(E|^R&B) – this is asking us: Given the hypothesis that there is not a cReator, and our background information (everything we know, bar fine-tuning), what is the likelihood of our evidence (fine-tuning)?

P(^R|B) – this is asking us: Given our background information (everything we know, bar fine-tuning), what is the likelihood of there not being a cReator?

On the left of the equation is P(R|B&E), which asks us: Given our evidence (fine-tuning) and our background information (which is, cumulatively, everything we know), what is the likelihood of a cReator?

The value of this equation relies very heavily on two questions having already been answered, namely the likelihoods of there being a cReator and not being a cReator, given what we know, apart from fine-tuning.  It also relies, rather heavily, on the assumption that fine-tuning doesn’t follow necessarily from what we already know.  If we were, in the future, to discover that B→E (if B then (necessarily) E), then B&E would equal B, so the left had side of the equation would become P(R|B).  This would naturally follow because P(E|R&B) = P(E|^R&B) = 1 and P(R|B)+P(^R|B)=1.

Therefore, there is an assumption that fine-tuning is consistent with our background (everything we know, bar fine-tuning) but our background is insufficient.

Now, we should make clear something about “background”.  Barnes’ says, of background, “tell me everything” and warns that information should not be arbitrarily ignored.  So, my question is this: is it arbitrary, given that no time related caveat is placed on the cReator hypothesis, to limit “background” to that which we know now?  How extensive is this “everything” of which you speak?  Is it possible that, in the future, we will discover that the fine-tuning we observe is a necessary consequence of relatively simple, yet entirely natural laws?  It would seem that the answer to that question, according to an apologist, should lie somewhere between “maybe” and “I don’t know” – perhaps somewhat closer to “maybe” given that “I don’t know” is saying that it isn’t necessarily impossible, and is therefore possible, making the answer an unambiguous “yes, it is possible”.

So, it seems to be unreasonable to assume that our background is always going to be insufficient to explain fine-tuning.  The assumption might be valid if we presupposed an interventionist god, or if there is some natural limit on the information that we can glean about the universe.  In the case of the latter, the argument by apologists is unacceptably stacked in favour of their god (assuming the existence of god, what is the likelihood of god?)  In the case of the latter, such a limit would imply that the question of the existence of a god may never be resolved, a god may never be proved but it may also never be disproved.

This is, I guess, a wonderful conclusion for apologists.  Potential job security until the end of time!

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I think that I am now ready to assign tentative probabilities to each of the terms in the equation.  I’m going to be as charitable as I can to the apologetic cause.

P(E|R&B) – we don’t know

P(R|B) – we don’t know

P(E|^R&B) – we don’t know

P(^R|B) – we don’t know

Plugging those values in, we arrive at P(R|B&E) = P(R|B) = we don’t know.

So, we could argue endlessly about how to manipulate the identities in the Bayesian calculations, and how likely or unlikely fine-tuning itself is, but at the end of the day, we merely arrive at “we don’t know”.  Sure, an apologist may immediately transmute that “we don’t know” into “god exists” via the subtle alchemy of an appeal to ignorance.  The more intellectually honest among us, however, are left with a mystery to investigate – why does the universe appear to be fine-tuned? – without any real need to worry about the superstitious wretches who continue to dog our investigative heels.

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It’s vaguely possible that someone is going to be upset that there were no jellybeans in this article.  I’m sorry, but the probabilities are so nebulous that I didn’t see any point in assigning any, even tentatively.

If someone else is keen to do an analysis using the jellybean model, feel free.