Collins vs. Stenger

Robin Collins has written a paper responding to some criticisms Victor Stenger made of the Fine Tuning Argument.

Collins starts out by conceding to Stenger that many of the claimed fine tunings do not qualify  as such. He focuses on a few examples where he thinks Stenger's arguments fail, basing his argument on a close consideration of the physics involved. Collins is a philosopher but, according to his CV, did some grad work in physics.  Stenger is himself a physicist. Collins accuses Stenger of getting the physics wrong. So who's right?

For this post, I'm only going to consider their remarks about the relative strengths of the various physical forces. I haven't read Stenger's book, The Fallacy of Fine Tuning (FOFT), so I'm basing my comments on this paper and Collins's claims about FOFT. I also should make clear that I think the Fine Tuning Argument is a bad argument overall. But I think it might be worthwhile for me as another physicist to try to evaluate the physics part of these arguments.

On the strength of gravity, Stenger writes,

The reason gravity is so weak in atoms is the small masses of elementary particles. This can be understood to be a consequence of the standard model of elementary particles in which the bare particles all have zero masses and pick up small corrections by their interactions with other particles.

Collins responds,

Although correct, Stenger’s claim does not explain the fine-tuning but merely transfers it elsewhere. The new issue is why the corrections are so small compared to the Planck scale. Such small corrections seem to require an enormous degree of fine-tuning, which is a general and much discussed problem within the Standard Model.

Collins is correct: the only natural energy scale in terms of fundamental physical constants is the Planck scale, and we have as yet no understanding of why the proton and neutron masses should be so small compared to the Planck scale. (I should point out, though, that when physicists talk of a parameter being "fine-tuned" it has nothing to do with being fine tuned for the existence of life. Rather, it is a matter of fine tuning for the observed physics of the universe.)

With regard to the relative strength of gravity compared to other forces, Stenger writes,

The gravitational strength parameter α_G is based on arbitrary choice of units of mass, so it is arbitrary. Thus α_G cannot be fine-tuned. There is nothing to tune.

Now, I have to say I find this statement very unclear.  α_G is a dimensionless parameter: it doesn't depend on any choice of units. It is defined as

α_G ≡ G(m_p)²/ℏc,

where G is the gravitational constant, m_p is the proton mass,  ℏ is Planck's constant, and c is the speed of light. No matter what system of units you use to measure those quantities,α_G will have the same value.

Collins, who has read FOFT, says that Stenger means the we can replace the proton's mass in α_G by the mass of some other fundamental particle. Collins, correctly, points out that this is irrelevant to the question of whether α_G as defined is fine tuned. In the absence of any reasonable alternative interpretation I have to agree with Collins again: changing from one parameter to a different parameter can't save you from fine tuning of the original parameter.

Collins goes on to give a rather involved discussion of how various physical properties scale as we allow α_G to change. This is a sophisticated bit of argument; Collins pulls in arguments based on biology, plate tectonics, and planetary science. I tried hard to find some flaws in this analysis, but only came up with a few minor quibbles.

Stenger does make an important point that Collins simply ignores. He points out that if we just change one parameter, that parameter might appear to be fine-tuned. But if we allow for two (or more) parameters to vary at the same time, there might be a much wider range of values that allow for life. For instance,

The relative values of α and the strong force parameter α_S also are important in several cases. When the two are allowed to vary, no fine-tuning is necessary to allow for both nuclear stability and the existence of free protons.

As I said, Collins makes no comment about this claim. There is an obvious counter to it, though: if we increase the number of parameters that vary, we also increase the available parameter space. Even if the life-permitting range of some value is increased in this way, the relative volume of parameter space might still be small.

What's worse, Stenger goes on in the very next paragraph to step on his own toes:

There are two other facts that most proponents of fine-tuning ignore: (1) the force parameters α, α_S, and α_W are not constant but vary with energy; (2) they are not independent. The force parameters are expected to be equal at some unification energy. Furthermore, the three are connected in the current standard model and are likely to remain connected in any model that succeeds it.

If Stenger is right here, then the values of α and α_S cannot be varied independently. So which is it?

First off, I don't know what Stenger means by, "the three are connected in the current standard model." In the current standard model, the three are independent parameters and can be varied independently.

Second, it is true that these couplings change with the energy scale at which they are measured: physicists call this "running coupling constants." But it's not clear to me why Stenger thinks this is relevant. Is he suggesting that at some vastly different energy scale, they might again have the correct ratios to allow for life? I'm not sure what the point of this remark is.

Thirdly, "The force parameters are expected to be equal at some unification energy." This is true in grand unified models (GUTs) and in some supersymmetric models, but these have not been verified experimentally and so remain highly speculative. Anyway, this causes problems for Stenger, because if these parameters are related by physical theory then they can't be varied separately and so his argument about varying two parameters at the same time is no longer available. 

Finally, let's return to Collins. He writes,

Next, I define a constant as being fine-tuned for ECAs [embodied conscious agents] if and only if the range of its values that allow for ECAs is small compared to the range of values for which we can determine whether the value is ECA-permitting, a range I call the “comparison range.” For the purposes of this essay, I will take the comparison range to be the range of values for which a parameter is defined within the current models of physics. For most physical constants, such as the two presented here, this range is given by the Planck scale, which is determined by the corresponding Planck units for mass, length, and time.

Taking the Planck scale as defining the comparison range is badly wrong, for two reasons.

First, the Planck scale sets a limit on current physics in the sense that we expect it to break down around that scale. But in fact we have good reason to think current physics breaks down very much before that scale. Physicists have high hopes that the LHC will reveal "new physics," at an energy that is a factor of 10¹² below the Planck energy. This has not yet happened, unfortunately. But to suppose that we can understand physics at energies all the way up to the Planck energy is just way off.

Secondly, even apart from the issue of new physics, it's absurd to suggest that we can determine whether ECAs are possible for values of parameters that differ greatly from the values we know as the actual ones. Think about it like this: if someone handed you the equations of the Standard Model and of general relativity, together with the values of the constants therein, would you be able to predict the existence of complex life forms? Certainly there are some ranges of some parameters that let us rule out complex life. For instance, if the cosmological constant is to big, then the universe will expand so fast that matter will never be able to clump together into stars and planets. But changing the ratio of (say) electromagnetic to gravitational force is a very delicate matter, and all sorts of unforeseen possibilities might arise, especially for values very far from the true values. Sure, you could say that life like ours would be impossible under those parameters. But the argument is supposed to be about embodied conscious agents in general, not just life like ours.

What's strange is that Collins himself took a much more modest view of the comparison range in a previous paper. There he showed a sophisticated appreciation of both of the points I just made. For example, he writes,

One limitation in the above calculation is that no detailed calculations have been performed on the effect of
further increases or decreases in the strong and electromagnetic force that go far beyond the 0.5 and 4 per
cent, respectively, presented by Oberhummer et al. For instance, if the strong nuclear force were decreased
sufficiently, new carbon resonances might come into play, thereby possibly allowing for new pathways to
become available for carbon or oxygen formation.

He introduces the "epistemically illuminated range" for a parameter: that range for which we can calculate with reasonable assurance of success whether a given value allows the formation of complex life. He applies this procedure to the fine tuning of the strong force for carbon and oxygen production in stars, and comes up with a not-very-fine-tuned value of 0.1. Here, too, he treats only of the possibility of there being life like ours, and makes no attempt to address whether some very different sort of complex life might arise.

To sum up, I think Collins has done a pretty good job of pointing out problems with Stenger's analysis. His treatment of the physics here is a big improvement over some of his earlier work. But his arguments aren't enough to establish his claim. Collins's chosen "comparison range" is certainly too large to be reasonable. And his arguments only address the possibility of life that is substantially similar to ours. Yet vastly different forms of life might be possible in other parameter regions: we simply don't have the sophistication to predict their existence from bare physical laws. (It's possible that life-permitting regions might be scattered, fractal-like, through the parameter space, so that at any life-permitting point small changes don't allow life, while overall the probability of life is quite large.)

Contingency

Tyler has brought up the cosmological argument from contingency and linked to a Philosophy of Religion (POR) article and a paper by Alexander Pruss. The latter is a long article and will take me a while to read and digest. So I'm just going to post some comments on the first article by way of starting (I hope) a discussion.

The argument runs like this:

(1) Everything that exists contingently has a reason for its existence.
(2) The universe exists contingently.
Therefore:
(3) The universe has a reason for its existence.
(4) If the universe has a reason for its existence then that reason is God.
Therefore:
(5) God exists.

I have two immediate objections to the argument, which I'll call the Nature of Necessity objection and the Quantum Mechanics objection. I've already discussed QM and reasons in my debate with Prof. Feser (see here and here), so in this post I'll just address the Nature of Necessity objection.

Cosmological arguments always begin by implicitly carving out a "God exception."

• - "Nothing can be beginningless - except God."
• - "Nothing can exist without a cause - except God."
• - "Nothing can be undesigned - except God."

Here we have "Nothing can exist necessarily - except God."

Properly speaking, "necessity" and "contingency" are terms that apply to propositions. Necessary truths are those that cannot fail to be true: the usual examples are mathematical and logical truths. Contingent truths could fail to be true. "It is raining right now" might be true, but it could have been the case that it didn't rain today.

The argument from contingency rips these terms out of their proper context and attempts to apply them to things. It asserts that there are contingent things - those that could possibly have not existed - and necessary things - those that could not have not existed. The problem is, no one ever seems to be able to point to something that exists necessarily - except God.

"Exists necessarily" is supposed to mean "exists in all possible worlds." But what is a possible world? Philosophers distinguish different types of possibility. Physical possibility means that which, according to the laws of nature, could happen. Logical possibility means anything that is not logically incoherent. (There are other types of possibility, but these are enough for discussion.) In making a modal argument - one based on what might happen in other "possible worlds" - it makes a big difference whether we are talking about physically possible worlds or logically possible worlds. So, it might be logically possible for the universe not to have existed, while at the same time it is physically impossible for the universe not to have existed. (That would be the case if the laws of physics somehow guaranteed that a universe spring into existence. I'm not claiming that they do guarantee this - only saying that some set of laws might do so.)

The POR article considers logically possible worlds and suggests that it seems logically possible that the universe not exist. This is, of course, true. Among the logically possible worlds is the empty world, in which nothing exists. So, no universe.

But also, no God. Because when necessary existence is construed according to logical possibility, it is an empty concept. Nothing exists in the empty world. So there is nothing that exists in all possible worlds. So there is nothing that exists necessarily.

The Nature of Necessity objection was articulated by Bertrand Russell a long time ago, so I'm sure someone has thought up a response to it. If you know of one, let me know!

I'm having a good discussion about my anti-fine-tuning argument with Tyler Journeaux over at his blog, Third Millenial Templar. Which is a great name for a blog, by the way. (Reminds me of the need for better atheist nicknames.) Thanks to Grundy for pointing me to Tyler's blog.

Though a Christian, Tyler is unimpressed with Swinburne's argument for God. (Of course I agree with him here.) Tyler thinks that there are good deductive arguments for God - specifically, the cosmological argument from contingency. Now, it seems to me that even the theistic philosophers of religion have abandoned the hope for a convincing deductive argument for God (e.g. Swinburne and Alvin Plantinga - Ed Feser and William Lane Craig are the only exceptions I know of). So Swinburne's approach - a cumulative argument for God - would seem to be the only approach that has any hope of being convincing.

Attention, Everyone!

This is Somewhat Abnormal, the personal blog of Robert Oerter. It is where I write about things I am reading and thinking about and comment on them. It is not to be confused with the similarly named Journal of Somewhat Abnormal Philosophy, or the esteemed Proceedings of the Somewhat Abnormal Society. Sometimes I write about science, something I know a little bit about. I occasionally attempt some amateur philosophical commentary. Other times I remark on things I find interesting or amusing. Read at your own risk.

Ed Feser has written a long post in response to my very brief one about his recent paper on Aquinas and inertial motion. I really don't think my little remark is worth all this boring argument, but as Feser accused me of dishonesty in the comments of my post, I feel compelled to respond. I am often wrong, I sometimes say stupid things, and I sometimes don't make my point as clearly as I might have. But I am not dishonest.

Wherein lies the supposed dishonesty? Feser begins by complaining that I ignored the whole first half of his paper. Well, I did! That wasn't the funny part! Again: this is a blog, not a philosophical journal. I comment on what I want to comment on, in whole or in part. I am not obliged to analyze his whole paper in order to make my silly little point. If Ed think otherwise then I think he misunderstands the nature of a blog.

He goes on to say

In the second half of the paper I examine, without endorsing, several ways of construing the relationship between the two principles...

and lists three of these ways. Well, my post concentrated on just one of the three possibilities, but explicitly mentioned that he treated of other possibilities. So I can't be accused of misrepresentation on that point.

What about the case I made fun of? Did I misrepresent what he wrote in any way? No, Feser says, both in his comments on my post and in his own blog post, that I interpreted him correctly in that

...I do discuss (though I do not endorse) the idea that angelic substances are the cause of inertial motion.

 He complains that

Needless to say, the idea has nothing whatsoever to do with wings, golden hair, white robes and the other stuff of children’s books.

Well, guess what? I didn't write a word about wings, golden hair, blah blah. Such dishonesty, Prof. Feser! (OK, I did make a parenthetical jab about dancing and pins, but that could hardly be resisted under the circumstances.)

Now, as far as endorsment: Feser says he didn't endorse any of the three possibilities. So if I had chosen any of the other possibilities, or even if I had criticised all three, he could still have responded "Well, I didn't endorse any of those solutions, I merely mentioned them." But for the case in question, here is what he wrote (emphasis added):

Hence the only possible cause of inertial motion—again, at least if it is considered to involve real change—would seem to be a necessarily existing intelligent substance or substances, of the sort the earlier Aristotelian tradition thought moved celestial objects. (Unless it is simply God Himself causing it directly as Unmoved Mover.)

So, imagine I wrote a physics paper, in which I wrote

There are three possibilities for the Higgs: Supersymmetric models, grand unified models, and the Standard Model.... In the case of the Standard Model, the only possible cause of the Higgs couplings would seem to be that they are the result of the action of intelligent fairies.

 Now, if someone wrote a blog post saying, "Seriously, Robb? Intelligent fairies?" how should I respond? "What dishonesty! I didn't endorse that possibility, I only mentioned it. And you completely ignored my treatment of the supersymmetric and grand unified cases!"

Again: Feser suggested angels as a serious possibility - indeed, the only possibility - for the cause of inertial motion for the case under consideration. I think that's worthy of a comment. And a chuckle.

Alright, I almost regret having written the post, since, as I said, this is all a rather boring argument. But what made it all worthwhile was the 344 (!) comments on Feser's blog in which Feserite dittoheads demonstrate their philosophical acumen by writing, "Yeah, that Oerter's a complete idiot/jerk/brainless GNU." Ah, it warms the cockles of my heart.

Feser finally complains that I am "tossing some red meat to the New Atheist mob", who will now endlessly repeat "Feser claims that asteroids are moved around by angels!" Well judging by the comments here, my readership consists mainly of Feserite Thomists, so I can hardly be accused of playing to the audience. And I can only dream of having that kind of clout in the atheist blogosphere - I've never had 344 comments on any post, ever. I'm fairly sure my silly little jibe would have sunk without a trace had not Ed brought attention to it. So if what he fears comes to pass, he will only have himself to blame - in more ways than one.

... We Have Heard On High

Ed Feser has a new paper out explaining why Newton's First Law of Motion is not incompatible with Aquinas's principle that "whatever is in motion is moved by another." In it he expands on some comments he made in response to my criticism of his book, The Last Superstition.

Newton's law states that anything that is in motion will remain in motion unless acted on by an outside force, so the two principles seem to be directly contradictory, at least at first glance. Newton says that an object that is completely isolated, so that it has no external influences on it, will continue to move. Aquinas denies this.

So how does Feser resolve the conflict? Easy! The object in uniform motion is moved along by....

(wait for it)

ANGELS!

Yes, angels are necessary to keep a moving object moving. I'm not making this up, he really says it:

So, it is difficult to see how inertial motion, when interpreted as involving real change, could have a physical cause. But as we implied above, even if its lacks a physical cause, there is nothing in the principle of inertia that rules out a metaphysical cause. Indeed, if inertial motion involves real change, then given the principle of motion together with the absence of a physical cause, such a metaphysical cause is necessary.

Of course, that raises the question of what exactly this metaphysical cause is....

If inertial motion involves real change, then, only a metaphysical cause external to the moving object could be the ultimate source. And we already have a model for such a cause in the Aristotelian tradition. For the motions of celestial bodies were in that tradition regarded as unending, just as inertial motion is (barring interference from outside forces) unending; and while this view was associated with a mistaken astronomy, a metaphysical kernel can be extracted from the obsolete scientific husk. Now the causes of celestial motion in this earlier Aristotelian tradition were, of course, intelligent or angelic substances....

Hence the only possible cause of inertial motion—again, at least if it is considered to involve real change—would seem to be a necessarily existing intelligent substance or substances, of the sort the earlier Aristotelian tradition thought moved celestial objects. (Unless it is simply God Himself causing it directly as Unmoved Mover.)

Here Feser is considering inertial motion as "real change." He also considers what happens if you consider inertial motion as a "state" that doesn't involve any real change: no actualization of a potential. Feser seems to be getting confused by the way physicists use the term "state": the "state" of a (classical) object refers to its location and its rate of change (velocity), so by definition it involves change. Ultimately, though, the question of whether inertial motion is or is not "real change" is not a physical question but a metaphysical one. One would think that Feser's Aristotelian-Thomian metaphysics would tell us which it is. That it cannot just shows how useless that metaphysics is.

The idea that angels are responsible for inertial motion raises a whole (heavenly) host of questions. Presumably, an object at rest doesn't need any angelic mover. However, in Newtonian physics, any uniformly moving reference frame can be considered to be at rest (Galilean relativity). If we have two objects in uniform motion relative to each other, which one does the angel need to guide? If we consider object A at rest, then the angel must move B. But if we consider object B at rest, then the angel must move A. What's a poor angel to do?

And how many angels are needed for this heavenly guidance? If an asteroid is being guided by an angel, and suffers an impact that splits it in two, does the angel recruit another angel to guide the second piece? Or can the first angel handle both pieces? What if the asteroid gets shattered into smaller and smaller fragments? Maybe each elementary particle has its own angel? How many angels are needed to guide a fragment the size of a pin? (And do they dance?)

Once again we see the Sophisticated Theologian in action. When the world doesn't work the way you want it to, just invent some invisible, undetectable beings to fill the gap.

I have to thank Prof. Feser for this paper; it shows more clearly than anything I could write what absurdities result when you try to force the world into a pre-conceived metaphysics.

Assumptions, Assumptions

So, I pointed out my FTAN (Fine Tuning Argument for Naturalism) to Alexander Pruss of Prosblogion, who was kind enough to respond in the comments of his post on fine tuning vs. the problem of evil. Alexander is not just some random blogger. All the folks at Prosblogion are Genuine Sophisticated Theologians - philosophy professors, no less. So, I was glad to get the opinion of an expert on my version of the fine tuning argument. Here's what he wrote (in part, I think I am fairly representing his responses with my excerpts here, but see the original post for his full remarks):

The FTA needs an assumption that there is a significant value to a universe that with very few exceptions, if any, follows orderly and elegant mathematical laws of nature. Such an assumption is compatible with miracles.

Now, this is exactly the sort of thing I was complaining about in my Purple Pachyderm post, and that Carl Sagan was complaining about in his Dragon in the Garage, and so on. For any argument against the existence of God, the theist simply introduces an arbitrary and unfounded assumption in answer.

So I pointed out that in a universe with any miracles at all, my FTAN would still work. For instance, on an earth that was too close to its sun for life to exist, God could prevent the excess radiation from reaching earth, thus allowing life to exist. The exception to energy conservation would be localized, satisfying the "few exceptions" assumption.

Alex responded:

Leibniz argued against Newton/Clarke that it would be inappropriate for God to rely on on-going miracles for the ordinary operation of the universe.
One way to defend this is to say that God has reason to avoid miracles. This reason can be overridden, of course.

OK, so now we have a new assumption: that miracles should not be on-going. Dragon in the garage once again.

 Unfortunately for Alex, this new assumption still doesn't answer the objection. Even with one-time miracles, there will still be infinitely more possible life-containing universes if there is an omnipotent God than if there is not. One example I pointed out was if the laws of chemistry don't allow for chemical evolution of life, but do allow for the existence of life. Then a single miraculous intervention by God could get life started. But there are infinitely many ways God could make this intervention, so there are infinitely many more possible life-containing worlds under the theistic assumption. So my FTAN still works.

Also, this new assumption flies in the face of an argument that theists have been making for centuries:  that it takes God's on-going miraculous intervention to sustain the universe. Here, for example, is Pope John Paul II discussing proofs of God's existence  (emphasis added):

Without such a supreme Cause, the world and every movement in it would remain "unexplained" and "inexplicable", and our intelligence would not be satisfied. The human mind can receive a response to its questions only by admitting a Being who has created the world with all its dynamism. and who continues to maintain it in existence. 

The theist wants to have it both ways. On-going miracles? Proof of God! No on-going miracles? That's proof of God, too!


Alex answered:

• 1. Dougherty and Poston in the paper I linked to argue that one can't consistently run both the FTA and ID-type biological design arguments. Your point is similar, though not the same.
• 2. I think both your and their point is somewhat weakened, but not destroyed, on the supposition that God would have good reason to minimize the number of miracles, subject to other desiderata.
• 3. But in any case, I think many of the proponents of the FTA would say that a number of the constants going into the FTA are such that not only need the values be "just right" (tough making sense of that rigorously, but there is an intuition there that many theists and non-theists find compelling) for life to begin, but for life to persist.

In (2) Alex is saying, I think, that God would prefer to create a life-containing universe without using miracles rather than one that requires miracles.Yet another new assumption. But Alex recognizes that that even this assumption does not "destroy" my point.

Anyway, isn't God supposed to want us to know about him? Wouldn't these miracles be evidence of a God? So why would God want to avoid them?

In (3), Alex is just saying that you can run the FTA (for God) on those parameters that allow life to persist. But this is irrelevant to my argument, which takes precisely the fine-tuned nature of those parameters as an argument against God.

So I have to say, I'm not too impressed with the Sophisticated Theologian's response to my counter-argument. Of course, with enough additional assumptions you can neutralize any argument. But the very need to make those logical contortions reveals how weak the theist's position is.

RP: Fine Tuning Supports Naturalism

The following seems worth re-posting, as some folks still seem impressed with the fine tuning argument. It seems like a fairly obvious point, yet I haven't seen it mentioned much in the fine tuning discussions I've read. I'd be grateful if anyone can show me the glaring flaw in the argument that I'm missing. At the Prosblogion link, Alexander Pruss kindly responded to my remarks; I'll have some comments on his response soon.

I should say again that I don't think the following is a very good argument for naturalism - it's just a way of showing why the fine tuning argument for God is hollow.

Originally posted on Thursday, October 13, 2011.

Garren's comments on the previous post got me thinking more about fine tuning. There are lots of reasons to dislike fine tuning arguments for God, but it occurred to me that we can turn the fine tuning argument around and show how it actually supports naturalism, not theism. Let me explain.

The usual fine tuning argument goes like this: Our universe is governed by natural laws that involve certain numerical parameters - the cosmological constant, the strength of the nuclear force, etc. Some of these parameters must lie in a very narrow range in order for life to exist:

PU = Possible Universes
FTU = Fine-Tuned Universes

So, given a naturalistic hypothesis (N) and general background knowledge (K), the probability of a fine-tuned universe is small:

P(FTU|N&K) = Area(FTU)/Area(PU)  << 1

On the other hand, given the theistic hypothesis (T), we would expect the universe to be suitable for life: P(FTU|T&K) is not small, or at least not as small as P(FTU|N&K).

One of the (many) problems with this argument is that we can't assert that the probability is given by the ratio of the areas without making many additional assumptions: that the values of parameters 1 and 2 are randomly chosen from the space of all parameters, for instance. But that's not the objection I want to pursue. Rather, I want to point out that the probability envisioned in the fine tuning argument is a sort of prior probability that ignores some of our background information: namely, the fact that life actually exists. That is, we have to take (K) to mean "general background knowledge not including the knowledge that life exists."

But we actually do know that life exists (L), and it is perfectly legitimate to include this knowledge along with our other background knowledge. If we add this knowledge back in, then trivially P(FTU|N&K&L) = 1: under the naturalistic hypothesis, the only way that life can exist is for the universe to have parameters that allow the existence of life.

But that is not true if God exists! Indeed, under theism, there is no reason to expect that the universe will be fine-tuned.

Remember that God is, by hypothesis, omnipotent. That means that God could  have caused life to arise by miraculous means, even in a universe that was not fine-tuned. Say, for example, that the universe had a value of the cosmological constant that caused it to expand too fast for galaxies to form. God could have prevented a galaxy-sized region from expanding in order to allow our Milky Way to form. Or God could have inserted a pre-made galaxy. Or he could have inserted an additional force that operated only within our galaxy and that countered the effects of the expansion. Or any number of other possibilities, because God can do anything.

So, under theism, the diagram looks like this:

That is, the probability of a fine-tuned universe under the theistic hypothesis is:

P(FTU|T&K&L) = Area(FTU)/Area(PU)  << 1

Conclusion: given that we know that life exists, the probability of discovering we are living in a universe with parameters fine-tuned for life is much higher under the naturalistic hypothesis than under the theistic hypothesis.