But what if the constants are necessary?

On the fine-tuning argument for the existence of God.

Before you are prejudiced, please note your answers to the following question. @hat is your credence that the physical constants are necessary, e.g. that there is no possible world with the same laws of physics as ours except where the fine-structure constant has a different value than it does? Write it down, or leave it in a comment before liking and smashing that subscribe button.

So, the fine-tuning argument for the existence of God. Read this post if you’re unfamiliar with it. In sum, it works as follows. Supposedly, there are various physical constants such that, if they were just a tiny bit different, life in this universe would be impossible. Moreover, there is little to no a priori reason to suspect these values for the constants are especially likely—the only thing special about the values is that they allow for the existence of life, and the probability of the constants having sufficiently close values to what they do is super duper tiny. So, conditional on their being no God (and no other perhaps impersonal force that prefers the existence of life), it seems super unlikely that life would exist. Conditional on God, though, maybe it’s still unlikely material life would exist, but not as unlikely. Therefore, the existence of life in our universe is strong Bayesian evidence for God.

Lots of different numbers show up for how unlikely fine-tuning would be depending on which constants are under discussion, so let’s say that the probability of getting fine-tuned constants by chance is something like 10^-30, which seems representative for what the proponents of this argument claim. Actually, proponents often boast much smaller probabilities; but 10^-30 will be small enough for our purposes.

As I suggested, there are views other than theism that might predict fine-tuning, like axiarchism, the idea that things are the way they are simply because it is good that they are this way (but not through the actions of a God). To simplify the discussion, I will ignore those hypotheses and pretend the only hypotheses at play are theism and normal, naturalistic, Richard Dawkins-style atheism. When I say “If God doesn’t exist…,” note that I am saying “If store-brand naturalistic atheism is true….” You may replace “God” with “God, or the Good, or whatever else is the kind of thing that might orient the universe towards life.”

So, to formalize, let G be the proposition that God exists, and let F be the proposition that the constants are fine-tuned for life. Then we have:

\(\frac{P(G|F)}{P(\lnot G | F)} = \frac{P(F|G)}{P(F|\lnot G)}\frac{P(G)}{P(\lnot G)}\)

(if you do not understand this formula, then give me money to learn the Way of Bayes. Or use your free trial. Or read the Wikipedia article for Bayes’ theorem.)

The quantity on the left is how likely theism is compared to atheism given fine-tuning (the posterior odds). The first factor on the right is how much theism predicts fine-tuning compared to atheism (the likelihood ratio). The second factor on the right is how likely God’s existence is compared to atheism before taking fine-tuning into account (the prior odds). Now, maybe you find theism super duper implausible a priori. Maybe it has, like, a one in a million chance of being true before we look at the empirical evidence. Or surely, at least, a 1 in 10¹⁰ probability. As for P(F|G)? Maybe you think the only reason we think theism predicts fine-tuning is that we’re biased in favor of thinking God would totally want to create us, biased perhaps by the narratives of popular religions. Maybe he’d only probably only create angels, or something. But surely there is at least a 1 in a million chance he would want to create life like us? Or at least 1 in 10¹⁰? Finally, there is P(F|~G). This will be one of the tiny numbers that theists boast about how unlikely for the constants to be what they are assuming a naturalistic world—10^-30, we are supposing. Therefore, we have

\(\frac{P(G|F)}{P(\lnot G|F)} = \frac{10^{-10}}{10^{-30}}\cdot 10^{-10} = 10^{10}\)

That is, given these numbers, given that we observe fine-tuning, God existing is 10¹⁰ times more likely than not. So if the argument works, you should take fine-tuning to be incredibly strong evidence for God! If you think even 10^-10 is an implausibly large estimate for the two quantities, I think you are probably overconfident or scope-insensitive, but I also remind you that the fine-tuning proponents often boast much smaller numbers than 10^-30, and you should look at their arguments in more detail.

For today, let us suppose that almost everything about the fine-tuning argument works: there really is fine-tuning, the values of constants we observe are super unlikely on naturalism, even compared to the prior odds of God existing and of him fine-tuning the universe for life. Today, I discuss just one objection: what if the physical constants are necessary? What if alpha, the fine-structure constant, just could not have been anything else, and a more developed physical theory will reveal this fact? Then, it may seem, the probability of the constants being what they are given naturalism will be 1, so fine-tuning is no longer comparatively likely given God’s existence.

The standard response to this objection is that this is a Bayesian argument. The probabilities above are meant to reflect our uncertainty, not any kind of objective likelihood. Water is H₂O,¹ and this fact is metaphysically necessary, but my confidence that water is H₂O is not 1; maybe the scientists are drastically mistaken, or I am misremembering what I learned, etc. Or at the very least, a few hundred years ago, a reasonable person’s confidence that water is H₂O would not even be close to 1. Yet it was still just as metaphysically necessary; it was of the essence of water to be H₂O before anyone knew so. It is the degree of uncertainty that the fine-tuner cares about, not anything else.

I will get to why I ultimately think “The constants could be necessary” is a bad objection, but I don’t think the standard response works (and, do note, that the standard response doesn’t work is my only thesis for this post). For while it is true that the constants being necessary doesn’t change the prior (low) probability that they are what they have to be for life to exist, it does change the relevant relationships of evidential dependence, such that if the constants are necessary, then the fine-tuning argument doesn’t work.

E is said to be evidence for H if the probability of H given E is greater than the prior probability of H. Formally: P(H|E) > P(H). A proposition S is said to screen out the evidence E for H provided that learning S would make E no longer evidence for (or against) H. Formally: S screens outs the evidence E for H provided that P(H|E) > P(H) but P(H|E,S) = P(H|S). For example, it being Spring is evidence that my car is wet, since it rains more in the Spring. But if I learn that it did in fact rain today, then its being Spring is no longer evidence for or against my car being wet. (Intuitively: learning whether it’s raining already subsumes all the evidence I’d get for my car being wet from the season). Therefore, the evidential dependence between the season and my car’s wetness is screened out by my observation that it is raining. Learning that it is raining destroys the ability of the season to be evidence for or against my car’s wetness.

Let us suppose that an oracle tells us that N = the constants are metaphysically necessary as the atheist alleges, just as it is metaphysically necessary 1+1=2. Let us, now, take the our two pieces of evidence—fine-tuning and the necessity of the constants—into account at the same time, and see how they bear on God’s existence. We have:

\(\frac{P(G|F, N)}{P(\lnot G | F, N)} = \frac{P(F\land N|G)}{P(F\land N|\lnot G)}\frac{P(G)}{P(\lnot G)} = \frac{P(F|N,G)}{P(F|N,\lnot G)}\frac{P(N|G)}{P(N|\lnot G)}\frac{P(G)}{P(\lnot G)}\)

This is a point where I might be making an oversight, but it seems to me that whether God exists, by itself, has little evidential bearing on whether the physical constants are metaphysically necessary, just like how, if an oracle told me whether God exists or not would not, I don’t think I’d very much change my credence in the proposition that 1+1=2, water is H₂O, two things can’t be in the same place at the time time, etc. are metaphysically necessary.² Therefore, I assume the middle term on the right is 1. Please push back if that assumption seems unjustified. We have, then, that

\(\frac{P(G|F, N)}{P(\lnot G | F, N)} \approx \frac{P(F|N,G)}{P(F|N,\lnot G)}\frac{P(G)}{P(\lnot G)}\)

As before, I assume the prior odds of God’s existence are not super extreme. Maybe you find it a priori very unlikely, but I doubt it’s anything like 10^-30 unlikely.

What is P(F|N,G)? This is where things get interesting. I claim that this quantity is simply equal to P(F|N): the probability that the metaphysically necessary values of the constants, whatever that may be, turn out to be the fine-tuned ones that allow for life. Intuitively, I think this is true because, on the assumption that the constants are necessary, God cannot control their values.³ The reason that, forgetting about the necessity of the constants, fine-tuning is more expected on God’s existence is because it is not-insanely-unlikely that God desires to create a physical universe fine-tuned for life. But if the constants are metaphysically necessary, then God’s desires would have no influence on their values, and indeed not be evidence regarding their values.⁴ Don’t get me wrong, P(F|N) still seems insanely low. Whatever deeper physical or mathematical truths render the constants necessary, it seems like they would have no regard for the existence of life, so it would seem like a metaphysical miracle that the necessary values of the constants just happens to fall in the tiny range that allows for life. But my claim, here, is simply that P(F|N,G) = P(F|N).

For the same reasons, it seems that P(F|N,~G) = P(F|N). Perhaps there are some deeper physical or mathematical truths such that, once we discover them, we’ll see alpha just had to have the value it actually does. But it doesn’t seem like learning God doesn’t exist would change your credence that, given that the constants are necessary, they have the fine-tuned values, since presumably whatever process or theoretical results the atheist imagines that explains the necessary values of the constants isn’t sensitive to God’s existence. Like how the mathematical explanation for why the 100^th digit of e is 7 will give the same answer regardless of whether God exists.

Recall our previous formula for the odds of God’s existence given fine-tuning and the necessity of the constants:

\(\frac{P(G|F, N)}{P(\lnot G | F, N)} \approx \frac{P(F|N,G)}{P(F|N,\lnot G)}\frac{P(G)}{P(\lnot G)}\)

If I am right that P(F|N,G) = P(F|N) and P(F|N,~G) = P(F|N), then the likelihood ratio is 1, and then this reduces to

\(\frac{P(G|F, N)}{P(\lnot G | F, N)} \approx \frac{P(G)}{P(\lnot G)}\)

Or, in other words, the odds of God existing given fine-tuning and the necessity of the constants is just whatever you originally thought the odds of God’s existence were before. This is to say, if you already believed that the constants are necessary, then observing fine-tuning doesn’t give you evidence for God relative to your prior probability.

The argument can be made more cleanly. The claim that fine-tuning in conjunction with the necessity of the constants don’t provide evidence for God is just

\(P(G) = P(G | F,N)\)

This, in turn, follows from two assumptions (check my work):

\(\begin{align} (1)&\,\,\,\,\, P(N|G) = P(N)\\ (2)&\,\,\,\,\, P(F|N,G) = P(F|N) \end{align}\)

(1) states that learning that God exists doesn’t give evidence for or against the constants being necessary. This can be doubted for the reasons described in footnote 3, but when it comes to the atheist who says “the constants might be necessary,” I have in mind someone who thinks a deeper theoretical explanation (and nothing referring to the choice of God) will show the constants have to be what they are, like how deeper theoretical explanations show that c² = 1/μ₀ε₀. If we have in mind this sort of hypothesis when we refer to N, then (1) seems true by comparison to similar cases.

(2) is what I argued for with the control argument. Given that the constants are necessary in the way the atheist imagines, God’s existence would be no evidence for or against the constants being fine-tuned. For, again, the reason we have an evidential dependence between God and fine-tuning is because we expect a not-super-tiny probability that God would want a fine-tuned universe. But conditional on the constants being necessary, he cannot control their values, and so God desiring a fine-tuned universe is not evidence for the constants being fine-tuned.

The conclusion is: if an oracle were to tell us that the constants are necessary in the relevant manner, then the fine-tuning argument would not work. We don’t have oracles, but if you find a really good reason to think the constants are necessary, then that should correspondingly diminish the compelling of the fine-tuning argument.

Richard Dawkins will read this (I am very famous) and then cry tears of joy. “Aha! I can just believe the constants are necessary, and then defeat the fine-tuning argument!”

Not so fast, bucko. Here’s an important point: as far as our subjective uncertainty goes, going from our prior probability (so, before we know about fine-tuning), it seems like whether the constants are necessary will be evidentially independent of whether they’re fine-tuned. If you’re Boltzmann brain suddenly popping into existence who doesn’t know physics and who also hasn’t observed the physical world, and then an oracle tells you that the universe is fine-tuned and God doesn’t exist (and all the other non-naturalistic life-oriented hypothesis are false), your reaction wouldn’t be “Hm, guess the constants are necessary.” No, you’d think a massive and lucky coincidence happened, and your consequence that a lucky metaphysical coincidence happened would not increase. Indeed, from (1) and (2) above, it follows that

\(\begin{align} (1')&\,\,\,\,\, P(N|\lnot G) = P(N)\\ (2')&\,\,\,\,\, P(F|N,\lnot G) = P(F|N) \end{align}\)

and from this it follows that

\(\begin{align*} P(N | F,\lnot G) &= \frac{P(F\land N\land \lnot G)}{P(F\land \lnot G)}\\ &= \frac{P(F\land N\land \lnot G)}{P(N\land \lnot G)}\frac{P(N\land \lnot G)}{P(F\land \lnot G)}\\ &=^{(1')} \frac{P(F\land N)}{P(N)} \frac{P(N\land \lnot G)}{P(F\land \lnot G)}\\ &= P(F|N) \frac{P(N | \lnot G)}{P(F | \lnot G)}\\ &= \frac{P(F|N)}{P(F|\lnot G)} P(N|\lnot G) \end{align*}\)

Consider the fraction in the last line. Unless you think there is some particular reason why we should a priori expect why constants in a godless universe are more likely to be fine-tuned for life than metaphysically necessary constants, that fraction is no less than one. Indeed, I would say it’s equal to 1: both the probability distribution of possible constants conditional on the constants (whatever they are) being necessary and the distribution conditional on atheism are both just whatever that distribution is when we ignore the influence of any entity that can cause the universe to be hospitable to life. The constants in a godless universe and those in a universe with constants necessitated by deeper physical truths are equally indifferent to life. Nevertheless, if the fraction is no less than 1, we have

\(P(N|F,\lnot G) \leq P(N | \lnot G)\)

This means that, if you are an atheist hearing the fine-tuning argument for the first time—even if you’re super confident God doesn’t exist—you should not react by raising your confidence that the constants are necessary while maintaining your confidence God doesn’t exist.

Even though it is true that if the constants are necessary then the fine-tuning argument does not work, that does not mean fine-tuning is evidence that the constants are necessary, even if you go in super confident that God doesn’t exist. So you should only reject the argument on these grounds if you antecedently thought the constants are likely to be necessary. Unfortunately, at the beginning of this post, I tricked you into admitting that your antecedent confidence in that claim is low, and if you try to go back on that, I will Dutch Book you into oblivion.

Okay, this is a small point, so who cares? The objection people say doesn’t work doesn’t work. Well, I have a secret reason for wanting to write this. There are a lot of these Bayesian-type arguments for God, of the form “The universe is fortunate in these super-duper-unlikely ways, but they are not super-duper-unlikely conditional on God, so we have strong evidence for God.” And I have a suspicion that the analogue of “What if the constants are necessary” actually works in some other cases. I suspect it works in the case of the argument from psychophysical harmony, as I have high antecedent confidence that it is metaphysically impossible that anyone in my physical state has a different mental state from me. But you will have to wait for a future post.

Anyway, the takeaway: I don’t think “The constants might be necessary” is a good response to the Fine-Tuning Argument, since the constants probably aren’t necessary (physicists can chime in here, but my impression is that the specifics of our world will probably still be due to free parameters in a more complete theory). But you should not reply to this objection by saying “This is about epistemic possibility, not metaphysical possibility, so the necessity of the constants makes no difference.” As far as I can tell, you either have to address whether the constants are in fact necessary, or say something more complicated like what is addressed below.

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You can stop reading here unless you are starving for an extra helping of philosophy. I got some nice comments on the above from Joe Schmid of the amazing YouTube channel The Majesty of Reason, and I should reply to them here. First, let us consider two analogous arguments to the Fine-Tuning Argument. The first is what I will call the “Flo-Tuning Argument”, and the second was called the “Awesome Theological Argument” by Luke Barnes.

The Flo-Tuning Argument: Flo noticed that if you multiply μ₀ (the strength of the magnetic force) by ε₀ (the strength of the electrical force), you get units of one over velocity squared. So Flo picked her favorite velocity, the speed of light c, and calculated the dimensionless quantity φ = c²μ₀ε₀, which she dubbed “Flo’s constant.” What’s more, she proved that if φ where even a tiny bit off from the value it actually has, all sorts of catastrophe would result and life would be impossible. Therefore, she reasoned, it is likely that the value of φ was fine-tuned by God.

So, I think the Flo-Tuning Argument is not good, even if we grant that life would be impossible if φ had a slightly different value. The reason is that φ is equal to exactly 1, and it had to be that way given how physics works. Taking Maxwell’s equations you can deduce that the electric and magnetic fields form a wave, and the velocity of the resulting wave is the square root of 1/μ₀ε₀. But an electromagnetic wave is just what light is, so the speed of light is given by c² = 1/μ₀ε₀, so φ = 1. Sure, if you make an assumption that violates the laws of physics, maybe you can prove from that that life would be impossible⁵—that is not a surprising result, and so we should not feel lucky or surprised that φ = 1. I bring this up because this sort of thing is what I have in mind with the atheist who supposes the values of the constants are necessary, though necessary in a less obvious way than above.

The Awesome Theological Argument: One night, the stars in the sky seem to miraculously spell out the entire Prologue to the Gospel of John in Koine Greek. Everyone sees this, and the event is confirmed by all astronomical measurements, so the idea of it being a wide group hallucination is ruled out. Such an event is extremely unlikely on naturalism, but not extremely unlikely on theism, so the event provides strong evidence for theism.

I take it that the Awesome Theological Argument is good—or at least, it would be good if the relevant events actually happened. Sure, we could argue about whether it really proves God exists; maybe demons or aliens or our simulators are trying to trick us. But such an event would certainly be strong evidence for the existence of God.

The reason people like to bring up the Awesome Theological Argument is because a lot of objections to the Fine-Tuning Argument also rule the former out. “God’s existence does not have a well-defined prior probability”; if such a point rules out the Fine-Tuning Argument, it also rules out the commonsense reasoning “The stars spelling out the Gospel of John is a lot more likely if God exists, so this seems to be evidence God exists.” “The constants might be necessary”; if someone concluded it might be metaphysically necessary that the stars are arranged just as they are, that would seem to be an ad hoc refusal to confront the evidence. The lesson: if you have an objection to fine-tuning, make sure it doesn’t also rule out the cases that would most obviously count as evidence for the existence of God.

We’ll get back to the Awesome Theological Argument and the Flo-Tuning Argument. A very important point that Joe raises is that even if you come in with antecedently high confidence that the constants are necessary, the datum of fine-tuning might count as evidence against the constants being necessary. He gives a fun analogy demonstrating why this would be reasonable:

Here’s an analogy. We’ve heard about large rocks on No Name Island. No one in our community knows for sure whether they’re movable, as none of us has ever been there to confirm with certainty. We’ve just heard various testimonial reports of varying quality from others outside our community. Some philosophers in our community hypothesize that the rocks are really just large outgrowths of the mountain underneath and so are immovable by humans. Other philosophers hypothesize that the rocks are instead boulders that could be moved by humans cooperating to push them around. You, Flo, are the foremost philosophical proponent of the immovable rocks hypothesis, pointing to the solid testimony in its favor from several reputable sources. But suppose you accompany me as we travel for the first time to No Name Island. As we’re about to land, we see from our helicopter those large rocks arranged to spell out “Welcome to No Name island! Enjoy your stay :)”.

Clearly, the arrangements of the rocks is so arbitrary from a natural point of view that we should conclude they are not immovable and that humans arranged them to be as they are. Sure, if an oracle told us the rocks were immovable with credence 1, the strange pattern of the rocks would no longer be evidence that they were fine-tuned by humans. But we do not assign probability 1 to immovable rocks, and it seems on any reasonable priors the observation will be strong evidence against immovable rocks.

This is compatible with the letter of what I argued: conditional on necessity of the constants, fine-tuning is not evidence for God. But conditional on our actual evidence, including our uncertainty of the necessity of the constants, fine-tuning might be evidence that the constants aren’t necessary and thereby count as evidence for God, even if you come in with high confidence that the constants are necessary. So the atheist is in a worse position than even I suggested above.

It seems to me that, in the case of fine-tuning, Joe is right. The possibility of large-scale complex structures, let alone life, is arbitrary from the point of view of fundamental physics, so having constants fine-tuned for such seems to be strong evidence that the constants are not necessary (not that I, personally, needed that evidence). But I must say I am not confident in this verdict, in particular when it comes to the Flo-Tuning Argument. I do not see what applies in the case of the fine-structure constant that does not apply to φ.⁶ I get the sense that if we really saw how the constants are necessary (assuming such is true), and we could see that they had to be what they are to the same extent that we can see φ has to be exactly 1, then we would no longer find the reasoning under the supposition that the constants are different to be particularly meaningful. As far as things seem to me, the reason it seems like fine-tuning is evidence against necessary constants just reduces to incredulity at the idea of their not being free parameters (or derivable from other free parameters). Justified incredulity, I think, but I don’t know if the considerations here should move the atheist who for some reason really expects we’ll fine more fundamental reasons for the values of the constants along the lines of why φ = 1. So, I suppose, I might need help from a reader in identifying what might make the Flo-Tuning case non-representative.

Joe gives another reply to me, arguing that even conditional on the necessity of the constants, we expect a higher chance of the constants being what they are conditional on theism (note he said these things in the context of the psychophysical harmony argument, so I have made the relevant substitutions):

I’ve been toying with the thought that even if God doesn’t have control over the [values of the constants] due to their necessity, their [fine-tuned] character can still significantly favor theism over naturalism. The (rough) reason is that, on theism, it’s not super-duper unlikely that many necessary truths are somehow grounded in, dependent on, or explained ultimately by God’s perfect essence.

…

And even if these claims have a low probability conditional on theism (which will result in a low probability of [fine-tuning] conditional on theism), I suspect that it won’t be overwhelmingly, fantastically low — which is arguably how likely [fine-tuning] is on naturalism (even supposing that, whatever the laws happen to be, they’re necessarily that way, which doesn’t boost the probability of their having any particular character). So, if we follow this line of thought, [fine-tuning] can still be serious evidence for theism even if the [values of the constants] are necessary.

My reply here is similar. It seems unlikely that, if it were shown that φ not being 1 would lead to catastrophe, this would give us evidence that Maxwell’s equations reflect God’s nature. If there is a disanalogy here with the fine-structure constant, then again, I will need help from the reader to find it.

Perhaps what is going on is this. A possibility I have been supposing is that, in the case where a constant is necessary, assuming it has something other than its necessary value could be shown to lead to catastrophe. Again, if I am wrong about this in the case of e.g. φ, then please correct me (I only have a fake undergrad degree in physics). But assume this is so. Then finding out that some constant having a different value would be catastrophic would, I think, be good evidence that its value its necessary, like how φ = 1 is necessary. More generally, it seems apparently-fine-tuned constants would be evidence that either they are arbitrary parameters set by God or they are necessary.

If it turns out that assuming φ is not 1 could not plausibly be shown to lead to catastrophic consequences, then I wholly concede Joe’s argument in the case of fine-tuning.

Lastly, Joe rightly asks me to consider what I say in the case of the Awesome Theological Argument, the case where the prologue of the Gospel of John is written in the stars. What I say is this. The sort of necessity the atheist envisions when they suppose the constants are necessary is similar to that which explains why φ = 1. So if we supposed that we found out that the writing in the stars is similarly necessary—that is, we have deep theoretical reason showing it had to be the case, enough that we would expect the prologue of John to be written in the stars even conditional on atheism or Islam being true—then, yeah, it seems like the writing in the stars wouldn’t be evidence for God/Christianity anymore. Our justified incredulity that there could ever be a case where the writing in the stars isn’t evidence for God seems to reduce to justified incredulity that we could find out that such an arrangement of the stars is necessary in the required manner; such incredulity does not seem to reflect what counts as evidence for God conditional on finding deeper theoretical explanation for why things have to be the way they are.

One way we can compare the two cases is as follows. If a genius physicist came along and purported to show that the writing in the stars is as necessary as that φ = 1 and is to be expected even conditional on atheism, I don’t think I could ever become convinced he didn’t screw up somewhere. But if a genius physicist came along and showed that a physical constant has to be what it is just as φ had to be 1, it wouldn’t take much after that for me to be convinced that he’s right.

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I think, ultimately, what I want to say about the Fine-Tuning Argument stands. The atheist who supposes the constants are necessary cannot be replied to by simply saying he’s confusing metaphysical and epistemic possibility, since in fact the necessity of the constants would screen the evidential connection between fine-tuning and God. But the atheist cannot get out of the argument in this manner unless he had an antecedently high confidence that the constants are necessary, before seeing the fine-tuning argument. Indeed, based on what Joe said, it seems pretty likely that fine-tuning should actually decrease his confidence in such a claim.

What does this say about psychophysical harmony? We will have to wait.

1. I know what many will say in response to this example, and I do not negotiate with terrorists.

2. I do not claim that all statements of metaphysical necessity would be largely unaffected. For example, if I learned with credence 1 that God exists, I would become highly confident that God necessarily exists. But the case of the constants seems more like the 1+1=2 case.

3. The control argument was briefly brought up by Brian Cutter in this interview (at about 1:03:00) on the argument from psychophysical harmony (thanks to Joe Schmid for this reference). Cutter replies that, in order for necessity to screen out evidence for God, we would have to be essentially certain of the necessity claim, which seems unreasonable. Why would we need near-certainty? The idea is that, given the four hypotheses (concerning the existence of God and the necessity claim), only God + contingency doesn’t have a teeny tiny probability of getting psychophysical harmony/fine-tuning. This is essentially the same as the point Joe gave to me, that fine-tuning is evidence against the necessity of the constants. I’ll talk about that later.

But what is important is that, assuming the reply made by Cutter works, we cannot reply to the atheist who brings up the necessity claim by saying “That only concerns metaphysical possibility, but the argument only talks about epistemic possibility,” which Cutter did briefly before the control argument was addressed. You’d need to address how well no God + necessity predicts the relevant datum. (In the case of psychophysical harmony, I must admit, my prior probability conditional on a posteriori physicalism that intrinsically-undesirable-feelings will correlate with avoidance-behavior etc. is pretty high. But that is a matter for another post).

4. I should be careful here. It is not unreasonable to think: “God’s existence is metaphysically necessary. God necessarily desires to create the best of all possible worlds, since he is necessarily good. Therefore, the features of our world in virtue of which it is the best—including fine-tuning—are metaphysically necessary. Yet they are still only necessary because they depend on what God necessarily desires. In particular, learning God’s desires will be evidence for how the world necessarily is.” In reply, I assume that conditional on God’s existence, some thing are necessary because of God’s necessary choices, and some things are necessary irrespective of God’s choice. In the latter category, I believe we have things like 1+1=2. I take N to be the proposition that the constants are necessary in that latter sense; this is in fact what the atheist has in mind when they say “Maybe the constants are necessary.” Now, if you’re one of the kinds of theist who think the second category of necessary truths isn’t real—if you, like Descartes, believe that God created the laws of mathematics and even logic—then I have to concede that nothing in this post should be persuasive to you, and the truth of your position would be enough to rebut the atheist. This is, from my understanding, a relatively marginal view, which doesn’t mean it’s wrong, but it does make me comfortable to limit my scope in this post.

5. Perhaps I am overestimating how likely it is such an argument could be made. If any physicists want to weigh in and tell me “There’s no way assuming that φ isn’t 1 would lead to the sorts of conclusions people make about the constants in the Fine-Tuning Argument,” please do!

6. One thing to note is that 1 is a much more natural value than the value of the fine-structure constant, so we have a reasonable high a priori probability that a given dimensionless constant will be 1. We could even imagine physicists inferring that there must be some principled reason for φ to be exactly 1, even before going through the reasoning. But—and I could be wrong here, so again, please correct me if you’re a physicist—I think I could have chosen an example with a less-obviously-natural value than 1, indeed perhaps with a level of naturalness that could plausibly be had by e.g. the fine-structure constant.