Fine-tuning, possibility, and probability

One of the most popular arguments for the existence of God makes no sense.

One of the most popular arguments for the existence of God is the “fine-tuning argument.” This argument begins from the observation that life exists, and that exists at least in part because the fundamental laws of physics allow for the existence of life; if they were different, life would be impossible. For instance, if gravity were weaker, stars and planets would never form, because it is gravity that pulls matter together into the cosmic structures we’re all familiar with. A universe with weak gravity would be a universe of scattered cosmic dust. Yet if gravity were stronger, the mass of the universe would pull together too strongly and everything would collapse into one massive black hole. Neither of those universes — the universe of scattered dust or the universe of one massive black hole — is a universe where life could ever have existed. In modern physics, the strength of gravitational force is determined by a number called the “gravitational constant.” And if we look at all possible values of the gravitational constant, we find that the vast majority of them lead to either scattered dust or black holes. It’s only a vanishingly small number of values that allow life to exist. Yet the actual gravitational constant is in that vanishingly small set of life-permitting values. In this sense, the gravitational constant is “fine-tuned” for the existence of life.

Similar considerations hold for all of the other fundamental physical constants: if they were substantially different, then the universe would not sustain life of any kind. And of all the possible values of these constants, the vast majority of them would result in life-inhospitable universes. So it’s not just the gravitational constant; all of the fundamental physical constants are “fine-tuned” to allow for the existence of life.

The probability of this happening by chance is miniscule. So the physical constants can’t have arisen by chance. They were actively finely tuned by a cosmic fine-tuner. And that cosmic fine-tuner is God. So these fine-tuned physical constants make it overwhelmingly likely that God exists.

Although this argument is popular, it really doesn’t make any sense if you think about it. There are two related flaws. First, a central idea in the argument is that, “of the possible values” for the physical constants, only a small number support life. But what does that mean? What are the “possible values” of the physical constants? People who support the cosmological argument typically think that the physical constants are numbers, so any number is a “possible” value of one of the physical constants. There’s an (uncountably) infinite amount of numbers, so there’s an infinite number of possible values for the physical constants. This is a bit weird! It’s a bit like if I held up a bag of marbles and asked you how many marbles are in the bag, and you said, “Well, there’s some number of marbles in the bag. And there’s an infinite number of numbers, any of which are equally possible. So I’ll guess fifty trillion marbles, since ‘50 trillion’ is a number and is therefore possible — and just as possible as any other number.”

…Ok, that’s not a great analogy; there are a number of differences between the “bag of marbles” case and the fine-tuning of the physical constants. The point is simply to highlight a certain pattern of reasoning: “Any number is possible because all numbers are numbers, and we’re just talking about numbers.” That kind of reasoning sounds bizarre in any other context, and I think that it sounds just as bizarre in the case of the fine-tuning argument. And the fine-tuning argument does depend on this kind of reasoning. “If we simulate what the universe would be like with different numbers plugged in for the physical constants, the vast majority of simulations don’t result in life-permitting conditions.” That’s the only argument given for the idea that the vast majority of possible physical conditions don’t support life. But that argument relies on the idea that any number for a physical constant represents a real possibility. And, again, that’s weird.

In fact, the marbles case shows that there’s a deeper reason why it’s absurd to talk about an infinite range of possible numbers for the physical constants. Why don’t we say that there could be fifty trillion marbles in my small bag? Well, because 50 trillion marbles couldn’t fit. Now, they could fit — if they overlapped. But marbles can’t overlap; two things can’t be in the same place at the same time. Yet this is because of how physics works: the forces between the atoms in the marbles push those marbles apart so they can’t phase through one another to overlap. The lesson here is that when we say what is or isn’t possible, we are usually talking about what is or isn’t possible given the laws of physics. But the laws of physics include the fundamental physical constants. Given the laws of physics, then, only one set of physical constants is possible. So, given the laws of physics, it’s not the case that a huge range of physical constants is possible. Given the laws of physics, the only possible physical constants are the actual ones.

Now sometimes when we talk about what’s possible, we aren’t taking the laws of physics as given. We might be talking about what’s “logically possible” rather than what’s “physically possible.” There is only one set of physical constants that are physically possible, but there are an infinite number of constants that are logically possible. But it’s also logically possible that there are an infinite number of marbles in the bag. In our actual reasoning about the world, it’s bizarre to take anything that is logically possible as a real possibility. So why should it matter that there are an infinite number of logically possible values for the physical constants?

In general, then: in what sense are there an infinite number of “possible” values for the physical constants? And why does it matter for our reasoning about the world that there are an infinite number of physical constants in that sense (whatever it is)? There’s no particularly good answer to those questions. “There sure are a lot of numbers” is about as sophisticated as the fine-tuning argument actually gets.

The second way that this argument doesn’t make sense is in the way it evokes the notion of probability. “There are an infinite number of possible values for the physical constants, so the probability of those constants being in the narrow fine-tuned range is very low.” Why think this?? What theory of “probability” are we assuming here?

One popular theory of probability is the frequentist theory of probability that says that the probability of some event is (the number of times that event occurs divided by the number of times an event could have occurred). So if you flip a coin 100 times and it lands heads 48 times, then the probability of that one of those coin flips lands heads is 48%. On this frequentist theory of probability, what is the probability that the constants are what they are? The physical constants have not been fixed more than one time; there is one set of physical constants. Those physical constants are life-allowing 1 out of 1 times, 100%. So it’s not highly improbable that the constants are life-allowing. Quite the opposite!

Now perhaps that just goes to show that we shouldn’t be accepting a frequentist interpretation of probability. But (1) some people think that the frequentist theory of probability is the only one that makes sense, and so the fine-tuning argument is committed to those people being wrong. But, more importantly, (2) even if we reject the frequentist theory of probability, then what theory of probability should we accept when thinking about the fine-tuning argument?

Another popular theory of probability is the subjectivist theory, where the probability of some event is just how confident you are that it occurred. Well, I’m 100% confident that the physical constants are life-allowing. (I’m alive, and I wouldn’t be if they weren’t.) Everyone else who thinks about this for a moment will come to the same conclusion. So on a subjectivist theory of probability, it’s not highly improbable that the constants are life-allowing. Again, quite the opposite.

The only major theory of probability on which the probability that the physical constants are life-allowing is not very high is a logical theory of probability, where we assign an equal probability to every possible outcome within a defined set of possible outcomes. But accepting a logical theory of probability has all of the same problems with accepting a logical theory of possibility. There are an infinite number of logical possibilities, and thus an infinite number of things that have some non-zero logical probability. But almost all of those logical possibilities are irrelevant for any of our reasoning about the world.¹ So again: why should it be relevant that there are an infinite number of numbers?

I think that these errors with the fine-tuning argument have a common flaw. Advocates of the fine-tuning argument seem to assume a sort of weird story where the physical constants were fixed at some point. At one point, there were no physical constants, but then something happened and the physical constants got fixed. That fixing either happened via God (who wants there to be life) or via a sort of cosmic random-number-generator that could have outputted any number as a value for the physical constants, but just so happened to select life-permitting constants. How miraculous!

But this is silly. Not just because there is no cosmic random number generator, but because it’s not at all clear that there was any event where the physical constants were fixed. Theists like to say that God is eternal, He exists out of time and thus was never created and never could have been created. It’s a kind of category mistake to think about the idea of God’s being created; he’s not the kind of thing that could be created. Similarly, I suggest, the numerical values of the physical constants should be understood as eternal in the same sense. While it’s clear that the values of the physical constants correspond to something in reality, it’s not at all clear what exactly they do correspond to, and no reason to think that that aspect of reality is something that must have been fixed, created, or otherwise determined at some point.

The idea that there was any process that “tuned” the physical constants (finely or otherwise) is a dogma that makes little sense; what would be involved in tuning the physical constants anyway? And the idea that every possible number is a “possible” value for the physical constants, which thereby implies that the actual numbers are highly “improbable” is another dogma; why are we taking all numbers to count as relevant, live possibilities? So the fine-tuning argument as a whole is equally dogmatic. It’s perhaps an acceptable ritual for believers to chant it for one another. But it doesn’t amount to a seriously persuasive argument for any reasonable skeptic.

1. A point about math: If there are an uncountably infinite number of possibilities — and, according to the usual logic behind the fine-tuning argument, there are an uncountably infinite number of possibilities — then the probability of any number being correct isn’t low, it’s zero. So according to the usual logic, the probability that the physical constants are what they are is 0%. But the physical constants are what they are! This is a further reason to think that the usual logic is wrong.