The Fine-Tuning Argument and the Base Rate Fallacy.

0. Introduction

The Fine-Tuning Argument is used by many apologists, such as William Lane Craig. It is a common part of the contemporary apologetical repertoire. However, I argue that it provides no reason to think that the universe was designed. One does not need to look in too much detail about actual physics, and almost the whole set up can be conceded to the apologist. The objection is a version of the base-rate fallacy. From relatively simple considerations of the issue, it is clear that relevant variables are being left out of the equation which results in the overall probability being impossible to assess.

The Fine Tuning Argument starts with an observation about the values of various parameters in physics, such as the speed of light, the Plank constant and the mass of the electron, etc. The idea is that they are all delicately balanced, such that if one were to be changed by even a very small amount, this would radically alter the properties of the universe. Here is how Craig explains the point, in relation to the gravitational constant:

“If the gravitational constant had been out of tune by just one of these infinitesimally small increments, the universe would either have expanded and thinned out so rapidly that no stars could form and life couldn’t exist, or it would have collapsed back on itself with the same result: no stars, no planets, no life.” (Quote taken from here)

This phenomenon of ‘fine-tuning’ requires explanation, and Craig thinks that there are three possible types of explanation: necessity, chance or design.

Craig rules out necessity by saying:

“Is a life-prohibiting universe impossible? Far from it! It’s not only possible; it’s far more likely than a life-permitting universe. The constants and quantities are not determined by the laws of nature. There’s no reason or evidence to suggest that fine-tuning is necessary.” (ibid)

Chance is ruled out by the following:

“The probabilities involved are so ridiculously remote as to put the fine-tuning well beyond the reach of chance.” (ibid)

The only option that seems to be left on the table is design.

So the structure of the argument is as follows (where f = ‘There is fine-tuning’, n = ‘Fine-tuning is explained by necessity’, c = ‘Fine-tuning is explained by chance’, and d = ‘Fine tuning is explained by design’):

  1. f
  2. f → (n ∨ c ∨ d)
  3. ~n
  4. ~c
  5. Therefore, d.

1. Tuning

It seems from what we currently know about physics that there are about 20 parameters which are finely tuned in our universe (if the number is not exactly 20, this doesn’t matter – for what follows I will assume that it is 20). For the sake of clarity, let’s just consider one of these, and assume that it is a sort of range of values similar to a section of the real number line. This would make it somewhat like radio-wave frequencies. Then the ‘fine-tuning’ result that Craig is referring to has a nice analogy: our universe is a ‘radio station’ which broadcasts on only an extremely narrow range. This range is so narrow that if the dial were to be moved only a tiny amount, the coherence of the music that was being broadcast becomes nothing but white noise. That our universe is finely balanced like this is the result that has been gained from physics.

It is important to realise that this fine-tuning is logically compatible with there being other radio stations which one could ‘tune into’. Imagine I tune my radio into a frequency which is broadcasting some music, and that it is finely-tuned, so that if I were to nudge the dial even a tiny amount it would become white noise; from that it does not follow that there aren’t other radio stations I could tune into.

It is plausible (although I don’t know enough physics to know) that if one varied only one of the 20 or so parameters, such as gravity, to any extent (not just a small amount), but kept all the others fixed, then the result would be nothing other than white noise. Maybe, if you hold all 19 other values fixed, every other possible value for gravity results in noise. However, it doesn’t follow from this fact (if it is a fact at all) that there is no combination of all the values which results in a coherent structure. It might be that changing both gravity and the speed of light, and keeping all the others fixed, somehow results in a different, but equally coherent, universe.

In mathematics, a Lissajous figure is a graph of a system of parametric equations. These can be displayed on oscilloscopes, and lead to various rather beautiful patterns. Without going into any of the details (which are irrelevant), the point is that by varying the ratio of the two values (X and Y), one produces different patterns. Some combinations of values produce ordered geometrical structures, like lines or circles, while others produce what looks like a messy scribble. There are ‘pockets’ of order, which are divided by boundaries of ‘chaos’. This could be what the various combinations of values for the 20 physical parameters are like.

Fine-tuning says that immediately on either side of the precise values that these parameters have in our universe, there is ‘white noise’. But it does not say that there are no other combinations of values give rise to pockets of order just as complex as ours. It doesn’t say anything about that.

2. The problem of fine-tuning 

It might be replied that there could be a method for determining whether there are other pockets of order out there or if it is just white noise everywhere apart from these values, i.e. whether there are other radio stations than the one we are listening to or not. And maybe there is such a method in principle. However, it seems very unlikely that we have anything approaching it at the moment. And here the fineness of the fine-tuning turns back against the advocate of the fine-tuning argument. Here’s why it seems unlikely we will be able to establish this any time soon.

We are given numbers which are almost impossible to imagine for how unlikely the set of values we have would be if arrived at by chance. Craig suggests that if the gravitational constant were altered by one part in 10 to the 60th power (that’s 10 with 60 ‘0’s after it), then the universe as we know it would not exist. That’s a very big number. If each of the 20 parameters were this finely tuned, then each one would increase this number again by that amount. The mind recoils at how unlikely that is. This is part of the point of the argument, and why it seems like fine-tuning requires an explanation.

However, this is also a measure of how difficult it would be to find an alternative pocket of order in the sea of white noise. Imagine turning the dial of your radio trying to find a finely-tuned radio station, where if you turned the dial one part in 10 to the 60th power too far you would miss it. The chances are that you would roll right past it without realising it was there. This is Craig’s whole point. It would be very easy to scan through the frequency and miss it. But if you wanted to make the case that we had determined that there could be no other coherent combination of values to the parameters, you would have to be sure you had not accidentally scrolled past one of these pockets of coherence when you did whatever you did to rule them out. The scale of how fine the fine-tuning is also makes the prospect of being able to rule out other pockets of coherence in the sea of noise almost impossible to do. It would be like trying to find a needle in 10 to the 60th power of haystacks. Maybe there is a method of doing that, but it seems like an incredibly hard thing to do. The more the apologist adds numbers for the magnitude of fine-tuning, the more difficult it is to rule out there being other possible coherent combinations of values out there somewhere.

Thus, it seems like the prospects of discovering a fine-tuned pocket of coherence in the sea of white noise are extremely slim. But this just means that it seems almost impossible to be able to rule out the possibility that there is such additional a pocket of coherence hidden away somewhere.

Think about it from the other side. If things had gone differently, and the values of the parameters had been set differently, then there might be some weird type of alien trying to figure out if there were other pockets of coherence in the range of possible values for the parameters, and they would be extremely unlikely to find ours, precisely because ours (as Craig is so keen to express) is so delicately balanced. Thus the fine-tuning comes back to haunt the apologist here.

We have a pretty good understanding of what the values for the parameters are for our universe, although this is obviously the sort of thing that could (and probably will) change as our understanding deepens. But I do not think that we have a good understanding of what sort of universe would result throughout all the possible variations of values to the parameters. It is one thing to be able to say that immediately on either side of the values that our universe has there is white noise, and quite another to be able to say that there is no other pocket of coherence in the white noise anywhere.

The fine tuning result is like if you vote for party X, and your immediate neighbours on either side vote for party Y. You might be the only person in the whole country who votes for party X, but it doesn’t follow that this is the case just because you know that your neighbours didn’t.

If the above string of reasoning is correct, then for all the fine tuning result shows, there may be pockets of coherence all over the range of possible values for the parameters. There are loads of possible coherent Lissajous figures between the ‘scribbles’, and this might be how coherent universes are distributed against the white noise. There could be trillions of different combinations of values for the parameters which result in a sort of coherent universe, for all we know. And the magnitude of the numbers which the apologist wants to use to stress how unlikely it is that this very combination would come about by chance, is also a measure of how difficult it would be to find one if it were there.

3. The meaning of ‘life’

It seems that if the above reasoning is right, then other pockets of coherence are at least epistemically possible (i.e. possible for all we know). Let’s assume, just for simplicity, that there are at least some such alternative ways the parameters could be set which results in comparably stable and coherent universes as ours. Let’s also suppose that these are all as finely tuned as our universe is. For all we know, this is actually the case. But if it is the case, then it suggests a distinction between a universe is finely-tuned, and one that is fine-tuned for life. We might think that those other possible universes would be finely tuned, but not finely tuned for life because we could not exist in those universes. We are made of matter, which could not exist in those circumstances. It might be that something else which is somehow a bit like matter exists in those universes, but it would not be matter as we know it. Those places are entirely inhospitable to us.


But this doesn’t mean that they are not finely-tuned for life. It just means that they are not finely-tuned for us. The question we should really be addressing is whether anything living could exist in those universes.

Whether this is possible, of course, depends on precisely what we mean by ‘life’. This is obviously a contentious issue, but it seems to me that there are two very broad ways we could approach the issue, which are relevant for this discussion. Let’s call one ‘wide’ and one ‘narrow’.

Here is an example of a wide definition of ‘life’. For the sake of argument, let’s say that living things all have the following properties:

  • The capacity for growth
  • The capacity for reproduction
  • Some sort of functional interaction with their environment, possibly intentional

No doubt, there will be debate over the conditions that could be added, or removed, from this very partial and over-simplified list, and the details do not matter here. However, just note one thing about this list; none of these properties require the parameters listed in the usual presentations of the fine-tuning argument to take any particular value. So long an entity can grow, reproduce and interact with its environment, then it is living, regardless of whether it is made of atoms or some alien substance, such as schmatoms. Thus, on such a ‘wide’ definition of ‘life’, there is no a priori reason why ‘life’ could not exist in other universes, even if we couldn’t.

On the other hand, we might define ‘life’ in terms of something which is native to our universe, such as carbon molecules, or DNA. If, for example, the gravitational constant were even slightly different to how it is, then DNA could not exist. Thus, if life has to be made of DNA, then life could not exist in any pocket of coherence in the sea of white noise apart from ours.

So there are two ways of answering the question of whether an alternative set of values to the parameters which resulted in a coherent universe could support life – a wide and a narrow way. On the wide view the answer seems to be ‘yes’, and on the narrow view the answer is definitely ‘no’.

It seems to me that there is very little significance to the narrow answer. On that view, the universe is fine-tuned for life, but only because ‘life’ is defined in terms of something which is itself tied to the physical fine-tuning of the universe. The meaning of ‘life’ piggy-backs on the fine-tuning of the physical variables. And this makes it kind of uninteresting. The same reasoning means that the universe is fine-tuned for gold as well as life, because the meaning of ‘gold’ is also tied to specific things which exist only because of the values of the variables, i.e. atoms and nucleus’, etc. Thus, if we want to say ‘fine-tuned for life’ and have that mean something other than just ‘fine tuned’, then we should opt for the wide view, not the narrow one.

But then if we go for the wide view, we are faced with another completely unknown variable. Just as we have no idea how many other potential pockets of coherence there may be in the sea of white noise, we also have no idea how many of them could give rise to something which answers to a very wide definition of ‘life’. It might be that there are trillions of hidden pockets of coherence, and that they are all capable of giving rise to life. We just have no information about that whatsoever.



5. Back to the argument

What the preceding considerations show is that the usual arguments taken to rule out the ‘chance’ explanation are missing something very important to the equation. I completely concede that our universe is extremely finely-tuned, to the extent that Craig explains. This means that if the values of the parameters were changed even a tiny amount, then we could not exist. However, because we don’t have any idea whether other combinations of values to those parameters would result in coherent universes, which may contain ‘life’, we have no way of saying that the chances of a universe happening with life in it are small if the values of these parameters were determined randomly. It might be that in 50% of the combinations there is sufficient coherence for life to be possible. It might be 90% for all we know. Even if it were only 1%, that is not very unlikely. Things way less likely happen all the time. But the real point is that without knowing these extra details, the actual probability is simply impossible to assess. Merely considering how delicately balanced our universe is does not give us the full picture. Without the extra distributions (such as how many possible arrangements give rise to coherent universes, and how many of those give rise to life) we are completely in the dark about the overall picture.

This makes the argument an instance of the base-rate fallacy. The example on Wikipedia is the following:

“A group of police officers have breathalyzers displaying false drunkenness in 5% of the cases in which the driver is sober. However, the breathalyzers never fail to detect a truly drunk person. One in a thousand drivers is driving drunk. Suppose the police officers then stop a driver at random, and force the driver to take a breathalyzer test. It indicates that the driver is drunk. We assume you don’t know anything else about him or her. How high is the probability he or she really is drunk?”

Because the ‘base-rate’ of drunken drivers is far lower than the margin for error in the test, this means that if you are tested and found to be drunk, it is a lot more likely that you are in the group of ‘false-positives’ than not. There is only one drunk person in every 1000 tested, and (because of the 5% margin for error), there are 49.95 false positives. So the chances that you are a false positive is far greater than that you are the one actually drunk person. It’s actually 1 in 50.95, which is roughly a probability of 0.02. Thus, without the information of the base-rate, we could be fooled into thinking that there was a 0.95 chance that we had been tested correctly, whereas it is actually 0.02.

With the fine-tuning argument we have a somewhat similar situation. We know that our universe is very delicately balanced, and we know that we could not exist if things were even slightly different. But because we effectively lack the base-rate of how many other possible combinations of values give rise to different types of life, we have no idea how unlikely it is that some such situation suitable for life could have arisen, as it were, by chance. As the above example shows, this rate can massively swing the end result.

6. Conclusion

The fine-tuning of the universe is a fact. This does not show that the universe is fine-tuned for life though. It also does not show that the universe must have been designed. It is impossible to know what the chances are that this universe happened ‘by chance’, because we do not have any idea about the relevant base-rate of coherent and (widely defined) life-supporting universes there could be. Thus, we have no idea if we can rule out the chance hypothesis, because we have no idea what the chances are without the information about the base rate.