Fine tuning, and divine attributes

0. Introduction

I’ve been thinking a lot about fine tuning recently. One way the fine tuning argument (FTA) is presented is by Robin Collins. He writes a lot about fine-tuning, and sometimes the argument is presented differently. Sometimes the idea is that the probability of fine-tuning is low on naturalism, but not low on theism. That version of the argument is presented here (we will come back to it later). Alternatively, the idea is that given fine-tuning, the probability of a life-permitting universe (LPU) is more likely given theism than given naturalism. I am going to look at an example of the second version of the argument in this post. You can see it being elaborated here.

Collins says that the ‘core’ fine-tuning argument is that:

“given the fine-tuning evidence, LPU strongly supports T over the NSU [naturalised single universe]” (p. 205).

The ‘fine-tuning evidence’ he refers to is the finding in contemporary cosmology that

“the laws and values of the constants of physics, and the initial conditions of any universe with the same laws as our universe, must be set in a seemingly very precise way for the universe to support life” (p. 204).

Given this evidence, the fact that there is life is more likely given theism than given naturalism (or the naturalised single universe hypothesis). We can put this as follows. The fact that the universe is life permitting (LPU) is more likely given theism than given naturalism:

i)   P(LPU | T) > P(LPU | N)

If i) is true, the LPU is evidence of theism over naturalism.

This uses what is sometimes called the ‘Likelihood Principle’, according to which evidence e counts supporting a hypothesis h1 over h2 if the probability of e given h1 is greater than the probability of e given h2. In our case, the fact that this universe is life-permitting counts as evidence for theism over naturalism because the probability that the universe would be life-permitting given theism is higher than the probability given naturalism. Fine-tuning is evidence of theism over naturalism because i) is true.

It is not just that LPU is more likely under theism than naturalism for Collins. He claims that the probability given naturalism is vanishingly small, whereas it is not vanishingly small under theism. This means that it is vastly more likely on theism than naturalism.

We can state the argument like this (where x << y means that x is “much, much less than” y):

1.    P(LPU | N) << 1
2. ~(P(LPU | T) << 1)
3. Therefore, LPU strongly supports T over N

So the argument goes.

 

1. The problem of elaborated hypotheses

Collins explains one way that the argument can be objected to at this stage is by building more into the hypotheses. He explains this as follows (p. 209):

“One problem with using simply the Likelihood Principle is that whether or not a hypothesis is confirmed or disconfirmed depends on what one builds into the hypothesis. For example, single-universe naturalists could prevent disconfirmation of their hypotheses by advocating the elaborated naturalistic single-universe hypothesis (NSUe), defined as NSU conjoined with the claim that the universe that exists is life-permitting … Similarly, theists could avoid any question about whether LPU is probable on T by constructing an elaborated theistic hypothesis (Te) which builds in the claim that God desired to create such a universe: Te = T & God desires to create a life-permitting universe.” (p. 209)

The way this works is like this. We had said that the probability of a life permitting universe given naturalism, P(LPU | N), was (much) lower than given theism, P(LPU | T). But if we expand N to include the claim that the universe is life permitting, then its probability equals 1. That’s just because P(LPU | N & LPU) = 1; the probability that the universe is life-permitting, given naturalism and the fact that the universe is life-permitting, is 1. Thus, we can manufacture a very high probability (a maximally high probability) by elaborating the N hypothesis in this way.

Interestingly, Collins doesn’t do quite the same thing when it comes to the elaborated theistic hypothesis. He doesn’t simply conjoin T and LPU. Rather, he combines T with a claim about God’s intentions. This produces the result that the probability goes to 1, just like with the elaborated naturalistic hypothesis, but in a slightly more circumspect manner.

Collins’ definition of the T hypothesis is just this (p. 204):

“there exists an omnipotent, omniscient, everlasting or eternal, perfectly free creator of the universe whose existence does not depend on anything outside itself.”

The implicit idea seems to be that if God is omnipotent, then whatever he wants to be the case follows by necessity. An omnipotent being couldn’t fail to actualise something they intended to actualise, for this would be a failure and thus a lack of power. Something like this seems to be going on here. If so, then adding on a claim about God’s desires has the consequence that the desired thing happens. So “T & God desires to create a life-permitting universe” entails LPU.

We will come back to this, but for now just note that to be exactly paralleling the move made when elaborating the naturalistic hypothesis, Collins should have made the elaborated theistic hypothesis simply T & LPU. That way, P(LPU | T & LPU) = 1, just like with the elaborated naturalistic hypothesis.

So far, the idea with elaborated hypotheses, however they are constructed, is that one can make LPU given the elaborated hypothesis have a maximally high probability by packing in more information to the conditional hypotheses. This would be a way of denying premise 1 of the argument, and denying i); we would be denying that LPU given naturalism is much less than 1, because it would be exactly 1, and we would be denying that the probability of LPU is greater given theism than given naturalism, because both elaborated hypotheses would be exactly 1. If we allowed the elaborated hypothesis move, the fine-tuning argument grinds to a halt with a stalemate, with both parties having epistemically equivalent hypotheses.

2. Probabilistic Tension

The way Collins proposes to deal with the problem of elaborated hypotheses is via the notion of ‘probabilistic tension’. He is saying that there is a way of telling between N and T; elaborated-N suffers from probabilistic tension, but elaborated-T does not. And he thinks that suffering from probabilistic tension is a ‘black mark’ against a hypothesis. If he is right about this, we would be able to discard elaborated-N and break the stalemate.

He defines probabilistic tension as follows:

“A hypothesis h suffers from probabilistic tension if and only if h is logically equivalent to some conjunctive hypothesis, h1 & h2, such that P(h1|h2) << 1: that is, one conjunct of the hypothesis is very unlikely, conditioned on the other conjunct.”

His example to bring out the idea here is with a murder trial. Imagine that fingerprints matching Alvin’s are found on the murder weapon. This strongly confirms the ‘Alvin is guilty of the murder’ hypothesis over the ‘Alvin is innocent of the murder’ hypothesis, because the probability that fingerprints matching Alvin’s would be found on the weapon given the innocence hypothesis is very low compared with given the guilt hypothesis. However, Collins goes on to say:

“Such matching [of fingerprints], however, does not confirm the guilt hypothesis over what could be called an “elaborated innocence hypothesis” – that is, an innocence hypothesis constructed in such a way that the matching of the fingerprints is implied by the hypothesis. An example of such a hypothesis is the claim that the defendant did not touch the murder weapon conjoined with the claim that someone else with almost identical fingerprints touched the weapon. This hypothesis entails that the fingerprints will appear to match, and hence by the Likelihood Principle the apparent matching could not confirm the guilt hypothesis over this hypothesis.”

So the idea is that we build into the innocence hypothesis the claim that Alvin did not touch the weapon (~A) and that his identical hand twin, Calvin, did touch the weapon (C). The elaborated innocence hypothesis is: ~A & C. This conjunctive hypothesis entails the evidence about the fingerprints, and means that the evidence about the fingerprints being on the weapon are not higher on either elaborated innocence or guilt hypotheses. They are equal.

However, Collins goes on to explain what he thinks is wrong with this:

“Nonetheless, this elaborated innocence hypothesis suffers from severe probabilistic
tension: one conjunct of the hypothesis (that some other person with almost identical fingerprints touched the weapon) is very improbable on the other conjunct (that the defendant is innocent) since it is extremely rare for two people to happen to have almost identical fingerprints.”

If I knew that Alvin has an identical hand twin who touched the weapon, then finding out that fingerprints that match Alvin’s would not make the elaborated innocence hypothesis seem surprising. It isn’t particularly surprising, given the fact that Calvin did touch the weapon, that Alvin is innocent and did not touch the weapon. The evidence doesn’t make this look bad at all. So one way of conditionalising the propositions doesn’t generate probabilistic tension.

However, if we conditionalise the hypotheses the other way round, things look very different. If I know that Alvin is innocent and didn’t touch the weapon, then I would still be surprised to find out that he had an identical hand twin. It is so unlikely that he would have an identical hand twin, that I would expect some other explanation of the fingerprints. Maybe someone messed up the lab results, or that the police are trying to set Alvin up by faking the fingerprint evidence, etc. My knowing that fingerprints matching Alvin’s are on the murder weapon does not lead me to expect that he has an identical hand twin who touched it. It is for this reason that the elaborated innocence hypothesis suffers from probabilistic tension. One hypothesis conditional on the other is very unlikely.

3. Fine Tuning and probabilistic tension

How does this relate to our previous topic? It works like this. The elaborated naturalistic hypothesis is simply the conjunction of the naturalistic hypothesis, N, and the claim that the universe is life permitting, LPU, i.e. elaborated-N = N & LPU. But, as premise 1 of Collins argument claims, the probability of LPU given N is very close to 0. Thus, the two conjuncts that comprise elaborated-N possess probabilistic tension. One of them, conditional on the other, is very unlikely.

However, claims Collins, the elaborated theistic hypothesis does not suffer from this problem. That hypothesis is comprised of the theistic hypothesis, T, conjoined with the claim that God desires to create a life permitting universe. If we were to conditionalise one on the other, we would find that their probability were nowhere near 0, and thus the elaborated theistic hypothesis would not suffer from probabilistic tension. This would allow us to distinguish between the two elaborated hypotheses and avoid the stalemate we found above.

Here is where I want to object. I have two objections.

Firstly, if we mirrored the elaborated naturalistic hypothesis, we would find ourselves in the same boat, and we would not avoid the stalemate. What I mean is that if the elaborated theistic hypothesis were merely the conjunction of T and LPU, then we have reason to think that the hypothesis does suffer from probabilistic tension. Let’s remember what the T hypothesis is. Collins defines the hypothesis as the claim that:

“there exists an omnipotent, omniscient, everlasting or eternal, perfectly free creator of the universe whose existence does not depend on anything outside itself.” (p. 204)

This thing has no intentions stipulated at all. It might desire a life-permitting universe, but it could desire anything. Without any information about what it desires, we should assign an equal probability to each possible universe that it could desire to create. So if we conditionalise LPU on T, we have no reason to expect the probability to be high. The probability that a God with no particular intentions would create a life-permitting universe is just the probability that this universe would come about by pure chance. The probabilities become exactly the same as on the original naturalistic hypothesis, which Collins was keen to stress is very, very close to 0. This would make premise 2 of Collins’ argument is false.

Think about it like this. Say there are two ingredients in my fridge, jam and spam, out of which there is enough to make a single-ingredient sandwich. You know that Alvin is a spam enthusiast, and that Calvin is a jam guy. Each of them likes their ingredient as much as the other likes theirs, and each hates what the other likes as much as the other hates what they like. The probability that the sandwich has spam in it, given that Alvin made it, is higher than given that Calvin made it:

P(S | A) > P(S | C)

Also, the probability that Alvin made the sandwich, given that it has spam in it is also higher than if it had jam in it.

P(A | S) > P(A | J)

This much is clear.

But if we consider the hypothesis that (Alvin or Calvin) made a sandwich, then we have no way of preferring either sandwich ingredient. The probabilities of either sandwich ingredient, given the disjunctive hypothesis is the same:

P(S| A v C)  =  P(J |A v C)

You would have to treat each possible ingredient of the sandwich as having equal probability. Without knowing what the sandwich maker wants, you can’t say what he will put in it.

Same thing with God, it seems to me. If we mirror the elaborated naturalistic hypothesis, then we don’t have any information about God’s desires in the hypothesis. T doesn’t mention his desires at all. We can suppose that he has some desires or other, if you insist, and then T becomes a disjunctive hypothesis, like with the sandwich example. We are effectively treating T as (either God who desires rocks, or God who desires black holes, or God who desires to be the only thing in existence…). Given such a hypothesis, we cannot expect any particular type of universe at all. For this reason, I think that premise 2 is false. The probability that the universe would be life-permitting, given the God hypothesis that Collins defines, is the same as if we picked one at random.

Of course, this is not how Collins went. He didn’t build the extended theistic hypothesis as (LPU & T). He said that the extended theistic hypothesis was the conjunction of T with a claim about God’s intentions. This would be like picking one of the disjuncts from my big disjunction above to go into the hypothesis; giving us information about what type of sandwich God desires to make.

But the elaborated naturalistic hypothesis suffered from probabilistic tension. If he wants to use the extended theistic hypothesis in place of the original premise 2, so as to avoid my objection from above, he better be able to avoid probabilistic tension. To establish this, he has to show that conditionalising T on the claim that God desires to create a life-permitting universe, or vice versa, is not very very close to 0. And it seems to me that it is. And this is where my second objection comes in. The extended theistic hypothesis is riddled with probabilistic tension.

Think about the probability that God has those very desires, given that he exists;

P(God desires LPU | T)

For all I know, God could have any desires. If I assume that I know that T is true, I should be extremely surprised to find out that he desires for life to exist. After all, he could have desired anything. As we saw already, the hypothesis T does not include any information about his desires, after all. Thus, out of all the possible things to desire, such as rocks, black holes, to be the only entity in existence, for there not to be life, etc, etc, he desired for there to be life. There aren’t just two possible sandwich ingredients. There is a seeming unlimited number of sandwich ingredients, and he happened to pick spam.

Knowing that “an omnipotent, omniscient, everlasting or eternal, perfectly free creator of the universe whose existence does not depend on anything outside itself” exists and then finding out that it desires life, it seems to me, is easily as surprising as knowing that Alvin didn’t touch the murder weapon and then finding out that he has an identical hand twin. There are just so many alternatives, and compared with the combined weight of all of them, God having any one particular desire is incredibly unlikely. Thus, I think that even on his own terms Collins’ strategy here fails. We should consider the original theistic hypothesis used in premise 2 to be false, and the extended theistic hypothesis, even if it doesn’t mirror the extended naturalistic hypothesis, to be full of probabilistic tension.

4. Ad hocness

Interestingly, Collins makes a move earlier on in the chapter which seems to anticipate this sort of response. He advocates for what he considers to be a restricted version of the likelihood principle:

“The restricted version limits the applicability of the Likelihood Principle to cases in
which the hypothesis being confirmed is non-ad hoc. A sufficient condition for a hypothesis being non-ad hoc (in the sense used here) is that there are independent motivations for believing the hypothesis apart from the confirming data e, or for the hypothesis to have been widely advocated prior to the confirming evidence.”

What he is advocating here is a restriction to the likelihood principle which means that you do not say that evidence supports hypotheses which are ad hoc, even if the evidence is more probable given the ad hoc hypothesis. He has a nice example to explain this, which I will quote in full:

“To illustrate the need for the restricted version, suppose that I roll a die 20 times and it comes up some apparently random sequence of numbers – say 2, 6, 4, 3, 1, 5, 6, 4, 3, 2, 1, 6, 2, 4, 4, 1, 3, 6, 6, 1. The probability of its coming up in this sequence is one in 3.6 × 1015, or about one in a million billion. To explain this occurrence, suppose I invented the hypothesis that there is a demon whose favorite number is just the aforementioned sequence of numbers (i.e. 26431564321624413661), and that this demon had a strong desire for that sequence to turn up when I rolled the die. Now, if this demon hypothesis were true, then the fact that the die came up in this sequence would be expected – that is, the sequence would not be epistemically improbable. Consequently, by the standard Likelihood Principle, the occurrence of this sequence would strongly confirm the demon hypothesis over the chance hypothesis. But this seems counterintuitive: given a sort of commonsense notion of confirmation, it does not seem that the demon hypothesis is confirmed.”

One way of thinking about the points I was raising above is that conjoining the T hypothesis with some particular fact about God’s intentions is ad hoc in exactly the way that the daemon hypothesis is for the dice rolls. We can make the example even more straightforward. Imagine I roll a die once and it is a 6. What is the probability that this would happen given naturalism? Presumably, the chances are one in six, or 0.16666…, which is just to say that it has the probability of happening by chance. What about on the elaborated T hypothesis which consists of T & God desiring for this die to land 6? Well, it wouldn’t be surprising at all for an omnipotent being who desired the die to land 6 to ensure that it landed 6. Far more likely than me rolling a 6 by chance anyway. So we should think that me rolling a die and it landing 6 is evidence of God, which is absurd.

If Collins wants to say that the daemon hypothesis is ruled out for being ad hoc, he should also say that the ‘God who desired me to roll a 6’ hypothesis should be ruled out because it is ad hoc as well. But it is far from clear that he can say that his elaborated theistic hypothesis is not ad hoc. He makes the following remarks:

“Now consider a modification of the demon case in which, prior to my rolling the die, a group of occultists claimed to have a religious experience of a demon they called “Groodal,” who they claimed revealed that her favorite number was 2643156432162441366, and that she strongly desired that number be realized in some continuous sequence of die rolls in the near future. Suppose they wrote this all down in front of many reliable witnesses days before I rolled the die. Certainly, it seems that the sequence of die rolls would count as evidence in favor of the Groodal hypothesis over the chance hypothesis. The relevant difference between this and the previous case is that in this case the Groodal hypothesis was already advocated prior to the rolling of the die, and thus the restricted Likelihood Principle implies that the sequence of die rolls confirms the Groodal hypothesis”

The difference between the first daemon hypothesis and the second is that in the first we roll the die and then construct the hypothesis afterwards, whereas in the second the group of occultists have received their number in advance of the rolling of the die. This stops the hypothesis being ad hoc; it wasn’t generated merely to fit the data. It made a  prediction that was extremely unlikely to be verified, but was.

But let’s think about Collins’ extended theistic hypothesis, T & God desires a life permitting universe. That surely makes no prediction. It is ad hoc in exactly the way that the first daemon hypothesis was – being constructed after the event merely to explain the data we already had. There cannot be a hypothesis postulated before the discovery that this universe is life permitting, and this means that there cannot be a claim about God’s intentions that raises the probability that this universe is life permitting that avoids being ad hoc in the way that Collins describes. So, not only does it suffer from probabilistic tension, it is also ad hoc. It violates both conditions he sets out. Even the non-elaborated theistic hypothesis does not raise the probability of LPU, as I argued above.

One might appeal to a prior notion of God that involves moral goodness, or appeal to an argument that purports to prove not only that God exists but that he has moral goodness. Possibly. It seems to me that simply already thinking that God is good, or already thinking that he already exists and is good, shouldn’t be what stops a hypothesis from being ad hoc. If always happen to irrationally believe that it is exactly 8:30 in the morning, and then I find a stopped clock on the beach that says it is 8:30, I cannot use my prior belief that it is 8:30 as reason to think that the clock happens to be showing the right time. Even though I already hold the belief, I should expect that the clock is showing the wrong time. This would be completely different if my prior belief in what time it was had a good independent reason to it. That would license me from inferring that the clock happens to be showing the right time. If Collins wants to say that his conception of God just happens to have the notion that he wants to create LPU, then unless he has a reason for this prior belief, it cannot be used to avoid the ad hoc charge, it seems to me. You don’t get to justify your belief merely with the fact that you already believe it. And it seems to me that the belief that there is a good God who really exists is not supported in anywhere near as good terms as the occultists had for Groodal.

5. Background knowledge

My guess here is that Collins would reply that the conjunction of T with God’s desiring to create a life-permitting universe is not ad hoc because it is part of his background information. In this Collins makes the slightly different version of the argument I mentioned at the very start of this blog post. In this alternative formulation, premise 1 is:

“The existence of the fine-tuning is not improbable under theism”

So now we are conditioning fine tuning on theism (rather then LPU on theism). In a section where he outlines the support for the premises, Collins makes the following remarks, which look like they might apply to our premise 2:

[It] is easy to support and fairly uncontroversial. The argument in
support of it can be simply stated as follows: since God is an all good being,
and it is good for intelligent, conscious beings to exist, it not surprising or
improbable that God would create a world that could support intelligent life.
Thus, the fine-tuning is not improbable under theism.”

This new comment is from an older paper; in fact it is from a paper that is 10 years older – it is from The Fine Tuning Design Argument (1999), whereas we have been focusing on The Teleological Argument: An Exploration of the Fine-Tuning of the Universe (2009). So it seems that the evolution of Collins’ thinking has been to take the goodness of God out of the theistic hypothesis, because in ‘The Teleological Argument’ the theistic hypothesis was just “there exists an omnipotent, omniscient, everlasting or eternal, perfectly free creator of the universe whose existence does not depend on anything outside itself”, with no mention of God’s goodness or intentional states at all. Maybe he made this move in order to avoid problems like my second objection. If so then it is out of the frying pan into the fire, because the situation is just as bad without it.

6. Conclusion

So let’s take a step back for a moment and think about where we are. If we take the ‘bare’ theistic hypothesis as Collins’ describes it, then there is no mention of God’s desires. For this sort of entity, we have no reason to think that he would make any of the seemingly infinite number of possible sandwiches (so to speak) that he could make rather than any other. Each of them is equally vanishingly unlikely. Thus, premise 2 is false. But if we add in a particular intention, and modify premise 2 to avoid the problem, then we find that this solves that problem only by making the hypothesis both probabilisticly tense, and ad hoc by Collins’ own lights. No Christian has grounds anywhere near as good as the occultists had for believing in Groodal, and so I cannot see how the belief is anything other than wishful thinking here.