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.


Fine tuning and consciousness

0. Introduction

The fine-tuning argument begins with the observation of fine-tuning, which is the phenomena that if the values of the parameters in fundamental physics were varied by even a tiny amount, the universe would be inhospitable. As Craig puts it:

“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.”

This couldn’t merely be a product of chance, as the chances are so remote. Neither could it be a matter of necessity, as it seems paradigmatically contingent. Thus, it must be the result of design; it must be the product of some intentional process by the designer of the universe.

Here I want to point out a move that is made in a certain part of the argument, and a concession that it tacitly requires which rules out the conclusion.

  1. Minds and brains

It seems pretty certain that if one varied the values of some of the fundamental physical parameters, the result would be a universe that was inhospitable to complex physical objects, like our bodies. Let’s set aside the question of whether ‘life’ with radically different types of bodies could exist in these weird circumstances. Let’s assume that the answer to this is also: no. Let’s just grant for the sake of the argument that the only situations in which they could occur is in situations very similar to this one.

I think that even when we have made these concessions, what we have established is that physical objects, of a certain complexity, could not exist if we altered the value of gravity, by even a tiny amount, for the sorts of reasons Craig outlines above.

But at this stage there may be a response here along the following lines. Showing that physical objects like brains could not exist in these circumstances, one might think, does not show that minds could not exist in these circumstances. After all, one might believe that the mind and the body are distinct. One might be a substance dualist, or an idealist, for example. One might believe that the soul continues to exist after the demise of the body, either by being reincarnated in a new body or by existing in an immaterial realm, like heaven. If one held any of these views, then merely showing that brains couldn’t exist if gravity were different would not establish that minds could not exist in those circumstances. After all, minds can exist without bodies (or so the substance dualist, idealist or believer in the afterlife, will maintain).

The FTA argument at this stage would have an inferential step in it that looks like this:

  1. Complex physical objects (like brains) could not exist if gravity were different
  2. Therefore, minds could not exist if gravity were different

The dualist (or idealist, etc) is merely pointing out that the conclusion does not necessarily follow from the premise. If minds can exist without bodies, then 1 can be true even if 2 is false. Thus, the inference is invalid.

What is required to bridge the gap from the claim that complex physical objects couldn’t exist in circumstance C, to the claim that minds could not exist in circumstance C, is the further premise that minds could not exist without bodies. Then the argument would become:

  1. Complex physical objects (like brains) could not exist if gravity were different
  2. Minds cannot exist without complex physical objects (like brains)
  3. Therefore, minds could not exist if gravity were different.

Without the new second premise, all fine-tuning established (even if we grant everything the apologist says about fine-tuning) is that brains could not exist if things were different. If minds can exist without bodies, then minds can exist regardless of the values of the fundamental parameters of physics. This would mean that the existence of minds is independent from the fine-tuning of the universe. Thus, for the FTA to be considered successful, we seem to be required to hold that minds depend on complex physical objects (like brains).

2. The importance of minds

Minds, as opposed to brains, we might think, are what is really important to God’s overall plan behind the design. Most forms of traditional theism hold that people are judged by God either by their works (whether they perform moral or immoral actions) or on the basis of their acceptance of Jesus as their personal saviour (the faith they have in Jesus). But it is minds that have the capacity to form intentions, which can be either moral or immoral. It is minds that can form the belief that Jesus is the saviour of the human race. It seems that all that is needed for this, on either the works or faith account, is that minds exist. And if that is the case, then the physical constants of the universe are irrelevant to this larger design. The existence of the physical universe doesn’t even seem to be required at all. In Berkeley’s idealism, for example, there are just minds, and no physical bodies at all. Yet, he thought that in this setting the divine judgement of human agent’s behaviour still makes sense. Faith in God and Jesus still makes sense for Berkeley, even though he thought that there was no physical universe (including physical brains) at all.

So for fine-tuning to have any relevance at all here, the apologist seems to have to insist that minds could not exist without bodies. Then, the fact that bodies (in particular brains) could not exist if physics were slightly different would also mean that minds also could not exist in those circumstances. And that would mean that moral assessments would be impossible, and so would the assessment of the level of faith that a person has, and with it the realisation of the whole divine plan would be impossible.

So the apologist wants to say something like this: look, God wants to have free agents who make moral choices, and have faith in Jesus (etc), and if gravity were even slightly different this would be impossible. That’s why it’s reasonable to infer design behind the fine-tuning.

3. Implications

Now, it seems to me that already there is a tension here. The proponent of the FTA seems to have to insist that brains are required for minds to exist. Otherwise, there argument doesn’t seem to have any relevance for the designed plan. Yet, if they do make this insistence, then they cannot consistently also maintain that there is an immaterial afterlife. You cannot say both that minds require brains, but that minds can exist even after the brain does not. If minds require brains, then you cannot have one without the other.

But the problem is deeper than this. Maybe the apologist will shrug this off somehow. Maybe in the afterlife we do have physical bodies of some sort (perfect ones, perhaps). But unless they want to say the same about God’s mind, they seem to be in a tricky situation. In this video clip, Craig affirms his belief that God is an immaterial yet intentional being. In doing so, he is making a very standard claim about God. God is, in some sense, a mind, but does not have a body (he is immaterial).

But this is precisely the sort of thing that our premise 2, which was required for the argument to go through, rules out. Just as you cannot rule out minds existing without the body, and then go on to affirm an immaterial afterlife, you also cannot rule out minds existing without the body and then go on to affirm that the universe was designed by an immaterial mind. If minds require bodies, then there are no minds without bodies, including God’s.

Thus, the proponent of the FTA is in a dilemma. Either minds can exist without bodies, in which case the physical fine-tuning of the universe is irrelevant to the existence of agents that God is interested in, or they cannot exist without bodies, in which case God (a mind without a body) cannot exist. Either fine-tuning is irrelevant, or God does not exist.

Epistemic extremism

On the most recent Atheist Experience (here), I think the hosts (Matt and Jamie) make some comments which go too far. I’m not sure if I have missed this before, or if it is a change in tone that has come up recently. Anyway, it seems to me to be a case of epistemic extremism.

In the show, they were talking to a recently de-converted ex-Christian, Ethan, about his newfound atheological engagement with missionaries and apologists. Ethan was explaining how he is now of the belief that there is no god. The caller had been trying to argue for this point in his conversations with Christians, rather than merely arguing that there is no good reason to believe in god. At about 28:17, the caller (wrongly in my opinion) suggests that “at some point eventually you have to make the decision about whether there is a god or there isn’t”. The hosts object to this comment quite strongly, both repeating “No” several times and shaking their heads.

It is at this point that Matt makes the following remark:

“I can be not convinced that there is a god and not convinced that there isn’t a god for my entire life”.

Now, what struck me about this is the use of the word ‘convinced’. It is a pretty strong epistemic modifier. To me, the modifier marks out the extreme ends of epistemic positioning. For instance, if p is the proposition that “some god exists”, and if epistemic confidence runs from 0 through to 10, then being convinced that p is true means something like being a 10. It really means you couldn’t be more confident of p. Similarly, being convinced that p is not true, means having a confidence level of 0 in p being true. Being convinced that p, or convinced that not-p, means being at the extremes of the epistemic scale for p.

When put like that, Matt is saying that you could be some number between 1 and 9 through your whole life. And that is true. I don’t think that for each and every proposition, you should take up either a 0 or a 10 degree of belief for it. Almost every belief I have is somewhere between 1 and 9, so I am not convinced of very much really. So, as far as that goes, I agree with Matt’s statement.

But it also seems clear to me that this notion of being convinced of p is different (and should not be muddled together with) the notion of believing that p. For instance, last night put my bike in the bike shed in my garden, and I have not yet gone to look at it this morning. I certainly do believe that the bike is in the shed. But, I am not convinced that the bike is in the shed. Unfortunately, bike thieves do operate in this area from time to time. I think it is unlikely, though possible, that my bike has been stolen. I believe it is in the shed, but I am less than convinced about that.

In a similar manner, I am of the belief that god (the Christian God anyway) does not exist, but I would not say that I was convinced that he doesn’t exist. It seems very unlikely to me (less likely than my bike being stolen, even), but it is possible.

I believe without being convinced that my bike is in the shed; and I believe without being convinced that god does not exist.

Just like with my bike, I am pretty confident about whether god exists, but I am not at the extreme far end of the scale. Maybe my degree of belief is like a 1.5 out of 10, or something like that.

I think that Matt probably has a very similar position to me on this question. He is probably of the belief that the christian god doesn’t exist, without being convinced. We’ve talked several times about this sort of thing, so I feel like I know where he is coming from.

Richard Dawkins put himself as a six out of seven on his scale of disbelief. Dawkins own self-description is:

“Very low probability, but short of zero. De facto atheist. ‘I cannot know for certain but I think God is very improbable, and I live my life on the assumption that he is not there.'” (Richard Dawkins, God Delusion, p. 50-51).

It seems to me that Dawkins is not convinced that god does not exist, but he is pretty solidly believing that God does not exist. He has a very strong belief, but he is not an extremist.

On the other side of the fence, we have William Lane Craig (about as far away from Dawkins as we can reasonably expect on the scale). Yet, even Craig declines to go all the way to the extreme of the scale. In this clip, he clearly states that he is not certain that god exists. Obviously, Craig thinks he has very good reasons to believe that god exists, and he does believe pretty strongly that god exists. Yet, it is wrong to put him at the extreme end of the scale either.

In some very important sense then, neither Dawkins nor Craig are convinced (in either direction) about whether god exists. While there may be people who do land on the epistemic scale at a point which is more extreme that either Dawkins or Craig, I think it is safe to assume that the vast majority of people are somewhere in between these two. Hardly anyone is more convinced than these guys, and even they are not convinced.

Matt’s criteria, of not being convinced either way, is so weak that it ends up covering people with such diverse opinions on the same topic as Dawkins and Craig, both of whom come under the description of being “not convinced that there is a god and not convinced that there isn’t a god”.

[As an aside, the definition of an atheist as someone who is “not convinced” that there is a god, is kind of absurd if it ends up classifying William Lane Craig as an atheist.]

Matt goes on to make the courtroom analogy:

“This person has been accused of a crime. Do you think he is guilty? No. Do you think he is innocent? No. Do you ever have to make up your mind? No.

Now, if we consider the standard of evidence in a court of law for very serious crimes, like murder, the standard used is ‘reasonable doubt’. It is true that given this standard, I would not be able to ‘convict’ most propositions as either being true or of being false. There is a ‘reasonable doubt’ about whether my bike is in the shed. Until I go and look to see if it is there, I am not able to make such a strong claim. Yet, I still believe (quite strongly) that my bike is in the shed. So I might not convict someone of being guilty of murder, yet still believe that they are guilty.

This makes me think that the courtroom analogy, and the notion of being ‘not convinced’ about the truth of a proposition, just obviously don’t track with the everyday sense of believing in things. We often believe things that we are not convinced in, and of which we wouldn’t be able to use the reasonable doubt standard to overcome. And I don’t see that this alone is irrational in any way. Am I being irrational for believing that my bike is in the bike shed, even though I am not convinced of it? I don’t think that is irrational at all.

Ethan replies to these comments, by referring to Jordan Peterson, who he claims just ‘tap dances around’ an issue, instead of laying out reasons to think it is true. At this point, Jamie jumps in and says:

“But if he is going to tap dance around, can’t he tap dance around and show weaknesses in the way that you have presented evidence for your claim? Wouldn’t it be better if you made him play defence on a battleground that very clearly he can’t hold?”

Jamie is clearly suggesting that Ethan shouldn’t make the claim that god doesn’t exist, but instead try to make his interlocutor ‘play defence’ for their claims. Then Matt joins in by saying:

“Ethan, by making the claim [that god does not exist], you have put yourself on a battleground that you can’t win”.

Here is where I think the main disconnect really kicks in. Matt’s claim clearly presupposes the idea that being convinced, or being beyond reasonable doubt, is the standard we should be using. But, if the claim is merely a belief claim, then this just seems wrong.

If I make a claim, like “I believe that god does not exist”, I do have a rational requirement to be able to justify that claim if someone challenges me on it. If I have no reason whatsoever, then (perhaps) that means that I cannot be rational in holding the belief. I could also have something which is a bad reason for having the belief. I need to be able to say something better than “Because I flipped the coin and got heads-up” for why I believe the proposition. So something is required (not nothing), and it needs to be a ‘good reason’ (not just flipping a coin, etc). But does it have to be enough to convince me? It seems obvious to me that the answer to that is: no. I can rationally believe something without being convinced of it. Think of the bike example. These make up the vast majority of our beliefs. Do we want to say that the vast majority of our beliefs are irrational, just because we are not convinced that they are true? I don’t think we do. Saying that we do sounds like epistemic extremism to me. It sounds antithetical to the sceptical, scientific, rational outlook the hosts usually try to defend.

But now Matt goes on to make some even more bizarre comments. He says to Ethan:

“Prove to me that you are not a mass murderer”

Ethan falters and confesses that he could not provide a proof of this that would convince Matt. But hold on a minute. What is the standard supposed to be here? Is Ethan only supposed to make claims that he has good enough reason to be convinced of, or to only make claims that he has good enough reason to convince Matt of? Which one is it?

Presumably, Ethan can be very confident, and have excellent reasons, to hold the belief that he is not a mass murderer. It seems almost unimaginable that you could forget such a thing. It’s logically possible, but it is way less likely than my bike being stolen, and there is nothing wrong with believing that the bike is in the shed. Ethan clearly has good enough evidence to rationally justify his own belief that he is not a mass murderer.

Can he justify it to Matt to the same extent? Well, possibly, but not over the phone in 2 minutes. What sort of significance are we supposed to derive from the fact that Ethan cannot summon up evidence over the phone to a complete stranger that he is not a mass murderer? Should we use this as a standard which means that Ethan shouldn’t claim to not be a mass murderer? This seems wrong to me. Ethan can certainly have the belief that he is not a mass murderer, and should be able to say outloud that he has the belief.

If I claim to be thinking about the number 7 right now, there is nothing (in principle) which could convince you beyond all doubt that I really am thinking of it. The same goes for all claims about the contents of our consciousness, such as that I am cold, or hungry, or like jazz music, or have a headache etc. I can be immediately aware of it, and to that extent I really am convinced of it, but I can give you no evidence beyond telling you. If you don’t believe me, there is nothing I can do to persuade you. But does that mean that we are not allowed (rationally) to report to others what we feel like, or what we are thinking about from time to time? Am I breaking a rule of sceptical discourse if I do so? I think not. Yet this does not meet Matt’s demand. I cannot prove to him that I am thinking of the number 7.

The standard for making a claim (most of the time) is not that you have enough evidence to convince your interlocutor. You do not have to be able to persuade them beyond a reasonable doubt. If you merely believe a proposition, without being convicted of it, then you have some justificatory burden if you make the claim, but it is not the same burden as it would be if your belief was at the extreme end of the epistemic scale.

If I said I was convinced that my bike was in the shed, it would be reasonable to expect that I have very good reason for the belief, such as that I was watching a live-feed camera showing the bike in the shed, etc. But if I merely claim to believe that it is in the shed, I need something less than that. I don’t need to convince a jury beyond a reasonable doubt to justify a belief in a proposition. I need some justification, but it needs to fit my confidence in the claim. So I believe the bike is in the shed because I remember putting it in there last night, I haven’t heard any noises that sound like bike thieves, I know that the crime level is low, etc. These are good reasons for having the belief. They justify the belief, even though they do not convince me. I have not “put myself on a battlefield I cannot win” by making the claim. Winning means having a reason that is proportionate to your degree of belief, not ‘being able to convince my interlocutor beyond a reasonable doubt’. So I just think Matt is wrong here. It isn’t a battlefield we cannot win on. If you believe god doesn’t exist, you can make that claim. You need something to justify it (to be rational), but you don’t need to convince me, and you don’t need to convince yourself.

Part of the reason for the seeming slide towards epistemic extremism may be simply sloppy presentation on the live show. We have all misspoken before, of course. But part of it seems to me like it might be caused by the apologetical atmosphere in general. An apologist has a very ambitious goal in mind, most of the time. They are not just defending the rationality of their beliefs, but actively trying to persuade non-believers. If your goal is to persuade me to change my mind about the truth of p, you need to have a very good justification for thinking that p is true. You need to have a better justification than you do to justify the claim that you merely believe that p.

Yet, we can see the epistemic extremism on display in the Atheist Experience in this episode as a conflation of these two different standards. Ethan can claim to believe that god does not exist, and he needs to have something to say about why he has this belief for it to be rational. But he does not have to produce the level of evidence that would be required to convince someone else to believe. These things are distinct.

Aquinas’ Third Way argument II – Another counterexample

0. Introduction

In the previous post, I looked at Aquinas’ third way argument, as presented by apologist Tom Peeler. He proposed a causal principle, similar to what Aquinas proposed. Aquinas said:

“that which does not exist only begins to exist by something already existing”.

Peeler said:

“existence precedes causal influence”.

But basically, they are arguing for the same principle, namely:

Causal Principle) For something to begin to exist, it must be caused to exist by some pre-existing object.

From now on, let’s just call that ‘the causal principle’. Peeler was using this principle to support the first premise of his argument, which was:

“If there was ever nothing, there would be nothing now”.

The idea is that if Peeler’s principle were true, then the first premise is true as well. In the previous post, I argued that even if we accept all this, the argument does not show that an eternal being exists. Rather, it is compatible with an infinite sequence of contingent things.

In this post, I want to make a slightly different point. Up to now, we have conceded that the causal principle entails that there are no earlier empty times. However, I want to insist that this is only true if time is discrete. If time is continuous, then the causal principle dos not entail that there are no earlier empty times. I will prove this by constructing a model where time is continuous and at which there are earlier times which are empty, and later times which are non-empty, yet there is no violation of the causal principle.

  1. The causal principle

I take the antecedent of this conditional premise, i.e. “there was ever nothing”, to mean ‘there is some time at which no objects exist’, which seems like the most straightforward way of taking it. Therefore, if the causal principle is to support the premise, the causal principle must be saying that if an object begins to exist, then it must not be preceded by a time at which no objects exist.

Strictly speaking, what the principle rules out is empty times immediately preceding non-empty times. Take the following model, where we have an empty time and a non-empty time, but at which they are not immediately next to one another on the timeline. Say that t1 is empty, and t3 is non empty:


In order to use the causal principle to rule this sort of model out, we need to fill in what is the case at t2. So let’s do that. Either t2 is empty, or it is not. Let’s take the first option. If t2 is empty, then t3 is immediately preceded by an empty time, and we have a violation of Peeler’s principle. Fair enough. What about the other option. Well, if t2 is non-empty, then t3 is not a case that violates Peeler’s principle, because it is not immediately preceded by an empty time. However, if t2 has some object that exists at it, then it is a case of a non-empty time immediately preceded by an empty time, because t1 is empty. Therefore, this second route leads to a violation of Peeler’s principle as well.

The point is that if all we are told is that there is some empty time earlier than some non-empty time, without being told that the empty time immediately precedes the non-empty time, we can always follow the steps above to rule it out. We get to a violation of the causal principle by at least one iteration of the sort of reasoning in the previous paragraph.

However, this whole way of reasoning presupposes that time is discrete rather than continuous. If it is continuous, then we get a very different verdict. That is what I want to explain here. If time is continuous, we actually get an even more obvious counterexample than model 2.

2. Discrete vs continuous

Time is either discrete, or it is continuous. The difference is like that between the natural numbers (like the whole integers, 1, 2, 3 etc) and the real numbers (which include fractions and decimal points, etc). Here is the condition that is true on the continuous number line, and which is false on the discrete number line:

Continuity) For any two numbers, x and y, there is a third number, z, which is in between them.

So if we pick the numbers 1 and 2, there is a number in between them, such as 1.5. And, if we pick 1 and 1.5, then there is a number in between them, such as 1.25, etc, etc. We can always keep doing this process for the real numbers. For the natural numbers on the other hand, we cannot. On the natural numbers, there just is no number between 1 and 2.

A consequence of this is that there is no such thing as the ‘immediate successor’ of any number on the real line. If you ask ‘which number is the successor of 1 on the real number line?’, there is no answer. It isn’t 1.01, or anything like that, because there is always going to be a number between 1 and 1.01, like 1.005. That’s just because there is always going to be a number between any two numbers on the real number line. So there is no such thing as an ‘immediate successor’ on the real number line.

Exactly the same thing imports across from the numerical case to the temporal case. If time is continuous, then there is no immediately prior time, or immediately subsequent time, for any time. For any two times, there is a third time in between them.

This already means that there cannot be a violation of Peeler’s principle if time is continuous. After all, his principle requires that there is no non-empty time immediately preceded by an empty time. And that is never satisfied on a continuous model just because no time is immediately preceded by any other time, whether empty or non-empty. However, even though the principle cannot be violated, this doesn’t immediately mean that it can be satisfied. It turns out, rather surprisingly, that it can be satisfied.

2. Dedekind Cuts

In order to spell out the situation properly, I need to introduce one concept, that of a Dedekind Cut. Named after the late nineteenth century mathematician, Richard Dedekind, they were originally introduced as the way of getting us from the rational numbers (which can be expressed as fractions) to the real numbers (some of which cannot be expressed as fractions). They are defined as follows:

A partition of the real numbers into two nonempty subsets, A and B, such that all members of A are less than those of B and such that A has no greatest member. (

We can also use a Dedekind cut that has the partition the other way round, of course. On this version, all members of B are greater than all those of A, and B has no least member (A has a greatest member). This is how we will use it from now on.

3. Model 5

Let’s build a model of continuous time that uses such a cut. Let’s say that there is a time, t1, which is the last empty time, so that every time earlier than t1 is also empty. The rest of the timeline is made up of times strictly later than t1, and they are all non-empty:


The precise numbers on here are just illustrative. All it is supposed to be showing is that every time up to and including t1 is empty, and that every time after t1 is non-empty. There is no first non-empty time, just because there is no time immediately after t1 at all. But there is a last empty time, which is just t1.

This model has various striking properties. Obviously, because it is a continuous model, there can be no violation of Peeler’s principle (because that requires time to be discrete). However, it is not just that it avoids violating the principle in this technical sense. It also seems to possess a property that actively satisfies Peeler’s causal principle. What I mean is that on this model, every non-empty time is preceded (if not immediately) by non-empty times. Imagine we were at t1.01 and decided to travel down the number line towards t1. As we travel, like Zeno’s tortoise, we find ourselves halfway between t1.01 and t1, i.e. at t1.005. If we keep going, we will find ourselves half way between t1.005 and t1, i.e. t1.0025, etc. We can clearly keep on going like this forever. No matter how close we get to t1 there will always be more earlier non-empty times.

So the consequences can be expressed as follows. Imagine that it is currently t1.01. Therefore, it is the case that some object exists. It is also the case that at some time in the past (such as t1) no objects existed. Whatever exists now could have been brought into existence by previously existing objects, and each of them could have been brought into existence by previously existing objects, and so on forever. So, it seems like this model satisfies Peeler’s version of the causal principle, that existence precedes causal influence, and Aquinas’ version of the principle, that “that which does not exist only begins to exist by something already existing”. Both of these are clearly satisfied in this model, because whatever exists has something existing earlier than it. However, it does so even though there are past times at which nothing exists.

4. Conclusion

The significance of this is as follows. If we assume that time is discrete, then the causal principle entails that there are no empty earlier times than some non-empty time. So if t1 is non-empty, then there is no time t0 such that t0 is empty. So if time is discrete, then the causal principle entails premise 1 of the argument (i.e. it entails that “If there were ever nothing, there would be nothing now”).

But, things are different if time is continuous. In that case, we can have it that the causal principle is true along with there being earlier empty times. The example of how this works is model 5 above. Something exists now, at t1.01, and there are times earlier than this which are non-empty. Every time at which something exists has times earlier than it during which some existing thing could have used its causal powers to bring the subsequent thing into existence. There is never any mystery about where the causal influence could come from; it always comes from some previously existing object. However, there are also empty times on this model, i.e. all moments earlier than or equal to t1. This means that the antecedent of the conditional premise is true (“if there ever was nothing”), but the consequent is false (“there would be nothing now”). So even though the causal principle looks true, the first premise is false. So if time is continuous, then the causal principle (even if granted for the sake of the argument) does not entail the first premise, and so does not support it being true.

Aquinas’ Third Way Argument

0. Introduction

I recently listened to a podcast, where the host, David Smalley, was interviewing a christian apologist, Tom Peeler. The conversation was prefaced by Peeler making the claim that he could prove that God existed without the use of the bible.

The first argument offered by Peeler was essentially Aquinas’ ‘Third Way’ argument, but done in a way that made it particularly easy to spell out the problem with it. In fact, Peeler gave two arguments – or, rather, I have split what he said into two arguments to make it easier to explain what is going on. Once I have explained how the first argument fails, it will be obvious how the second one fails as well. The failures of Peeler’s argument also help us to see what is wrong with Aquinas’ original argument.

  1. Peeler’s first argument

Peeler’s first argument went like this (at about the 23 minute mark):

  1. If there were ever nothing, there would still be nothing
  2. There is something
  3. Therefore, there was never nothing

As Peeler pointed out, the argument is basically a version of modus tollens, and so is definitely valid. But is it sound? I will argue that even if we grant that the argument is valid and sound, it doesn’t establish what Peeler thinks it does.

Here is the sort of consideration that is motivating premise 1. In the interview, Peeler was keen to stress that his idea required merely the fact that things exist and the principle that “existence precedes causal influence”. There is an intuitive way of spelling out what this principle means. Take some everyday object, such as your phone. This object exists now, but at some point in the past it did not exist. It was created, or made. There is some story, presumably involving people working in a factory somewhere, which is the ‘causal origin’ of your phone. The important part about this story for our purposes is that the phone was created via the causal powers of objects (people and machines) that pre-existed the phone. Those pre-existing objects exerted their causal influence which brought the phone into existence; or, more mundanely, they made the phone. The idea is that for everything that comes into existence, like the phone, there must be some pre-existing objects that exert causal influence to create it. As Aquinas puts it: “that which does not exist only begins to exist by something already existing”.

One way to think about what this principle is saying is what it is ruling out. What it is ruling out is that there is a time where no objects exist at all, followed immediately by a time at which some object exists.

Imagine that at time t0, no objects exist at all. Call that an ‘empty time’. Then, at t1 some object (let’s call it ‘a‘) exists; thus, t1 is a ‘non-empty time’. This situation violates Peeler’s causal principle. This is because a has been brought into existence (it has been created), but the required causal influence has no pre-existing objects to wield it. We can picture the situation as follows:


At the empty time, t0, there is nothing (no object) which can produce the causal influence required to bring a into existence at t1. Thus, the causal influence seems utterly mysterious. This is what Peeler means by ‘nothing can come from nothing.’ So we can understand Peeler’s causal principle in terms of what it rules out – it rules out things coming into existence at times that are immediately preceded by empty times, or in other words it rules out non-empty times immediately following from empty times. Let’s grant this principle for the sake of the argument to see where it goes.

If we do accept all this, then it follows that from the existence of objects, such as your phone, that there can never have been a time at which no objects existed (i.e. that there are no empty times in the past). That’s because of the following sort of reasoning. If this time has an object, such as your phone, existing at it, then this time must not be preceded by a time at which no objects existed. So the phone existing now means that the immediately preceding time has objects existing at it. But the very same reasoning indicates that this prior time must itself be preceded by a time at which objects existed, and so on for all times.

We can put it like this: if this time is non-empty, then so is the previous one. And if that time is non-empty, then so is the previous one, etc, etc. Thus, there can never be an empty time in the past if this time is non-empty.

This seems to be the most charitable way of putting Peeler’s argument.

2. Modelling the argument

For all we have granted so far, at least three distinct options are still available. What I mean is that the argument makes certain requirements of how the world is, for it’s premises and conclusion to be true. Specifically, it requires that a non-empty time not be immediately preceded by an empty time. But there are various ways we can think about how the world is which do not violate this principle. A model is a way that the world is (idealised in the relevant way). If the model represents a way that the world could be on which the premises and conclusion of an argument are true, then we say that the model ‘satisfies‘ the argument. I can see at least three distinct models which satisfy Peeler’s argument.

2.1 Model 1

Firstly, it could be (as Peeler intended) that there is a sequence of non-necessary objects being caused by previous non-necessary objects, which goes back to an object which has existed for an infinite amount of time – an eternal (or necessary) object. Think of the times before t1 as the infinite sequence: {… t-2, t-1, t0, t1}. God, g, exists at all times (past and future), and at t0 he exerted his causal influence to make a come to exist at t1 alongside him:


On this model, there are no times in which an object comes into existence which are immediately preceded by an empty time, so this model clearly does not violate Peeler’s principle. Part of the reason for this is that there are no empty times on this model at all, just because God exists at each time. Anyway, the fact that this model doesn’t violate Peeler’s causal principle means that there is at least one way to model the world which is compatible with Peeler’s argument. The world could be like this, for all the truth of the premises and conclusion of Peeler’s argument requires.

But, this is not the only option.

2.2 Model 2

Here is another. In this model, each object exists for only one time, and is preceded by an object which itself exists for only one time, in a sequence that is infinitely long. Each fleeting object is caused to exist by the previous object, and causes the next object to exist. On this model there are no empty times, so it is not a violation of Peeler’s principle. Even though it does not violate the principle, at no point is there an object that exists at all times. All that exists are contingent objects, each of which only exists at one time.

Think of the times before t1 as the infinite sequence { … t-2, t-1, t0, t1}, and that at each time, tn, there is a corresponding object, bn:


Thus, each time has an object (i.e. there are no empty times) and each thing that begins to exist has a prior cause coming from an object. No object that begins to exist immediately follows from an empty time. Therefore, this model satisfies Peeler’s argument as well.

2.3 Model 3

There is a third possibility as well. It is essentially the same as the second option, but with a merely finite set of past times. So, on this option, there is a finitely long set of non-empty times, say there are four times: {t-2, t-1, t0, t1}. Each time has an object that exists at that time, just like in model 2. The only real difference is that the past is finite:


In this case, t-2 is the first time, and b-2 is the first object.

However, there might be a problem with this third option. After all, object b-2 exists without a prior cause. It isn’t caused to exist by anything that preceded it (because there are no preceding times to t-2 on this model). Doesn’t this make it a violation the causal principle used in the argument?

Not really. All that Peeler’s causal principle forbids is for an object to begin to exist at a time immediately following an empty time. But because there are no empty times on this model, that condition isn’t being violated. Object b-2 doesn’t follow an empty time. It isn’t preceded by a time in which nothing existed. It just isn’t preceded by anything.

Now, I imagine that there is going to be some objection to this type of model. Object b-2 exists, but it was not caused to exist. Everything which comes into existence does so because it is caused to exist. But object b-2 exists yet is not caused to exist by anything.

We may reply that object b-2 is not something which ‘came into existence’, as part of what it is for an object x to ‘come into existence’ requires there to be a time before x exists at which it does not exist. Seeing as there is no time before t-2, there is also no time at prior to t-2 at which b-2 does not exist. So b-2 simply ‘exists’ at the first time in the model, rather than ‘coming into existence’ at the first time. Remember how Aquinas put it: “that which does not exist only begins to exist by something already existing”. There is no prior time at which b-2 is “that which does not exist”. It just simply is at the first time.

No doubt, this reply will seem to be missing the importance of the objection here. It looks like a technicality that b-2 does not qualify as something which ‘comes into existence’. The important thing, Peeler might argue, is that b-2 is a contingent thing that exists with no cause for it. That is what is so objectionable about it.

If that is supposed to be ruled out, it cannot be merely on the basis of Peeler’s causal principle, but must be so on the basis of a different principle. After all, Peeler’s principle merely rules out objects existing at times that are preceded by empty times. That condition is clearly not violated in model 3. The additional condition would seem to be that for every non-necessary object (such as b-2), there must be a causal influence coming from an earlier time. This principle would rule out the first object being contingent, but it is strictly more than what Peeler stated he required for his argument to go through.

However, let us grant such an additional principle, just for the sake of the argument. If we do so, then we rule out models like model 3. However, even if we are kind enough to make this concession, this does nothing to rule out model 2. In that model, each object is caused to exist by an object that precedes it in time, and there are no empty times. Yet, there is no one being which exists at all earlier times (such as in model 1).

The existence of such an eternal being is one way to satisfy the argument, but not the only way (because model 2 also satisfies the argument as well). Thus, because model 2 (which has no eternal being in it) also satisfies the argument, this means that the argument does not establish the existence of such an eternal being.

So, even if we grant the premises of the first argument, it doesn’t establish that there is something which is an eternal necessary object. It is quite compatible with a sequence of merely contingent objects.

2. Peeler’s second argument

From the conclusion of the first argument, Peeler tried to make the jump to there being a necessary object, and seemed to make the following move:

  1. There was never nothing
  2. Therefore, there is something that has always been.

The fact that the extra escape routes are not blocked off by the first argument, should give you some reason to expect the inference in the second argument to be invalid. And it is. It is a simple scope-distinction, or an instance of the ‘modal fallacy’.

There being no empty times in the past only indicates that each time in the past had some object or other existing at it. It doesn’t mean that there is some object in particular that existed at each of the past times (such as God). So long as the times are non-empty, each time could be occupied by an object that exists only for that time (as in our second and third models), for all the argument has shown.

The inference in the second argument is like saying that because each room in a hotel has someone checked in to it, that means that there is some particular individual person who is checked in to all of the rooms. Obviously, the hotel can be full because each room has a unique individual guest staying in it, and doesn’t require that the same guest is checked in to every room.

When put in such stark terms, the modal fallacy is quite evident. However, it is the sort of fallacy that is routinely made in informal settings, and in the history of philosophy before the advent of formal logic. Without making such a fallacious move, there is no way to get from the conclusion of Peeler’s first argument to the conclusion of the second argument.

3. Aquinas and the Third Way

In particular, medieval logicians often struggled with scope distinctions, as their reasoning was carried out in scholastic Latin rather than in symbolic logic. That they managed to make any progress at all is testament to how brilliant many of them were. Aquinas is in this category, in my view; brilliant, but prone to making modal fallacies from time to time. I think we can see the same sort of fallacy if we look at the original argument that is motivating Peeler’s argument.

Here is how Aquinas states the Third Way argument:

“We find in nature things that are possible to be and not to be, since they are found to be generated, and to corrupt, and consequently, they are possible to be and not to be. But it is impossible for these always to exist, for that which is possible not to be at some time is not. Therefore, if everything is possible not to be, then at one time there could have been nothing in existence. Now if this were true, even now there would be nothing in existence, because that which does not exist only begins to exist by something already existing. Therefore, if at one time nothing was in existence, it would have been impossible for anything to have begun to exist; and thus even now nothing would be in existence — which is absurd.” Aquinas, Summa Theologiae, emphasis added)

This argument explicitly rests on an Aristotelian notion of possibility. The philosopher Jaakko Hintikkaa explains Aristotle’s view:

“In passage after passage, [Aristotle] explicitly equates possibility with sometime truth, and necessity with omnitemporal truth” (The Once and Future Seafight, p. 465, emphasis added)

This is quite different from the contemporary view of necessity as truth in all possible worlds. On the contemporary view, there could be a contingent thing that exists at all times in some world. Therefore, being eternal and being necessary are distinct on the modern view, but they are precisely the same thing on the Aristotelian view. We will come back to this in a moment. For the time being, just keep in mind that Aquinas, and by extension Peeler, are presupposing a very specific idea of what it means to be necessary or non-necessary.

We can see quite explicitly that Aquinas is using the Aristotelian notion of necessity when he says “…that which is possible not to be at some time is not”. This only makes sense on the Aristotelian view, and would be rejected on the modern view. But let’s just follow the argument as it is on its own terms for now.

The very next sentence is: “Therefore, if everything is possible not to be, then at one time there could have been nothing in existence.” What Aquinas is doing is imagining what would be the case if all the objects that existed were non-necessary objects. If that were the case, then no object would exist at every time, i.e. each object would not exist at some time or other. That is the antecedent condition Aquinas is exploring (i.e. that “everything is possible not to be”).

What the consequent condition is supposed to be is less clear. As he states it, it is “at one time there could have been nothing in existence”. We can read this in two ways. On the one hand he is saying that if everything were non-necessary, then there is in fact an earlier time that is empty. On the other hand, he is saying that if everything were non-necessary, there could have been an earlier time that is empty.

Let’t think about the first option first. It seems quite clear that it doesn’t follow from the assumption that everything is non-necessary that there is some time or other at which nothing exists. Model 2 is an example of a model in which each object is non-necessary, but in which there are no empty times. If Aquinas is thinking that “if everything is possible not to be, then at one time there could have been nothing in existence” means that each object being non-necessary implies that there is an empty time, then he is making a modal fallacy. This time, the fallacy is the other way round from Peeler’s example: just because each guest is such that they have not checked into every room of the hotel, that does not mean there is a room with no guest checked in to it. Think of the hotel in which each room has a unique guest in it. Exactly the same thing applies here too; just because every object is such that it fails to exist at some time, that does not mean that there is a time at which no object exists. Just think about model 2, in which each time has its own unique object.

Thus, if we read Aquinas this first way, then he is committing a modal fallacy.

So let’s try reading him the other way. On this reading he is saying that the assumption that everything is non-necessary is compatible with there being an empty time. One way of reading the compatibility claim is that there is some model on which the antecedent condition (that every object is non-necessary) and the consequent condition (that there is an empty time) are both true. And if that is the claim, then it is quite right. Here is such a model (call it model 4):


On this model, there are two objects, a and b, and they are both non-necessary (i.e. they both fail to exist at some time). Also, as it happens, there is an empty time, t2; both a and b fail to exist at t2. So on this model, the antecedent condition (all non-necessary objects) and the consequent condition (some empty times) are both satisfied.

However, while this claim is true, it is incredibly weak. The difference is between being ‘compatible with’ and ‘following from’. So for an example of the difference, it is compatible with me being a man that my name is Alex; but it doesn’t follow from me being a man that my name is Alex. If we want to think about the consequent following from the antecedent condition, we want it to be the case that every model which satisfies the antecedent condition also satisfies the consequent condition, not jus that there is some model which does. But it is clearly not the case that every model fits the bill, again because of model 2. It satisfies the condition that every object is non-necessary, but it doesn’t satisfy the condition that there are some empty times.

So what it comes down to is that the claim that there are only non-necessary objects is compatible with the claim that there are empty times, but it is equally compatible with the claim that there are no empty times. Being compatible with both means that it is simply logically independent of either. So nothing logically follows from the claim that there are only non-necessary objects about whether there are any empty times in the past or not.

So on the first way of reading Aquinas here, the claim is false (because of model 2). On the second way of reading him, the claim is true, but it is logically independent of the consequent claim. On either way of reading him, this crucial inference in the argument doesn’t work.

And with that goes the whole argument. It is supposed to establish that there is an eternal object, but even if you grant all of the assumptions, it is compatible with there not being an eternal object.

4. Conclusion

Peeler set out an argument, which was that if nothing ever existed, there would be nothing now. The truth of the premises and the conclusion is satisfied by, or compatible with, model 2, and so does not require that an eternal object (like God) exists. The second argument was that if it is always the case that something exists, then there is something which always exists. That is a simple modal fallacy. Lastly, we looked at Aquinas’ original argument, which either commits a similar modal fallacy, or simply assumes premises which do not entail the conclusion.


Getting an ought from an is

0. Introduction

In the Treatise of Human Nature, Hume outlined the ‘is-ought’ problem, sometimes referred to as ‘Hume’s Guillotine’. The idea is that it is not possible to argue validly from ‘descriptive’ statements (about how things are) to ‘normative’ conclusions (about how things ought to be). 

Hume describes how he often notices a change that takes place when he is reading certain passages on moral philosophy:

“I am surprised to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with an ought, or an ought not. This change is imperceptible; but is, however, of the last consequence” (Section 3.1.1)

Examples of this switch include the move from 1 to 2 in the following examples:


  1. X makes people happy
  2. Therefore, people ought to do X


  1. God commands people to do X
  2. Therefore, people ought to do X

If we want to turn A) into a valid argument, we would naturally want to add another premise, as follows:

  1. X makes people happy
  2. People ought to do what makes them happy
  3. Therefore, people ought to do X

Now the argument is valid. But now the conclusion follows from a set of premises which are not all descriptive. Our new premise 2, needed to make the argument valid, is normative (because it is about what ought to be the case, not just what is the case). Therefore, it is not a case of getting ‘an ought from an is’; but of getting ‘an ought from an ought and an is‘. Hume’s point is that without the addition of a normative premise, like 2, an argument like A or B cannot be made valid.

We can state the is-ought problem as follows:

There is no valid argument such that the premises are purely descriptive, and the conclusion is normative.

A counterexample to this would be a valid argument with purely descriptive premises and a normative conclusion.

1. A counterexample to the is-ought problem

Consider the following example:

  1. The conclusion of this argument is true
  2. Therefore, we ought to do X

This inference is valid; there is no way the premise could be true without the conclusion also being true. After all, the premise says that the conclusion is true; so the only thing that makes the premise true is the conclusion being true.

The premise is seems to be quite clearly descriptive. It doesn’t include the word ‘ought’ or any synonym of the word.

On the other hand, the conclusion clearly is normative, involving the word ‘ought’ quite explicitly.

This means we have a valid argument with purely descriptive premises and a normative conclusion. This makes it a counterexample to the is-ought principle as stated above. In some sense, it shows that it is possible to derive an ought from an is, after all.

Molinism and the Grounding Objection, Part 1

0. Introduction 

Molinism is the view that there are true counterfactuals involving agents making libertarian free choices, and that these counterfactuals are known by God. See this for more background.

Perhaps the most common objection to Molinism is referred to as the ‘grounding problem’. The issue is just that there seems to be nothing which explains why true Molinist counterfactuals are true. They seem to be just true, but not true because of anything in particular. Here is how Craig puts it in his paper Middle Knowledge, Truth–Makers, and the “Grounding Objection” (henceforth MK, and from which all the Craig quotes will come in this post):

“What is the grounding objection? It is the claim that there are no true counterfactuals concerning what creatures would freely do under certain specified circumstances–the propositions expressed by such counterfactual sentences are said either to have no truth value or to be uniformly false–, since there is nothing to make these counterfactuals true. Because they are contrary–to–fact conditionals and are supposed to be true logically prior to God’s creative decree, there is no ground of the truth of such counterfactual propositions. Thus, they cannot be known by God.”

One way of thinking about this issue is that the grounding problem itself presupposes the ‘truth-maker’ principle. According to this principle, every true proposition is made true by something. If the truth-maker principle is correct, and if nothing makes Molinist counterfactuals true, it follows that they are not true. Hence, it follows that there are no such truths for God to know.

In response to this, a Molinist can either deny the truth-maker principle, or accept it and provide a truth-maker for the counterfactuals. As Craig makes explicit, he believes he can make the case that either strategy is plausible:

“For it is far from evident that counterfactuals of creaturely freedom must have truth-makers or, if they must, that appropriate candidates for their truth-makers are not available.”

Craig gives reasons that one might want to deny the truth-maker principle in general. He also explains how one might think about Molinist counterfactuals not having truth-makers. He also offers an account of how they could have truth-makers. If any of these works, it seems that the grounding objection has been rebutted. In this series I will look at his proposals, and argue against them. In this first post, I will just look at the positive case that Craig sets out for Molinism.

  1. The (supposedly) intuitive case

Craig mentions a comment from Plantinga that he agrees with, about how plausible it is that there should be true Molinist counterfactuals:

“No anti–Molinist has, to my knowledge, yet responded to Alvin Plantinga’s simple retort to the grounding objection: “It seems to me much clearer that some counterfactuals of freedom are at least possibly true than that the truth of propositions must, in general, be grounded in this way.””

Craig goes on to say that the grounding problem is:

“…a bold and positive assertion and therefore requires warrant in excess of that which attends the Molinist assumption that there are true counterfactuals about creaturely free actions.”

Plantinga is saying that the fact that there are Molinist counterfactuals is more plausible than the truth-maker principle. To show that we should prefer the truth-maker principle to Molinist counterfactuals, we need warrant for the truth-maker principle “in excess” of that for Molinist counterfactuals. Not an easy job, thinks Craig, who says that the warrant for Molinist counterfactuals is “not inconsiderable”.

In his ‘Warrant for the Molinist Assumption’ section of MK, Craig provides three aspects of the case which supposedly shows that Molinist counterfactuals have ‘not inconsiderable’ warrant already. These are as follows:

  1. First, we ourselves often appear to know such true counterfactuals.”
  2. Second, it is plausible that the Law of Conditional Excluded Middle (LCEM) holds for counterfactuals of a certain special form, usually called “counterfactuals of creaturely freedom.””
  3. Third, the Scriptures are replete with counterfactual statements, so that the Christian theist, at least, should be committed to the truth of certain counterfactuals about free, creaturely actions.”

In this post, I will focus on the first of these three.

2. The epistemic objection – Molinist counterfactuals are unknowable

The first one of these, along with the third and Plantinga’s quote from above, are all related. They are rebutted by what I will call the ‘epistemic objection’.  According to this objection, even if they were true, it isn’t possible for an agent to know Molinist counterfactuals.

It seems to Craig to be obvious that we “often appear to know” Molinist counterfactuals to be true. Yet, there seems to be good reason to think that we cannot know Molinist counterfactuals.

In order to help explain things, I want to make an important distinction, which is between Molinist counterfactuals and what I will call ‘probably-counterfactuals’. So, an example of a Molinist counterfactual is:

a) Had Louis been tempted, he would have given in.

An example of a probably-counterfactual is:

b) Had Louis been tempted, he probably would have given in.

The difference between a) and b) is merely the word ‘probably’. The difference it plays is huge though. I think that it makes the difference between being crucial to rational reasoning generally (like b), and being utterly useless (like a). I think that Craig’s claims about Molinist counterfactuals only really make sense if they are ultimately being made about probably-counterfactuals, and I will explain why I think this in what follows.

First of all, Craig thinks that we “often appear to know” Molinist counterfactuals, like a). But this is strange. Maybe God could know them (although, I don’t think that can be maintained either), but how could a mere mortal like me know them? All I can really know, we might suppose, is i) what I have some kind of access to empirically (a posteriori), and ii) what I can reason about abstractly (a priori). And neither of these routes can get me to the conclusion that Louis would have freely chosen to give in to the sin had he been tempted.

I don’t have empirical access to counterfactual situations, so that rules out the first epistemological route; nothing about the empirical world that I can investigate can tell me which of the two options Louis would have freely chosen to make.

But mere abstract reasoning cannot ever decide which of two options an agent with libertarian free choice would make either; it doesn’t follow logically from any purely a priori antecedent conditions. Thus, Louis’ choice seems literally unknowable to an agent like me. Not only that, but all Molinist counterfactuals become unknowable for the same reason.

On the other hand, knowing b) seems relatively straightforward, at least in principle. Let’s suppose Louis has a strong track record of giving in to sin when tempted, and that I know this because I have witnessed it personally. Perhaps he has also told me about how much he hates living in the stuffy confines of the monastery and yearns for some temptation to give into. Any number of scenarios like this could support the idea that I could come to believe with good reason that he probably would have given in had he been tempted.

Thus, a) seems literally unknowable, whereas b) is eminently knowable. They are therefore, epistemically asymmetric.

3. The utility objection – Molinist counterfactuals are useless

Craig says:

“Very little reflection is required to reveal how pervasive and indispensable a role such counterfactuals play in rational conduct and planning. We not infrequently base our very lives upon the assumption of their truth or falsity.”

He is right about the fact that counterfactuals play a “pervasive and indispensable” role in “rational conduct and planning”. But where is wrong is that it is probably-counterfactuals which are doing most of the work, and Molinist counterfactuals do none (and indeed, could not do any). The reason for this difference in utility is because of the epistemic asymmetry between probably-counterfactuals and Molinist counterfactuals.

Here is an example to play with to make this point clear. Imagine I am deciding whether or not to leave my bike unlocked or not while I go into the library. Let’s suppose that I see the well-known bike thief, Louis, lurking just round the corner. I decide to lock my bike up. When I return after finding the book I want, I am glad to find my bike is still there. I begin to unlock my bike, and at this point you ask me: “Why did you lock your bike up?” My answer is going to be something like this:

c) Had I not locked up my bike, Louis probably would have stolen it.

It is the likelihood of Louis stealing the bike that motivated me to lock it up. My reasoning process included the fact that I had good reasons to think that e) was true. The place that the probably-counterfactual plays in my reasoning is completely clear. It makes perfect sense for a probably-counterfactual to be what I am using here to come to my decision to lock the bike up.

The idea that I used a Molinist counterfactual is almost unintelligible though. Imagine my reply had been the following:

d) Had I not locked up my bike, Louis would have freely chosen to steal it.

It would be bizarre for me to say that, because there is no way for me to know that d) is true rather than false. Given that Louis has libertarian free will, he could have chosen to steal the bike, but he could have also chosen not to steal the bike. The scenario where he freely chooses to steal the bike, and the scenario where he freely chooses refrain from stealing the bike, are literally identical in every respect up to the point where he makes a decision. There is nothing at all, even in principle, that could justify my belief that one would happen rather than the other. Possibly, God knows something I don’t, but it is clear that I do not. Thus, there is no way it can be part of my (rational) decision making process, for I have no reason to think that it is true rather than false.

If this wasn’t bad enough, we can develop the worry. Imagine that standing next to Louis is Louise, who I know has never stolen a bike, or indeed anything, in her entire life. My belief is that she is unlikely to steal my bike. Her presence is therefore not a consideration I took into account when I locked my bike up. If you asked me when I got back to my why I did not consider her presence, I would have said that it was because of something like the following:

e) Had I not locked up my bike, Louise probably would not have stolen it.

I was under the belief that even if I had not locked my bike up, Louise probably wouldn’t have stolen it. While the presence of Louis plays a role in my reasoning, and the presence of Louise does not, and this is easily cashed out in terms of probably-counterfactuals.

But when we come to consider that it wasn’t probably-counterfactuals, but Molinist counterfactuals that were part of my reasoning, we run into a problem. This is because an entirely symmetric Molinist counterfactual can be created for Louise:

f) Had I not locked up my bike, Louise would have freely chosen to steal it.

Given that Louise has libertarian free will, she could have chosen to steal the bike, but she could have also chosen not to steal the bike. The scenario where she freely chooses to steal the bike, and the scenario where she freely chooses refrain from stealing the bike, are literally identical in every respect up to the point where she makes a decision. Each of Louis and Louise are perfectly symmetrical in this respect, so there is no reason for me to believe both that e) is true and f) is false. But unless I do have this (non-Molinist) asymmetric view about e) and f), my inclination to treat them differently utterly inexplicable.

The very thing that the counterfactual would need to do to be an ‘indispensable’ part of my reasoning process is inexplicable if they are Molinist counterfactuals.

4. A possible reply

There is a possible reply that could be made on behalf of the Molinist at this point though. Clearly, our Molinist friend might reply, we cannot know for sure whether a Molinist counterfactual like a) or d) or f) is true rather than false. Only God can know that for certain. However, I have set the bar too high. We can reasonably infer such counterfactuals from the truth of the probably-counterfactuals, which I already conceded are not problematic to know. So, for example, it is from the premise that Louis probably would have stolen the bike, that I infer that he would have freely chosen to steal the bike. Obviously, this is not a deductive inference (for it is not deductively valid), but it is a reasonable inductive inference.

Here is the inference:

  1. Had I not locked the bike, Louis probably would have stolen it
  2. Therefore, had I not locked the bike, Louis would have freely chosen to steel it

This reply has a lot going for it. Things can be known via such inductions. I think that premise 1 is true, and that it’s truth can be plausibly construed as something which increases the (epistemic) probability of 2. Thus, the inference, though inductive, seems pretty good.

I actually don’t think that 2 could be true, but that is for semantic reasons that we do not have to get into here. Let’s just say that for the sake of the argument, I accept this type of move. Where does it get us?

It might be thought that Molinist counterfactuals can indeed be known (via inductive inference from known probably-counterfactuals). Thus, the epistemic objection seems to have been countered. Indeed, once we make this move, counterfactuals like d) (i.e. had I not locked up my bike, Louis would have freely chosen to steal it) can be believed by me with justification. Thus, it is now no longer problematic to see how they might fit into my reasoning process. I believe (via inference from a probably-counterfactual) that Louis would have freely stolen my bike, and that belief is what motivates me to lock it up. Thus, the utility objection has a rebuttal as well.

5. The redundancy reply

As I said,  I think this is a good line of response. I think it is about the best there is to be had. But even if we concede it, I don’t think much has happened of any importance. Ultimately, they rescue Molinist counterfactuals at the cost of making them redundant. If they can known and can be put to work in decision making, then they necessarily do not need to be used, because there will already be something we believe (or know) which does all of their work for them.

Even if Molinist counterfactuals, like d), can be inductively inferred from probably-counterfactuals, like c), it is not clear that they can be derived from anything else. Consider the case where someone believes that Louis will freely choose to steal the bike, but does not believe that he probably will steal the bike. Such a belief can be had, but surely it is irrational. It is like holding that this lottery ticket is the winner, even while believing that it is unlikely to be the winner. Such beliefs may be commonplace (and maybe it is beneficial to believe that you will beat the odds when fighting with a disease, etc), but they are paradigmatically irrational nonetheless. Unless you believe that something is probably going to happen, you should not believe (i.e. should lack a belief) that it is going to happen.

If that is right, then it has a similar consequence for Molinist counterfactuals being used in rational processes. Unless I have inferred it from a probably-counterfactual, I cannot reasonably believe a Molinist-counterfactual. But the only way I can use a belief in a Molinist counterfactual as part of a rational decision-making process is if I reasonably believe it. Therefore, the only way I can use a belief in a Molinist counterfactual as part of a decision making process is if I already believe the corresponding probably-counterfactual.

Here is an example to make this clear.

Let’s say that I can infer that ‘Louis would freely choose to steal the bike if left unlocked’ from the premise that ‘he probably would steal the bike if left unlocked’, and from no other premise. Let’s also say that I use believe that ‘he would freely choose to steal the bike if left unlocked’, and that I use that as part of my decision process to lock the bike up. It follows that because I used that belief as part of my rational process, that I must also believe that he probably would steal the bike.

This means that even if Molinist counterfactuals played the role that Craig thinks they do in decision making, they must come with an accompanying belief about the corresponding probably-counterfactual.

And this means that, maybe Molinist counterfactuals can be known, and maybe they can be used in reasoning processes, but they can do so only if there is a reasonably believed probably-counterfactual present as well. This makes Molinist counterfactuals completely dependent on probably-counterfactuals from both an epistemic and decision theoretic point of view. You never get to rationally believe a Molinist counterfactual unless you already believe the corresponding probably-counterfactual. And you can never use your belief in a Molinist counterfactual in some reasoning process unless you also already believe the corresponding probably-counterfactual.

And as we saw, probably-counterfactuals can already do all the explanatory work in explaining why I decided to lock my bike up. I don’t need Molinist counterfactuals if I have the right probably-counterfactual, and I never have a Molinist counterfactual unless I already have the right probably-counterfactual. That makes them necessarily redundant. Maybe they can play the role Craig wants them to play, but only if the need not play it.


6. Conclusion

Craig’s first aspect of the warrant for Molinist counterfactuals was that we commonly know such counterfactuals. However, I showed how it seems quite hard to see how we could know such counterfactuals directly. They are not things we can experience ourselves, and they are not deducible a priori. Probably-counterfactuals, on the other hand, are eminently knowable. Craig also claimed that Molinist counterfactuals play an indispensable role in decision making, however their disconnection from our direct ways of knowing their truth-values makes them irrelevant to decision making, unlike probably-counterfactuals.

The only response to this seems to be to claim that Molinist counterfactuals can be known via inference from probably counterfactuals. While this may be true (although I still have problems with that), all it would get a Molinist would be something which can only be known because the probably-counterfactual was also known, and only does any work explaining decision making if that work could be done by the epistemically prior probably-counterfactual. They can only be saved by being made redundant.