Short Article (6): Can God Create any Logically Possible World?

God’s omnipotence is a tricky beast to define, and very often the notion of logical possibility is used in defining it. In a recent discussion concerning the problem of evil I was asked which of two premises I rejected – that God, since he’s omnipotent, can do anything logically possible, or that God should remove suffering if it’s logically possible to do so. I reject both, but was specifically asked to say why I reject the former. This short article is an expanded explanation of what I said in response.

It is my contention that there are states of affairs which, though they be logically possible, are such that God cannot bring them about. Before I offer the two examples I gave it might be useful to be clear about what a logically possible world (LPW) actually is. As I understand and use the term a LPW is a complete description of reality as it could be. Take the set of all propositions that might or might not obtain, eg: A, B, C, D, E….n. A LPW will be a state of affairs in which every single one of these propositions – or their denial – obtains. So, one possible world would be:

A, B, -C, D, E, etc.

Or

-A, B, -C, D, -E, etc

But we could not have:

-A, B, -B, C, -D, E, etc,

Because this contains a logical contradiction by trying to include both B and –B.

To take a concrete example: I have a son who is 10 years old. However, in some other LPW I have no son, but three daughters. There is no LPW in which I have a son and don’t have a son at the same time.

With this brief sketch of LPWs in mind, let’s look at my examples:

(1) Libertarian Free Will (LFW)

If human beings have LFW then there are LPWs God cannot bring about. Take, for instance, Judas Iscariot’s betrayal of Christ. There is a LPW in which Judas, under certain conditions, chooses to betray Christ, and another in which he chooses to remain faithful. In either case we will have a complete description of reality. The former LPW contains the proposition “Judas betrayed Jesus” whilst the latter contains the proposition “Judas did not betray Jesus.” However, (if human beings have LFW) which of these worlds becomes actual is not up to God. It’s up to Judas. Under these precise circumstances Judas chose to betray Jesus, but he really could have chosen not to betray. God couldn’t force him to act freely in either direction; this was Judas’s move as a free agent. Calling the former world PW(B) and the latter PW(-B) we can say that PW(B) was actualisable but PW(-B) was not. So, God could not actualise PW(-B), despite the fact that it is a LPW. This distinction between logically possible and actualisable is subtle but significant, and sadly the two are often conflated.

(2) Temporal Creation

My second example doesn’t require LFW. Take any two universes God could create: U-X and U-Y. Let’s say further than He desires to create two different universes, one after the other. There are two kinds of LPWs here:

(i) PW-Y1 – in which God creates U-Y first and then U-X,

Or

(ii) PW-X1 – in which God creates U-X and then U-Y.

Now, both of these worlds are LPWs, that is they are complete descriptions of reality in which every proposition is either affirmed or denied. However, God can only create one of them. If he chooses PW-Y1 then he cannot create PW-X1. They exclude each other, and yet both are LPWs.

Now, it might be objected (and in fact during my previously mentioned discussion it actually was) that PW-Y1 and PW-X1 are only LPWs before God creates anything. In other words, once God chooses to create PW-X1 then PW-Y1 is no longer a LPW. This is incorrect and blurs again the subtle distinction between actualisable worlds and logically possible worlds. PW-Y1 remains a LPW. It remains a complete description of reality. It’s represents a way reality really could have been. However, it is no longer actualisable.

It seems to me then that definitions of omnipotence that rely on the notion of logical possibility can’t be quite right since it seems clear enough (to my mind anyway!) that there are LPWs that even an omnipotent being couldn’t create. This also means that arguments against God’s existence – such as some versions of the problem of evil – which rely on the notion that God can do anything logically possible are flawed and need to be revised or abandoned.

Stephen J. Graham

The Curious Incident of the Pony in the Nighttime

^Mark Marx – of leg-growing faith-healing fame – recently made another rather intriguing claim:

“Well, it seems God heals animals too. We’ve seen a flock of sheep healed, and now a pony!”

Sadly Marx refuses to engage with me, but another kind tweep was able to get the story from him, which is quoted unedited and in full below:

“Here’s the story, with kind permission to share… “Hi, I would just like to thank the lovely ladies who prayed for my very sick pony a few weeks ago. I know it sounds strange praying for a pony, but i cared a lot about him and the worry was affecting my health. He became v sick with Strangles and his throat swelled up so he couldn’t eat properly. He was seen by 2 different vets and given antibiotics but nothing helped. Both vets thought he would die. This went on for a few weeks and the 2nd vet said to give him till July and then he would be a loss. He also said there would probably be complications with his throat if he did survive. I went to the healing on the streets and some lovely women prayed with me for the stress and anxiety I was suffering from, and also prayed for a miracle for my pony. She prayed that that night he would be galloping about the field. Well, that evening, with 3 witnesses, my wee pony came galloping up to the field gate! He previously had been lying down or slowly walking about. I was so thankful. Just before July, the infection finally left him and he was able to eat. He has since put on loads of weight, is very bright eyed and full of life. Last week he galloped about the field non-stop for 5 minutes, a happy, healthy boy. The results have just come back from the vet that he is all clear. I am v thankful for the healing prayers he received. God cares for all creation, not just ourselves.””

Now, there’s not too much we can do with anonymous anecdotes except to analyse what little we have, without being able to follow up and ask questions of the various relevant parties.

On the face of it the story is probably enough to convince many people that the power of prayer was instrumental in healing this afflicted beast. To my mind, however, the story simply illustrates the problem with trying to use such anecdotes to defend miracles. A careful reading of the story suggests a much more simple explanation beneath the surface. Sadly, many people don’t bother to read carefully (few people have the time for that these busy days, I guess), and I suspect the story will be passed on as a simple “pony at death’s door – got prayed for – was healed – galloped in celebration” story. Perhaps in a few years we’ll hear also how eyewitnesses saw it turn into a horse, sprout wings, and fly. But let’s have a more careful reading.

Firstly, the pony was “very sick” with a condition called Strangles. Now, how many people will hear this story and bother to find out what Strangles is and how it’s treated? Very few, I suspect. But it sure does sound horrible, doesn’t it? It sounds like the sort of killer disease that would torment a poor beast, finally killing it through asphyxiation or starvation. That’s not quite what it is. Granted, like any health ailment, it isn’t pleasant, but in most cases it simply runs its course and the animal recovers in time. There can sometimes be complications, but the disease is very rarely fatal.

Which brings me to the second point: how sick was this particular animal? The anonymous owner says “very sick,” but notice that she was suffering from stress and anxiety. As a fellow-sufferer of these scourges I know only too well the reality-warping effects they can have. On several occasions I was truly convinced I was “very sick” – dying of cancer, in fact – due to the appearance of some otherwise common physical symptoms. Sufferers of anxiety tend to catastrophize, and one’s judgment is not terribly reliable under such circumstances. “But, wait a minute, Stephen,” I hear you cry, “didn’t this woman’s judgment get confirmed not only by one but two vets?” I’m glad you asked, this brings us to the third point.

The answer is “not quite.” Notice how this woman says “both vets thought he would die.” But this can’t be quite accurate since she also reports that one of them “said to give him till July and then he would be at a loss.” [Emphasis mine] So, this vet at least had not lost all hope. Seemingly in his professional opinion the animal could still get well again. Note that later on the woman tells us “just before July the infection finally left him,” which is in keeping with the vet’s prognosis.

These words bring us to the fourth point. After the pony was prayed for he was up and able to run over to a gate. But the woman appears to imply he wasn’t fully healed even at this stage. It seems to be a much more gradual recovery before “the infection finally left him” and the vet was able to give him the all clear. Perhaps the antibiotics that the woman had spoken of previously had begun kicking in, and the disease was now fading out – as one of the vets seems to have expected.

Upon our closer reading then it seems that what we really have here is a case of a pony with a disease that tends to run its course, (though this animal may have suffered some complications or perhaps for longer than is normal), and which recovered in the time frame laid down by at least one vet, after receiving treatment which included the use of antibiotics. The woman – suffering stress and anxiety as a result of her sick animal – was clearly incredibly relieved that the animal got well and, being a religious person, quite naturally attributed the recovery to a supernatural intervention.

It would be interesting to get the testimony of one of the vets rather than have to go on an interpretation of their words by a woman suffering stress and anxiety. Patients frequently have a very different understanding of their illness from that of their doctor – typically thinking they are in worse shape than they actually are. There are other questions we could ask: What was the time frame of the illness? How long after being prayed for did he fully recover? Did the vets think this within the parameters of what is normal in the circumstances? These are all questions that naturally arise on the back of a more careful reading of the story. Only by ignoring all these relevant details can anyone sensibly claim that what we have here is a case of a pony being miraculously healed by God. Sadly I suspect Mark Marx won’t care one jot about being careful, nuanced, and critical. It gives him another wonderful anecdote to share as he travels the world seeking to amaze the masses.

Stephen J. Graham