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.


-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,


(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



Filed under God, Possible Worlds, Problem of Evil

3 responses to “Short Article (6): Can God Create any Logically Possible World?

  1. I’d just like to clarify the objection to the temporal example you used.
    PW-Y1 and PW-X1 only become incompatible after god chooses one or the other.

    I can still say that both are LPW but that one can no longer be actualized now, but god could have actualized either world, but can no longer do so now that one was actualized vs. the other.

    And this only works given the acceptance of some conception of time, with god being “in-time” rather than outside of time so that before and after relations could actually apply to what god actualizes. This is itself a controversial issue though less so than LFW!

    As for the meatier objection with LFW, well I think molinism complicates the defense since even if it is “up to Judas” whether PW(B) or PW(B-) happens GIVEN certain circumstances C. Molinism treats LFW quite very deterministicly, saying that Judas will always do PW(B) actions given circumstances C1, but will always do PB(B-) in circumstances C2. The key is that god is the one who chooses to actualize circumstances C1 vs. C2.

    The difficulty I have with calling saying god can’t actualize a LPW is only because we’ve made a kind of assumption that:

    Judas will PW(B) in C1
    Judas will PW(B-) in C2

    Given those additional axioms/assumptions, then we’ve effectively axiom’ed our way out of a possible world: Judas will PW(B) in C2 since we’ve said that world can’t exist via an assumption.

  2. How did ideas like “evil” and “sin” even enter the mind of a perfectly good being like God? Or were they a complete surprise to God? Can God be surprised?

  3. How does one define “libertarian free will,” except as the ability to make decisions other than the ones that one would have normally arrived via less absolutely free means, such as via using one’s current knowledge, experiences, ingrained habits, prejudices and cognitive biases, acquired in one’s lifetime, and including also any number of minuscule tipping factors like the butterfly’s wing effect.

    Instead of libertarian free will, I think decisions can be explained, they have sufficient causes. For instance, when it comes to making changes in one’s life, people change when the pain of remaining the same becomes too great. Nor does “will” have to be “free” in the absolutely “free” libertarian philosophical sense to simply be will. Every animal makes decisions, and keeps moving and reacting to stimuli, and makes more.

    Besides, there’s no way to test for absolutely free libertarian free will since there is no way to place someone in exactly the same space-time situation more than once including every other factor duplicated, so we can never know if anyone has the capacity to “chose differently.” And if they DID choose differently given exactly the same circumstances, what then? The ability to make such unpredictable decisions is as worthless as a roll of the dice or a spin of a wheel of fortune. Better to have sufficient causes behind one’s decisions, even if it is difficult to ever be fully conscious of why one has made some of one’s choices.

    I also think that concentrating on making well informed decisions is more important than concentrating on defending libertarian free will decision-making.

    Because let’s say we COULD make the experiment I mentioned above, putting a person in exactly the same space-time place and we could see that person make a totally different decision even with all of the zillion factors remaining exactly the same. That might only prove that one’s “will” functioned unpredictably like spinning a wheel of fortune, making every decision a gamble, based on no solid connections even with your own memories and past experiences. And that’s not a meaningful way to live. Better to stress the benefits of remaining well informed in our decision making, remaining connected to the past and future. So, get to know others and yourself, read literature, study history and nature, look through telescopes, study and learn, and we will make more well informed decisions, or at least better informed ones over time.


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