Category Archives: Possible Worlds

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

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