LCA: Responding to 3 important challenges

I intend to discuss three problems here:

1. In what sense does God have a will, since God necessarily chooses the best possible world.

2. In what sense are there possible worlds, since God necessarily creates only the best possible world.

3. In what sense is God omnipotent, since God in some sense can only bring about the best possible world, and no others.

These problems are serious ones, and do need to be responded to. This is especially important given the large corpus of literature claiming that these problems spell the end of contingency arguments, or for any conception of theism.

First, let’s run a little thought experiment. Suppose we have a deterministic chess AI, name it A: given the same position, and the same outside factors like underlying hardware and time remaining, it will always make the same move. There is no randomness inside the AI. Suppose that A’s opponent is a fairly weak engine, and A has been able to perfectly predict all of their opponent’s moves. There is a sense in which A “knows” about all these possible outcomes and futures, despite the fact that none of them can come about.

Now I don’t think that at this point it’s too controversial to extend the thought experiment. Suppose that A is not just deterministic, but is actually necessary. That is: not only can it not do otherwise given the nature of its programming and its situation, but those programs and situations could not be different. Does this fundamentally change A’s knowledge? I don’t see how it does. The internal state of A is identical, it’s just a fact about the external world that has changed. But not, in a sense, A’s world. Since A’s world consists only of the board, the rules, and the opponent.

Even though A is necessary, there is a sense in which it “knows” about “possible” future outcomes. How can this be? I claim this: A’s “knowledge”, though it appears to be based on counterfactuals, does not depend on possible worlds at all. This knowledge that A has is not based on any kind of access to “possible worlds” since A and its opponent are necessary.

An agent, when considering the impacts of their actions, can simulate possible outcomes of all the actions that agent could take. Even if the agent is necessary, it can simulate these outcomes, since that agent itself is the thing that determines them. Now perhaps you and I do not, because our knowledge is imperfect. But our chess AI has in a sense a perfect knowledge of its world, and God has a perfect knowledge as well. So God can perfectly internally simulate the outcomes of the actions that He could take. And note that this is true regardless of whether God necessarily takes a particular action. Each of these simulations is technically metaphysically impossible: God, being perfectly good, won’t choose to create them. But that’s the only impossibility present in them: they contain no other contradictions. God’s will, God’s choice, is the only thing restricting these worlds from being possible. And so God can perfectly simulate them.

Now we have reconstructed a possible world: not as a meaningfully real metaphysical possibility, but as a specific kind of thought in God’s mind. And using these possible worlds, we can engage in all our normal counterfactual reasoning, which we have come to love Lewisian worlds for. But now, possible worlds aren’t primitive, God’s knowledge and God’s power are ontologically prior.

Where did that notion of power come from? Again, worlds are simulations of the consequences of God’s actions. And so the totality of all those actions in each of those worlds is the totality of God’s power. Normally we want to frame omnipotence as “the ability to bring about any possible world”, but now we’ve gone the other way: omnipotence is primitive, and a possible world is a simulation of the consequences of an action of which God is capable. So now: what is omnipotence? What makes God omnipotent rather than just very potent?

It is the density of possible worlds. The denser they are, the more powerful God is. If there are only, say, 3 possible worlds, God is not very powerful. But if they are more unrestricted perhaps every logically possible world, or every world that would be metaphysically possible apart from God’s will, then God is more powerful. What we have now is: God’s power is as unrestricted as His knowledge, and God’s knowledge is as unrestricted as His power. So now an argument for omniscience also suffices for omnipotence. Arguments for God’s omniscience have been given elsewhere, and perhaps they will be elaborated on further later. But for now, we will move on.

God’s will is mixed in here too: God must will because God has a reason for one world becoming the actual world, and God acts on that reason. That reason being that that world is the best possible world. Seems like having a reason and a goal, simulating outcomes, and choosing an action is having a will. God chooses among alternatives based on His beliefs (or in this case, knowledge) and desires. The content of those desires is moral goodness, and God is necessarily good, so God necessarily creates the best possible world. But despite (and in my argument, because of) this, God chooses, and God has a will.

Why believe this? So far all I’ve done is tell you a story about the attributes. I hope I’ve convinced you that they are possible, compatible, and reinforce and illuminate one another. But so far, I’ve given you no reason to think God has them.

Here’s one: We need counterfactuals to ground our everyday reasoning. But given the PSR, as Van Inwagen argues, there is modal collapse. Only one truly possible world, therefore necessitarianism. So there are no other possible worlds to ground our counterfactuals. Are we dead?

No: possible worlds do exist, but only in the mind of God. And that’s the only place they could exist: no other being can simulate these “almost possible” worlds, since no other being is the means by which they are possible or impossible. It is solely because of God that they are possible or impossible, so only God can have proper simulations of them. But under that, the only way we can ground our counterfactual reasoning (if we rely on possible worlds) is via God. So God is a necessary part of our everyday reasoning. Combined with the rest of the LCA, we ought to believe in God.

LCA – Points 2 to 4

In our previous post on Leibniz’ Cosmological Argument, we examined the first premise, the PSR. I would summarize the PSR with the claim “reality is fundamentally intelligible”, though we go into more technical detail in that previous post. To remind you, here is the full argument:


  1. Every contingent fact has an explanation.
  2. There is a contingent fact that includes all other contingent facts.
  3. Therefore, there is an explanation of this fact.
  4. This explanation must involve a necessary object.
  5. This necessary object is God.


Here we will examine points 2 to 4. These are reasonably simple, and although they are sometimes disputed there shouldn’t be anything too controversial here. Most skeptics who deny this argument will take issue with premises 1 or 5.

(2)               There is a contingent fact that includes all other contingent facts.

It is at this point that we must define what a “contingent” fact is. Briefly, a contingent fact is a fact that does not explain itself. For example, we might say “a cat exists”. Is that self-explanatory? Can we coherently ask “why does a cat exist?”. In the case of my cat, explanations may include: me and my brother asked my parents for one, and also the cat has parents, and also the cat is composed of molecules, and also the species “cat” was created by God. These are all partial explanations for the contingent fact “my cat exists”. Here, a contingent fact is any fact like this, any fact X that has an explanation Y, where Y and X are not identical.

This definition is a bit vague, and purposefully so. There are multiple conceptions of precisely how we cash out contingency, and I want my argument to be general enough to cover all of them. But if you are after a more specific definition, try this one: a contingent fact is a fact that is true in some possible worlds, but not all possible worlds. There are some worlds in which there is no cat (or no matter), and some that include a cat. Note that I am not talking about a multiverse here, some worlds contain one universe, some contain multiple, some contain none. A possible world is a way that reality could have logically possibly been, but isn’t. A possible state of affairs that could have attained, but didn’t. If this is a new idea for you, perhaps study this SEP article. We will occasionally make use of this definition during our argument, but I will attempt to stay as general as possible.

Some of you are necessitarians and reject possible worlds. I am. If that is you, then we will need a different notion of contingency. I intend to publish my thoughts on that once we have completed the entire LCA series.

The actual premise is relatively easy. If it’s true that “x is a fact” and “y is a fact”, then it’s true that “both x and y are facts”. So we can construct a true statement such as “x is a fact and y is a fact and……..” and so on until we’ve covered every contingent fact. This fact that we’ve constructed is contingent because all of the incorporated facts are contingent. If any of them could possibly be different, then so could the constructed fact. In some other literature, this fact is called the BCF or BCCF (Big Contingent Fact, or Big Collected Contingent Fact).

There is a minor concern here that the BCF could be self-referent. That is, the BCF includes the BCF. Some of you will be familiar with Russel’s Paradox, which relies on this kind of self-reference. So there are two solutions, I think either works. Either we say that this isn’t a set, and we call it a “collection” or something, and then we aren’t bothered by self-reference. Or we construct the BCF by including every contingent fact that isn’t the BCF, we include every other contingent fact. This is a relatively minor issue, it is in a sense just nitpicking. But it seems important to include it so people don’t get grumpy at me.

(3)               Therefore, there is an explanation of this fact.


This follows from (1) and (2). Every contingent fact has an explanation due to the PSR, so the fact we just constructed has an explanation

(4)               This explanation must involve a necessary object.

Let’s suppose it isn’t true, suppose the BCF is explained by a contingent fact. Given the PSR, then this explanation still has to exist. We’re supposing it’s not necessary, which means it must be contingent. But if it’s contingent, then it’s part of the fact that we’re trying to explain.

This means that the explanation is its own explanation. It doesn’t depend on anything else to be true. This means it’s not contingent, and is instead necessary. So by reductio, the explanation for the constructed contingent fact must be necessary.

Some complain that I’ve equivocated between “fact” and “object” here. But this is not a big problem, like the self-reference above. Every fact refers to at least one object, and for every object X we have the fact “X exists”. We can travel between “facts” and “objects” freely. I choose the term which best primes the intuition of the person reading it.

This will conclude the middle section of the LCA. Next time, we will investigate what the necessary explanation is, we will work out what properties and attributes it must have, and end up concluding that it is God.