Sometimes it is said that God has libertarian freedom. The argument for this often goes like this:
- God freely chose to create the world.
- The world is not necessary.
- Therefore, God’s free act of creating of the world was not determined.
- Therefore, God has libertarian freedom.
This argument is actually quite popular, but it is invalid. For the sake of the argument, I’ll grant we can validly get to (3). However, the jump to (4) assumes a suppressed premise, something like:
- 3a. If a free act A is not determined, then A is libertarian free.
But that is false. It assumes that indeterminism is sufficient for libertarianism, when it’s actually only necessary for libertarianism. What is needed instead is something like this:
- 3a′. Freedom is incompatible with determinism.
But with this addition, the argument would then assume incompatibilism. (1)–(2) at best get you indeterminism, but what is needed to secure the conclusion that God’s freedom is libertarian is an argument for incompatibilism, not an argument that assumes incompatibilism.
Analytic Theology, et cetera. 
There is at least one way to tighten up the move from 3-4. Here it is – granting the inference from 1&2 to 3:
1. God freely chose to create the world.
2. The world is not necessary.
3. Therefore, God’s free act of creating of the world was not determined.
Supplying what is needed to get to conclusion above – call this the a se premise:
4. God cannot be caused in any way in which he is not himself in control of being caused.
5. Therefore God has libertarian freedom.
OK. Obviously the move from 4-5 is sketchy. To make it less sketchy – but sketchy nonetheless – the premise says that there is no world in which God is caused where he is not himself responsible for his being so caused. So it is no possible that God is caused in a way where he is determined by anything outside of himself. But God is sometimes free. Hence, God has libertarian freedom.
Response: But maybe God’s *nature* or *character* (those are not the same thing!) determines what he does.
Reply: Nope. See premises 1 and 2.
There is something wrong with the above argument and the error is easier to spot than a jumbo jet.
Typically, those who offer the argument in the main post do so to support our having libertarian free will. But the ‘a se’ premise, as you’ve articulated it, would seem to disallow our having that kind of freedom.
That’s right. It would at least *seem* to imply God’s having that kind of freedom. Where the error in the argument I ran is that God’s being free to do x or ~x is not the result of God’s having a certain type of freedom, but is a result of aseity. That is, it is not in the nature of God’s freedom itself that allows for the contracausal power but in the nature of something else, i.e., another one of his properties.
The central move I typically challenge is the move from *God has some feature F* to *we have some feature F*. The best shot at making that inference, as far as I know of, involves appealing to the imago dei; but then we just need to ask whether God’s having that freedom counts as one of the communicable or incommunicable attributes. And there’s no argument I know of that the imago dei itself gives us a reason to think God’ freedom is reflected in that.
That’s good. Another problem with the imago dei move is if we view the attributes in a course-grained vs. a fine-grained way. So, suppose God is free. Suppose this is communicable. As far as I can see, that only entails that we are free. Here I say nothing about the nature of the freedom. Suppose that god has a sui-generis freedom (neither narrowly circumscribed by a compatibilist nor libertarian analysis), he’s still free. I may have compatibilist freedom, I’m still free. I image God in being free. It’s not clear that we must image God in fine-grained rather than course grained ways. To see the point with a non-controversial example, take a look at rationality or knowledge. We are rational and able to know, but it’s not according to the way God knows. Suppose we know in accord with a design plan, yadda yadda. God doesn’t know like this, he’s not designed!