In a recent discussion, it was brought to my attention that causing some act is not doing some act. I suppose that in considering two different senses that's quite true. First, if I press "play" on my DVD player, I am not doing the action of reading the disc (even though I caused it). But these are two different senses of "cause." In the physical sense, I did cause the button to press which placed a series of intermediate physical causes resulting in the desired effect of the DVD playing. Anyone who insists I did not play the DVD is just mistaken.
Let's consider a thought experiment. Suppose there is a nuclear bomb, a single domino, and a mad scientist supervillain. She wants to destroy the region of the world where she is, but has a whimsical side as well. She sets the scenario so that when she flicks her finger on the domino, it falls and triggers the bomb (suppose she has enough time to get away or does not care if she dies). Has she detonated the nuclear bomb? Of course she has. She has both caused and performed the action.
Now let's add one more domino, and line it up so that when our supervillain scientist strikes the first domino, it, in turn, strikes a second, and that second domino detonates her nuclear bomb. Has the addition of the second domino affected the causal or "doing" relationship? It seems not. For the mechanism was still caused to run by the supervillain. Moreover, the counterfactual truth of "if the first domino were to strike the second, it would fall and trigger the bomb" is not a sufficient cause of the bomb's being detonated. Now add a third, and a fourth, and so on, until an infinite series of dominos are set up so that each one triggers the next to fall, until eventually the nuclear bomb is triggered. Even in the case of an infinite number of intermediate causes, the mad scientist supervillain has still caused and done the action of detonating the nuclear bomb.
The same goes for God in hard determinism. In this case, God causes each and every action (including sinful ones). It would not matter if he used one or many intermediate causes to bring the action about; he has done it (especially since, on hard determinism, the subject lacks free will). What of soft determinism and compatibilism? This fares no better. Think back to the DVD analogy. According to compatibilism, human beings can only act in accord with their nature. It is the same as when the power button is pressed on the remote; the DVD player can only act in accord with its nature. But if I have caused and done the action of playing the DVD, then God has caused and done the actions of human beings, including sin. In this case, we now have an argument:
1. If determinism is true, then God causes and does acts of sin.
2. Determinism is true.
3. Therefore, God causes and does acts of sin.
4. God cannot cause and do sin.
5. Therefore, determinism is not true.
Obviously, we have a reductio; we can hold (1, 2, and 3) or we can hold (1, 4, and 5), but we cannot hold all of the premises. The first part of this post substantiates (1), so that can be safely accepted. (3) and (5) are entailed conclusions, and so cannot themselves be denied. So, we can safely create another premise:
6. Either determinism is true or God cannot cause and do sin.
The only obvious way of escape is to claim that God can, indeed, sin. I am not sure if anyone would take this escape route. If anyone would, it's worth remembering that God would therefore not be the paradigm of moral goodness. There is another way. (1) can be denied on the grounds of theological voluntarism. That is to say, while (1) is true in that if determinism is true, then God causes and does acts that for humans would be a sin, these are not sins for God. This is because God can simply will to do them, and whatever God wills is right. There are a number of consequences to this. First, the other horn of the Euthyphro dilemma comes to light: morality is not really objective, but arbitrary. That not only seems absurd on its face, but one would have a hard time even coherently defining such nonsense. Second, it would mean obviously absurd things, such as that God could will the torturing of babies, or that God could lie, or any number of things. In any case, it seems much more plausible that God cannot cause and do sin than that determinism is true!