Arminians are strange birds at times (but maybe so are we Calvinists). They hold to something that has commonly been referred to as libertarian free will (LFW), which is basically the ability to choose between alternatives with equal ease. It’s also been referred to as the power of contrary choice. They argue (or just assert) that without LFW man cannot be morally accountable for his choices. If they argue, it goes something like this. If man is morally accountable, then he can choose contrary to how he will. Man is morally accountable, therefore, he can choose contrary to how he will. (Principle of Alternative Possibilities - PAP)
Here is a very user-friendly refutation against LFW:
1. Choices are either caused or uncaused.
2. If a choice is uncaused, then it comes from nothing and is, therefore, morally irrelevant.
3. Choices are morally relevant.
4. Therefore, choices are caused (and, therefore, necessary by definition).
5. The causes of choices are chosen or not chosen.
6. If causes of choices are chosen, then an infinite regress of choices and antecedent-causes precede any choice.
7. An infinite regress of causes and choices is impossible, therefore, the causes of choices are not chosen.
8. Choices are causally necessitated by something not chosen. (4 & 7)
9. LFW is false because choices are caused by something other than the agent's choice.
2. If a choice is uncaused, then it comes from nothing and is, therefore, morally irrelevant.
3. Choices are morally relevant.
4. Therefore, choices are caused (and, therefore, necessary by definition).
5. The causes of choices are chosen or not chosen.
6. If causes of choices are chosen, then an infinite regress of choices and antecedent-causes precede any choice.
7. An infinite regress of causes and choices is impossible, therefore, the causes of choices are not chosen.
8. Choices are causally necessitated by something not chosen. (4 & 7)
9. LFW is false because choices are caused by something other than the agent's choice.
Now where many Calvinists get a bit uncomfortable is when the tables are turned back on them. Does God have LFW? Well, most Calvinists will say no, God does not have LFW. Yet what they give with one hand, they take away with the other. They don’t want to say that God has LFW, but they don’t want to say that God is unable to choose contrary to how he chooses.
Again using the proof, though with some modification, let’s see if God could have not chosen to create:
1. Choices are either caused or uncaused.
2. If a choice is uncaused, then it comes from nothing and is, therefore, morally irrelevant.
3. Choices are morally relevant.
4. Therefore, choices are caused (and, therefore, necessary by definition).
5. The causes of choices are chosen or not chosen.
6. If causes of choices are chosen, then an infinite regress of choices and antecedent-causes precede any choice.
7. An infinite regress of causes and choices is impossible, therefore, the causes of choices are not chosen.
8. Choices are causally necessitated by something not chosen. (4 & 7)
9. Creation is caused by choice.
10. Creation is a caused by something causally necessitated and not chosen. (8 & 9)
11. Something caused by something that is causally necessitated would itself be equally causally necessitated (and therefore could not be otherwise by definition).
12. Creation is something
13. Creation could not be otherwise. (10 – 12)
Calvinists will sometimes say things like “If creation was necessary, then creation has claim on God.” That was actually said to me several years ago by John Frame. My reply was simply that creation does not have a claim on God but his eternal intentions do. Why should it seem strange that God cannot act contrary to what he wants most to do? After all, if it is actually true that agent A will do X in state of affairs S, then it is also true that agent A must be inclined to X in S in order for X to obtain, lest pure contingency (i.e. something from nothing) obtains. Yet if it is true that A can refrain from X in S, then it is false that A must be inclined to X in S (for the possibility of of refraining from X implies that A need not be inclined to X); yet the truth of X presupposes that A must be inclined to X in S. Therefore, since inclination is necessary for X, then X is caused.
Calvinists can introduce mystery into the mix along with the creator-creature distinction and even paradox if they like, but nothing can change the fact that LFW is a philosophical surd and no amount of mystery, creator-creature distinction, or paradox (whatever that might mean to someone) can undermine what is patently false. The only thing left to say, as Frame said to me, is "Well, maybe God has an unrevealed attribute that is somewhere between pure contingency and necessity, something like LFW but not really LFW." (I paraphrase but that's pretty close to it.)
Finally, in common parlance someone even like myself might say without contradiction something like "I could have chosen differently," but that simply underscores that the choice in view was made according to liberty, a freedom to choose as as one likes, which is nothing akin to the radical "freedom" that LFW contemplates.