Paul claims some libertarian philosophers deny PAP (Principle of Alternate Possibilities). He cites Timothy O' Connor, David Hunt and William Lane Craig. (link) This topic is somewhat tangential to our determinism/choose debate, but it's interesting so I thought I would address it. I tend to disagree with PAP but I also disagree with some of Craig's recent comments. I don't think O'Connor was denying PAP and I find Hunt's comments prima-facia inconsistent, so I will only address Craig.
PAP and Frankfurt Examples
PAP is the idea that a person is morally responsible for what he has done only if he could have done otherwise. (Free will Handbook. Fisher. Frankfurt-Type Examples and Semi-Compatiblism. p283.) Note that not just some, but all events for which we are accountable must be free and not necessary under PAP. So for example those holding to PAP must deny we are morally accountable for our actions that result from prior free choices but are themselves not free. Understood this way, not just some, but a great deal of libertarian thinkers deny PAP. Arminius' commentary on Romans 9:19 reveals he denies PAP: If, indeed, the man commits that which deserves hardening of free-will, he is subjected to blame, and is worthy of wrath, even if he may be hardened by that will, which can not be resisted. For resisting and that freely, the divine will, revealed in the word, which can be resisted, he is brought into that necessity of the divine decree, also revealed in the word, which can not be resisted, and so the will of God is done in reference to him, by whom the will of God is not done. (link) On the other hand, denying PAP is very different then saying man never has alternative possibilities (AP) or even that AP is necessary for moral responsibility.
Here's a Frankfort example: Suppose Jones is in a voting booth deliberating about wheater to vote fro Gore or Bush. After reflection, he chooses to vote for Gore and does vote for Gore by marking his ballot in the normal way. Unbeknownst to him, Black, a liberal neurosurgeon working with the Democratic Party, has implanted a device in Jones's brain which monitors Jones's brain activities. If he is about to choose to vote Democratic, the device simply continues to monitoring and does not intervene in the process in any way. If, however, Jones is about to chose to vote, say, Republican, the device triggers an intervention that involves electronic stimulation of the brain sufficient to produce a choice to vote for the Democrat (and a subsequent Democrate vote). (ibid. 282)
The Frankfort example has numerous problems, such as 1) there is no "sign" beforehand indicating what the choice will be, 2) there's no such thing as a "forced choice" so no device could trigger a choice, 3) the will is part of our immaterial soul, so no physical device could monitor and manipulate it. However, the interesting question is if the Frankfort example can be fixed. Let's look at Craig's attempt.
Response to William Lane Craig
William Lane Craig: "But as you note, I’m a libertarian who thinks that causal determinism is incompatible with freedom. That doesn’t imply that I hold to the Principle of Alternative Possibilities (PAP), which states that a free agent has in a set of circumstances the ability to choose A or not-A. I’m persuaded that so long as an agent’s choice is not causally determined, it doesn’t matter if he can actually make a choice contrary to how he does choose. Suppose that God has decided to create you in a set of circumstances because He knew that in those circumstances you would make an undetermined choice to do A. Suppose further that had God instead known that if you were in those circumstances you would have made an undetermined choice to do not-A, then God would not have created you in those circumstances (maybe it would have loused up His providential plan!). In that case you do not have the ability in those circumstances to make the choice of not-A, but nevertheless your choice of A is, I think, clearly free, for it is causally unconstrained—it you who determines that A will be done. So the ability to do otherwise is not a necessary condition of free choice." (link)
I disagree with Craig's statement - while he patches some of the problems in the prior Frankfort example, he creates some new ones. Middle knowledge looks like it could successfully replace "the sign" and Molinism could replace the "forced choice" and work with an immaterial soul. So it seems the initial Frankfort problems are fixed. However, Craig has some new problems.
First, Craig defines PAP in a much broader sense than Fisher; Craig's not just going after responsibility, he's going after AP. Both Fisher and Craig deny PAP, but given their different definitions of PAP, Fisher denial entails actions that are "necessary but responsible", Craig's denial entails actions that are "necessary but free". For Fisher, the issue is "do you have to have AP in all cases of responsibility?" For Craig, the issue is "do you have to have AP in any cases of freedom?"
The problem with Craig's argument is that middle knowledge entails AP. Everything God knows via His middle knowledge is possible (included within God's natural knowledge). God could not know, via His middle knowledge, that you would choose something that would "louse up His plan", because God's plan totally failing is strictly impossible and not an object of His natural knowledge. This falls into the same category as God sinning. It's logically inconsistent to have a Sinning Holy One, so such scenarios are self-contradictory, logically impossible, and not part of God's natural knowledge. Only in a relative sense (removing some of God's attributes from view) can we even talk about such things without sliding into incoherence.
Nor could God still have middle knowledge of Jones voting democratic without the possibility of Jones voting republican because it would louse up His plan. By middle knowledge God knows which of two or more possibilities would obtain under various circumstances. If nothing else is possible, middle knowledge is unnecessary and superfluous, since God already knows what "would" happen - the only thing that can happen.
If you remove the "it would louse up God's plan" aspect, and just say God chooses not to create that world, then such a choice leaves man with AP. The person can, but will not (and would not) choose otherwise. So Craig's replacement of "the sign" was unsuccessful; it was replace by something that entailed AP - the very element he attempted to remove.
Further, causal indeterminism entails AP; it's the core element of AP. The deterministic/indeterministic distinction is broader than the agent/event causation distinction. Thus, even agent causation may be deterministic or indeterministic. If the agent doesn't have alternative possibilities, then his nature determines him to one and only one action. Although there is a difference between this and deterministic event causation, it's still deterministic, not indeterministic.
Finally, Craig's example doesn't rule out AP. Now God couldn't get me to vote for republican (since I wouldn't do so), but He could create a world where I live in Timbuktu. So there are three possible worlds: vote republican, vote Democrat, and riding a Camel in the Sahara. Now Craig goes further and says what if my voting Democrat messes up His sovereign plan. So God has to put me in the Sahara; permitting me to vote Democrat is impossible (since it would be unwise for God to do so). Oddly enough, we still have alternative possibilities: vote republican or ride a Camel in the Sahara. Not what I had in mind when I entered the voting booth, but twofold possibilities none-the-less, so it's still not deterministic. Even under the assumption that God wouldn't create me at all, "possible me" (the object of God's natural knowledge that did not get actualized) would still have had alternative possibilities.
Now don't get me wrong, I like Craig and still recommend his books. I have no idea how these recent statements he has made could be reconciled with his earlier works. In his chapter "Within One's Power Once More" in his book Divine Foreknowledge and Human Freedom: The Coherence of Theism : Omniscience, Craig states "But assuming that our actions are not causally determined, we have the ability to act in ways other than we in fact act" p. 161. But it seems this recent statements are mistaken.
Why I Reject PAP
I agree with Arminius on the hardness of hearts, but while such acts are voluntary they seem like they are less than choices. Recall Aristotle said: "Choice is manifestly a voluntary act. But the two terms are not synonymous, the latter being the wider. Children and the lower animals as well as men are capable of voluntary action, but not of choice. Also sudden acts may be termed voluntary, but they cannot be said to be done by choice." (Aristotle, Nicomachean Ethics (ed. H. Rackham) II.3) Thus, rejecting PAP harmonizes with my choose arguments.
Futher, PAP seems to be interpreted too specifically for my taste. You must be able to vote Democrat or Republican. You must be able to do good or evil. You must be able to eat chocolate or vanilla... Aquinas broke freedom down into two parts: exercise and specification. "Now a power of the soul is seen to be in potentiality to different things in two ways: first, with regard to acting and not acting; secondly, with regard to this or that action. Thus the sight sometimes sees actually, and sometimes sees not: and sometimes it sees white, and sometimes black." (link) For me, it's enough to choose A or not - I don't need to extend things to the ability to choose A or B. Now this issue is mostly perception not real. Some determinists like to specify "B" and then show B is impossible. But both "A or not" and "A or B" are alternative possibilities. It's just one is more specific than the other.