First the argument in nuce, then a detailed explanation.
P1. I am morally responsible for at least some of my actions and omissions.
P2. I cannot be morally responsible for an action or omission unless I am libertarianly free with respect to that action or omission.
C. I am libertarianly free with respect to at least some of my actions and omissions.
2. Moral responsibility is to be distinguished both from causal responsibility and from legal responsibility. Suppose I have just passed my stress EKG with flying colors and have no reason to think I have heart disease. But I have a heart attack while driving home from the doctor's office and kill a pedestrian. Surely I am not morally responsible for the death. And it would be a draconian law indeed under which I would be held legally responsible. On the other hand, I am morally responsible for the entertaining (if not the initial occurrence) of evil thoughts such as the thought of running down a man who has insulted me, but not legally responsible for them inasmuch as there are no — and should not be — any positive laws regulating what one thinks. (Positive laws are those posited by legislatures.)
3. An action-omission is a failure to act. Example: I promise to meet you at Insufficient Grounds coffeehouse for chess at an agreed upon time, but fail to show up or notify you of my inability to be present.
4. That (P1) is true I take to be either self-evident or more evident than the load-bearing premises of any argument the conclusion of which is its negation. That we take credit for some of our actions/omissions shows that we take ourselves to be morally responsible for them. This credit cannot be accounted for in terms of mere causal or legal responsibility. And the same applies when we blame ourselves and others for actions and omissions.
5. (P2) will be rejected by compatibilists. They will hold that moral responsibility does not require libertarian freedom of the will (LFW). I suggest we define LFW disjunctively in a manner to accommodate the distinction between 'leeway' and 'source' incompatibilism:
LFW. An agent S is libertarianly free with respect to an action A iff (i) S does A, and (ii) either S could have done other than A while all other conditions remain the same, or S is the ultimate source of the action, or both.
An incompatibilist is one who maintains that moral responsibility is logically incompatible with the truth of (causal) determinism understood as the thesis that the actual past together with the actual laws of nature render only one present nomologically possible. Determinism has two consequences: it deprives the agent of alternative future possibilities, and it insures that the agent is not the ultimate source of any action. For if determinism is true, the agent himself is nothing other than an effect of causes that stretch back before his birth, so that no part of the agent can be an ultimate origin of action.
A 'leeway' incompatibilist holds that moral responsibility requires alternative possibilities, while a 'source' incompatibilist holds that the agent's being the ultimate source of his action sufficies for moral responsibility.
Compatibilists believe that moral responsibility can be had 'on the cheap' if , roughly speaking, a person is free in the sense of not being constrained to act or refrain from acting by anything external to the agent. Here is an example of a compatibilist analysis of freedom. Person P is free to do action A if and only if
P wills (wants, desires, chooses, etc.) to do A.
P's willing (wanting, etc.) to do A is unencumbered by any internal or external impediment, or subject to any internal or external compulsion.
P's willing (wanting, etc.) to do A is motivated by reasons.
The existence of an action done freely in the above sense is consistent with the truth of determinism. For one could act freely in the above sense even if one is not the ultimate source of one's action, and there are no alternative possibilities of action.
But this is not the sense of 'free' in which we morally responsible agents are free. Facing a morally relevant choice, I experience myself as free in the sense that it is 'up to me' what happens, that what I do is determined by me, and that when I do A rather than B (both being possible), I could have done B. Thus I experience myself as both the ultimate source of the action, and as as having an open future. Note that even if Frankfurt-type counterexamples show that moral responsibility does not require an open future, that does not suffice to show that moral responsibility does not require LFW, for if I am not the ultimate source of an action, then I cannot be morally responsible for it.
6. One might try to argue that this sense of libertarian freedom, and the sense of moral responsibility that rests upon it, are illusory. I do not believe that it makes any sense to view these phenomena as illusory, but this is a separate question.
7. The argument given above is not compelling, but then few, if any, arguments for substantive philosophical theses are compelling. (If you think you have a compelling argument, present it to me and I will show you why it is not compelling.) But I do claim that the above argument renders the belief in libertarian freedom of the will rationally acceptable.