We could call your whole mind –all of your beliefs, desires, and emotions and whatever else is in your introspective phenomenal field- “you.” This is a reducible self because it is at once "you" -a self- and contains beliefs and desires that we could omit from the set of considered elements while still calling that set "you": hence, reducible self. There is also a part of your mind that we cannot pare anything away from while still calling the set of considered items "you." This is your irreducible self. The notion is difficult to pin down, but it has sufficient objective content for us to communicate about it. I have some idea of what I mean when I talk about my self as opposed to particular beliefs and desires, as I think most people do.

Though really, it doesn't matter whether we are talking about your irreducible self or one of your reducible selves for the purposes of the argument. All that matters is whether some part of whatever we end up calling your self does what I need it to do for my argument.

An object bumping into an object would be understood as simple motion if you did not have a preexisting concept of physical causation. So would any introspective event (barring the volitions I’m talking about, obviously). So the motion must be generated by, and its generation must be directly observed by, the irreducible self.

This must be done freely because otherwise it is not *generation* of motion. The motion is already there, and the self is just obeying it like a child tossed by a wave. It would be processed as simple motion like any other phenomenon in the absence of the concept of physical causation. You have to observe that you did something novel to your body or mind.

Please clearly explain the impact of this.

Correlation would not produce the "because of" that the concept of physical causation includes. "A, then B" is the only thing you could get from correlation. This is different from "A, then B because of A."

Correct. But we could only infer that after we had the concept of physical causation to apply to the bat. The question is where the concept of physical causation came from in the first place. I do not know how we could derive the concept from the sorts of interactions you are describing. It seems like we would infer simply "balls change direction when they contact a solid object," not "balls change direction when they contact a solid object, because of the contact with the solid object." We need to explain how we arrive at the ability to structure the observation with a "because of," i.e., with a generation of force by the solid object rather than just a change in motion.

Correct. Once we have the concept of physical causation, we are more strongly inclined to posit a physical cause in cases like this. However, I am asking where we got the notion of a physical cause -as against a correlation- at all, and it is not obvious that the situation you describe would particularly advance that.

My argument is compatible with the existence of a concept of physical causation in infants. It simply requires that the self be capable of performing volitions when an infant.

I agree that it would "make sense" for evolution to hardwire our DNA with a concept of physical causation, but that isn't decisive. Notice that it would also "make sense" for evolution to have hardwired our DNA with concepts like, say, the concept "red," the concept "two" or the concept of agriculture. That is not evidence that we have any of those concepts because we are hardwired by evolution to have them from birth.

Further, even if you think evolution probably did equip us with a concept of physical causality, there is a sense in which evolution could equip us with the concept without hardwiring it into our DNA. Evolution could do this by designing us so that we are likely to pick up the concept very quickly after birth. In fact, if my argument is correct, then we do pick up the concept pretty quickly: after our very first volition, perhaps making it the first concept we ever form.

Now, I admit that it would be difficult to tell the difference between a concept that we picked up very early in life, and a concept that we had from birth. But the facts remain: (1) so far as I know, we haven't got proof or even evidence that the concept of physical  causality is genetic, and (2) all of the concepts I'm aware of having picked up, I picked up consciously, after birth. This warrants me in expecting a non-genetic source for the concept of physical causality.

I am not sure what the impact of this section is on my argument.

Choices certainly are the "outcome of" and "based on" those things, but that isn't obviously incompatible with free will, so long as those things don't necessitate particular outcomes all of the time. Introspection seems to show that they don't, in fact. Even with more-or-less perfect knowledge of my own mind, I notice that I am not 100% confident of exactly what I will be doing in five minutes, even though I probably will not acquire any terribly important new beliefs or desires between then and now.

The choices made by the self are neither entirely determined by anything other than the self nor random. I think this because it is seemingly an accurate description of what I experience upon introspection, and on the basis of the argument that I present in the OP. 

Clearly, our brains are adept at recognizing patterns. Doesn't repeated correlation demonstrate that A and B are related?

I agree that we have a mechanism that could form patterns of association. I do not see how this would, at some point, transmute those patterns of observation into the concept of physical causation. A pattern of association could only provide “if A moves, then B always moves”, not “if A moves, then B always moves, because of A’s motion.” You need to explain why such patterns of association would ever provide a concept of physical causation.

You cite abstraction and model building to explain the origin of the concept. Abstraction can only omit elements from particular observations (though we may of course manipulate and recombine the abstractions derived thereby). For example, we may observe a red car, then a blue car, then omit the particular colors of the cars to arrive at the abstraction “car.” But in no case does removing elements like this provide us with qualitatively new conceptual material – nor could it. You cannot arrive at a concept of physical causation by omitting elements from instances of simple motion, unless those instances already contain the “because of” element on the perceptual level. As I pointed out in the OP, however, when we observe instances of simple motion, there is no perceptual element of causation. Nor could building mental models create the additional “because of” element, as a mental model obviously cannot draw on concepts that we don’t already have and that cannot be created from concepts that we already have.

The sort of free will that this argument concludes with explains the existence of our concept of physical causation and tells us that we have an irreducible self with the ability to generate motion in ways that are neither determined nor random.

But there is also a self that has beliefs and desires, and to whom these experiences occur. I am not sure how you could make sense of a belief as a belief (or an experience as an experience, or a desire as a desire, etc) without a self that has the belief (experience, desire, etc).

To be clear: I am not referring to an a-personal process involving beliefs and desires. I am referring to what has the beliefs and desires. The existence of the self is at least as clear as the existence of the beliefs and other phenomena that you are talking about. Likewise, the referent of the phrase “the self” is at least as clear as the referents of the concepts “belief,” “experience,” etc. Admittedly that referent is difficult to isolate in language, but this is a problem for many concepts, particularly those derived from introspection, and does not change the fact that we do know more or less roughly what we mean when we say “the self.”

Introspection confirms that decisions are based on beliefs and desires and so on, but it also confirms that the decision is based on them in some way that permits the decision to be neither determined nor random. This is volition, which I have claimed is the contribution of the irreducible self.

First, “there are multiple selves when the brain has a physical pathology” is not the same as “there are always multiple selves.” Introspection says the opposite.

Second, even if there were multiple selves, my argument would still hold so long as those selves do what the argument requires. We are more interested in whether free will exists than whether there are ten selves with free will or one.

I will be happy to examine the evidence in question, when you present it.

You are correct that we may not need the concept of physical causation that I am talking about to "build up workable knowledge of reality." That isn't the issue. The fact is that we have this (perhaps unnecessary) concept, and we use it, and we think it refers to something in the real world. I am trying to figure out where it came from, and I think it couldn't exist unless free will also exists.

I'm not saying that. I'm just wondering where the concept came from. I do not know what it would even mean to "prove" a concept. I am pretty sure you can only prove a proposition.

The mental slips that you describe clearly only employ conceptual elements that already exist in the mind. I agree that the concept of physical causation is conceptually "close" to the concept of simple motion, but these mental slips are not a plausible mechanism for bridging the two. We would have to bring in something other than standard mental slips, something capable of spontaneously generating qualitatively new concepts. Whatever that thing might be, I know of no evidence for its existence.

There is a sense in which I can agree with your account of concept formation. I simply disagree that it could give rise to any qualitatively new concepts, as there is not an obvious way that we could arrive at qualitatively new concepts simply by rearranging linguistic bits.

The size of the distance between the two is not the issue, the existence of any distance at all is. A concept that contains an element which is qualitatively dissimilar from all conceptual elements available to a given mind is, to all appearances, just not available to that mind.

I agree, but I think you would have to acquire the idea of causation first, to know that hitting the golf ball would have the desired result.

I suspect these basic concepts may be acquired by infants, by some combination of observation of others actions, attempts to imitate those actions, and the effects of the random movements of their arms and legs when they contact movable objects in their environment. Imitation, in particular, is an important part of learning such things. Many animals learn by imitation to perform actions which 'cause' other things to happen. Birds have been observed to drop objects onto hard surfaces to break them open, so whether they have any conscious awareness of the principle of causality, they certainly have acquired the ability to deliberately employ it.

Even more significantly, birds have been observed placing food objects they are trying to break open onto busy roadways, since they have learned somehow, presumably by combinations of accident and observation, that cars will eventually run over the objects and break them open. It seems quite unlikely that such specific behavior evolved to be purely instinctively driven.

Alternatively, if such behavior, which clearly involves some level of awareness of the effect of particular actions, can come to be instinctive, it further weakens the concept that it requires any higher consciousness.

IOW, I think the evidence is that such intentional behavior is often learned by imitation, without any higher 'metaphysical' thoughts on causality - those ideas follow, when we consciously contemplate our observations. Our higher cognitive abilities then allow us to extrapolate our observations to different but analogous situations. So it seems pretty well established that there are various sources outside our internal conscious reasoning for us to acquire the ability to deliberately employ cause and effect relationships. Even crows can do it: see here.

 I suggest you check out: 

http://www.youtube.com/watch?v=aKLAbWFCh1E

In short, your definitions and False dichotomies are probably inaccurate.

We have a limited free will. There are certain naturally predestined events, but between them there is a variety of choices how and when these predestined events will happen. Not even the wisest being is infallible in prediction.
The causation is there, I mean, there are impacts of previous causes affecting us. But they don't affect us totally. We can choose to be totally determined by them, or we can choose to withstand them and act from our own inner will, which is more diffcult, but also a progressive thing to do.

Unfortunately, modern psychology is still not modern enough about this subject. There is a knowledge of physical and emotional causes, cognitive also, but the higher states of mind are crowned with ignorance, as for the academic science. People with a low consciousness are pretty much deterministic, but it is not a rule for everyone. We have to recognize their existence and study them. This will probably happen when enough of scientists will spontaneously experience what can not be pinned down in any existing textbook of psychology. Then we will discover and verify much of what is the free will really about. Until then, it is a speculation with insufficient data.

Btw, I've heard, that the brain actually makes a decision before we consciously realize it. Is it true? What does it mean for the concept of free will, good or bad?