Surely reason is deterministic.
If I can take the same input, use the same process and produce more than one result, surely reason is useless. More over, surely there is a cause for when I do not apply reason, or when my reason is imperfectly implimented. Whatever this concept of LFW is, it is seemingly a very naive attempt to rectify the understanding that humans have predispositions with the Christian doctrine that we can choose to obey or disobey God.
That is where believers in libertarian free will differ from your perspective. They do not believe necessarily that reason is deterministic, or they did not think so for the longest time. But even if they do see reason as deterministic, they view the will as being able to choose between the deterministic dictates of reason and other alternatives. That does not make reason useless. Reason may well provide the best possible course of action, but they do not see us as bound by reason. From their perspective, reason may tell me not to embezzle that $40 million from my company's coffers but I still do it. From your perspective I would do it because I have another drive that overshadows reason, call it greed. From their perspective I have some perversity of the will that allows me to see another course and choose, call it greed.
So libertarian free willers can view reason as part of the will, in which case they would say that reason is not deterministic. Or they can see the will as independent of reason, in which case they can follow the dictates of reason or not. Reason is not useless, again, in that situation because it is simply the means by which we arrive at one possible outcome. It does not dictate the outcome. The will does that job. And the will is perceived as acausal.
Now, personally, I think this is silly. I can destroy your will with a properly placed incision in the anterior cingulate gyri (it needs to be bilateral). I think we have excellent empirical evidence that the will results from neural action (yes, that sentence relies on dualistic thinking because that's just our language). I cannot, on logical grounds, deny the possibility of free will. If it were that simple there would be no debate. The debate rages because we have ideas about freedom of the will and empirical evidence and a conceptual framework that contradicts it.
I see three possibilities. (1) The universe is dualistic/pluralistic and free will is possible for all thinking creatures (this includes all those forms of "neutral monism" that try to cheat free will out of their system); but this conception depends critically on linking acausal "stuff" with causal "stuff", and I don't see how to do that. (2) The universe is a monism and everything is deterministic with no possibility of free will -- the usual way of thinking about materialism. (3) The universe is a monism and the ground of existence provides the one possible free will -- this is usually expressed as a form of idealism, but I suppose could also be viewed as a form of pantheism if one thought that everything is divine. The only one of those that I think is very, very unlikely is the first. I see no way of determining which of the latter two are correct. In one way of looking at it number two is just a restricted view -- we look only within the universe and do not consider the ground of existence in the equation. But I don't see how we could really understand much about the ground of existence.
The other possibility, I guess, is Kane's view -- that we may think of free will in the wrong way. He conjoins the deterministic parts of "us", which includes reason, to non-deterministic happenings in the quantum world. In his way of thinking about it, if a non-deterministic event is used by deterministic forces (say, our reason, for example), then we cannot properly speak of the outcome as determined. That outcome would not be purely random and would not be purely determined. Would it, then, be free? I don't think so, but he does.
ETA:
Whatever this concept of LFW is, it is seemingly a very naive attempt to rectify the understanding that humans have predispositions with the Christian doctrine that we can choose to obey or disobey God.
With that I strongly agree, though there are exceptions. Most ways of looking at Christianity dictate a dualistic perspective that allows free will. There are few Christians who see problems with this perspective, though, like the philosophers who are also believers -- like Robert Kane among others -- try to work out a system that allows free will within a deterministic framework. They are driven to it by the problem of evil.
There are others, as well, who are not Christians who simply want to justify what they feel must be true because they seem to experience it all the time. Let's face it. We feel free. Probably because we don't think back to first principles in our daily life - how tedious would that be? When we get down to it, though, it seems pretty clear to me that nothing happens except on some sort of framework. I don't see how libertarian free will can make sense, but I am not willing to state categorically that there is no possibility of free will in the universe because I have no clue how the universe is constructed.
ETA again:
The other thing to keep in mind is that this construct we use -- causality -- may simply be a construct. We certainly bring it to the table as a way of making sense of the world whether or not it reflects reality. It is how our brains work. But if we take quantum mechanics seriously and take uncertainty seriously, then the universe is built on a much weirder foundation than we are seemingly willing to admit in most discussions. We say that at the macro level there is determinism and only at the very micro level is there indeterminancy. But this macro level determinism may simply be the way that we look at things, the only way that we can see them because of the way that we are made. None of this speaks to the problem of free will. I add it only as clarification to anything that I said above.
