Ian,
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I certainly deny that the physical world is closed.
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And you are quite right about this; every scientist would sell his right arm to find an unified theory of physics...
But this not leds to free will being outside the our known physics.
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So I'd ask the same question as I did to Stimpy. If some of our actions are partially mentally caused would this be determined? Obviously I wouldn't deny that my actions are determined by myself, but if what I am myself is not physically determined, what other factors are determining me to be what I am?
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Of course, a system partially determined is not a deterministic system. Only the determined parts are.

But, why do you supose there are un-deterministic parts? Our observation of this system only showed some sub-atomic randomness which is probably meaningless...
Anyway, I was not asking you about if our will is determined or not; I was asking about why you think our free will is "libertarian" ...
A less fuzzy question:
Why do you think free will have some quality not avalaible under our known physics and brain models?
If we define the will as the capability of making a decision, let's list some factors we already know are present:
- Input recognition; we reckon the situation matching our vision, ear, etc... with previous memory, that can inform us about some options.
- Previous experience; we remenber previous decissions, they add to the balance.
- Purpose. We can have some general purpose which make us select the best option for it.
- Mood; our mood seems to influence in our decisions also.
- Unkown factors; most times we don't know why did we chose this option instead of that other. However, the complexity of the brain itself it's already a cause of an unpredictable (currently) behaviour.
I can find a place for all these factors in neural models; so, which factor does you make think human will can't fit it? Why do you feel human will is not determined by our brain?