Ian,
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I admit I'm very tired but I really have no idea what you mean by describing free will as complex. I mean the concept of complexity can only legitimately be applied to physical things can't it?
Moreover with my intepretation of free will it is meaningless to ask how it works because it is a basic existent.
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Not, complex is an abstract concept; you can aply it to mathematics, logic, art, whatever.
I mean, you can perceive the will has different parts. In fact, in your examples you are providing good examples about how many factors add to end in a decission.
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The question is not the fact that my behaviour is determined by my desires or what I intrinsically am, but why I am what I am to have those desires in the first place. Er . . isn't it?
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You are pushing my english level here...

I don't see the conection of free will with this question, sorry.
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Maybe a thought just suddenly acausally popped into my head thinking "Hey, I really fancy kippers, but I'm going to have porridge to prove I have (libertarian) free will" LOL. Of course maybe that thought needn't have arisen wholly acausally as perhaps I might be the sort of person prone to such sudden maverick thoughts. But this doesn't mean to say that my behaviour could be encapsulated by any algorithm.
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The problem of your example is:
It doesn't mean to say that your behaviour could be encapsulated by any algorithm.
But...
We know this kind of behaviour could be encapsulated in an algorithm because we got there from computers studying.
In other words, unexpected thoughs and decissions are not proof of an external free will. In a complex algorithm this kind of unexpected behaviour is pretty normal.
You have to think that a human brain is a huge system full of balancing mechanisms, chained. Impulses happens and you are not going to be capable of mentally rebuilding these process.
Why? Because a system can not have full knowledge of itself, this is and old & established principle...
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Even if it could be, the algorithm would just describe my behaviour, it would just describe what I freely choose to do. This is different from if physicalism/materialism is true because then the algorithm wouldn't just describe my behaviour, it would lead it
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I don't know too much about materialism, or your vision of materialism, but in modern neurology the mind is both the dinamic & static configuration of the brain.
BTW, an algorithm is a description of a process, not a description of the results of this process. An algorithm which draws a circle doesn't resemble the description of a circle (except in some implementations) and partial understanding of it can lead you easily to think in something different of a circle as a result.
In other words, an algo. which generates something similar to human will would be intuitively unrelated to human decissions. You would read it and you would't believe that piece of code could produce such results...
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So it seems to me to be a bit of a phony free will. Within the free will I have outlined, what is my free will circumscribed by apart from the type of person I am? And if the type of person I am is wholly determined, what is it wholly determined by? (given my belief that what I really am is non-physical).
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If we want to understand "human will" we will have to create an understable description of it. This is an universal problem which idealism, dualism, and some other models don't address despite its appearances. I would say these models are build to avoid addressing it, especially idealism.
About the type of person you are, it's determined by thousands of things (physical) which you already know...I don't understand which problem do you see there.(?)
PD: Edited to correct some silly error