Yeah, you almost lost me there but I got back on track. This isn't any kind of a worry for me. If a religionist wants to introduce "an extra cause", it would be pretty evident what they were up to. Its just like this "intelligent design" crap. Obviously an intelligent designer would have to be powerful enough to create the whole universe, who do they think they're kidding? An extra cause, as you put it, either means something that is just some part of natural reality that we haven't discovered yet, almost certainly because its effect is so small that it is basically insignificant and irrelevant, or it needs to have some truly magical capablities which would need some truly magical instigator with vast powers and... OMG, you just found God! Pfff
I'm not sure how all the terms are being defined but i'll give it a go:
I am of course not a dualist! So, within my world view, everything that makes a human being what ,or more to the point, who they are is defined bodilly in naturalistic terms. I assume that we're considering free will to be a property of a sentient being,regardless of whether it's organic (such as a human being) or "synthetic" (such as in a massivly complex computer).
A computer, for instance, is a machine which deals in logic and data. However, a computer must have input in order "make decisions"-keep in mind that I'm using "make decision" colloquially. The computer cannot have free will under conventional concepts of it.
If I view a human being as being analagous to a computer, I can view the brain as being a pragmatically congruent machine. The input we experience comes from the five senses and is processed by whatever "software" we have(whether it be innate or learned or a little of both).
It may be that we are just incredibly complex machines which react to stimulae from the senses which might imply that we don't have free will.
in a function f:
In this function, we have input (the x) and output (f(x)).
the output of the function can only be of one value due to the input.
Perhaps we have an analagous function, of much more complexity with much more in the way of independent variables, which provides the output.
Maybe it'd look something like:
Eyes(cat,bowl empty)=feed cat
or something of the sort.
I guess it's just stuff for me to think about.