For those of you interested in this sort of thing, J. R. Lucas wrote "Minds, Machines and Gödel" and The Freedom of the Will several decades ago, in which he argued that Gödel's Incompleteness Theorems would apply to any physical deterministic system. Any such system should have a Gödel sentence, which is basically the proposition, "This proposition is not provable within this system", which is true but not provable (if it were provable, then it would be false; and if it were false, it would be provable). Mechanistic systems cannot recognize their Gödel sentence as true, because they can only "comprehend" truth as a matter of provability. This is not the case for human beings: we can see that Gödel-type sentences would be true, even though they are inherently unprovable (within their respective systems). Therefore, human beings cannot be explained in purely physical, deterministic terms. Nor can any mere physical system, i.e. computers, be able to duplicate the functions of the human mind -- since they would not be able to recognize their Gödel sentences as true.
At his website, Lucas has most of his contributions to this debate, and the online journal Etica e Politica published several of the more important essays by both Lucas and his detractors. Interesting stuff.
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