It’s bad form to say this up front, but I don’t think you actually have terribly deep understanding of the phenomena you glibly reference. (You could, of course, prove me wrong; it’s just that an inductive inference from the history of the Internet suggests that most people making similar references don’t really know what they’re talking about). All the same, I’m going to discuss them as if you have more than a passing acquaintance.
[QUOTE=Iknewit]
The Halting Problem can not be solved by any physically possible mind. Look it up. It is an impossibilty. It has been confirmed as undecideable. It can not be explained by the human brain. It is impossible. It is confirmed as such.
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The Halting Problem, for those who don’t know, is the general question of determining which computer programs halt and which don’t. It’s fairly easy to show that no computer program can solve this. (Indeed, this generalizes; for reasonable classes of processes P, it’s easy to show that no P-process can determine which P-processes halt). But there’s nothing preventing physical processes from solving the general Halting Problem for computer programs. It is an open question whether any physical processes, or for that matter the human brain, can solve the general Halting Problem for computer programs, though most believe they cannot. But it is pretty much a mathematical certainty that there is no describable physical machine which takes in descriptions of other physical machines, goes into motion for a bit, and then either flashes a “Yes, that machine eventually comes to a halt” light or a “No, that machine never halts” light, immediately afterwards “halting” itself.
Well, subject to certain conditions, this is fair enough, but more general than you imply. I would reword it as the fact that no system at all, whether mind, machine, or mathematical construct, “formalizable” or not, can be both sound and complete (i.e., always give correct answers) with respect to a language with the ability to speak about the system itself, in an appropriate sense.
But what’s essentially going on with both the Halting Problem and Goedel’s Incompleteness Theorem is that you go to some system S and mention a statement something like “S doesn’t think this statement is true” (worded in such a way that one doesn’t need explicit self-reference to pull off the same effect). Clearly, whatever S thinks about such a statement, it’s fucked (no matter what kind of thing S is). It’s unclear what genuine relevance any of this has to the current discussion, though. But perhaps you can make the point more strongly.