Â Â Â Â Computationalism
is the view that human minds are essentially computing machines. Stronger forms of the position claim that anything computable with the mind is possible with some equally powerful theoretical computer (typically idealized in the form of a Turing machine
). In other words, for each human mind, there is a Turing machine isomorphic to that mind. The Church-Turing thesis
is one such position, claiming that everything that is calculable is calculable with a Turing machine.
Â Â Â Â Hypercomputationalism is the contrary position that humans are capable of computation beyond the capabilities of a Turing machine. For instance, a human mind may solve a problem in a finite period of time which would take a Turing machine an infinite amount of time.
Â Â Â Â This is a PDF of an article arguing for hypercomputationalism.
Â Â Â Â I'm particularly interested in discussing the merits and flaws of the argument articulated in this article, though I also welcome any general thoughts on the issue of computationalism vs. hypercomputationalism. The article isn't too long, but it's fairly dense and highly technical.
Â Â Â Â With regard to the article's argument, I think the fatal flaw is in its third premise. I think it's unlikely that humans will always be able to find âˆ‘(n + 1) when they solve âˆ‘(n). At the very least, I have little reason to believe that is the case except for the optimistic claims of the researchers writing the article. Furthermore, I'm unconvinced that even if humans can
employ a bootstrapping technique without limit that a sufficiently complex Turing machine couldn't be constructed to mimic such techniques. For those reasons, I find the argument unconvincing.
Â Â Â Â I am inclined intuitively to accept the Church-Turing thesis. And since I have no real reason to suspect any physical or logical law-breaking properties of the human brain, I intuit that the human mind is probably just a very, very complex Turing machine (or isomorphic to one). I suppose Douglas Hoffstadter's GÃ¶del, Escher, Bach
and I Am a Strange Loop
have had a significant influence on my formation of that opinion.