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billswift comments on Reason as memetic immune disorder - Less Wrong
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That fellow Bringsjord seems to me an obvious kook, e.g. he claims to have proven that P=NP.
He claims to have an argument that P=NP. He's a philosopher, so "argument" != proof. Although approaching P=NP as a philosophical argument does strike me as kooky.
Better proof of kookhood is that he was at AGI mainly to present his work on hypercomputing, which he claimed was a computational system with more power than a Turing machine. One element of his argument was that proofs using hyperset logic (which he said is an entire field of logic nowadays; I wouldn't know) use a notation that can not even theoretically be represented by a Turing machine. These proofs were published in two-dimensional journal articles, in black-and-white print. I did not notice any fractal fonts in the proofs.
I came across a wikipedia article on hypercomputing a while back, http://en.wikipedia.org/wiki/Hypercomputation , the whole theory doesn't seem at all well supported to me.
It is a field with an imaginary object of study.
It would be nice though, if outsiders could show some respect by demonstrating, as is probably demonstrable but difficult, that its object of study is incoherent, not just imaginary.
I'm not really sure it makes sense to talk about mathematical objects as being imaginary but not incoherent.
Respectful outsiders?
Is that a reference to the inner sanctum of the Hypercomputation sect? ;-)
I'd be very surprised if this Universe was super-Turing, but you think it's actually incoherent? I can definitely conceive of a hypercomputational cellular automata, what is it about the idea of our Universe being hypercomputational that seems incoherent to you?
I think that it is very common for things that we casually think we can definitely conceive of to actually be incoherent. I also think that almost everyone else underestimates how common it is.
I think I'm correcting for that. Do you agree that the halting oracle function itself is well-defined? If so, what seems inconceivable about a cellular automaton whose rules depend on the output of that oracle? OK, you have to stretch the definition of a cellular automaton to allow it, perhaps by allowing cells to have unbounded state, but the result is a wholly defined and therefore surely in-principle-conceivable Universe which is super-Turing. No?
It's not incoherent. There could be such a thing as Hypercomputation.
However, nobody has found any evidence that it exists so far - and maybe they never will.
Hypercomputation enthusiasts claim that its existence doesn't matter too much - and that it's a valuable concept regardless of whether it exists or not. Maybe.
I don't disagree (i.e., I don't see any positive reason to doubt the coherence of hypercomputation – though Michael sounds like he has one), but remember not to confuse subjective conceivability and actual coherence.
And, now I see why I am skeptical of hypercomputation. It seems to all necessitate some form of computation over an infinite number of steps. This would require some severe bending of the rules or constraints of physics, wouldn't it?
timtyler's comment below mine seems to be appropriate:
Doesn't Newtonian gravity require computation over an infinite number of steps?