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From that article: > So, the objection that humans cannot solve every problem only shows that humans might not be complete halting oracles, but cannot show tha
by baddox 8y ago
From that article:
> So, the objection that humans cannot solve every problem only shows that humans might not be complete halting oracles, but cannot show that humans are not partial halting oracles.
I don't get it. We can already easily making Turing machines that answer the halting problem for certain infinite sets of Turing machines, so there's nothing unique about the human brain in this regard.
- yters 8y agoThe previous sentence to the one you quote explains: > We can even remove an infinite number of problems from the set and still have an infinite and undecidable set. It is an undecidable set, so cannot be described by a TM.
- baddox 8y agoOh okay, I guess that entire paragraph is just a complicated way of rephrasing their claim, which is that there is at least one TM for which no TM can possibly answer the halting problem, but for which humans can. So then, the claim is that it's at least conceivable that humans can do this, because you can remove a finite or even infinite number of elements from an infinite set and still be left with an infinite set. I still don't understand how this is a remotely useful insight or in any way an indication that humans may have super-Turing abilities.
- yters 8y agoThat's correct. It does not prove that humans have this capability. It just shows that a common counter argument fails, and then the article goes on to explain how it would make an empirical difference if humans are partial halting oracles.