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Jayson_Virissimo comments on The Strangest Thing An AI Could Tell You - Less Wrong
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"All mathematical reasoning involving "infinities" involves self-evident contradictions, but human mathematicians have a blind spot with respect to them." -Eliezer Yudkowsky
I'm going to lose sleep over this one...Is there anything to this?
There needn't have been in order for this to be a reasonable example, but perhaps Eliezer is not-so-subtly hinting that he actually expects an AI to say this.
But it's really no different than "all reasoning by mathematicians about X is wrong" where X is any mathematical concept you please.
yes. at least, i assume that it's related to intuitionist or constructivist logic (which you can google - for example http://en.wikipedia.org/wiki/Intuitionistic_logic)
the flip side is that apparently you can do an awful lot of maths without the law of the excluded middle (which is what is necessary to reason with infinities).
actually, the wikipedia article for intuitionism is more helpful - http://en.wikipedia.org/wiki/Intuitionism (it has a section directly addressing infinities)
No - check the infinities in CGT - e.g. "Mathematical Go: Chilling Gets the Last Point".