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andrewcooke comments on The Strangest Thing An AI Could Tell You - Less Wrong
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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)