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komponisto comments on Rationality Quotes: October 2009 - Less Wrong
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But surely "we ate X" can mean "X = {Y: We ate Y}", as in "we ate a set of fried chicken legs" -- and this would allow one to analyze "we ate nothing" to mean "we ate X" for X = emptyset.
Let "nothing" be the empty set, and say that "we ate X" means that X is the set of all things that we ate? How would that handle the sentence "No robot took off its hat"? My semantics say that that's equivalent to "for no robot X, (X took off X's hat)"; yours would say something like "(the set of no robots) took off (some value that isn't a set of hats)".