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cousin_it comments on The two meanings of mathematical terms - Less Wrong
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Re the last quote: I didn't expect Eliezer to say something like that. Has he actually ever seen a finite set?
Perhaps he meant "seen" in the sense of "visualized." What happens when we try to introspect on our visualization of some mathematical terms?
Well I can't visualize an infinite set, but neither can I imagine a finite set, nor the number 5 for that matter. I can imagine five dots, or five apples, but not 5. In terms of my visualization, "5" seems to be an unfinished utterance. My mind wants to know, "5 what?" before it will visualize anything, or else it just puts up 5 black circles or whatever.