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cousin_it comments on The two meanings of mathematical terms - Less Wrong
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Please see this previous comment of mine.
The point here is that it "1+1=2" should not be taken as a statement about physical reality, unless and until we have agreed (explicitly!) on a specific model of the world -- that is, a specific physical interpretation of those mathematical terms. If that model later turns out not to correspond to reality, that's what we say; we don't say that the mathematics was incorrect.
Thus, examples of things not to say:
"Relativity disproves Euclidean geometry."
"Quantum mechanics disproves classical logic"
"I am an infinite set atheist - have you ever actually seen an infinite set?"
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.