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Polymeron comments on How to Convince Me That 2 + 2 = 3 - Less Wrong
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The core issue is whether statements in number theory, and more generally, mathematical statements are independent of physical reality or entailed by our physical laws. (This question isn't as obvious as it might seem, I remember reading a paper claiming to construct a consistent set of physical laws where 2 + 2 has no definite answer). At any rate, if the former is true, 2+2=4 is outside the province of empirical science, and applying empirical reasoning to evaluate its 'truth' is wrong.
I don't think this is at all the core issue.
Eliezer's original post stated that beliefs need to come from mind-reality entangling processes.
If math is a part of "reality", then Eliezer's point stands and empirical reasoning makes perfect sense.
If math is not a part of "reality", then we would expect it to influence nothing at all, including our beliefs. Or even suppose that knowledge came from somewhere and could influence belief but still did not otherwise correlate with reality: Then it would be irrelevant. This, of course, is not the case - as anyone who's ever used any mass-manufactured device as well as bridges and roads, should realize. Math DOES have utility in real life. And I daresay that if it suddenly stopped helping us reliably predict the load-bearing limit of bridges, we'd treat is as suspect and false.
The ACTUAL core issue remains that a belief that cannot be reversed is useless.