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chaosmosis comments on Causal Reference - Less Wrong
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Meditation:
If we can only meaningfully talk about parts of the universe that can be pinned down inside the causal graph, where do we find the fact that 2 + 2 = 4? Or did I just make a meaningless noise, there? Or if you claim that "2 + 2 = 4" isn't meaningful or true, then what alternate property does the sentence "2 + 2 = 4" have which makes it so much more useful than the sentence "2 + 2 = 3"?
2+2=4 isn't a cause. It's a tautological description. Describing things is useful, though.
I agree...PA was invented based on our observations; our observations aren't just magically predicted by some arbitrary set of rules. PA has only existed since 1889; reality had existed long before that.