mbrubeck comments on The Useful Idea of Truth - Less Wrong
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Koan answers here for:
I think this one gets more complicated when you include beliefs about things like theorems of logic, e.g., "Any consistent formal system powerful enough to describe Peano arithmetic is incomplete." It seems to me that this belief is meaningful, yet independent of any sensory experience or physical law. That is, it's not really a belief about "the universe" of atoms or quantum fields or whatnot. Perhaps it would be better to talk about these "beliefs" as a separate category.
They are truisms - in principle they are statements that are entirely redundant as one could in principle work out the truth of them without being told anything. However, principle and practice are rather different here - just because we could in principle reinvent mathematics from scratch doesn't mean that in practice we could. Consequently these beliefs are presented to us as external information rather than as the inevitable truisms they actually are.