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cousin_it comments on Truth and the Liar Paradox - Less Wrong Discussion
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Can you explain in more detail why no single formal theory can express every part of math that you care about?
I just wrote a post on a related but simpler question, about math beliefs rather than math values. It might apply to your question as well.
I assume he's claiming to care about a great deal of math, including at each stage the equivalent of Morse-Kelley as a whole rather than just the statements it makes about sets alone.
But I don't know what post Wei Dai referred to, and I doubt I read it. Quick search finds this comment, which seems grossly misleading to me - we could easily program an AI to reason in an inconsistent system and print out absurdities like those we encounter from humans - but may have something to it.