Will_Sawin comments on Notion of Preference in Ambient Control - Less Wrong
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An agent that reasoned by proving things in ZFC could exist.
Stupid argument: "This program, computed with this data, produces this result" is a statement in ZFC and is provable or disprovable as appropriate.
Obviously, a real ZFC-based AI would be more efficient than that.
ZFC is nice because Newton's laws, for example, can be formulated in ZFC but aren't computable. A computable agent could reason about those laws using ZFC, for example deriving the conservation of energy, which would allow him to compute certain things.