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.
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.