And what if the propositions we want to reason about are self-referencing or say something about the system itself in a Godelian way? You need probabilistic rea

And what if the propositions we want to reason about are self-referencing or say something about the system itself in a Godelian way? You need probabilistic reasoning for that to actually work. Also, "simply prove/disprove the propositions" requires infinite computational resources (we don't know how long the proofs will be or if there are any). Logical induction does not.