Sure, but that’s an uninteresting tautology. If we define A as a set of conditions sufficient for B to happen then lo and behold! A implies B.
Come on, mathematics is sometimes interesting, right?
The VNM theorem posits that a utility function exists. It doesn’t say anything about how to find it or how to evaluate it, never mind in real time.
It’s like asking why humans don’t do the Solomonoff induction all the time—“there must be a reason, what is it?”
Yeah okay, I agree with this. In other words the VNM theorem says that our AGI has to have a utility function, but it doesn’t say that we have to be thinking about utility functions when we build it or care about utility functions at all, just that we will have “by accident” created one.
I still think that using utility functions actually is a good idea though, but I agree that that isn’t implied by the VNM theorem.
In other words the VNM theorem says that our AGI has to have a utility function
Still nope. The VNM theorem says that if our AGI sticks to VNM axioms then a utility function describing its preferences exists. Exists somewhere in the rather vast space of mathematical functions. The theorem doesn’t say that the AGI “has” it—neither that it knows it, nor that it can calculate it.
Come on, mathematics is sometimes interesting, right?
Yeah okay, I agree with this. In other words the VNM theorem says that our AGI has to have a utility function, but it doesn’t say that we have to be thinking about utility functions when we build it or care about utility functions at all, just that we will have “by accident” created one.
I still think that using utility functions actually is a good idea though, but I agree that that isn’t implied by the VNM theorem.
Still nope. The VNM theorem says that if our AGI sticks to VNM axioms then a utility function describing its preferences exists. Exists somewhere in the rather vast space of mathematical functions. The theorem doesn’t say that the AGI “has” it—neither that it knows it, nor that it can calculate it.
That’s what I meant.