My impression from your above comments is that we are mostly in agreement except for how much we respectively like mathematical logic. This probably shouldn’t be surprising given that you are a complexity theorest and I’m a statistician, and perhaps I should learn some more mathematical logic so I can appreciate it better (which I’m currently working on doing).
I of course don’t object to logic in the context of AI, it mainly seems to me that the emphasis on mathematical logic in this particular context is unhelpful, as I don’t see the issues being raised as being fundamental to what is going on with self-modification. I basically expect whatever computationally bounded version of probability we eventually come up with to behave locally rather than globally, which I believe circumvents most of the self-reference issues that pop up (sorry if that is somewhat vague intuition).
My impression from your above comments is that we are mostly in agreement except for how much we respectively like mathematical logic. This probably shouldn’t be surprising given that you are a complexity theorest and I’m a statistician, and perhaps I should learn some more mathematical logic so I can appreciate it better (which I’m currently working on doing).
I of course don’t object to logic in the context of AI, it mainly seems to me that the emphasis on mathematical logic in this particular context is unhelpful, as I don’t see the issues being raised as being fundamental to what is going on with self-modification. I basically expect whatever computationally bounded version of probability we eventually come up with to behave locally rather than globally, which I believe circumvents most of the self-reference issues that pop up (sorry if that is somewhat vague intuition).