So let’s talk about this word, “could”. Can you play Rationalist’s Taboo against it?
Testing myself before I read further. World states which “could” happen are the set of world states which are not ruled impossible by our limited knowledge. Is “impossible” still too load-bearing here? Fine, let’s get more concrete.
In a finite-size game of Conway’s Life, each board state has exactly one following board state, which itself has only one following board state, and so on. This sequence of board states is a board’s future. Each board state does not correspond to only a single previous board state, but rather a set of previous board states. If we only know the current board state, then we do not know the previous board state, but we know the set that contains the previous board state. We call this set the board states that could have been the previous board state. From the inverse of this, we know the set that does not contain the previous board state, which we call the boards which could not have been the previous board.
Going back up to our universe, what “could happen” is a set of things which our heuristics tell us contains one or more things which will happen. What “can’t happen” is a set of things which our heuristics tell us does not contain a thing that will happen.
A thing which “could have happened” is thus a thing which was in a set which our heuristics told us contained a thing that will (or did) happen.
If I say “No, that couldn’t happen”, I am saying that your heuristics are too permissive, i.e. your “could” set contains elements which my heuristics exclude.
I think that got the maybe-ness out, or at least replaced it with set logic. The other key point is the limited information preventing us from cutting the “could” set down to one unique element. I expect Eliezer to have something completely different.
Oh come on. Alright, but if your answer mentions future or past states, or references time at all, I’m dinging you points. Imaginary points, not karma points obviously.
Testing myself before I read further. World states which “could” happen are the set of world states which are not ruled impossible by our limited knowledge. Is “impossible” still too load-bearing here? Fine, let’s get more concrete.
In a finite-size game of Conway’s Life, each board state has exactly one following board state, which itself has only one following board state, and so on. This sequence of board states is a board’s future. Each board state does not correspond to only a single previous board state, but rather a set of previous board states. If we only know the current board state, then we do not know the previous board state, but we know the set that contains the previous board state. We call this set the board states that could have been the previous board state. From the inverse of this, we know the set that does not contain the previous board state, which we call the boards which could not have been the previous board.
Going back up to our universe, what “could happen” is a set of things which our heuristics tell us contains one or more things which will happen. What “can’t happen” is a set of things which our heuristics tell us does not contain a thing that will happen.
A thing which “could have happened” is thus a thing which was in a set which our heuristics told us contained a thing that will (or did) happen.
If I say “No, that couldn’t happen”, I am saying that your heuristics are too permissive, i.e. your “could” set contains elements which my heuristics exclude.
I think that got the maybe-ness out, or at least replaced it with set logic. The other key point is the limited information preventing us from cutting the “could” set down to one unique element. I expect Eliezer to have something completely different.
Oh come on. Alright, but if your answer mentions future or past states, or references time at all, I’m dinging you points. Imaginary points, not karma points obviously.