Of course, some elements of S might be in neither of them, that is, the agent ignores what the program outputs on them.
So on those statements, the program may either update or not, but at the time of choosing the program, the agent can’t predict those statements, so it can’t use the programs’ updatelessness or updatefulness in deciding which one to choose. Did I get that right?
The agent might commit to “only updating on those things accepted by program p”, even when it still doesn’t have the complete infinite list of “exactly in which things does p update” (in fact, this is always the case, since we can’t hold an infinite list in our head). It will, at the time of committing, know that p updates on certain things, doesn’t update on others… and it is uncertain about exactly what it does in all other situations. But that’s okay, that’s what we do all the time: decide on an endorsed deliberation mechanism based on its structural properties, without yet being completely sure of what it does (otherwise, we wouldn’t need the deliberation). But it does advise against committing while being too ignorant.
So on those statements, the program may either update or not, but at the time of choosing the program, the agent can’t predict those statements, so it can’t use the programs’ updatelessness or updatefulness in deciding which one to choose. Did I get that right?
First off, that S was supposed to be ¯S, sorry.
The agent might commit to “only updating on those things accepted by program p”, even when it still doesn’t have the complete infinite list of “exactly in which things does p update” (in fact, this is always the case, since we can’t hold an infinite list in our head). It will, at the time of committing, know that p updates on certain things, doesn’t update on others… and it is uncertain about exactly what it does in all other situations. But that’s okay, that’s what we do all the time: decide on an endorsed deliberation mechanism based on its structural properties, without yet being completely sure of what it does (otherwise, we wouldn’t need the deliberation). But it does advise against committing while being too ignorant.