You might be referring to actions taken by Tim-in-China. Tim-in-US chose to create Tim-in-China, so all actions taken by Tim-in-China are a consequence of choices made by Tim-in-US.

The thing is there's two ways of looking at this problem. Either creating Tim-in-China is just one option avaliable in an action-determined, everything he does is just a consequence which Tim-in-US predicted. In this case it isn't self-modification. Alternatively, he is an independent agent, in which case creating him is self-modification but the problem isn't action-determined.

I think I'm beginning to see that you're right, self-modification isn't a strictly defined concept. On the other hand, very few things are strictly defined, 'human' and 'AI' are certainly not but we wouldn't be wise to ignore them when solving Friendliness.

It is possible to set up mathematical models in which self-modification is well defined (in the same way that atoms aren't fundamental physical entities, but we can set up models in which they are and those models are useful). The basic idea is an agent is given a problem of some type, but prior to the problem we offer it the chance to have the problem faced by another agent instead of itself, if there is any other agent for which it would say yes then it self modifies on this problem.

You'll also have to choose something that leads to it not being action-determined, and something that's consistent with a definition of action-determined that doesn't lead to "action-determined" referring a useless or empty set of possibilities.

The set of real world strictly action-determined problems is empty, the concept is similar to that of an ideal straight line, it is a useful approximation not a real category.

The strict definition of action-determined problem is something like this:

• agent comes into existence, out of nowhere, in a way the is completely uncaused within the universe and could not have been predicted by its contents
• agent is presented with list of options
• agent chooses one option
• agent disappears

I think the last part may not be strictly necessary, but I'm unsure. The first is necessary, it is what separates action-determined problems from broader categories like decision-determined problems and identity-determined problems.