I'll bet you £100 that whatever conclusions the SIAI eventually draws about self modification will apply just as well to all kinds, I really cannot see how a silly distinction like the one you are making would find its way into a mathematical proof.

We're certainly agreed on that. I'm willing to go further -- I believe any mathematical conclusions that apply to self-modification (your definition) will apply to all possible actions. I don't think your definition carves out a part of the world that has any usefully special properties.

Worse, [self-modification interpreted as requiring a modification to the entity taking action] is not even well-defined, if an AI copies itself onto another computer, and alters the copy, is that self-modification? If it modifies itself, but keeps a copy of its old code around, is that self-modification? Where do you draw the line between the two?

Agreed.

I don't think your definition is well-defined either. Where's the important line between self-modification and making a toaster?

We appear to have no useful definition for the word. Time to stop using it, IMO.