You are saying that a GAI being able to alter its own "code" on the actual code-level does not imply that it is able to alter in a deliberate and conscious fashion its "code" in the human sense you describe above?

I am saying pretty much exactly that. To clarify further, the words "deliberate", "conscious" and "wants" again belong to the level of emergent behavior: they can be used to describe the agent, not to explain it (what could not be explained by "the agent did X because it wanted to"?).

Sure, but we could imagine an AI deciding something like "I do not want to enjoy frozen yogurt", and then altering its code in such a way that it is no longer appropriate to describe it as enjoying frozen yogurt, yeah?

Let's instead make an attempt to explain. A complete control of an agent's own code, in the strict sense, is in contradiction of Gödel's incompleteness theorem. Furthermore, information-theoretic considerations significantly limit the degree to which an agent can control its own code (I'm wondering if anyone has ever done the math. I expect not. I intend to look further into this). In information-theoretic terminology, the agent will be limited to typical manipulations of its own code, which will be a strict (and presumably very small) subset of all possible manipulations.

This seems trivially false - if an AI is instantiated as a bunch of zeros and ones in some substrate, how could Godel or similar concerns stop it from altering any subset of those bits?

Can an agent be made more effective than humans in manipulating its own code? I have very little doubt that it can. Can it lead to agents qualitatively more intelligent than humans? Again, I believe so. But I don't see a reason to believe that the code-rewriting ability itself can be qualitatively different than a human's, only quantitatively so (although of course the engineering details can be much different; I'm referring to the algorithmic level here).

You see reasons to believe that any artificial intelligence is limited to altering its motivations and desires in a way that is qualitatively similar to humans? This seems like a pretty extreme claim - what are the salient features of human self-rewriting that you think must be preserved?

Generally GAIs are ascribed extreme powers around here

As you've probably figured out, I'm new here. I encountered this post while reading the sequences. Although I'm somewhat learned on the subject, I haven't yet reached the part (which I trust exists) where GAI is discussed here.

On my path there, I'm actively trying to avoid a certain degree of group thinking which I detect in some of the comments here. Please take no offense, but it's phrases like the above quote which worry me: is there really a consensus around here about such profound questions? Hopefully it's only the terminology which is agreed upon, in which case I will learn it in time. But please, let's make our terminology "pay rent".

I don't think it's a "consensus" so much as an assumed consensus for the sake of argument. Some do believe that any hypothetical AI's influence is practically unlimited, some agree to assume that because it's not ruled out and is a worst-case scenario or an interesting case (see wedrifid's comment on the grandparent (aside: not sure how unusual or nonobvious this is, but we often use familial relationships to describe the relative positions of comments, e.g. the comment I am responding to is the "parent" of this comment, the one you were responding to when you wrote it is the "grandparent". I think that's about as far as most users take the metaphor, though.)).