IIUC, fixed point equations like that typically have infinitely many solution. So, you defined not one goodnew predicate, but an infinite family of them. Therefore, your agent will trust a copy of itself, but usually won’t trust variants of itself with other choices of fixed point. In this sense, this proposal is similar to proposals based on quining (as quining has many fixed points as well).
My belief is that this one was fine, because self-reference occurs only under quotation, so it can be constructed by modal fixpoint / quining. But that is why the base definition of “good” is built non-recursively.
Is that what you were talking about?
(Edit: I’ve updated the post to be clearer on this technical detail.)
IIUC, fixed point equations like that typically have infinitely many solution. So, you defined not one goodnew predicate, but an infinite family of them. Therefore, your agent will trust a copy of itself, but usually won’t trust variants of itself with other choices of fixed point. In this sense, this proposal is similar to proposals based on quining (as quining has many fixed points as well).
My belief is that this one was fine, because self-reference occurs only under quotation, so it can be constructed by modal fixpoint / quining. But that is why the base definition of “good” is built non-recursively.
Is that what you were talking about?
(Edit: I’ve updated the post to be clearer on this technical detail.)
Sorry, I was wrong. By Lob’s theorem, all versions of goodnew are provably equivalent, so they will trust each other.