In sound common sense, A()≠2 does not imply (A()=2 ⇒ U()=3^^^3).
Okay, then I don’t know what kind of reasoning system this “common sense” is or how to build an inference system that implements it to put as S in A(). As a result, discussing it becomes unfruitful unless you give more details about what it is and/or motivation for considering it an interesting/relevant construction.
(What I wanted to point out in the grandparent is that the wrong conclusion can be completely explained by reasoning-from-outside being separate from S, without reasoning-from-outside losing any standard properties.)
Okay, then I don’t know what kind of reasoning system this “common sense” is or how to build an inference system that implements it to put as S in A(). As a result, discussing it becomes unfruitful unless you give more details about what it is and/or motivation for considering it an interesting/relevant construction.
(What I wanted to point out in the grandparent is that the wrong conclusion can be completely explained by reasoning-from-outside being separate from S, without reasoning-from-outside losing any standard properties.)