Funny that you don't even reference the passage on 185, which is the root of all of this.
If you start trying to prove basic geometry theorems (about parallel lines, sum of angles in a triangle, etc.) it will also become circular. You need a starting point, a basic axiom that you assume but can not prove.
The "PC's make their own decisions" theorem is built upon the text of page 185*. If you ignore it, you're going to have a hard time reconstructing the proof.
But I think you know that.
*Which, admittedly, reinforces my own deeply held beliefs.