The class says you advance as a binder.
There is no disclaimer stating you need binder levels to advance.
I'm saying your entire argument is based on a comparison to things that don't really compare.
Actually, no, it wasn't my argument at all, nevermind my entire argument. It was an example of how the interaction works. You take a level in a PrC that advances casting, but you have no previous ability to cast spells. As such, you lose the casting ability of the class. Similarly, if you take a level of Anima Mage without any levels of Binder, you lose the advancement of the Binder class. The reason why is because you can't add 1 to null to get 1.
Lol so binding has to follow the patterns of spell casting because you say so? Assumption. Adding 1 to something you currently have none of somehow equals 0? Mathematical failure. Null ability to bind? Directly opposite rules text, which indicates anima mage levels stack as binder levels for binding vestiges. You're making up rules with absolutely no basis in the rules text.
You obviously have no clue what the mathematical concept of null is, as incredibly simple as it is, so spare me your criticism of my knowledge of mathematics.