User blog comment:PsiCubed2/How to make Deedlit's Mahlo-level notation more intuitive/@comment-27513631-20180807204248/@comment-30754445-20180807212212

Because:

(1) Deedlit's system is already using ψ. Since we are required, by the very nature of Mahlos, to use to kinds of functions, it is simpler to have them both of the same type.

(2) ψ is much more widely known (an IMO easier to learn) then θ.

(3) The most important feature here is not whether the collapse is ψ-type or θ-type. The main point of my suggestion is using the familiar letter I, instead of the mysterious χ. Notating Deedlit's I(3,7,6) as I(M2x3+Mx7+6) (or I(Mx3+7,6) if you insist) hardly requires any explanation. Write it as χ(Mx3+7,6) and most people won't understand what you're takling about.

Of-course, we could just tell people that this is how χ works, but why ask for this kind of trouble? The only reason Deedlit used χ is that Rathjen used χ, and Rathjen wasn't particularly interested in making his notation accessible to amateur mathematicians. So if using I instead if χ allows to save a few lines of explanations, why not?

BTW, this blog post, really, was in response to Rpkar's statement that Deedlit's notation is less intuitive that Username's OCF because of the χ function that he found difficult to understand. I was trying to show, that by notating the exact same function with a more familiar notation, its mystery can be dispelled.

(You have no idea how long it took me to realize that this is how χ works, even though Deedlit wrote it explicitly at the end of his post. Had he used I instead if χ, I would have understood it immediately)