>>16538515
>Classes don't exist because they're formulas. Formulas are meta-mathematical objects
Correct. Classes are a metamathematical things. You cannot quantify over all classes in mathematical claims. However, once you pick an individual class you can make mathematical claims related to it by substituting with the formula.
>You can say x = x when x is a set. It is meaningless to use the equals sign when either side is a formula
Technically correct. However, you can define X=Y to be a shorthand for the claim that for every x in X, x in Y and vice versa. Thus you're enabled to talk between sets and particularly chosen classes, or two particularly chosen classes.
>That isn't how math works, and you know it.
It's actually very common in math to skip things that the reader is assumed to have already covered.
>Here are Gödel's crimes: treating formulas as if they really existed
Formulas can be treated as mathematical objects and studied using mathematical methods. What is wrong with this?
>treating formula schemas as sets
Like where?

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Why do midwits extrapolate his incompleteness theorem to everything in the world outside of arithmetics for which he proved the incompleteness?