Lexicon of Arguments

 

IX 22
Individuals/Quine: Problem: if y and z are elementless, we obtain y = z due to the extensionality law as it is formulated here - i.e. there is only one single elementless thing - if it is the empty class, then individuals are not elementless - if individuals are elementless, and if they exist at all, then there is only one individual and not an empty class - solution: we do not have to regard individuals as elementless. They are identical with their class of one - and also with the class of one of this class, etc.
>Classes/Quine.
IX 199
Individuals/QuineVsFraenkel: individuals are not elementless - solution: individuals are identical with their classes of one - therefore "Tnx" is no longer needed to protect y from the flood of individuals. And now that the zero classes of all types are identified with each other, "Tnx" is no longer required to fend off the tide of zero classes - power set axiom/cumulative theoretical terms: we can now accept it without protection: Ey∀x(x ε y ↔ x ⊆ z). With this we are even more liberal than Zermelo.