Lexicon of Arguments

 

VII (e) 89
Extensionality/Quine: ((x ⊆ y ) u ((y ⊆ x) > (x = y)) - i.e. a class is determined by its elements. (s) If x and y are subsets of each other, then they are identical).
IX 22
Extensionality Axiom/EA (= extensionality law)/Quine: classes that are consistent in their elements are equal - ∀x(x ε y u x ε z) > y = z - Abbreviation for ∀x(x ε y u x ε z) u (y ε x z ε x)] - Problem:> Individuals.
IX 25
Extensionality Axiom/Quine: (according to the new identity definition): (y = z u y ε w) > z ε w.
IX 178
Extensionality/Quine: is that what distinguishes attributes from classes. Two attributes can be of different order and, therefore, certainly different, and yet be applied to the things, e.g. the attribute "j(j^x jy) where "j" has the order 1, an attribute solely of y - E.g. attribute ∀c(c^x cy), where "c" has the order 2, again an attribute solely of y, but one of the attributes has the order 2, the other has the order 3.
>Order/Quine.