Lexicon of Arguments

 

VI 124
Comprehension/paradoxes/Quine: that each element relation (each term) results in a set is not possible because of Burali-Forti, etc. - Solution: these element relations (conditions) may determine sets, or perhaps the last (outermost) classes - outer condition: cannot be an element in turn - are introduced layer after layer - for classical mathematics "true0" already suffices - everything is in one language - there is a hierarchy of truth predicates.
>Truth Predicate/Quine.
VII (g) 136
Paradoxes/Quine: no longer occur when the levels of language are distinguished, i.e. if one keeps out the expressions "true-in-L", "denotes-in-L", etc. of the language L itself.
IX 124
Burali-Forti/paradox/Quine: "the class of ordinal numbers does not exist": "NO ε ϑ": is the tamed version of Burali-Forti: that there must be a larger ordinal number and simultaneously it cannot exist. - Reductio ad absurdum of the comparability of the ordinal numbers - solution/today: we will not assume that every condition about the existence of an element relation determines a class.
X 70
Grelling paradox/Quine: "x does not fulfil itself" must not occur in the object language.
>Object Language/Quine.