Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
[german]


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Theses II

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VII (e) 97
Universe/v. Neumann/Set Theory/Quine: divides the universe (of discourse) into things that can be elements and those that cannot be.
What exists for Zermelo are von Neumann's elements.
For the existence of classes, elements and others there are further postulates, which satisfy every condition φ, whose bound variables are limited to elements as values.
- - -
IX 221
Universe/Quine: we get our expanded universe by adding classes to the extreme universe of new foundations. The resulting system is called an enlargement of the system of new foundations. - We cannot use the old comprehension schema of new foundations. Maintained because for example "(x: Fx} ε ϑ "(Fx stratified)) - "{x: x = x}" is now wrong. - ((s) Because not stratified.).

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