IX 21
Ontology/Class/Sets/Relations/Quine: Classes and relations as values of quantifiable variables must be regarded as real objects.
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Ontology/Quine.
IX 219
Set/Quine: the property to be a set only means that ∃z(x ε z) ((s), there is something that x is a part of) - then ∃y x(x ε y (Ez(x ε z) u Fx)) - since Ez(x ε z) x ε Uϑ. - Even narrower: a ∩ Uϑ ε ϑ - Uϑ is then the class of all sets. The point is that ϑ ε ϑ (if there are extreme classes), so Uϑ is still the most comprehensive class that exists. The condition of being a set: ∃y(z ε y).
III 318
Sets/class/von Neumann/Quine: (...) Classes are not sets.
IX 228
Set/Neumann/Quine: a class is a set if it is not larger than a certain set (sets can be an element, classes cannot).
IV 418
Ontology/Quine: Standards of ontological admissibility: two principles.
1. No entity without identity.
2. Ontological thriftiness.
According to Quine, there are physical objects and quantities.
V 149
Class/Set/Quantification/Quine: Classically, a quantification via classes is an object of quantification (referential quantification).
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Quantification.
Class: abstract terms for classes are singular terms.
Include/Epsilon/Quine: "ε" is a two-digit predicate or relative general term. "Is an element of." (Originates from the predication scope "is one").
Now we get the theorem of comprehension:
V 150
Comprehension/Quine:
(1) (EZ)(x)(x ε Z . ≡ Fx)
The compression set assigns a class to each element relationship.
III 293
Classes/Sets/Condition/spelling/Quine: we always have the need to assign of the class of all and to only assign those objects that fulfill a certain condition. We write this as x^.
III 294
Example x^~(x e a) the class of all non-elements of a.
These are abstracts.
