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Number/Wittgenstein: not a concept, but a logical form.
Numbers/cardinal/Wittgenstein: that there are infinitely many cardinals, is a rule that one sets up.
Number/Frege/WittgensteinVsFrege: a number is a property of a property. - Problem: E.g. for blue-eyed men in the room. - Then the five would be a property of a property - to be a blue-eyed man in the room - e.g. to express that Hans and Paul are two, they would then have a property in common, which not exactly belongs to the other. - ((s) each would have the property to be different from the other.) - Solution/Frege: the property of being Hans or Paul.
Number/Wittgenstein: are not merely signs. - One can have two items of the form three, but only one number. - ((s) WittgensteinVsFormalism).
Number/Definition/WittgensteinVsRussell: numerical equality is a prerequisite for a clear correspondence. - Therefore, Russell's definition of the number is useless. - ((s) because circular, if you want to define number via illustration).
Definition/Wittgenstein: instead of a definition of "number" we must figure out the rules of usage.
Number/Russell/Wittgenstein: has claimed, 3 is a property that is common to all triads. - ((s) Frege: classes of classes - does Frege not mean objects with classes (instead of properties)?).
Definition number/WittgensteinVsRussell: the number is an attribute of a function which defines a class, not a property of the extension. - E.g. Extension: it would be a tautology to say, ABC is three. - In contrast, meaingful: to say, in this room are three people.
Definition number/numbers/Wittgenstein/Tractatus: 6,021 - the number is the exponent of an operation.
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Waismann I 66
Def natürlichen Zahlen/Wittgenstein: diejenigen, auf die man die Induktion bei Beweisen anwenden kann.
Vorlesungen 1930-35 Frankfurt 1989
Das Blaue Buch - Eine Philosophische Betrachtung Frankfurt 1984
Tractatus Logico Philosophicus Frankfurt/M 1960
Einführung in das mathematische Denken Darmstadt 1996
Logik, Sprache, Philosophie Stuttgart 1976