Philosophy Lexicon of Arguments

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II 32
Number/Wittgenstein: not a concept, but a logical form.
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II 283
Numbers/cardinal/Wittgenstein: that there are infinitely many cardinals, is a rule that one sets up.
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II 343
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.
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II 344
Number/Wittgenstein: are not merely signs. - One can have two items of the form three, but only one number. - ((s) WittgensteinVsFormalism).
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II 360
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).
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II 361
Definition/Wittgenstein: instead of a definition of "number" we must figure out the rules of usage.
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II 415
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)?).
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II 416
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.
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IV 93
Definition number/numbers/Wittgenstein/Tractatus: 6,021 - the number is the exponent of an operation.
- - -
Waismann I 66
Def natürlichen Zahlen/Wittgenstein: diejenigen, auf die man die Induktion bei Beweisen anwenden kann.


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Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.

W II
L. Wittgenstein
Vorlesungen 1930-35 Frankfurt 1989

W III
L. Wittgenstein
Das Blaue Buch - Eine Philosophische Betrachtung Frankfurt 1984

W IV
L. Wittgenstein
Tractatus Logico Philosophicus Frankfurt/M 1960

Wa I
F. Waismann
Einführung in das mathematische Denken Darmstadt 1996

Wa II
F. Waismann
Logik, Sprache, Philosophie Stuttgart 1976


> Counter arguments against Wittgenstein
> Counter arguments in relation to Numbers



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Ed. Martin Schulz, access date 2017-06-25