Lexicon of Arguments

Philosophical and Scientific Issues in Dispute
 
[german]


Complaints - Corrections

Table
Concepts
Versus
Sc. Camps
Theses I
Theses II

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I 107
Def Zero/Frege: because nothing falls under the concept "unlike itself", we declare: 0 is the number that is equal to the concept "unlike itself".
>Concept, >Object, >Numbers.
I 110
0/1/zero/one/numbers/Frege: 0 is the object that falls under the concept "equal to 0" - thus an object (the zero) falls under the concept. Because an object falls under the concept, the concept is assigned the number 1 (1 object, the zero). On the other hand, 0: no object falls under the concept "equal to 0 but not equal to 0". Hence 0 is the number which corresponds to the concept.
- - -
IV 98
Subset/element/Frege: a subset must always be distinguished. FregeVsSchröder/FregeVsArea Calculus (German: Gebietekalkül). The zero must not be contained as an element in every class. Otherwise it would depend on the respective manifold. At one point it would be nothing, and then it would be something (e.g. negation of a). - Solution: zero as a subset (empty set).
>Empty set, >Subsets.
IV 100
Zero/0/empty set/FregeVsSchröder/Frege: the zero must not be contained as an element in another class (>Günter Patzig, introduction to Frege IV), but only subordinate as a class. (+ IV 100/101).
>Element relation.

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