|Zero: is a natural number that is used to express that no object meets a certain condition or that a measured value has this quantity with respect to a unit of measure._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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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".
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.
Subset/Element/Frege: must always be distinguished. FregeVsSchröder/FregeVsRegion Calculus - 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).
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). ((s) zero only contained as a subset in any other set)._____________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.
Die Grundlagen der Arithmetik Stuttgart 1987
Funktion, Begriff, Bedeutung Göttingen 1994
Logische Untersuchungen Göttingen 1993