|Number of... (Anzahl, amount): Result of counting unlike a number that has not yet been determined. Frege used "Anzahl" (amount) to define numbers._____________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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|Berka I 121
Definition Anzahl/original German: Amount/Number/extendend function calculus/Hilbert:(extendend function calculus: here also formulas are possible, which do not depend on any variables, which represent thus certain statements, for these one has to determine their correctness or falsehood.)
Definition number: a number is not an object, but a property. The individuals to whom a number belongs to as a property cannot be the counted things themselves, since each of the things is only one, so that a number that is different from one could not occur at all.
Correct: For example, it is a property of the predicate "being continent of the earth", which is true for exactly five individuals.
Numbers/Hilbert: numbers also appear as qualities of predicates.
Definition onself number/Hilbert: individual predicate function. In the extendend function calculus: ?? ?? ?? ?? ...................................... Will it be possible to include the number theory into the logic .
The numbers 0,1,2 are the functions 0 (F), 1 (F), 2 (F), etc._____________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.
K. Berka/L. Kreiser
Logik Texte Berlin 1983