Psychology Dictionary of Arguments

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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.

Author Concept Summary/Quotes Sources

David Hilbert on Number of (Amount) - Dictionary of Arguments

Berka I 121
Def Number of/amount/(German: "Anzahl")/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.
>Truth values
, >Truth.
Def number of: 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.
>Properties, >Predicates, >Objects.
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 of a definite number/Hilbert: individual predicate function. In the extendend function calculus: here it will 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.(1)
>Numbers, cf. >"Exactly One".

1. D. Hilbert & W. Ackermann: Grundzüge der theoretischen Logik, Berlin, 6. Aufl. Berlin/Göttingen/Heidelberg 1972, §§ 1, 2.

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. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Berka I
Karel Berka
Lothar Kreiser
Logik Texte Berlin 1983

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