# Philosophy Lexicon of Arguments

Numbers: whether numbers are objects or concepts, has been controversial in the philosophical discussion for millennia. The most widely accepted definition today is given by G. Frege (G. Frege, Grundlagen der Arithmetik 1987, p. 79ff). Frege-inspired notions represent numbers as classes of classes, or as second-level terms, or as that with one measure the size of sets. Up until today, there is an ambiguity between concept and object in the discussion of numbers. See also counting, sets, measurements, mathematics, abstract objects, mathematical entities, theoretical entities, number, platonism.

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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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I 170
Def Equinumerousness/Frege/Meixner: f is a property that is equinumerous with the property g, = Def for at least one two-digit relation R applies: - 1) Every entity that has f is in the relation R with exactly one entity that has g - 2) If entities that have f are different, so are entities with g - 3) inverse of 1: every entity that has g. - Number: can then be defined noncircularly: x is a natural number = Def x is a finite number property - Number/Meixner: conceived as a property they are typeless functions

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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.

Mei I
U. Meixner
Einführung in die Ontologie Darmstadt 2004

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Ed. Martin Schulz, access date 2018-02-23