Philosophy Lexicon of Arguments

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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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Books on Amazon
I 82
Number / definition / Carnap: "The number of the term f is two" means "there is an x ​​and there is a y such that x is not identical to y, x falls under f, y falls under f, and for every z holds: if z falls under f, then z is identical with x or with y. "


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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.

Ca I
R. Carnap
Die alte und die neue Logik
In
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996

Ca III
R. Carnap
Philosophie als logische Syntax
In
Philosophie im 20.Jahrhundert, Bd II, A. Hügli/P.Lübcke (Hg), Reinbek 1993

Ca IV
R. Carnap
Mein Weg in die Philosophie Stuttgart 1992

Ca VI
R. Carnap
Der Logische Aufbau der Welt Hamburg 1998

CA VII = PiS
R. Carnap
Sinn und Synonymität in natürlichen Sprachen
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982

Ca VIII (= PiS)
R. Carnap
Über einige Begriffe der Pragmatik
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982


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Ed. Martin Schulz, access date 2017-11-18