Philosophy Dictionary 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). Fregeinspired notions represent numbers as classes of classes, or as secondlevel 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. _____________ 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  Item  More concepts for author  

Bigelow, John  Numbers  Bigelow, John  
Black, Max  Numbers  Black, Max  
Carnap, Rudolf  Numbers  Carnap, Rudolf  
Chisholm, Roderick  Numbers  Chisholm, Roderick  
Field, Hartry  Numbers  Field, Hartry  
Frege, Gottlob  Numbers  Frege, Gottlob  
Geach, Peter  Numbers  Geach, Peter T.  
Genz, Hennig  Numbers  Genz, Hennig  
Gödel, Kurt  Numbers  Gödel, Kurt  
Hartmann, Nicolai  Numbers  Hartmann, Nicolai  
Hilbert, David  Numbers  Hilbert, David  
Logic Texts  Numbers  Logic Texts  
Mates, Benson  Numbers  Mates, Benson  
Meixner, Uwe  Numbers  Meixner, Uwe  
Mill, John Stuart  Numbers  Mill, John Stuart  
Piaget, Jean  Numbers  Piaget, Jean  
Poincaré, Henri  Numbers  Poincaré, Henri  
Prior, Arthur  Numbers  Prior, Arthur  
Quine, W.V.O.  Numbers  Quine, Willard Van Orman  
Tarski, Alfred  Numbers  Tarski, Alfred  
Wessel, H.  Numbers  Wessel, H.  
Wittgenstein, Ludwig  Numbers  Wittgenstein, Ludwig  
