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.

 
Author Item Excerpt Meta data

 
Books on Amazon
Berka I 539
Ordinals / ordinal numbers /o.n./ Tarski: we need them to classify characters of infinite order - it is a generalization of the concept of natural numbers - these are the smallest o.n. -
transfinite o.n.: since there are figures for every infinite sequence of o.n that are larger than any member of the sequence, there are particular numbers that are greater than all natural numbers - in every non-empty class of o.n. there is a smallest number - Omega / Omega / w: in particular there is the smallest transfinite o.n. w (Omega). the next largest is w + 1 and so on - the language of the general set theory is of order w.


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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.

Tarsk I
A. Tarski
Logic, Semantics, Metamathematics: Papers from 1923-38 Indianapolis 1983

Brk I
K. Berka/L. Kreiser
Logik Texte Berlin 1983


> Counter arguments against Tarski
> Counter arguments in relation to Numbers ...

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Ed. Martin Schulz, access date 2017-09-23