Philosophy Lexicon of Arguments

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Ordinal numbers: ordinals indicate the position of elements within a sequence (expressed by "first", "second", ...). In contrast, cardinal numbers (expressed by "one," two ", ...) indicate the size (cardinality) of sets. See also numbers, sets, order, well-ordering.

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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:
Bertrand Russell
Bertrand Russell Die Mathematik und die Metaphysiker 1901 in: Kursbuch 8 Mathematik 1967

18
Ordinal numbers: result from counting. Objects can only be counted when some come first, and others come afterwards.

Cardinal numbers: they are the basic numbers of the infinite numbers (not the ordinal numbers). They are not obtained by sorting and counting, but by a different method, which, if necessary, shows whether a quantity is bigger.
This method does not say in the same way as counting how many elements a set has! Each element is linked to a number in pairs. Thus, infinite sets are defined numerically.


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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.

R I
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986

R II
B. Russell
Das ABC der Relativitätstheorie Frankfurt 1989

R IV
B. Russell
Probleme der Philosophie Frankfurt 1967

R VI
B. Russell
Die Philosophie des logischen Atomismus
In
Eigennamen, U. Wolf (Hg), Frankfurt 1993

R VII
B. Russell
Wahrheit und Falschheit
In
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996


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Ed. Martin Schulz, access date 2017-11-22