|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._____________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. |
Bertrand Russell on Ordinal Numbers - Dictionary of Arguments
Bertrand Russell Die Mathematik und die Metaphysiker 1901 in: Kursbuch 8 Mathematik 1967
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._____________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. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986
The ABC of Relativity, London 1958, 1969
Das ABC der Relativitätstheorie Frankfurt 1989
The Problems of Philosophy, Oxford 1912
Probleme der Philosophie Frankfurt 1967
"The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202
Die Philosophie des logischen Atomismus
Eigennamen, U. Wolf (Hg), Frankfurt 1993
On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit"
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996