|Infinity, infinite, philosophy: infinity is a result of a not stopping procedure, e.g. counting or dividing, or e.g. the continued description of a circular motion. In life-related contexts, infinitely continuous processes, e.g. infinite repetition, or never ending waiting are at least logically not contradictory. A construction rule does not have to exist to give an infinite continuation, such as e.g. in the development of the decimal places of real numbers. See also boundaries, infinity axiom, repetition, finitism, numbers, complex/complexity._____________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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|Bertrand Russell Die Mathematik und die Metaphysiker 1901 in: Kursbuch 8 Mathematik 1967
Most numbers are infinitely large, and to infinity one can add additional numbers as often as one wants, without changing the character of the number.
Russell: there is also a largest infinite number: this is the number of objects in total, regardless of species and genus.
Cantor proved that there is no largest infinite number, and if he were right, the contradictions would appear again in refined form in the concept of infinity._____________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.
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986
Das ABC der Relativitätstheorie Frankfurt 1989
Probleme der Philosophie Frankfurt 1967
Die Philosophie des logischen Atomismus
Eigennamen, U. Wolf (Hg), Frankfurt 1993
Wahrheit und Falschheit
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996