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# Philosophy Dictionary of Arguments

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Paradoxes: are contradictions within formally correct statements or sets of statements that lead to an existence assumption, which initially seemed plausible, to be withdrawn. Paradoxes are not errors, but challenges that may lead to a re-formulation of the prerequisites and assumptions, or to a change in the language, the subject domain, and the logical system. See also Russellian paradox, contradictions, range, consistency.

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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 Concept Summary/Quotes Sources

Georg Cantor on Paradoxes - Dictionary of Arguments

Berka I 371
Antinomies/quantum theory/Cantor: (1895): "Antinomy of the set of all transfinite ordinal numbers".
Published first by Burali Forti in 1897.
"Cantor's antinomy": A of the greatest cardinal number" = ("A. of the set of all sets")
At that time the fundamental consequences were underestimated.
Russell: (Letter to Frege, 16.06.1902): Russell's antinomy as a further development of the Cantor's antinomy. This can also be derived from Frege's first volume of the basic laws of arithmetic.

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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. 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.

Berka I
Karel Berka
Lothar Kreiser
Logik Texte Berlin 1983

> Counter arguments against Cantor
> Counter arguments in relation to Paradoxes

Ed. Martin Schulz, access date 2022-06-26