|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correct statements or sets of statements that lead to an existence assumption, which initially seemed plausible, to be withdrawn.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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|Berka I 371
A) Semantic: Liar, Grelling/Nelson, Russellian A. of the designation.
B) syntactically (logically): antinomy of Cantor, of Burali Forti, Russell's set of all sets which do not contain themselves as elements.
Antinomies/Paradoxes/Solution/Berka: a) Axiomatization, (Fraenkel, v. Neumann, Bernays, Quine)
B) (Russell, König, Brouwer, Hilbert): Verification of the logical foundations of set theory and mathematics. > Type theory, > Separation of object and meta language.
F. P. Ramsey
The Foundations of Mathematics and Other Logical Essays 2013
K. Berka/L. Kreiser
Logik Texte Berlin 1983