|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correct statements or sets of statements that lead to an existence assumption, which initially seemed plausible, to be withdrawn.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._____________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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Comprehension/paradoxes/Quine: that each element relation (each term) results in a set is not possible because of Burali-Forti, etc. - solution: these element relations (conditions) may determine sets, or perhaps the last (outermost) classes - outer condition: cannot be an element in turn - are introduced layer after layer - for classical mathematics "true0" already suffices - everything in one language - hierarchy of truth predicates.
Paradoxes/Quine: no longer occur when the levels of language are distinguished, i.e. if one keeps out the expressions "true-in-L", "denotes-in-L", etc. of the language L itself.
Burali-Forti/paradox/Quine: "the class of ordinal numbers does not exist": "NO ε ϑ": is the tamed version of Burali-Forti: that there must be a larger ordinal number and simultaneously it cannot exist. - Reductio ad absurdum of the comparability of the ordinal numbers - solution/today: we will not assume that every condition about the existence of an element relation determines a class.
Grelling paradox/Quine: "x does not fulfil itself" must not occur in the object language._____________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.
Wort und Gegenstand Stuttgart 1980
Theorien und Dinge Frankfurt 1985
Grundzüge der Logik Frankfurt 1978
Mengenlehre und ihre Logik Wiesbaden 1967
Die Wurzeln der Referenz Frankfurt 1989
Unterwegs zur Wahrheit Paderborn 1995
From a logical point of view Cambridge, Mass. 1953
Bezeichnung und Referenz
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982
Philosophie der Logik Bamberg 2005
Ontologische Relativität Frankfurt 2003