Philosophy Lexicon 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correct statements or sets of statements that lead to an existence assumption, which initially seemed plausible, to be withdrawn.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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VI 124
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.
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VII 136
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.
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IX 124
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.
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X 70
Grelling paradox/Quine: "x does not fulfil itself" must not occur in the object language.

Q I
W.V.O. Quine
Wort und Gegenstand Stuttgart 1980

Q II
W.V.O. Quine
Theorien und Dinge Frankfurt 1985

Q III
W.V.O. Quine
Grundzüge der Logik Frankfurt 1978

Q IX
W.V.O. Quine
Mengenlehre und ihre Logik Wiesbaden 1967

Q V
W.V.O. Quine
Die Wurzeln der Referenz Frankfurt 1989

Q VI
W.V.O. Quine
Unterwegs zur Wahrheit Paderborn 1995

Q VII
W.V.O. Quine
From a logical point of view Cambridge, Mass. 1953

Q VIII
W.V.O. Quine
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982

Q X
W.V.O. Quine
Philosophie der Logik Bamberg 2005

Q XII
W.V.O. Quine
Ontologische Relativität Frankfurt 2003


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



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Ed. Martin Schulz, access date 2017-05-23