Philosophy Lexicon of Arguments

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Bertrand Russell
I XII
Def circle fault principle/Russell/Gödel: no totality can contain elements that can be defined only in terms of this totality or elements which include or imply this totality -" -viscious circle principle, VCP -
I XII
Circle fault principle/GödelVsRussell: the principia themselves do not fulfil the principle in their first edition if "definable" means "definable within the system" and no definition methods outside are known, except for those that include even more extensive totalities than those that occur in the system - Gödel: I would rather see this as proof that the circle fault principle is wrong than that classical mathematics is wrong - because one can argue that the reference to a totality necessarily implies a reference to all of its individual elements or, in other words, that "all" means the same as an infinite logical conjunction -" I XIV "all"/solution/Carnap:"All" alludes to analyticity or necessity or provability -" CFP/Gödel: seems to apply only to entities constructed by ourselves -" otherwise totality is nothing absurd -
I 55f
Circle fault principle/Russell: Propositions: only form multiplicities, no entities - (s) entities are formed by terms, i.e. that you cannot set up a sentence about "all of its elements". (> "Everything he said"/(s): "say" does not form a category like "next to", "similar" "son of"; "nothing" does not either nor does it form an entity, only a multiplicity. but "father of" (unambiguous) (Ru: function, not only relation)> Chisholm)
I 57
Circle/PM/Russell: arises when one allows values as possible arguments of a propositional function ​​that require the function -
I 61
Circle fault principle/circle/entitiy/totality/PM/Russell: there must be no propositions about all propositions - E.g. All propositions are false -" therefore two kinds of truth/falsehood: 1st kind: "j a is true" (special value) - 2nd kind "Every value of jx^ has truth of the 1st kind" -

R I
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986

R II
B. Russell
Das ABC der Relativitätstheorie Frankfurt 1989

R IV
B. Russell
Probleme der Philosophie Frankfurt 1967

R VI
B. Russell
Die Philosophie des logischen Atomismus
In
Eigennamen, U. Wolf (Hg), Frankfurt 1993

R VII
B. Russell
Wahrheit und Falschheit
In
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996


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Ed. Martin Schulz, access date 2017-05-25