# Philosophy Dictionary of Arguments

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Circularity: Circularity is an expression for the problem that something cannot be explained by itself. The problem arises, for example, when, in an attempted definition, no independent second expression is found for an object or for the relations of this object to other objects. See also circle, vicious circle principle, totality, wholes, type theory, self-reference.

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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

Bertrand Russell on Circular Reasoning - Dictionary of Arguments

I XII
Def vicious circle 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. - Vicious 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. - Circle Fault Principle/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) (Russell: function, not only relation).
I 57
Circle/Principia Mathematica/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/Principia Mathematica/Russell: there must be no propositions about all propositions. - E.g. All propositions are false - therefore two kinds of truth/falsehood: 1st kind: "φ a is true" (special value) - 2nd kind: "Every value of φx^ has truth of the 1st kind".

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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.

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

Russell II
B. Russell
The ABC of Relativity, London 1958, 1969
German Edition:
Das ABC der Relativitätstheorie Frankfurt 1989

Russell IV
B. Russell
The Problems of Philosophy, Oxford 1912
German Edition:
Probleme der Philosophie Frankfurt 1967

Russell VI
B. Russell
"The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202
German Edition:
Die Philosophie des logischen Atomismus
In
Eigennamen, U. Wolf (Hg), Frankfurt 1993

Russell VII
B. Russell
On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit"
In
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996

> Counter arguments against Russell

Ed. Martin Schulz, access date 2022-01-28