# Philosophy Lexicon of Arguments

Element relation, element relationship: the existence of a number within a set. In the broader sense the existence of an object (urelement) within a set. The element relation is to be distinguished from the subset relation. See also sets, classes, subsets, elements, set theory, empty set, universal class, paradoxes.

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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.

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IX 23
Element relation/identity/classes/individuals: "ε" before individuals has the property of "=".
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IX 113 ff
Definition element relation/ordinal: "E" stands for "{ : y ε z}". Ru: y is a number, but not z (z must be a quantity). Pair of number and quantity, also the number is part of the quantity. If this is true, it is an e-relation - E should arrange the ordinals.
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IX 119
NO: class of ordinal numbers (≠ ordinal numbers)
Element relation/ordinals/Quine: here, "ε" means "smaller" - interchangeable with "contains" with respect to ordinals - therefore x U {x} is the next ordinal after x if there are still ordinals behind x at all - it is not sufficient to meet the element conditions to belong to a class - the existence is necessary - proof of "NO ε ϑ ((s) the class of ordinals does not exist"). - It is now obvious: if NO existed, 23.9 and 24.3 (see above) would be a contradiction to 23.7 -> paradoxon of Burali-Forti.
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IX 219
Element relation/Epsilon/induction/Quine: the primitive predicate "ε" divides the determination of classes
(a) behind the Epsilon into the requirement of having elements and
(b) in front of the epsilon into the requirement of being an element.
Problem of Induction: always one with the existence of classes that have been used only for the requirement (a) - Induction: in order to derive it from the definition of n we need a class {x:Fx} or
N n {x: Fx} or
{x:x <= z u ~Fx}
as a value of a variable of this definition and this is a variable that stands only on the right hand side of "ε".

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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.

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

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Ed. Martin Schulz, access date 2018-03-20