Philosophy Lexicon of Arguments

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Empty set: an empty set is a set without an element. Notation ∅ or {}. There is only one empty set, since without an existing element there is no way to specify a specification of the set. The empty set can be specified as such that each element of the empty set is not identical with itself {x x unequal x}. Since there is no such object, the set must be empty. The empty set is not the number zero, but zero indicates the cardinality of the empty set.

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 218
Empty set/zero class/Quine: Λ is not equal to 0! (For Frege 0, namely {L}.
A propos IX 226ff
Empty set/zero class/(s): unlike definition gap (e.g. divide continuity through zero). - Real gap: a well-defined condition is not met, e.g. primes between 31 and 37: 5 natural numbers do not satisfy the condition, 0 natural numbers fulfill the condition.
For an infinite number of rational numbers and real numbers the condition is not defined - universal class/(s) if there is nothing that fulfills the condition it is questionable whether we can talk of a set (because it does not match a term). - The other way around: what is should be the condition for the universal class?

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.

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

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

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

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

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

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

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

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

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

W.V.O. Quine
Ontologische Relativität Frankfurt 2003

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Ed. Martin Schulz, access date 2018-03-18