# Philosophy Lexicon of Arguments

Quantifiers: in the predicate logic, quantifiers are the symbol combinations (Ex) and (x) for the set of objects to which one or more properties are attributed to. A) Existence quantification (Ex)(Fx) ("At least one x"). B) Universal quantification (x)(Fx) ("Everything is F"). For other objects e.g. y, z,… are chosen. E.g. (x) (Ey) (Fx > Gy). See also quantification, generalized quantifiers.

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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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Books on Amazon

X 121
Branched Quantifiers/Quine: normal: e.g. "(x) (Ey)"/everyday linguistic translation: "for every choice of x, a y must be chosen so that the following sentence is true." Various x may require different y - i.e. the choice of y depends in general on the choice of x - Problem: e.g. the phrase "Fxyzw": suppose we want to say: for each x there is a y and for every z there is a w such that Fxyzw - the choice of y should depend only on the x and the choice of w only on z - (1) (x) (Ey) (z) (Ew) Fxyzw - so the choice of w depends also on x - solution: branched quantifiers:
(X) (Ey)
Fxyzw
(Z) (EW)
- So you do not need functions as values ​​of variables (2nd order logic, HOL).

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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

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 2018-04-23