|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._____________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. |
|Gärdenfors I 237
Quantifiers/Langacker: (Langacker 2003) Thesis: Expressions like "any cat" function as special cases of concepts for fictional objects. These are points in the conceptual space.
a) proportional quantifiers: e.g. all, most, none.
b) representative quantifiers: e.g. each, any. "Some" is used in both ways.
Cognitive treatment of quantifiers/Langacker:
Any: random selection.
Every single/each: throughgoing single investigation of the elements.
All/every: here it is accepted that an individual examination is not possible. Here a picture is conjured that at the same time can be overlooked._____________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.
Ronald W. Langacker
Foundations of Cognitive Grammar Stanford, CA 1999
The Geometry of Meaning Cambridge 2014