Philosophy Lexicon of Arguments

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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:
Peter Gärdenfors
I 237
Quantifiers/Langacker/Gärdenfors: (Langacker 2003) Thesis: Expressions like "any cat" function as special cases of terms for fictional objects. These are points in the conceptual space.
Quantifiers/Langacker:
a) proportional quantifiers: e.g. all, most, none
b) representative quantifiers: e.g. each, any. "Some" is used in both ways.
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I 238
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 is to be overlooked.
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I 236
Quantifiers/Linguistics/Gärdenfors: a cognition-based semantics should be able to say something about the meaning of quantifiers like "all" and "some".
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I 237
Quantifiers/Langacker: (Langacker 2003) Thesis: Expressions like "any cat" function as special cases of terms for fictional objects.
Gärdenfors: These are points in the conceptual space.
GärdenforsVsLogic: the traditional truth-functional semantics sweeps a set of characteristics of quantifiers with respect to the context under the carpet.
E.g. "Everyone has come" does not mean that all mankind has appeared, but only a context-dependent group of individuals.
Grammar: Problem: the quantifiers function grammatically as singular, although the universal quantifiers relate to all elements of a set.
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I 238
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 is to be overlooked.


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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.

Gä I
P. Gärdenfors
The Geometry of Meaning Cambridge 2014


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Ed. Martin Schulz, access date 2017-10-17