Philosophy Dictionary of Arguments

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Quantification: is a function within the predicate logic, in which a property is attributed to an object yet to be determined. A) Existence quantification e.g. (Ex) (Fx) "At least one object x is F". It is assumed that the object denoted by x exists. B) Universal quantification (notation (x) ...) "For all x applies ...". Both forms of quantification can be negated, covering most of the everyday cases. In addition, a subject domain must be chosen, within which the statements that result from the insertion of objects are meaningful. See also existence, non-existence, existence assumption, existence predicate, universal quantification, existence quantification, domains, opacity, intensional objects.

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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Hans Kamp on Quantification - Dictionary of Arguments

Cresswell I 172
Quantification/Kamp: there are cases where the quantifier can be changed from the existence qu. to universal qu. If it does not bind any variable in the consequent, we have as a logical equivalence:
I 173
(x) (Fx> P) ↔ (ExFx> P) (s) bracket!) - N.B./(s): the existential quantifier extends only to the Fx, i.e. on the reverse reading, it then extends not to the consequence (left hand side of the equivalence). Ex (x) ((donkey x and Pedro has x)> Pedro proposes x - Problem: x here binds a variable in the consequent - Solution/Kamp: analyzed indefinite phrases (descriptions) as predicates (see above) - the universal quantifikation is part of the meaning of "if".

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.
The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Kamp I
From Discourse to Logic: Introduction to Modeltheoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory (Studies in Linguistics and Philosophy)

Cr I
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988

M. J. Cresswell
Structured Meanings Cambridge Mass. 1984

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Ed. Martin Schulz, access date 2021-02-25
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