# Philosophy Dictionary 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.

Author Concept Summary/Quotes Sources

Jaakko Hintikka on Quantifiers - Dictionary of Arguments

II 28
Branched Quantifiers/branching/stronger/weaker/Hintikka:
Example branching:
1st branch: there is an x and b knows ...
2nd branch: b knows there is an x ...
Quantification with branching quantifiers is extremely strong, almost as strong as 2nd level logic.
Therefore, it cannot be completely axiomatized (quantified epistemic logic with unlimited independence).
II 29
Variant: a variant would refer to simpler cases where the independence refers to ignorance, combined with a move with a single, un-negated, non-epistemic operator {b} K. Here, an explicit treatment is possible.

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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. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Hintikka I
Jaakko Hintikka
Merrill B. Hintikka
Investigating Wittgenstein
German Edition:
Untersuchungen zu Wittgenstein Frankfurt 1996

Hintikka II
Jaakko Hintikka
Merrill B. Hintikka
The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989

> Counter arguments against Hintikka
> Counter arguments in relation to Quantifiers

Ed. Martin Schulz, access date 2023-09-30