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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

Bertrand Russell on Quantifiers - Dictionary of Arguments

Hintikka I 173
Quantification/quantifier/acquaintance/description/Russell/Hintikka: in Russell, the quantifiers (or the domain of bound variables) go only via objects of the acquaintance. ((s) physically present things).
Description/Theory of Description/Russell: descriptions are eliminated in the context in favor of quantifiers. There are only quantifiers and bound variables.
Russell/Hintikka: one could paraphrase it as the following: the concept "is always true" is the only one occuring in propositions which originally contained certain descriptions.
Power/Russell/Hintikka: the force ((s) semantic force) of the reduced propositions depends on the individual range of the variable.
N.B./Hintikka: now it is only a part of the story that Russell has successfully eliminated non-existent objects (E.g., the current King of France is bald). His reduction continues:
Quantifier/Russell/Hintikka: the quantifiers go only via objects of the acquaintance. ((s) objects of which we only know by description are not allowed, they cannot be quantified via according to Russell, which is more than the elimination of non-existent objects because there are also existing objects which we know only by description).
Hintikka I 173
Denotation/Russell/Hintikka: N.B.: a brilliant feature of Russell's theory of the denotation of 1905 is that it is the quantifiers which denote!
Theory of Description/Russell: (end of "On Denoting") Thesis: contains the reduction of descriptions on objects of acquaintance.
I 174
Hintikka: this connection is astonishing. It also appears to be circular, only to admit objects of acquaintance.
Solution: we must see what successfully denotating phrases actually denote: they denote objects of acquaintance.
Ambiguity/uniqueness/Hintikka: it is precisely ambiguity that leads to the failure of the existential generalization.
E.g. Waverley/Russell/Hintikka: that only objects of acquaintance are allowed, shows his own example: "the author of Waverley" in (1) is actually a primary event, i.e. his example (2).
"Whether"/Russell/Hintikka: only difference: wanted to know "whether" instead of "did not know".
Secondary Description/Russell: can also be expressed in the way that George wanted to know from the man who actually wrote Waverley whether he was Scott.
I 175
That would be the case if George IV had seen Scott (at a distance) and had asked "Is that Scott?".
HintikkaVsRussell: why does Russell choose an example with a perceptually known individual? Do we not normally deal with individuals of flesh and blood, whose identity is known to us, rather than merely with perceptual objects?
Knowledge who/knowledge what/perception object/Russell/Hintikka: precisely in the case of perception objects, it seems as if the kind of uniqueness that we need for a knowledge-who does not exist.
Hintikka I 178
Quantifier/Quantification/HintikkaVsRussell: Russell systematically confuses two types of quantifiers. (A) of the acquaintance, (B) of the description.
Problem: Russell had not realized that the difference cannot be defined solely in relation to the actual world!
Solution/Hintikka: we need a relativization to sets of possible worlds, which change with the different propositional attitudes.
Hintikka I 180
Elimination/Eliminability/HintikkaVsRussell/Hintikka: in order to eliminate merely seemingly denotating descriptions, one must assume that the quantifiers and bound variables go via individuals that are identified descriptively. ((s) >intensional object ).
Otherwise the real Bismarck would not be an admissible value of the variables with which we express that there is an individual of a certain kind.
Problem: then these quantifiers must not be constituents of the propositions, for their range of values consists not merely of objects of acquaintance. So Russell's mistake was a twofold one.

1.
Quantifier/Variable/Russell/Hintikka: by 1905 he had already stopped thinking that quantifiers and bound variables are real constituents of propositions.
Definition apparent/Russell/Hintikka: = bound variable.

2.
Acquaintance/Russell: values of the variables should only be objects of the acquaintance. (HintikkaVsRussell).

Hintikka I 180
Quantifiers/HintikkaVsRussell: now we can see why Russell did not distinguish between different quantifiers (acquaintance/description): for him, quantifiers were only notational patterns, and for them it is not necessary to define the range of possible interpretation, therefore it does not make a difference when the domain changes!
Quantification/Russell: for him it was implicitly objective (referential), in any case not substitutional.


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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.

Russell I
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986

Russell II
B. Russell
The ABC of Relativity, London 1958, 1969
German Edition:
Das ABC der Relativitätstheorie Frankfurt 1989

Russell IV
B. Russell
The Problems of Philosophy, Oxford 1912
German Edition:
Probleme der Philosophie Frankfurt 1967

Russell VI
B. Russell
"The Philosophy of Logical Atomism", in: B. Russell, Logic and KNowledge, ed. R. Ch. Marsh, London 1956, pp. 200-202
German Edition:
Die Philosophie des logischen Atomismus
In
Eigennamen, U. Wolf (Hg), Frankfurt 1993

Russell VII
B. Russell
On the Nature of Truth and Falsehood, in: B. Russell, The Problems of Philosophy, Oxford 1912 - Dt. "Wahrheit und Falschheit"
In
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996

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


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Ed. Martin Schulz, access date 2022-01-28
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