Philosophy Dictionary of Arguments

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Variables, philosophy: variables are symbols in statements or logical formulas, in the place of which various, more precise determinations, such as constants or names of objects, can be inserted. In logic, free and bound variables are distinguished. Free variables, which are not bound by a quantifier such as (Ex) or (x), do not form a statement yet but a statement function such as e.g. "Fx" - "Something is F". Numbers or objects are not variable entities. The variability consists in the applicability of more than one possible value. See also free variables, bound variables, constants, individual constants, individual variables, substitution, substitutability, logic, statements, statement function, formulas.

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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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W.V.O. Quine on Variables - Dictionary of Arguments

V 129
Variables/Quine: Their archetype are the pronouns - in the relative clause the relative pronoun stands for the name of the object.
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VI 37/38
Variable/Quine: allows us to manoeuvre every occurrence of "a" into a context of "a =" and to treat the resulting context as an unanalysable predicate "A" that absorbes the singular term - singular term: can be re-introduced later as a description.
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VII (a) 13
Bound variable/Quine: instead of it, we can say that something is in the range of a pronoun.
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VII (f) 107ff
Variables/Quine: "F": not bindable - Only apparent predicates, vacancies in the sentence chart - "p", "q", etc. stand for whole expressions, they are sometimes viewed as if they needed entities whose names are these expressions (these are called propositions) - "p" "q", etc. are never bound variables! - "p>q" not a sentence, but a scheme.
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VII (f) 110
Not bindable variable/Quine: E.g. "p". If it were considered to be the name of some entity, it would have to be a bindable variable, which is not the case - e.g. "F" on a par with "p": if predicates are to be the names of some entity, they would have to be regarded as bindable variables, which they are not.
VII (f) 110
Variables/Numbers/Quine: in "x + 3 > 7" "x" should be regarded as a pseudo-number - "x + 3> 7" should be considered a pseudo-sentence or scheme. It cannot be quantified.
VII (f) 111
Variables/Quine: Greek letters: completely different status: they occur in a language about language: E.g.
(3) (∃a)(φ v ψ)
is on a semantically higher level than "x + 3> 7".
(3) is a name of a sentence or expression - Greek letters are standing for sentences here - they are quantifiable - "φ": grammatically substantival, occupies the place of names of sentences. - "p": grammatically sentential (sentence form): has the place of complete sentences.
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IX 194f
Universal variable/Systematic ambiguity/Quine: possibly at the expense of adding new and unreduced predicates "T0", "T1", "T2",... that are added to "ε", we can get rid of the special, indexed variables in favor of the universal variables x, y.... - in fact, "Tnx" can easily be expressed with help of "ε" and the logic: "∃z(x,y ε z)" ensures compliance of the type in x and y and vice versa ensures compliance of the type with x and y that xn, yn ε ϑ n + 1, that ∃z(x,y, ε z). - Thus disappears Russell’s grammatical constraint, that declared "xm ε y n" meaningless if m + 1 unequal n - "m ε y n" now becomes useful for all m and n - if m + 1 unequal n, so "xm ε y n" simply becomes wrong.
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X 95
Variables/Quine: quantifiable variables should never be in predicate places, but always in name places.


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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 [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.

Quine I
W.V.O. Quine
Word and Object, Cambridge/MA 1960
German Edition:
Wort und Gegenstand Stuttgart 1980

Quine II
W.V.O. Quine
Theories and Things, Cambridge/MA 1986
German Edition:
Theorien und Dinge Frankfurt 1985

Quine III
W.V.O. Quine
Methods of Logic, 4th edition Cambridge/MA 1982
German Edition:
Grundzüge der Logik Frankfurt 1978

Quine V
W.V.O. Quine
The Roots of Reference, La Salle/Illinois 1974
German Edition:
Die Wurzeln der Referenz Frankfurt 1989

Quine VI
W.V.O. Quine
Pursuit of Truth, Cambridge/MA 1992
German Edition:
Unterwegs zur Wahrheit Paderborn 1995

Quine VII
W.V.O. Quine
From a logical point of view Cambridge, Mass. 1953

Quine VII (a)
W. V. A. Quine
On what there is
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (b)
W. V. A. Quine
Two dogmas of empiricism
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (c)
W. V. A. Quine
The problem of meaning in linguistics
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (d)
W. V. A. Quine
Identity, ostension and hypostasis
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (e)
W. V. A. Quine
New foundations for mathematical logic
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (f)
W. V. A. Quine
Logic and the reification of universals
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (g)
W. V. A. Quine
Notes on the theory of reference
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (h)
W. V. A. Quine
Reference and modality
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VII (i)
W. V. A. Quine
Meaning and existential inference
In
From a Logical Point of View, , Cambridge, MA 1953

Quine VIII
W.V.O. Quine
Designation and Existence, in: The Journal of Philosophy 36 (1939)
German Edition:
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982

Quine IX
W.V.O. Quine
Set Theory and its Logic, Cambridge/MA 1963
German Edition:
Mengenlehre und ihre Logik Wiesbaden 1967

Quine X
W.V.O. Quine
The Philosophy of Logic, Cambridge/MA 1970, 1986
German Edition:
Philosophie der Logik Bamberg 2005

Quine XII
W.V.O. Quine
Ontological Relativity and Other Essays, New York 1969
German Edition:
Ontologische Relativität Frankfurt 2003

Quine XIII
Willard Van Orman Quine
Quiddities Cambridge/London 1987


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Ed. Martin Schulz, access date 2021-07-29
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