# Philosophy Lexicon of Arguments

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.

Author Item Summary Meta data
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 13
Bound variable/Quine: instead of it, we can say that something is in the range of a pronoun.
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VII 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 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.
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VII 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.
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VII 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.

Q I
W.V.O. Quine
Wort und Gegenstand Stuttgart 1980

Q II
W.V.O. Quine
Theorien und Dinge Frankfurt 1985

Q III
W.V.O. Quine
Grundzüge der Logik Frankfurt 1978

Q IX
W.V.O. Quine
Mengenlehre und ihre Logik Wiesbaden 1967

Q V
W.V.O. Quine
Die Wurzeln der Referenz Frankfurt 1989

Q VI
W.V.O. Quine

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

Q VIII
W.V.O. Quine
Bezeichnung und Referenz
In
Zur Philosophie der idealen Sprache, J. Sinnreich (Hg), München 1982

Q X
W.V.O. Quine
Philosophie der Logik Bamberg 2005

Q XII
W.V.O. Quine
Ontologische Relativität Frankfurt 2003

> Counter arguments against Quine

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Ed. Martin Schulz, access date 2018-06-21