V 129
Variables/Quine: Their archetype are the pronouns - in the relative clause the relative pronoun stands for the name of the object.
---
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.
---
VII (a) 13
Bound variable/Quine: instead of it, we can say that something is in the range of a pronoun.
---
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.
---
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.
---
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 x
n, y
n ε ϑ
n + 1, that ∃z(x,y, ε z). - Thus disappears Russell’s grammatical constraint, that declared "x
m 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 "x
m ε y
n" simply becomes wrong.
---
X 95
Variables/Quine: quantifiable variables should never be in predicate places, but always in name places.
