Lexicon of Arguments

 

I 30
Number variables/Prior: variables are no names. E.g. if exactly 3 things φ and exactly 4 things ψ, then more things are φ than ψ. Then "3" is no name but an inseparable part of the verb operator "Exactly 3 things __".
>Names, >Operators, >Predication, >Is, >Equality, >Equations, >Sets, >Set theory.
I 33
Bound variables/Quine: bound variables can only stand for names. So for things, not for sentences.
>Bound variables, cf. >Names of sentences, >Quantification,
>Objects.
QuineVsFrege: names are not for sentences, only for things. - E.g. "For a φ, φx" is the only way to read this, that there is at least one thing, so that x "does" this thing.
>Sentences, >"Stand for", >Names/Frege, >Sentences/Frege.
Quine himself does not do that but he has "ε" for "is element of".
>Element relation, >Is, >Predication.
I 35
Bound variable/name/Prior: E.g. open sentence "x is red-haired": what is x?
>Open sentences/propositional functions.
It depends on how we stand for" understanding:
a) x is for a name, such as "Peter" (Substitute)
b) or object Peter
PriorVsQuine: bound variables can also stand for sentences: "J. believes that p" (anything), then stands for a sentence.
ad I 93 (external):
Sentence variable/Wittgenstein: Tractatus: The term presupposes forms of all sentences in which it can occur - Tractatus 3.312: It is therefore represented by the general form of the sentences which it characterizes - Wittgenstein: namely in this form the expression will be constant and everything else can be variable - sentence variable: Aristotle's innovation "a" for a whole sentence.
I 148
Bound variables/Prior: bound variables represent logical proper names.
"For an x:
1. x φ-s,
2. nothing else than x φ-s and
3. it is not the case that x ψ-s".
I 164f
Bound variable/PriorVs some American logicians: not any bound variable stands for a name.