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Number variables/Prior: no names. E.g. if exactly 3 things j and exactly 4 things y, then more things are j than y. Then "3" no name but inseparable part of verb operator"Exactly 3 things __".
Variables/Quine: (bound) can only stand for names. So for things, not for sentences.
QuineVsFrege: names are not for sentences, only for things - E.g. "For a j, jx" is the only way to read this, that there is at least one thing, so that x "does" this thing - Quine himself does not do that but he has "E" for "is element of".
Bound variable/name/Prior: E.g. open sentence "x is red-haired": what is x? - 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.
A propos I 93 (external):
Sentece Variable/Wittgenstein: Tractatus: The term presupposes forms of all sentences in which it can occur - 3.312 It is therefore represented by the general form of the sentences which it characterizes - Witt.: namely in this form the expression will be constant and everything else can be variable - sentence variable: Aristotle innovation "a" for a whole sentence.
Prior I 148
Bound variables/Prior: represent logical proper names - "For an x: 1. x ft, 2. nothing else than x ft and 3. it is not the case that x yt".
Bound variable/PriorVsAmerican logicians: not any stands for a name.
Objects of thought Oxford 1971
Arthur N. Prior
Papers on Time and Tense 2nd Edition Oxford 2003