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Variable/description/deputy/GeachVsCarnap: in its rules for descriptions, e.g. ""___ ___ (ix)(...x...)___ ___" etc. the strokes do not function, as Carnap believes as vacancies (substitutes) but as variables! - Carnap thinks, however, if he renames them, he avoids his problems with variables.
I 199, 200
Variables/Constants/GeachVsCarnap: Carnap does not distinguish between them, as he himself says: E.g. Carnap: "If "Q" is a constant pr (determined or indeterminate), then the sentences (Prague)" (city),"Q(a)" are all equally derivable from "Q(x)". - Geach: "determined or undetermined", shows that the alleged "constant pr" is used as a variable. - Solution: "For all "Q" if ..." - but then we have a variable ""Q"" that contains quotes as part of itself.
Free Variables/Strawson: E.g. (A) In "x is a human", "x" is a free variable. - Here, "x" does not occur as a free variable - because "x" is "x is a human" occurs as a free variable, the theorem (A) is true. - If (A) contained a free variable, it would not be a statement, but a propositional function.
Bound Variables/Use/Mention/Geach: in e.g. "x is a human being", "x" is needed, therefore it is a bound variable! (Bound by the quotes) - at the same time the expression is the name of a description, even if it does not denote anything. (> Denote/designate). - Names do not denote anything.
Logic Matters Oxford 1972