As in the case of CONSTANT, we shall apply the terms VARIABLE and FORM
also in the construction of uninterpreted calculi, introducing them by
special definition for each such calculus in connection with which
they are to be used.  Ordinarily the symbols and expressions so
designated will be ones which become variables and forms in our
foregoing sense under one of the principal interpretations of the
calculus as a language.

It should be emphasized that a variable, in our usage, is a symbol of
a certain kind rather than something (e.g., a number) which is denoted
or otherwise meant by such a symbol.

Therefore, a variable (or more precisely, particular instances or occurrences
of a variable) can be written on paper---just as the figure 7 can be
written on paper, though the number 7 cannot be so written except in
the indirect sense of writing something which denotes it. And similarly
constants and forms are symbols or expressions of cetain kinds.
It is indeed usual to speak also of numbers and physical quantities
as "constants"---but this usage is not the same as that in which a constant
can be contrasted with a variable, and we shall avoid it in this book.

Mathematical writers do speak of "variable real numbers," or oftener
"variable quantities," but it seems best not to interpret these phrases
literally.  Objections to the idea that real numbers are to be divided
into two sorts of classes, "constant real numbers" and "variable real
numbers," have been clearly stated by Frege and need not be repeated here
at length.  The fact is that a satisfactory theory has never been
developed on this basis, and it is not easy to see how it might be done.