 Sometimes (as in the excluded-middle schema, above) the placeholders in a schema-template are marked by letters. It is important to keep in mind the distinction between, on one hand, an open sentence, such as ‘\((x + y) = (y + x)\)’; whose object-language numerical variables ‘\(x\)’ and ‘\(y\)’ range over the numbers and, on the other, a schema such as the number-theoretic commutativity schema whose template-text is ‘\((X + Y) = (Y + X)\)’; and whose side condition is that the two occurrences of ‘\(X\)’ are to be replaced by two occurrences of one and the same numeral, and likewise for the two occurrences of ‘\(Y\)’. The numerals belong to the object language, while the place-holders belong to the metalanguage. The variables in the object-language range over a domain of objects, while the ‘dummy letters’ in the template-text are just placeholders for syntactic substituends. (For a careful exposition of the distinction, see Quine 1945: sec. 1.)