," assuming that
is a function which has individuals for its arguments. Suppose, for example, that
is "always true"; let it be, say, the "law of identity,"
. Then we may substitute for "
" any name we choose, and we shall obtain a true proposition. Assuming for the moment that "Socrates," "Plato," and "Aristotle" are names (a very rash assumption), we can infer from the law of identity that Socrates is Socrates, Plato is Plato, and Aristotle is Aristotle. But we shall commit a fallacy if we attempt to infer, without further premisses, that the author of Waverley is the author of Waverley. This results from what we have just proved, that, if we substitute a name for "the author of Waverley" in a proposition, the proposition we obtain is a different one. That is to say, applying the result to our present case: If "