unthinking), the latter by a prefixed element (say, plural[27]-reform-er).  There are, of course, an unlimited number of other possibilities.  Even within the confines of English alone the relative independence of form and function can be made obvious.  Thus, the negative idea conveyed by un- can be just as adequately expressed by a suffixed element (_-less_) in such a word as thoughtlessly.  Such a twofold formal expression of the negative function would be inconceivable in certain languages, say Eskimo, where a suffixed element would alone be possible.  Again, the plural notion conveyed by the _-s_ of reformers is just as definitely expressed in the word geese, where an utterly distinct method is employed.  Furthermore, the principle of vocalic change (goose—­geese) is by no means confined to the expression of the idea of plurality; it may also function as an indicator of difference of time (e.g., sing—­sang, throw—­threw).  But the expression in English of past time is not by any means always bound up with a change of vowel.  In the great majority of cases the same idea is expressed by means of a distinct suffix (die-d, work-ed).  Functionally, died and sang are analogous; so are reformers and geese.  Formally, we must arrange these words quite otherwise.  Both die-d and re-form-er-s employ the method of suffixing grammatical elements; both sang and geese have grammatical form by virtue of the fact that their vowels differ from the vowels of other words with which they are closely related in form and meaning (goose; sing, sung).

[Footnote 26:  For the symbolism, see chapter II.]

[Footnote 27:  “Plural” is here a symbol for any prefix indicating plurality.]

Every language possesses one or more formal methods or indicating the relation of a secondary concept to the main concept of the radical element.  Some of these grammatical processes, like suffixing, are exceedingly wide-spread; others, like vocalic change, are less common but far from rare; still others, like accent and consonantal change, are somewhat exceptional as functional processes.  Not all languages are as irregular as English in the assignment of functions to its stock of grammatical processes.  As a rule, such basic concepts as those of plurality and time are rendered by means of one or other method alone, but the rule has so many exceptions that we cannot safely lay it down as a principle.  Wherever we go we are impressed by the fact that pattern is one thing, the utilization of pattern quite another.  A few further examples of the multiple expression of identical functions in other languages than English may help to make still more vivid this idea of the relative independence of form and function.