even customarily, be used as a word.  Thus, the hort- “garden” of such Latin forms as hortus, horti, and horto is as much of an abstraction, though one yielding a more easily apprehended significance, than the _-ing_ of singing.  Neither exists as an independently intelligible and satisfying element of speech.  Both the radical element, as such, and the grammatical element, therefore, are reached only by a process of abstraction.  It seemed proper to symbolize sing-er as A + (b); hort-us must be symbolized as (A) + (b).

[Footnote 1:  We shall reserve capitals for radical elements.]

[Footnote 2:  These words are not here used in a narrowly technical sense.]

So far, the first speech element that we have found which we can say actually “exists” is the word.  Before defining the word, however, we must look a little more closely at the type of word that is illustrated by sing.  Are we, after all, justified in identifying it with a radical element?  Does it represent a simple correspondence between concept and linguistic expression?  Is the element sing-, that we have abstracted from sings, singing, and singer and to which we may justly ascribe a general unmodified conceptual value, actually the same linguistic fact as the word sing?  It would almost seem absurd to doubt it, yet a little reflection only is needed to convince us that the doubt is entirely legitimate.  The word sing cannot, as a matter of fact, be freely used to refer to its own conceptual content.  The existence of such evidently related forms as sang and sung at once shows that it cannot refer to past time, but that, for at least an important part of its range of usage, it is limited to the present.  On the other hand, the use of sing as an “infinitive” (in such locutions as to sing and he will sing) does indicate that there is a fairly strong tendency for the word sing to represent the full, untrammeled amplitude of a specific concept.  Yet if sing were, in any adequate sense, the fixed expression of the unmodified concept, there should be no room for such vocalic aberrations as we find in sang and sung and song, nor should we find sing specifically used to indicate present time for all persons but one (third person singular sings).

The truth of the matter is that sing is a kind of twilight word, trembling between the status of a true radical element and that of a modified word of the type of singing.  Though it has no outward sign to indicate that it conveys more than a generalized idea, we do feel that there hangs about it a variable mist of added value.  The formula A does not seem to represent it so well as A + (0).  We might suspect sing of belonging to the A + (b) type, with the reservation that the (b) had vanished.  This report of the “feel”