It is well to recall that all languages must needs express radical concepts (group I) and relational ideas (group IV).  Of the two other large groups of concepts—­derivational (group II) and mixed relational (group III)—­both may be absent, both present, or only one present.  This gives us at once a simple, incisive, and absolutely inclusive method of classifying all known languages.  They are: 

A. Such as express only concepts of groups I and IV; in other words, languages that keep the syntactic relations pure and that do not possess the power to modify the significance of their radical elements by means of affixes or internal changes.[110] We may call these Pure-relational non-deriving languages or, more tersely, Simple Pure-relational languages.  These are the languages that cut most to the bone of linguistic expression.

B. Such as express concepts of groups I, II, and IV; in other words, languages that keep the syntactic relations pure and that also possess the power to modify the significance of their radical elements by means of affixes or internal changes.  These are the Pure-relational deriving languages or Complex Pure-relational languages.

C. Such as express concepts of groups I and III;[111] in other words, languages in which the syntactic relations are expressed in necessary connection with concepts that are not utterly devoid of concrete significance but that do not, apart from such mixture, possess the power to modify the significance of their radical elements by means of affixes or internal changes.[112] These are the Mixed-relational non-deriving languages or Simple Mixed-relational languages.

D. Such as express concepts of groups I, II, and III; in other words, languages in which the syntactic relations are expressed in mixed form, as in C, and that also possess the power to modify the significance of their radical elements by means of affixes or internal changes.  These are the Mixed-relational deriving languages or Complex Mixed-relational languages.  Here belong the “inflective” languages that we are most familiar with as well as a great many “agglutinative” languages, some “polysynthetic,” others merely synthetic.

[Footnote 110:  I am eliminating entirely the possibility of compounding two or more radical elements into single words or word-like phrases (see pages 67-70).  To expressly consider compounding in the present survey of types would be to complicate our problem unduly.  Most languages that possess no derivational affixes of any sort may nevertheless freely compound radical elements (independent words).  Such compounds often have a fixity that simulates the unity of single words.]

[Transcriber’s note:  Footnote 110 refers to the three paragraphs beginning on line 2066.]