Notes

¹ Maher (1966:9, note 3) names several works perpetuating the myth of a Darwinian linguistics; his inclusion of Greenberg 1957 is questionable.

² In a letter from Darwin to Lyell, dated September 23, 1860 (Francis Darwin 1888:341-344), there appears an upside-down version:

³ Chomsky and Halle (1968:295) are aware that such feature classes are "intersecting categories," though the redundancy rules inferred from the usual nonconverging feature hierarchy in works such as Chomsky 1965 do not appear to reflect this awareness.

⁴ This blending of two different theoretical statements about the same data is hinted at in Chomsky and Halle's distinction, for phonetic features, between a "classificatory function" and a "phonetic function" (1968:298). In the former, features are class-names and therefore abstract, and it is only in this use that their values are restricted to binary; in the latter, features correspond to aspects of phonetic reality and admit of n-ary gradations in value. Clearly, the fusion of these two uses is involved in the problem of lexical-feature hierarchy discussed above: it seems likely that the hierarchy imposed on feature-classes by reading down the tree belongs to the first, or abstract, use, while the redundancy rules or implicational relations to be got from the tree by reading up belong to the second, or practical use.

⁵ Allen (1953:8) draws a distinction between a syllabic "method of writing" and the essentially phonemic analysis "underlying it and actually set out ... in the varṇa-samām- nāy a.

⁶ Jespersen's an(t)alphabetic notation (1889) will not be considered here. The matrix does not appear in it, perhaps because the characters are concatenations rather than unit symbols, making a tabular arrangement unwieldy..

⁷ Conflation arrangements (as opposed to actual diagrams) of inflectional paradigms are often found in pedagogical grammars and are of long standing; see for instance Whitney's Sanskrit grammar, first published in 1879 (Whitney 1889). Such arrangements are arrived at by shifting the case endings for each paradigm until the result is blocks of like ending as in Jakobson1s diagrams.

⁸ Classification even along a continuum is difficult. For a notion of the model as central, see Black 1962, Campbell 1921, Hesse 1966, Toulmin 1953; for a notion of the model as peripheral, see Braithwaite 1953, Hesse's (1966) discussion of Duhem, and perhaps Nagel 1961. Lachman's (1963: 79-83) classification of the uses of models is evidence that all of these views are useful at one time or another.

⁹ With regard to whether the analogizing consists in illuminating the unfamiliar by comparing it with the familiar, or vice versa--a debate not to be pursued here--see Campbell (1921:84), Nagel (1961:107), Rosenblueth and Wiener (1945:317) versus Black (1962:233), Toulmin (1953:20). "Familiar" and "unfamiliar" are, after all, relative: the relation of material analogy remains the same whichever view is taken. Of the various types of models little need be said beyond the fact that this work deals with neither "physical" (or scale) models nor "formal" (or mathematical) ones. It is difficult to choose a name for the type of model it does deal with, variously termed "symbolic," "material," and "analogue." The subject of types of models is pursued in Beckner (1959: 33-36, 52-53), Black (1962:222-229), Chapanes (1963:109-110), Kaplan (1964:266-268), and Rosenblueth and Wiener (1945:317).

¹⁰ The difference is one of emphasis, reflecting the degree of concern about possible abuse of the model, either by choosing a poor one or by letting it usurp the place of the theory (Braithwaite 1953:93-96). Black (1962:236), Campbell (Hesse 1966:3-4, 98-99), Kaplan (1964:274-275), Kuhn (1962:184), Nagel (1961:112) , and Toulmin (1953:37-39) agree on these two functions, though their terminology differs.

¹¹ Extension and development correspond to the two directions suggested in the philosophy of science for the influence of the model on scientific theory; see Black (1962: 228-229, 241), Hesse (1966:98-99), Kaplan (1964:274-275), Kuhn (1962:24), Nagel (1961:112-114), Toulmin (1953:39).

¹² The reference in transformational theory of the term "extraposition" to the tree diagram itself is clear by contrast with Jespersen's use of the term. While Jespersen defines "extraposition" with reference to sentences--"a word, or a group of words, is placed, as it were, outside the sentence as if it had nothing to do there," as in As to an Abyssinian victory, that is out of the question (1937:35)--transformationalists define it with reference to the figure, as the placing of a group of constituents, usually an embedded sentence, on the outside (the extreme right-hand side) of the diagram.

¹³ All of these transformation-types are to be found in Stockwell, Schachter, and Partee (1973), as well as elsewhere in the literature.

¹⁴ Compare Lyons (1968:155-156) for a discussion of the meaning of "generative" as (1) "predictive;" and (2) "explicit."

¹⁵ Pruning has become a widely-accepted theoretical modification, not only for transformational-generative theoryper sebut also for other grammatical theories, such as dependency grammar: Robinson (197Ob:282), for instance, proposes a revised S-pruning convention.

¹⁶ Transformational-generative grammar is not, of course, the only theory current in linguistics to draw its terms from the model or from a metaphor attached to the model. Stratificational grammar, for example (the very name of which reflects a geological metaphor), employs terms like "knot pattern" that reflect what goes on graphically, in the diagrams (Lamb 1966). Other grammatical theories that make use of transformations tend also to name them from the figure--for example, the "infrajection" transformations of case grammar (Fillmore 1968:23, n. 29), the "raising" transformations of dependency grammar (Anderson 1971b).

¹⁷ The art elements go by different names, and not all treatments include them all. Kepes (1944:23) lists point, shape, line, position, color, value, texture; Anderson (1961), only line, shape, texture, color, and motion. Klee (1961:76) gives the "formal elements of graphic art" as simply "points, and linear, plane, and spatial energies."

¹⁸ The works of Anderson (1961), Kepes (1944), Klee (1961), and Scott (1951) are general treatments. More specific treatments, handbooks of graphic design and graphic designers1 manuals, are concerned with typography or with the application of design principles to advertising. It seemed best, therefore, to consult general works and construct from them a "handbook" for graphic representation in linguistics.

¹⁹ The principle of iconic relations is one of Chao's "ten requirements for good symbols" (1968:210-227); the others, applying chiefly to unit symbols such as orthographic characters, are not useful for our purposes.

²⁰ We shall leave Reed-Kellogg diagrams out of the discussion that follows. They defy classification, because they are, in both form and meaning, so very complicated. Their form is an elaborate code in the shape and slant of lines; their meaning comprises not only constituent analysis but also constituent function, and encompasses simultaneously deep and surface structure.

²¹ Though Robinson (1970b:260) asserts that Tesnière's is a dependency grammar, it differs somewhat from other versions of dependency grammar such as those of Anderson (1971b), Fillmore (1968), and Robinson. As these latter are more explicit regarding the reading of tree diagrams, the discussion that follows draws largely on them.

²² Dependency grammar has various theoretical affinities: with transformational-generative grammar (both employ phrase-structure rules and transformations); with tagmemics (Fillmore [1968:88] notes the ease of conversion between a dependency grammar and the slot-filler notion of tagmemic theory); with Reed-Kellogg school grammar (both are concerned to express notions of grammatical function--modification and government--and Reed-Kellogg diagrams are graphically the literal expression of slot and filler). It is important to note, however, that these are affinities of theory--of notions and concepts—rather than affinities of representation. Reed-Kellogg diagrams and tagmemic notation especially have little in common graphically with dependency trees.

²³ In Fillmore's original formulation (Fillmore 1968) of case grammar, it was by no means clear that the vertical dimension of his tree was to be construed as dependency; Robinson (1970a:64) substantiates Fillmore's suspicion that his base rules "mix categorical notions with relational (functional) ones in a way that Chomsky sought to avoid by defining functions in terms of configurations of categories, rather than by directly labelling them." Fillmore himself finally suggested a dependency reading for trees in case grammar and an alternative design for the tree so read. Since the case categories may well be, in actual function, simply " labels on the branches that link Ρ with the various NP's [italics his],11 then "one may just as well represent these relationships more directly by replacing the node Ρ by the V" (87) --as in the diagrams of dependency grammar in general.

²⁴ This need not necessarily mean lengthier constructions; for more complex notions of modification, more complex diagrams--for example,

²⁵ It should be noted that the mathematics here is of the most rudimentary sort: it is touched on at all only in order to illuminate the graphic nature of what we have been calling tree diagrams. There are treatments of graph theory and applications of these and other mathematical concepts to some of the representation used in linguistics (see, for instance, Zierer 1970). This book is not intended to replace them, but rather to approach the subject of linguistic representation from another angle--as the source of non mathematical models for linguistic science--and with another set of tools--the concepts of the philosophy of science and the principles of graphic design.

²⁶ Jespersen uses a directed graph as early as 1937:

(Jespersen 1937:121)