Tree diagrams

Provenience

The tree was introduced into linguistics by August Schleicher, whose Die deutsche Sprache, published in 1860, contains three linguistic Stammbäume (Maher 1966:7). Schleichers figure is a schematic tree:

(Schleicher 1888:82)

But if Schleicherזs tree is the prototype for the tree in linguistics, what is its own prototype?

Tree-like representation is of great age. Sometimes stylized, sometimes realistic, trees illustrate in medieval scholastic philosophy all kinds of taxonomies. Thus we find a tree for the seven liberal arts, grouping them into the Trivium and Quadrivium; a tree of virtues and vices, embellished with medallions. Not only taxonomie but also genealogical trees appear well before the nineteenth century--at least as early as the eighteenth (Barnes 1967:114). Most such early trees look like this one:

(Ong 1958:78)

But though we can say with certainty that tree-like representation of taxonomy and genealogy goes back well beyond Schleicher's day, we cannot with equal certainty see in it the direct ancestor of Schleicher's tree. For this we must consider three possibilities: tree diagrams in evolutionary biology; tree diagrams in human genealogy; and manuscript stemmata.

Greenberg (1957) , Hoenigswald (1963), and Mäher (1966) agree that the source of Schleicher's tree is not the one most often supposed, Darwinian evolutionary biology. The myth of a Darwinian linguistics originated with Schleicher himself (Hoe-nigswald, 6). So taken was he with the Origin of Species that in 1863 he wrote Die Darwinische Theorie und die Sprachwissenschaft, drawing a parallel between biological and linguistic evolution. Recapitulation by students of linguistics¹ magnified the resemblance until, by a sort of simile-huic-ergo-propter-hoc reasoning, Schleicher's tree appeared to be an offshoot of Darwin's.

This in itself of course does not disqualify Darwin's tree as the direct ancestor of Schleicher's. A more serious objection (Maher, 7) is that Die deutsche Sprache appeared a scant year after the Origin of Species. It is unlikely, therefore, that Schleicher knew Darwinian evolutionary theory before he formed his own theory of linguistic evolution. And in fact, the earliest version of Schleicher's tree appeared in 1853, well before the Origin of Species :

(Schrader 1883:69)

According to Schräder (1883 : 68), Schleicher called this earliest version a "'sich verästelnde Baum.'" Though not yet a "Stammbaum" (Schleicher did not christen his figure until 1863, in Die Darwinische Theorie und die Sprachwissenschaft), it conveys the same relationships as the tree from Die deutsche Sprache reproduced above. It simply replaces the letters standing for such hypothetical linguistic unities as Slavogermanen (b in the later version) and Lettoslaven (c in the later version) with the names for them. Schleicherfs use of the tree diagram to express linguistic evolution thus definitely antedates Darwin?s use of it to express biological evolution.

But the Origin of Species was not the débuteither of evolutionary biology or of the tree diagram. The first appearance of tree diagrams for evolutionary biology was probably in Lamarck's Philosophie zoologique (Simpson 1961:62). Lamarck's and Darwin's diagrams (given on the following pages) differ only slightly in form--Lamarck!s version is upside down ; Darwin's is not² -- and not at all in meaning: Lamarck (1809:462־ 464) and Darwin (1859:116-125) invest the figure with the same meaning, that of change through time. That Darwin's tree is not much earlier than Schleicherזs, then, does not mean that Schleicher's tree was not drawn from evolutionary biology. A tree that translated the meaning of change through time--the phylogenetic meaning -- had been in currency for nearly half a century by the time Schleicher's tree appeared.

The second possible source for Schleicher's tree, tree diagrams in human genealogy, is at least as likely as the first. For one thing, trees, as we have said, had been for centuries a common shorthand for the concept of genealogy; for another, the metaphor accompanying Schleicher's notion of linguistic evolution is that of human genealogy. Terms like "mother-," "daughter," and "sister-language" established this metaphor quite early in the development of Schleicher's theory, in Die sprachen Europas in

(Darwin 1859)

(Lamarck 1809:463)

1848 (Maher, 7). It is thus older than the figure itself. Moreover, it had already been employed as a metaphor for language history a century earlier by Leibniz (Maher, 8).

It may be, however, that human genealogy furnished the prototype for the tree diagram in linguistics only indirectly, through the agency of the third possible source, manuscript stemmata. An example is the following:

(Maas 1957:7)

In fact, both Hoenigswald (8) and Maher (8) claim this origin for the tree, pointing out that Schleicher, a pupil of Friedrich Ritsehl at Bonn, would have been trained in the construction of manuscript stemmata. Hoenigswald argues that Ritschl's theory of the construction of manuscript stemmata influenced the comparative method: the "doctrine of the shared error" is an instance.

Not much is to be gained from looking at the figures themselves. Direct inspection of the trees for historical linguistics, evolutionary biology, and textual criticism shows the greatest resemblance between Schleicher's later version and the one that appears in the Origin of Species. Both figures are right side up; both are highly stylized (compare Schleicher's earliest version; both mark junctures with Roman letters. A manuscript stemma, on the other hand, is upside-down and marks junctures with Greek letters. These differences, nevertheless, weigh little in the scales against the general similarity of the three figures in form and meaning. Moreover, neither the metaphor of evolutionary biology nor that of human genealogy can be finally discounted, for both have influenced the course taken by the theory of linguistic evolution since Schleicher.

Meaning

Dangerous as it is to divorce form from content, we must do so in the case of graphic representation in linguistics. Thus we shall consider first the form of tree diagrams: of what parts do they consist? How are the parts put together to form the whole? In doing so, it will of course be impossible to avoid speaking of meaning, but this is meaning of the most abstract sort--the very general meaning that attaches to the figure by virtue of the putting together of parts to form a whole. This is not the same thing as the meaning of a particular tree diagram--the message with which the figure is invested in a given instance, the statement it makes about a given set of data. That, as we shall see, is a different matter.

The graphic elements of a tree diagram are the vertical and horizontal dimensions--given by the medium itself--and nodes and branches. Vertical and horizontal have, respectively, paradigmatic and syntagmatic import: things arranged along the vertical dimension are mutually exclusive; things arranged along the horizontal dimension are not. Thus the units on the vertical axis are those that do not occupy the same time or space; the units on the horizontal axis are not subject to this restriction. If the latter are defined negatively, this is because what they are not is more significant than what they are, in terms of the structure imposed on the data by the tree diagram; units on the horizontal dimension are defined by the fact that they do not participate in the mutual exclusivity which characterizes units on the vertical dimension.

We have analyzed the form of tree diagrams into

Superimposed on this is the combination of node and branch, which gives the figure its inherent directionality. It has a beginning and an end, and these remain the same however the figure is set on the page, whether it is left-- to-right, top-to-bottom, or the reverse: one starts with the stem (the undominated node) and reads out to the bushiest part. The tree is always divergent, never convergent. Thus the meaning of node and branch is former unity--former, because the unity that exists somewhere in time or space (a node) is explicitly said not to exist somewhere else in time or space (the branches). So

says that something splits in two under conditions left to be stated.

Clearly, then, the basic, the most abstract, meaning of the tree leaves room for variation in meaning for given instances of the figure. Not only does the figure necessarily leave unstated the conditions under which its statement about the data holds; it is also unspecified for the domain of its application. For time and space may be variously construed. Is time, for instance, historical time, or conceptual time (as in morphological "processes")? Is space geographical space, or conceptual space (as in taxonomy)? It is true that the basic meaning of a figure to some extent circumscribes the possible meanings it can take on--to some extent sets limits to its mutability. Nevertheless, it is possible to distinguish between meanings that are a good fit for a figure and meanings that are not. The tree in linguistics bears (independent of purely graphic variation, like squared versus slanting branches) at least four meanings: genesis, taxonomy, componential analysis, and constituent analysis.

Genesis

Chronologically, the primary meaning of tree diagrams is, as we have seen, genetic. The genetic meaning construes the graphic elements of the figure in the following way. The vertical dimension represents time (Simpson 1961: 62)--"real" time, that is, historical time, time through which change occurs. Units on the vertical axis are therefore things that succeed each other in time; they are mutually exclusive with respect to time. Conversely, units on the horizontal axis are things that occupy the same time, that are not mutually exclusive with respect to time. To put units on the same horizontal says of them nothing more than that they do not succeed each other directly. The horizontal expresses not necessarily temporal identity--simultaneity--but temporal nondistinctness. The tree can be factored into what Schleicher happily named the Nebeneinander and the Nacheinander (Maher, 5); from a genetic tree we can read both the succession of stages (the vertical axis: the Nacheinander) and the array of entities at any single stage (the horizontal axis: the Nebeneinander). Schleicher put it this way:

(Schleicher 1888:59)

The combination of node and branch superimposed on that of vertical and horizontal expresses former unity; for the genetic tree, "former" is to be taken literally, as earlier in time. Branches then represent subsequent divergence, and the aggregate of branches f rom a single node constitutes the whole set of its descendants. Branches from a common node are more closely related to each other than to those farther off; thus

(Bloomfield 1933:312)

says (among other things) that Indie and Iranian are more closely related to each other than to any of the other languages, and so too Slavic and Baltic, each pair having passed through a period of unity.

The meaning of the whole figure, then, is the phylogenetic meaning: the development of a set of related entities by means of change through time. Besides the static meaning conveyed by the configuration of node and branches, the genetic tree has a dynamic meaning: the figure has a starting point and proceeds in one direction. The import of its dynamism is "time״ ; but it is , in Bronowski's words (1969:83),

not a forward direction in the sense of a thrust towards the future, a headed arrow. What evolution does is to give the arrow of time a barb which stops it from running backward.

This dynamism is often the focus of modified versions of the genetic tree--what might be called "details" from the whole figure--like those of Bloomfield :

(Bloomfield 1933:312)

and Trager and Smith:

(Trager and Smith 1950:64)

They are offshoot diagrams: at any given stage, only one entity occurs. Nowhere is there a set of two or more entities occupying the same horizontal, so that there is nothing that might properly be called the Nebeneinander. They focus on the Nacheinander--Bloomfield's on the successive stages in the development of a single language out of Indo-European, Trager and Smith's on the successive reduction of Indo-European as the daughter languages split off from it. If such offshoot diagrams have a destination--in Bloomfield's figure, English; in Trager and Smith's, Slavic-- it is something in the present or something already past, never something in the future. It is in this sense that Bronowski' s barbed arrow is appropriate.

Taxonomy

Related to the genetic meaning of tree diagrams is the taxonomie meaning. Because the graphic elements of the tree are construed differently for the two meanings, however, they are only related, not identical. The vertical dimension in a taxonomie tree diagram signifies not time, but space: points along the vertical axis represent not stages in the development of a language family out of a single parent language, but stages in the successive partitioning of a set. Units on the vertical axis are things that succeed each other in space--the conceptual space furnished by the set that is being partitioned--just as in a genetic tree diagram units on the vertical axis are things that succeed each other in time. They are in paradigmatic relation to each other, mutually exclusive with respect to space. Conversely, units on the horizontal axis are things that occupy the same space, that are not mutually exclusive with respect to space, that are in a syntagmatic relation. An example is Pike?s taxonomy of continuants :

(Pike 1943:142)

Frictionals and Nonfrietionals, a syntagmatic pair, share the same space--a space from which they have dislodged Continuants, so that the pair Frictionals/Nonfrictionals is in a paradigmatic relation with Continuants.

The graphic elements of node and branch set the boundaries of the relations among units. As in a genetic tree, branches from a common node are more closely related to each other than to those farther off; in a taxonomie tree this is proximity not in time but in space, and branches from a common node define subsets. In the example given above, for instance, Frictionals and Nonfrictionals are proper subsets of the set of Continuants, and together they exhaust the set.

We can restate our analysis of the taxonomie tree in terms of set theory. The set-theoretic definition of a taxonomy (Gregg 1954:47-51) is:

1. It is a hierarchy

2. It is a one-many relation

3. It has a "unique beginner"

4. No unit is equal to that dominating it

5. No two levels have members in common

6. It is an asymmetrical relation

7. It is an irreflexive relation

8. It is an intransitive relation

9. For any two members of its field, either y includes x, or x includes y, or they are mutually exclusive

10. ״The converse of a taxonomie system is never a taxonomie system"

Perhaps it will be useful to translate these theorems back into graphic terms. The first four theorems are implicit in our interpretation of the combination of node and branch. The tree figure is hierarchical by virtue of branching, which gives it a beginning and an end. A one-many relationship is what branching from a single node is. By definition the tree figure has a unique beginner--that is, it starts from a single node and is divergent, not convergent. No unit is equal to that dominating it, because a node, if it branches at all, must necessarily give way to two or more nodes. The fifth, sixth, seventh, eighth, and tenth theorems are implicit in our interpretation of the vertical dimension in the tree. Because units succeed each other along the vertical dimension, no two points on it can have members in common; nor can succession, by definition, be either symmetrical (two units each succeeding the other) or reflexive (a unit succeeding itself). Transitivity is not ruled out by definition; but if two units separated by a third are seen, in accord with the notion of hierarchy, as linked only through that third intervening unit, then transitivity too is impossible. And, of course, the converse of a taxonomie system cannot be a taxonomic system, for the tree proceeds in one direction and cannot be read backwards.

It is the ninth theorem, which states the admissible relations among units on the horizontal dimension, that is troublesome for the taxonomic tree in linguistics. We can interpret this theorem, following Kay (1970), in terms of Venn diagrams; for the admissible relations between taxa :

(Kay 1970:8)

for the prohited relation:

(Kay 1970:9)

Taxa--whether they are nodes or terminal elements--can be related in one of two ways. Either they participate in the paradigmatic relation, which we have defined as the vertical dimension, so that for any two units one is a proper subset of the other (the first two Venn diagrams above); or they participate in the syntagmatic relation, which we have defined as the horizontal dimension, so that any two units are wholly separate (the third Venn diagram). What they may not do is participate at once in both the paradigmatic relation and the syntagmatic relation. They may not constitute intersecting classes.

What about the taxonomie tree in linguistics? Here the definition of admissible relations among taxa becomes a problem. Compare B100mfieldfs (1933: 205) classification of nouns in English,

 I. Names (proper nouns)

II. Common nouns

 A. Bounded nouns

 B. Unbounded nouns

 1. Mass nouns

 2. Abstract nouns

with Chomsky's "subcategorization" of them:

(Chomsky 1965:83)

Taxonomie trees in linguistics usually fail the requirement that classes not overlap. Because the feature [± Animate] appears at more than one node, Chomsky's subcategorization shows four intersecting taxa :

That is, some common nouns denote animate objects, and some do not; some proper nouns denote animate objects, and some do not. Though this is clearly an accurate statement, it is not a proper taxonomy. B100mfieldfs classification is . It yields a taxonomic tree in which no feature appears at more than one node and in which, therefore, no classes overlap :

Pike proposes, as an alternative to the taxonomy of continuants we have looked at, a tree that fail the same requirement as Chomsky's subcate-gorization of nouns:

(Pike 1943:142)

He thereupon presents a dendrogram that faces in two directions at once:

(Pike 1943:144)

By representing his classification by a sort of Rorschach tree, Pike avoids putting features at more than one node; but overlapping classes are to be inferred--for instance,

It seems, then, that linguists do not follow a set theoretic definition of taxonomie classification. This is to be inferred from their graphic representation. Pike's Phonetics ,for example, is probably the most explicitly taxonomie of modern linguistic treatments; yet the meager taxonomy we looked at in the beginning of this section is the only diagram we have considered from it that is a proper taxonomy. Nida (1964:74) explicitly allows overlapping classes. Though there exists a taxonomic meaning for the tree, then, tree diagrams presented as taxonomies are often something else.

Hence the difficulty presented, for transformational grammar, by tree diagrams for feature hierarchies: because linguistic taxonomy allows overlapping feature-classes, the desired relations of implication that hold among features are not, as is often held, to be automatically and unambiguously inferred. The contention is that reading up the tree reflects logical implication. Yet this is true only for the left-hand branches in a semantic feature hierarchy like the one below:

(Bever and Rosenbaum 1970:6)

Thus [+Human] implies [+Animate] implies [-Plant]; but [-Human] does not necessarily imply [+Animate], nor does [-Animate] necessarily imply [-Plant]. What has gone wrong here is that these features name what are in reality, logically and semantically, overlapping classes.³ The class named by [-Animate], for example, embraces not only some of the members of the class [-Plant] , but also all of the members of the class [+Plant] and all of the members of the class [-Human]. Similarly, the class named by [-Human] embraces not only some of the members of the class [+Animate] but also all of the members of the class [-Animate] and all of the members of the class [+Plant].

Componential analysis

Trees expressing componential analysis look in every way like their fellows; but they do not mean the same thing. Like Chomsky1s subcategorization of English nouns, the lexical entry for bachelor applies features ([±Male] and [±Young]) at more than one node (see following page). It is a simple matter to make the figure conform to the criteria for taxonomy by reordering the features :

(Katz and Postal 1964:14)

To do so solves nothing, however, because the meaning of lexical entries is not taxonomy. Lexical entry and taxonomy are not synonymous.

The meaning of trees expressing componential analysis is in a sense the opposite of taxonomy. These trees are what are called ״keys" in biology and anthropology (Conklin, 1964 and personal communication). A key sets out a componential analysis of the units that are its terminal elements, an analysis in which the components are distinctive features. This is a schematic version of a key:

(Simpson 1961:52)

Here the analysis of units Լ₁ - L₈ is given in terms of the distinctive features a1, 2, b1,2, and c1,2--equivalent to [±a] , [±b] , [±c] . The element Լ1 is analyzed as [a1, b1,c1] , the element L2 as [a1, b2, c2] , and so on. The beginner, d, is a dummy feature; it is not distinctive within the analysis, but simply defines the whole set Լ₁- L₈. The lexical entry tree forbachelor is actually a telescoped version of the following key:

Chomsky's subcategorization of nouns--because it violates the set-theoretic restriction on overlapping classes-- is also a telescoped version of a key:

The sequence of features along the vertical is the same for the original diagrams as for the full keys, and so is the sequence of terminal elements along the horizontal. The original diagrams are telescoped in comparison with the full keys in the sense that elements along both dimensions are omitted.

We can call the diagrams both of Katz and Postal and of Chomsky keys, because both construe the graphic elements of the tree in the same way as keys. Keys, like taxonomie trees, construe the vertical dimension as conceptual space, within which a set is successively partitioned; keys, like taxonomie trees, construe the combination of node and branch as set and subsets. But whereas taxonomic trees do not--or should not--allow overlapping classes, keys require them. A full key has them on every row; a telescoped key like the ones we have been looking at usually has at least some. Because of this, keys lack the directionality of genetic and taxonomie tree diagrams. In a full key, every terminal element is specified for every feature. Whether we read from top to bottom or bottom to top makes no difference. The analysis of each terminal element comes out the same: to say that Լ₁ = a₁ + b₁ + с₁ is the same as saying that a₁ + b₁ + c₁ = Լ₁. It is only the figure, as a graphic design, that has directionality; the meaning of componential analysis as expressed in a key has none. The fact that directionality is inherent in the design of tree diagrams lets the key incorporate a hierarchy of features. The sequence of features in the lexical entry for bachelor, for instance, is the sequence in which, according to this semantic theory, these features are hierarchically arranged; but as Simpson (1961 : 55) points out, this order "is derived from the corresponding hierarchic classification and is not inherent in the key as such."

So it is that reordering the features on the tree for bachelor is useless. For one thing, the order in which features occur is fixed; for another, it is only accidental that the tree for bachelor converts to a true taxonomy. The subcategorization of English nouns that we looked at earlier, having overlapping classes, does not. And it is unimaginable for, say, Halle's key for the sounds of Russian:

(Halle 1959:46)

Yet the problem for linguistics is even more complicated than this: beyond the confusion that results from employing the same diagram to represent the two different meanings of taxonomy and componential analysis, there is the confusion that results from employing the same features for the names of both taxa and components. The difficulty of drawing all and only the proper inferences regarding implicational relations among feature-classes from such a tree as the one from Bever and Rosenbaum discussed above--a difficulty that follows from allowing overlapping classes-- is compounded by this confusion. It is therefore only partially solved by representing the classi- fication as what it properly is in componential- analysis terms, a key--with blank spots where inadmissible feature-combinations occur :

Such a representation is only a partial solution precisely because of the confusion, both graphic and terminological, of taxonomy and componential analysis: what is intended, what is in fact desired here, is a blending of the two. For linguistics, it must be possible to read off from such a tree not only an artificial, analysis-imposed classification--a taxonomy--that ignores the practical reality of overlapping classes, but also simultaneously an accurate statement of the implicational relations that hold among the criteria for classification--the components--for any given single instance of real analysis.⁴ We shall reserve a more detailed discussion of this problem for a later consideration of the possibility of representing graphically such a double meaning.

Constituent analysis

This might more properly be called immediate constituent analysis (1С analysis). An example is the following, a tree for 1С analysis at the level of the sentence:

(Chomsky 1957:27)

Analysis of the graphic elements in each of the other three kinds of tree diagrams showed their meanings to be related. Taxonomy results from, and often recapitulates, phylogeny; componential analysis implies a prior taxonomy (that is, a hierarchical classification of the features employed). The first three meanings are thus related in a sort of chain. Constituent analysis, however, stands apart from this chain. It has in common with the others only the basic meaning of the tree design itself.

The vertical dimension expresses succession; not succession in time or space, but simply succession. In the example above, NP, for instance, gives way to Τ and N; VP gives way to Verb and NP; and so on. The relation expressed by the combination of node and branch is thus to be read, not "becomes" (as in a genetic tree), nor ״includes" (as in a taxonomie tree), nor Mis divided into" (as in a key), but simply "may be replaced by.?f This is the technique of immediate constituent analysis itself: it is the process of substitution. (The reading of "becomes" that is attributed to the vertical dimension of the tree in generative grammar is a misreading. It results from misconstruing the meaning of the tree as something other than constituent analysis-- usually as "generative process" or speech production. The meaning of tree diagrams of sentences in generative grammar is substantially the same as in structural linguistics: description, not production [Chomsky 1965:9], the description of a sentence in terms of its constituents.) The horizontal dimension of trees for constituent analysis expresses syntagmatic relatedness; in the example above, Τ and N form one syntagm, Verb and NP another, and so on. Units in the same row are not mutually exclusive, not substitutable one for another. In 1С trees, then, the significance attributed to the vertical and horizontal dimensions adds nothing to the expression of hierarchy already conveyed by the combination of node and branch.

Node and branch also express constituent function (Chomsky 1965:68-74). The difference between Subject and Object, for instance is conveyed by

The figure entails this difference: it is automatic.

There is a further difference between 1С trees and other kinds, and that is the fact that no units need appear at the nodes of the tree.

(Nida 1966:21)

Here, just as in the first example, the meaning is immediate constituent analysis. Its expression is unhampered by the lack of category symbols like NP, VP, and so on; which terminal units are constituents of which constructions at which level is quite clear.

The four meanings of tree diagrams, then, are genesis, taxonomy, componential analysis, and constituent analysis. Even the modest collection of diagrams we have accumulated here shows the existence of homonymy for graphic representation in linguistics :