¹ I am indebted to Rulon S. Wells for several valuable discussions of this paper, and to C. F. Voegelin and Bernard Bloch for helpful criticisms. In view of the fact that methods as mathematical as the one proposed here have not yet become accepted in linguistics, some apology is due for introducing this procedure. However, the advantage which may be gained in explicitness, and in comparability of morphologies, may offset the trouble of manipulating the symbols of this procedure. Furthermore, the proposed method does not involve new operations of analysis. It merely reduces to writing the techniques of substitution which every linguist uses as he works over his material. One works more efficiently when one thinks with pencil and paper.

² And, of course, phonemic constituents of suprasegmental ‘morphemes’ (if we wish to call them that), e.g. stress, intonations, and pauses.

³ The conditions may be phonemic or morphological.

⁴ In effect, such a treatment of concord takes some of the features of selection, e.g. the fact that all nouns in the Hebrew phrase agree as to the article, and puts these facts into the phonemic form of the repeated morpheme. As a result, not only the physical recurrence of a repeated phoneme, but also its special position (e.g. before every noun of the phrase), is now given when we describe that morpheme. Such treatment permits a simpler syntactic statement, because the information about the recurrence of the repeated morpheme would otherwise have to be given somewhere in the course of the syntactic description. The syntactic equations to be offered below will suffice to describe what morphemes occur together and in what order, but will not be able to describe conveniently the agreements among the morphemes in a sequence. To do so would require various devices; e.g. instead of writing N N (N for noun), we would have to write something like ^haN^haN, meaning that we can have either NN or haN haN but not haNN. Hence it is preferable to get as much of this information out of the way as possible before we attack the sequences. Not only the obvious cases of repeated morphemes but also more complicated types of agreement can be stated as being merely the special forms of particular morphemes. For further discussion of this treatment of repeated morphemes as single morphemes, see Lang. 21.121-7 (1945).

⁵ If poem and house are placed in one class N, overlooking the difference in their distribution, then write and, say, wire (I'm wiring a whole house this time) would be placed together in a class V since the distributional difference between them corresponds to that between poem and house. We would then obtain a statement connecting N and V. If we kept poem and house in separate classes, and write and wire in separate classes, we would obtain two statements, one connecting write and poem, and another connecting wire and house. These two statements together would equal the one statement about N and V.

⁶ The criterion which decides for -ing, and against un-, as the relevant environment in determining substitution classes is therefore a criterion of usefulness throughout the grammar, a configurational consideration. It will be seen below that the classes defined on the basis of -ing can be replaced by certain sequences of classes, which is not the case for any classes based on the un- environment. Special statements will have to be made later about the selection of un-, which in part will run across the boundaries of the classes set up on the basis of -ing, etc.

⁷ With variant -ren plus vowel change for plural -s.

⁸ This would give us a class V including cover, note, find, think, and a class N including cover, note, find, child. It would permit individual morphemes to be members of more than one class. Alternatively, we could put cover, note, find into a class G, think into V, child into N. Then each morpheme could only belong to one class, and morphemes having wider distributions, or having the distributions of two classes, would find themselves in a new class. Bernard Bloch uses yet another solution in his analysis of Japanese. He would regard the noun cover, which occurs in positions of N, and the verb cover, which occurs in positions of V, as two independent morphemes whose homonymy is syntactically irrelevant. That is, he uses class membership as a necessary condition for morpheme identity. Any of these methods of classification can be followed rigorously, and may be advantageous for particular purposes. Any one of them can be used in the method discussed below without affecting the final result.

⁹ Such substitutions as certainly for know John can be precluded by analyzing the utterance into immediate constituents. However, the analysis into immediate constituents requires a technique different from that used in this paper, a technique based on comparing the apparent structures of utterances and parts of utterances. In this paper, on the other hand, we seek to arrive at a description of the structure of an utterance, without having any prior way of inspecting these structures or of saying whether two utterances are equivalent in structure. Therefore., the analysis into immediate constituents is not used here, and we must state other methods of excluding such substitutions as certainly for know John.

¹⁰ This does not mean that every member of the class occurs in all the positions in which any other member occurs (fn. 5). A particular morpheme may occur in several classes (fn. 8). Some morphemes occur in two or more classes in the list below; cf. class-cleavage in Leonard Bloomfield, Language 204 (New York, 1933). The statement of the environments of each morpheme class given here is far from complete, and is merely sufficient to identify the class.

¹¹ In such expressions as the one I saw, a good one.

¹² If subdivisions are not recognized here they will have to be dealt with as special types of selection (§7.6).

¹³ We may include have and be in R in some environments, e.g. in relation to not: have not taken parallel to will not take as against don't get going. Note that when do, have, or be have -ing after them they are in the position of V, not of R.

¹⁴ There are special utterances like the here and now, but in general these limitations hold.

¹⁵ For the remaining morpheme classes of this type, the analogous statement of environment will not be made, since the class mark (-Na, Na-, etc.) is sufficient indication.

¹⁶ This is true only within the broad limits of what utterances frequently occur in the culture. There are also limitations when man is preceded by an adjective A (e.g. young man). There would then be two adjectives, the A of good boy, and the A of young man, which together should yield young good boy (A A N = A N = N). The conditions under which the two adjectives would occur next to each other in this way are mentioned in §4.32.

¹⁷ The standard procedure being as follows : since D A = A permits us to substitute D A for A wherever A appears, we write D A in place of the first A in this very equation: if D A = A, then D D A = A, i.e. D D A = D A = A.

¹⁸ We determine that it is A² rather than A ¹ in this equation by testing whether peculiar (A¹) can be replaced by older, oldish (A²). In constructing all these equations we may use either of two working procedures. One is to obtain a large amount of data, including many sequences which have the same environment as N ¹; we may then sort out, from among these, those sequences which consist of A followed by N, and see whether the A is always A ¹ or also sometimes A²: e.g. we see whether among the sequences having the same environment as senator we have not only peculiar fellow but also older fellow. The other procedure is to set up equations as working hypotheses, on the basis of whatever data we have, and then try various substitutions for each symbol in our equations, until we discover which symbols are mutually substitutable. Thus on the basis of He's a peculiar fellow we may write tentatively A N ¹ = N ¹. Then we would test to see if A is A ¹ or A ² by seeing if we can substitute older for peculiar and still get an English utterance. The two procedures are, of course, epistemologically equivalent.

¹⁹ See George L. Trager and Bernard Bloch, The Syllabic Phonemes of English, Lang. 17.228 (1941).

²⁰ When we have the stress pattern the medially-stressed morpheme is in class D: pretty young is D A in She's a pretty young girl to be out this time of night. It parallels very young in He's a very young fellow. The addition of emphasis stress, and other changes in the environment, complicate these stress statements. Exact statements will be necessary, however, since various morphemes (e.g. first) occur in both A and D.

²¹ V! can substitute for N V in many utterances: Come into the house! for He came into the house. Therefore V! can be considered as equalling N V, with the morphemic intonation ! substituting syntactically for N. This cannot be done for N!, since the stretch of speech immediately following N! has the complete intonation of an independent minimum utterance: John, why don't you come! Therefore N! too must be taken as an independent minimum utterance.

²² The position of this phrase in the sentence may be seen in II 5, p. 205, of R. H. Lowie, Z. Harris, and C. F. Voegelin, Hidatsa Texts (Indian Historical Society, Prehistory Research Series 1.6, May 1939), from which volume most of the Hidatsa examples given here have been taken. The analysis in §§5.1-3 is tentative.

²³ Ibid. II 31, p. 207.

²⁴ Ibid. I 49, p. 195.

²⁵ This is also done, in essence, by Bloomfield's class cleavage (Language 204), and by his functions of form classes (ibid. 196), which in essence provide for the syntactic equivalence of words and sequences of words (phrases). Needless to say, the whole procedure described here owes much to Bloomfield's method.

²⁶ It may be necessary to point out that this positional analysis is strictly formal, as compared with form-and-meaning analyses like the one in Otto Jespersen's Analytic Syntax (Copenhagen, 1937).

²⁷ Of course, from the formula N V we derive many sequences that occur: e.g. T A N V (The old order changeth) since T A N — N, and so on.

²⁸ Some of these limitations can be included by giving the signs more than one alternative value depending on the value of the other signs, somewhat as phonemic letters are given various allophonic values. We could say that after N ⁴, English V ⁴ has two values : simple V ⁴, and V ⁴ IV⁴. The utterance sequence N V could represent both N V and N V N (see §4.4). The more limitations of selection we wish to indicate by these equations, the more raised numbers we may need. This may not always be the case; but if we wished for example to indicate which noun stems occur with which -Nn suffixes we would require a long list of equations, involving several numerically differentiated resultant N's, before the first N ¹ -Nn = N ¹ equation of §4.3.

²⁹ Bloomfield, Language ch. 13. Note also Kenneth L. Pike, Taxemes and Immediate Constituents, Lang. 19.65-82 (1943), and the method of analysis used for Japanese by Bloch, Studies in Colloquial Japanese II, Lang. 22.200-48 (1946).

³⁰ Cf. also a comparable brief analysis of Kota in Lang. 21.283-9 (1945), based on the data supplied in M. B. Emeneau, Kota Texts, Part I (Berkeley and Los Angeles, 1944).

^30a In a private communication.

³¹ All members of V_f are also members of V_d: V_d are verbs which occur before N, V_f are verbs which occur before N N (as well as before N). Cf. §4.1.

³² We can check this by noting that if in the first V ⁴ we substitute a verb which is not a member of V_f, we get a sequence which hardly ever occurs, and whose meaning is not changed by the substitution of N ⁴ P_e N ⁴ : She bought him a good husband would not differ in meaning (if it occurred) from She bought a good husband for him. But if we try another member of V_f, for instance think, we find again that the substitution gives a ‘meaningless’ (non-occurring) utterance, or in any case one with a greatly altered meaning: She thought him a good husband as against She thought a good husband for him. Verbs in V_f are therefore verbs which involve obvious change in meaning when the N ₁ P_c N substitution is imposed upon them; verbs not in V_f do not involve any reportable change in meaning under that substitution. Therefore the made in made him a good husband functions as a member of V_f.

³³ Such families of morphemes came to my notice in Stanley Newman's and Morris Swadesh's material on English.

³⁴ See, for example, Edward Sapir, Language 86 ff. (New York, 1921):