¹ The details of transformational analysis which the present paper summarizes have appeared or are to appear in various issues of Transformations and discourse analysis papers (Department of Linguistics, University of Pennsylvania) and of Papers on formal linguistics (Mouton & Co., The Hague). I wish to thank Henry Hiż for valuable criticisms of the present manuscript.

² This is a simplified statement, omitting various restrictive conditions.

³ The immediate-constituent analysis would give:

with a sample and is and of value eventually appearing as heads. The existence of a sentence A sample is of value, and its relation to the analyzed sentence, are not expressed by the constituent analysis.

⁴ A distinction should also be made here between hierarchical operations and simple classification. The fact that some strings are partially similar, or that some strings occur in the same positions, may be expressed by collecting these strings into a class or schema. This serves only for an abbreviation of a linguistic description that could be made without such classification, so that there is no hierarchical linguistic operation here.

⁵ This is not to say that there are no further subtleties of sentence structure which have yet to be treated. There remain problems concerning morphological and other restrictions on the application of transformations, concerning quasi-idiomatic constructions, concerning classifier-relations between words, etc.

⁶ The pitting of one linguistic tool against another has in it something of the absolutist postwar temper of social institutions, but is not required by the character and range of these tools of analysis.

⁷ The complete statement is a bit more complicated, because certain sentences have a string structure different from the one shown here (though closely related to it); e.g. This I like. Correspondingly, certain transformations produce or act upon these other string structures. The actual transformations of a language are of course a small subset of the ones admitted by the above statement, a subset distinguished by certain additional string restrictions and by the essential transformational properties described below in this paper.

⁸ Because of the mass of idiomatic and quasi-idiomatic expressions in language, each type of description has to treat of various special small categories of words, and in some cases even of unique words. But in the case of string and transformational analyses, and less adequately in the case of constituent analysis, the statements for aberrant and idiomatic material can be made in the terms of the given description (constituent, string, or transformation) or in limited extension or weakenings of the rules of that description. In these analyses, the treatment of difficult material does not require us to go completely outside the terms of the given description into the terms of another or into the metalanguage.

⁹ A program for string analysis by computer exists, and a transformational program has been designed. A transformational program can utilize in part the results of a string analysis. The less detailed program which analyzed sentences on the Univac in 1959 used a combination of string analysis and constituent analysis.

¹⁰ This applies, for example, to the formulation of grammar in terms of partially ordered homomorphisms which was sketched in Z. S. Harris, ‘From morpheme to utterance’, Lg. 22.161–83 (1946), and which has been given an explicit form in Noam Chomsky's rewriting rules; also to the precise theory of generative grammar proposed and formulated by Chomsky in a series of major papers, especially in his Syntactic structures (The Hague, 1957). Cf. also his interesting ‘Three models for the description of language’, IRE Transactions on information theory, IT-2 (1956).

¹¹ This formulation has to be extended, as it readily can be, to two further cases: where the second sentence form lacks one of the word categories (due to zeroing); and where we start with two sentence forms, A ₁ and A ₂, each with its own scale of satisfiers, plus a connective, and compare with a sentence form B containing the word categories of both (or at least, allowing for zeroing, the word categories of one form) where the acceptability-order of the n-tuples of B is summed in some regular way (related to the connective) from the acceptability-order of the corresponding n-tuples of A ₁ and A ₂. This criterion of a preserved acceptability-ordering is not easy to investigate and use. However, it clearly holds for all the pairs of satisfier-sets X, Y, where we would clearly want a transformational relation between X and Y. And if we find n-tuples which satisfy one form (with satisfiers X) with different acceptability-ordering than when they satisfy another form (with satisfiers Y), we indeed do not wish to call Y a transform of X, e.g. we may hesitate to consider the use of the passive form in scientific writing as a passive transform of the active.

¹² Such extension of a type of analysis into parts of the language where the analysis could not have been independently established does not make the analysis arbitrary. The existence of the relation in question has already been established over a large part of the language. Once we have seen, in this large part of the language, what are the effects of this relation, we may be able to show that similar effects exist in the rest of the language and may be attributed to the same relation.

¹³ One might say Can Helen Keller see a person with her fingers?, but the acceptabilite would be rather special, and even more so for a simple Did Helen Keller see John? Thery is also Can Helen Keller ‘see’ a person with her fingers?; but this can be derived, by a transformation that produces quotation, from something like Can Helen Keller do something which is called seeing a person with her fingers?

¹⁴ One might propose, as such a property: personal names used purely as examples for this discussion, and not identified with any real or fictional person. But such n-tuples have no acceptability difference among them in any sentence-form, so that they do not provide a basis for saying that (9) ↔ (10).

¹⁵ Note in particular the formulations proposed by Henry Hiż in ‘Congrammaticality, batteries of transformations, and grammatical categories’, Proceedings of Symposia in Applied Mathematics, vol. 12 (American Mathematical Society, 1961); also in his ‘The role of paraphrase in grammar’, Monograph series on languages and linguistics, vol. 17 (1964). The definition of transformation can also be adjusted for various purposes. Starting with transformations defined as an equivalence relation between satisfier-sets (the X and Y above), we can speak of transformations between sentences (corresponding members of these sets) or between sentence forms (for certain n-tuples satisfying them). In a different way, we can speak of transformations operating on sentences, or operating on elementary sentences and on transformations (§3.5 below).

¹⁶ This holds also for the transformations as they appear in the theory of Noam Chomsky and in the applications by his students, even though in this case they are set up formally not as a relation between sentences but as instructions in the course of generating sentences (from already-generated simpler sentences). See Noam Chomsky, ‘A transformational approach to syntax’, in A. A. Hill, ed., Proceedings of the Third Texas Conference on Problems of Linguistic Analysis in English, 1958 124–58 (1962), reprinted in J. A. Fodor and J. J. Katz, edd., The structure of language (1964).

¹⁷ Acceptability-difference is a refinement of the criterion of cooccurrence, which had been used in the original formulation of transformations by Z. S. Harris, ‘Distributional structure’, Word 10.146–62 §12 (1954); ‘Cooccurrence and transformation in linguistic structure’, Lg. 33.283–340 (1957). The criterion of cooccurrence presented difficulties, because it is doubtful if we can say that a certain n-tuple does not occur at all in a given sentence form. A more important reason for seeking a refinement on cooccurrence is that transformation preserves not only the occurrability of n-tuples but also the degree to which they can occur and the sense and nuance with which they occur. See end of fn. 11.

¹⁸ The specific lists for English, on which the present commentary draws, are given in various papers, from Z. S. Harris, ‘Discourse analysis’, Lg. 28.1–30 §7.3 (1952), and through various issues of the Transformations and discourse analysis papers. In the following discussion, the terminology of operations and the symbol → will often be used instead of the terminology of (equivalence) relations and the symbol ↔. This is only because once we have a transformational relation between forms A and B, it is convenient (in order to define a useful set of base transformations, §5) to develop a formulation in which B is obained from A by an operation, with A being the simpler or descriptively prior form. In terms of the elementary operations (§5), the primitive is no longer the equivalence relation but a set of incremental and zeroing operations (§5.1), which produce one form out of another, A → B. However, this direct operational formulation does not suffice for the extensions of §5.3.

¹⁹ Vn for nominalized verb, i.e. V with zero or other affix occurring in the positions of N; and so for Va, etc. (P) in the formulas below indicates that some cases covered by the formula have P and others do not. S for sentence. The words ‘subject’ and ‘object’ (or Ω) represent not constituents but the pre-t and post-V material in the elementary sentence forms, and material brought into these positions by specified operations on these forms.

²⁰ One could also analyze this structure not as N V or V Ω operating on S, but as N V X and X V Ω (as sentences) with an S replacing the X. E.g. I know that he came = I know something plus He came. That he came is a fact = Something is a fact plus He came. Among the various difficulties with such an analysis is the fact that for some of these W verbs there is no natural X: e.g. I hope that he will come would require at best I hope for something. The difference in analysis is one of convenience of description. It does not affect the essential existence or properties of transformations.

²¹ More precisely, the if entry is if S ₁ or S ₂ … or S _n. There is a whether variant of if, and in certain situations a whether variant of that. Also, that N V Ω has the variant that N should V Ω and in certain positions necessarily for N to V Ω. Sn' is distinct from Sn, because it can contain Y: His having been present was denied. Sn includes Ving as well as Vn, with of before objects beginning with N: His purchasing of the books was deliberate, His retention of the report was deliberate. Sn can be taken to include also the deformation N's An (His quickness) from N is A, and N's Nn (His manhood) from N is N.

²² Other limited or variant objects of W can be seen in, for example, I prefer it that he should come. Also P N _i that N _i(t) V Ω has a variant N _i to V Ω: I believe about him that he is wrong, I believe him to be wrong, I know him to have come late; this variant is comfortable primarily if V = be or if Y has operated on V. For a particular subcategory of W, to be in this object is zeroed, yielding: I believe him wrong, I consider him an authority, I find him at fault. Note that I ordered them present is obtained here from I ordered (about them) that they be present, while I ordered them to be present is obtained from I ordered them that they be present (in the object list below); the latter means that the order was addressed to them, but the former does not.

²³ For the necessary zeroing of N_i's when the subject of W is N _i, see below.

²⁴ Among limited objects of particular W there is I let go of it (in addition to I let it go).

²⁵ This is a crude statement of the differences required by but.

²⁶ There is also a possibility of operating on three sentences at once, e.g. S ₁ related S ₂ to S ₃.

²⁷ A similar permutation in the question Would he see her? etc. will be seen below to be occasioned by the dropping of if. Permutations like This I like in the elementary sentence could also be considered to depend upon the addition of a stress morpheme, and so based upon an increment. The position of not in respect to tense in He did not go, etc., can be analyzed as the original position and not a permutation; but there are other special transformations on not.

²⁸ Or rather than D: second morpheme of V.

²⁹ This can happen as the result of permutation, as when the passive N ₁ t V N ₂ → N ₂ t Ven by N ₁ puts as the domain of the first N of the resultant the word category which had been the domain of the second N in the operand. It happens as the result of zeroing, as when the zeroing of P in p N of measure, N V P N → N V N, brings into the apparent Ω position to V a noun of measure which had not been in the domain of the Ω of that V (e.g. minute is in the domain of the Ω of tick off, as in The clock ticked off a minute → A minute was ticked off by the clock, but it is not in the Ω of pause, as in He paused for a minute → He paused a minute where ~∃ A minute was paused by him). It also happens as the result of adding constants, as in He smoked cigars → He began the smoking of cigars, where began becomes the value of V and we can say that the smoking becomes the value of ∃ in respect to any transformation which is defined on ∃ and accepts the smoking as ∃ of began.

³⁰ Since every transformation leaves its effect, if only in the choice of subcategory for a given category symbol, the precise statement of arguments and of operands and resultants for each transformation opens the way to computation of transformational decomposition. There exist cases of φ _i followed by a zeroing which has the effect of an inverse of φ _i, but these have to be recognized only when a trace has been left, i.e. when some φ _j has intervened (for an example, see end of §5.213).

³¹ Under W we have to include is A _m of manner, and also the binary verbs.

³² A sentence can be ambiguous because of the range of meanings of a word in it (e.g. I like the sound; I like the Sound) or because of a degeneracy (homonymity) resulting from transformations (e.g. They have shined shoes. ← They have shoes which are shined, by zeroing of which are ← wh (They have shoes. The shoes are shined.); and also They have shined shoes ← They shined shoes by the Y operator have Ven). In the former type, dictionary ambiguity, the ambiguity disappears when some of the other words in the n-tuple are varied (e.g. The boat sank in the Sound.) In the latter, grammatical ambiguity, the ambiguity remains no matter how the n-tuple is varied, so long as the altered n-tuples can occur at all in the two grammatical sources.

³³ For this analysis of the, see the papers of Beverly Robbins in the Transformations and discourse analysis papers.

³⁴ In this form we no longer have binary transformations. Each binary is the result of a divisor of type 3 (whose resultant is not a sentence) followed by a divisor of type 1 (operating on a sentence, with a deformed sentence as increment).

³⁵ ‘Local synonymity’ is used for synonymity in respect to the particular environing words in a structure.

³⁶ This is an extreme example of the fact that when a word occurs in a sentence, it does not carry its full dictionary meaning, but only such meaning as can constitute a normally-accepted (or, depending on the discourse, a jocular, shocking, etc.) meaning in relation to the other words with which it is grammatically juxtaposed.

³⁷ Though the determiners of X _ap may be the other words of the K, the zeroing does not occur in a K by itself, but only when one form is juxtaposed to another (as happens also in morphophonemics). Within a K or an insert or operator by itself there is no redundancy which is removable. In those K in which a particular subcategory of Ω, or a particular subject-object pair, determine that a particular V (or set of locally synonymous V) is the main one, the V may be replaced by a constant of low semantic specificity (e.g. have or be or is P); but the V will not be zeroed (something which would produce a new kind of V-less sentence): He wrote a poem → He did a poem; ~∃ He poem.

³⁸ Here the V _aping and to V _ap do not have the form of inserts. However, dropping them only changes the form of the subject or object to N, which is a respectable grammatical form. Note that the plural agreement is a late morphophonemic operation, after the zeroing.

³⁹ Although the evidence that one form has been derived from another by the dropping of some material is of the same kind here as throughout, it is less obvious in the cases discussed here. The evidence that (1) N ₁ caused N ₂ ← (2) The V _aping of N ₁ caused N ₂ is that for every sentence of form (1) there exists a sentence of form (2), the difference in acceptability between various N ₁, N ₂ choices in (1) being the same as in (2). Furthermore, this holds only for V = occur, happen, act, etc. and not for V = end, is brief, etc. In contrast, for N ₁ ate N ₂ we don't find The Ving of N ₁ ate N ₂. Hence cause here is not a V which simply occurs in a K, but is a sentence operator. I.e. its subject (and Ω) is a deformed K. When we find N (other than ‘human’ N) as its subject, this N is obtained from the deformed K by dropping the Ving; and the Ving drops only if it is the appropriate one for cause.

⁴⁰ Dropping to V _ap is different from zeroing repetitive V _i or to V _i after an antecedent to V _i (§5.22): I spoke and I expect him to.

⁴¹ Going beyond language to specialized subject-matter languages which contain greater restrictions, methods of this kind could be used to achieve more simply characterizable subjects, objects, etc. Thus to measure a room could be taken as reduced from to measure the length (etc.) of a room; to rig the convention from to rig the voting (or the activity etc.) of the convention, to load the gun from to load the cylinder of the gun. In this way the Ω of the V would also become more explicit.

⁴² Under certain sentence operators, the K is only (or primarily) of the be type; and after certain of these the be is then always dropped: I call him a fool; I consider him a fool, I consider him to be a fool.

⁴³ But if the V of K ₂ is not be or the appropriate verb, the wh-wordm reains: I saw the man who buys milk (unless this man has been familiarly regarded as being the person with a characteristic relation to milk, in this case an inveterate buyer of it: he might then be referred to as the milkman).

⁴⁴ The collecting of the disjunctional N, the formation of the wh-words, the N t permutation (when N is available, hence no permutation in Who will go?), are all transformations which appear elsewhere too. The W needed for the question are those that take if. The W needed for the imperative are those that permit please in the operand. That the lost subject of the operand is uniquely you is seen from Wash yourself! etc.; it is therefore zeroable as N _ap.

⁴⁵ We can define a set of proword substitutions which are similar to various types of zeroing, but operate under somewhat different conditions. Thus the disjunctions and conjunctions of §5.23 may be replaced by indefinite pronouns and by certain words operating as classifiers (e.g. people in the sense of someone; act in the sense of do something) in all syntactic situations, and by zero in only certain syntactic ones. Words of almost all categories (chiefly N) can be replaced by prowords of that category and by words that are semantically inclusive in respect to them; this is more likely to occur if the word is referent-repeating. The zeroing of repetitive material (§5.22) is similar only to this last, but occurs also in some syntactic situations in which pronouning does not occur (e.g. while Ving) and also in various categories which have no proword. The zeroing of ‘appropriate’ words (§5.21) is related to a much more general system of locally appropriate sub-categories, which includes synonyms and certain kinds of antonyms as well as sets of words based on looser local semantic similarity.

⁴⁶ This relation of zero to pronoun does not hold in §5.22, where a word is zeroed only if it is the same word as the antecedent; nor in §5.21.

⁴⁷ The ambiguity of Each place has been taken by someone arises from the two possible orderings of the disjunctional operation (which yielded someone) and the conjunctional operation (which yielded every). We begin with

If we first make a conjunction on the A (i.e. A ₁ place has been taken by N ₁ and A ₂ place has been taken by N ₁ … and A _n place has been taken by N ₁) we obtain

If here we make a disjunction on the N (i.e. Every place has been taken by N ₁ or every place has been taken by N ₂ … or every place has been taken by N _m) we obtain

in the sense of

However, if in the original sentence we first make a disjunction on the N, yielding

and on this a conjunction on the A, we obtain

in the sense of

⁴⁸ There is a possibility that this Ω-zeroing can be derived through the Sn form, where Ω has insert form.

⁴⁹ In the example given here, what can be replaced by whatever; and what has been dropped is anything, the things, etc., which are pronouns for disjunctions of N. However, there are also cases in which what can be replaced by the single thing that, or the like; in such cases, what has been dropped is a pronoun or a classifier N _c1 for a single N: I heard what he said and you heard it too; What he planted has grown to be quite a tree.

⁵⁰ A partly similar case is the rare dropping of pronoun or N _c1 which may occur after certain the A, where the the indicates a lost wh-insert connected to that N: the true ← the things which are true. This is mine ← This is my N ₁ or N ₂ … or N _n; This is his ← This is his N ₁ or N ₂ … or N _n.

⁵¹ X̆ for pronoun of X. S-N _i indicates S with N _i omitted.

⁵² The apposition with comma is different: It was (widely) read, what he wrote.

⁵³ Almost all, because there remain a few pure permutational (asyntactic) transformations. To derive these, we would have to add a fifth type of elementary transformation which carries out restricted permutations.

⁵⁴ See in particular Henry M. Hoenigswald, Language change and linguistic reconstruction (Chicago, 1960).

⁵⁵ As an example of a limitation on similarity, note that the It transformation does not extend to zero N plus wh-S: see the end of §5.23.

⁵⁶ [This article has not been proofread by the author.]