El aprendizaje y la enseñanza de la danza

Syntacticians study sentence-types, and sentence-types are abstract objects.¹ There are notations in which syntacticians write down their findings. What relationship is there between syntactic notation and the abstract objects they are studying? Often it is said that what syntacticians write down are ‘representations’ of the things that they are investigating. But the term ‘representation’ can be misleading. In one common way of speaking, a representation of an object bears a likeness to the object it represents, and we commonly think of representational likeness as relating two physical things, as in the case of portraiture. But there is no physical likeness between what a linguist writes down and an abstract sentence-type. If used in this context, the term ‘representation’ cannot connote portraiture.

Oddly, the verb ‘represent’ and its nominalization ‘representation’ differ in this respect. The verb ‘represent’ has one sense that seems appropriate to our case, as when we say Let ‘QB4’ represent the fourth square in the Queen’s Bishop file. Here no physical likeness is implied. The noun ‘representation’, on the other hand, tends to suggest physical resemblance; it seems a little odd to say: ‘QB4’ is a representation of the fourth square in the Queen’s Bishop file. Nevertheless, I propose to retain the term and tolerate any oddness it might occasion. Furthermore, I will call syntactic sentence-types ‘phrase-markers’, not ‘trees’, since the term ‘tree’ suggests a particular method of representation of syntactic sentence-types, and tends to foster a confusion between syntactic sentence-types and representations of them.²

Some notations are better, in certain respects, than others. On the suggested usage, a phrase-marker representation is accurate if and only if each item in the representation corresponds to some property of the sentence-type, and

¹ See Katz 1981.

² I won’t, however, be using the term ‘phrase-marker’ in the same sense that Chomsky (1955, 1975) uses it. There is, between that account and the one I offer here, a great terminological difference, and, perhaps, a great philosophical difference. For example, the objects of syntactic study in Chomsky (1955, 1975) are called ‘utterances’.

no property of the sentence-type goes unrepresented by some item in the representation. Ideally, in representations of syntactic sentence-types, all and only the syntactic properties of the sentence-type would be represented. On this view, an analogue to phrase-marker representations would be the traditional molecular models composed of colored spheres and sticks. Like phrase-marker representations, they are representations of structure, and reflect scientific claims about that structure. But at the same time the physicists tell us that molecular models such as these do not look like that which they represent. Neither do linguistic representations look like what they represent. Both embody specific theoretical claims, accurate to the extent that they correspond to the structures of molecules or to the structures of sentence-types.³

It is necessary to distinguish the representations of phrase-markers from the notation in which the representations are written. Phrase-markers have certain properties. In a complete representation, each of those properties must be represented. The notation in which a complete representation is written must allow the representation of all of those properties. But no notation is ever unique in that respect. There are always distinct notations that allow the representation of the same properties, which are called ‘notational variants’. One may use ‘C 4’ or ‘QB4’ to represent the fourth square in the Queen’s Bishop file; one may use trees or labeled bracketings to represent sentence-types. One task of syntactic theorizing is to produce a notation in which syntactic representations may be written. But there is no notation uniquely suited to the task.

As in the case of the term ‘representation’, the term ‘notation’ must be handled with care. There are differences between syntactic notation and other notations. Musical notational systems allow the representation of musical structure, but they also allow both the transcription of the structure of what has been heard, and the transcription of instructions to the musician. Syntactic notations serve neither of these functions. In particular, the syntactic constituency of a sentence-type is not something that we ‘take down’. We could only ‘take down’ syntactic constituency if syntactic constituency were open to inspection. But it is not. So there is no syntactic notation parallel to phonetic notation. Again, our understanding of syntactic structure is only inferential.

There is not only a tendency to confuse representations with the things they represent but also a tendency to think that representations represent things that they do not. Specifically, there is a tendency, when reading syntactic

³ There are many further issues. Suppose we wish to represent a complex object, indicating in the representation all of its parts, all of the properties of each part, and all of the relationships between those parts. And suppose the separation into objects, properties, and relations can at least in part be achieved empirically. We would wish, in our preferred theoretical talk, to refer to what we would take to be relations between parts. Should a term that refers to a relation be chosen (e.g. ‘attraction’), or should a relational term be chosen (‘attract’)? Does it matter? There are many questions such as this that I cannot entertain here.

Syntactic Notation 119 representations in one of the standard notations, to take the horizontal dimension as representing temporal priority. Tree structures and labeled bracketings both invite the idea that they notate representations of things that stand in time. But this cannot be right: phrase-marker representations are representations of sentence-types, which do not stand in time, not of utterances, which do. There is as little justification in reading phrase-marker representations as representations of things that stand in time as there would be in reading{2, 3} or <8, 6> as representations of things that stand in time. The things these notations represent are not temporal objects. I am, of course, specifically denying that phrase-marker representations represent utterances. Utterances are temporal; they have acoustic and articulatory structures, the first stated in terms of frequency against time, the second stated as a sequence of muscular gestures. Nothing could completely represent them that did not acknowledge their temporal nature. But utterances do not have syntactic structure, so no syntactic representation could correctly represent them.⁴

I will represent phrase-markers as sets of sets. Some parts of phrase-markers will be represented as ordered sets, and other parts will be represented as unordered sets. But no ordering indicated in the representation of a phrase-marker is temporal ordering. Sentence-tokens are ordered in time (or, in the case of written sentence-tokens, in space), but I am representing sentence-types, not sentence- tokens. Nevertheless, as I will argue directly, there is a kind of ordering that occurs in sentence-types that needs to be represented, a type of ordering that is neither temporal nor spatial. I will represent syntactic constituent-types that are ordered in this way as ordered sets. There are also syntactic constituent-types that are not ordered in this way, and these will be represented as unordered sets. By adopting set notation for syntactic ordering and its lack, I believe I can avoid the temporal confusions that have arisen from other notations. But since sentence-tokens are ordered in time, it will be necessary to state the relationship between the (atemporal) ordering (or lack of ordering) of linguistic expression-types and the temporal ordering of their tokens. I will take that up in due course.

In the fragment of syntactic theory that I present, much will be left unexamined. I assume, for example, that we are given a set of syntactic categories, but will not argue what the categories should be. It would be best, I think, if we could limit the theory to only two—a function category and an argument category—and much that I will have to say would go through if only this binary categorial distinction were allowed. The motivation for positing a syntactic category can only be given in syntactic terms; the tendency to ‘syntacticize’ all sorts of linguistic phenomena whose treatments more correctly lie in pragmatics, semantics, and even phonetics should be resisted.

⁴ As regards Chomsky (1955, 1975), the question would be whether he meant, by calling the objects of inquiry ‘utterances’, to be referring to things that stand in time.