Later —21; see section 6. But there is no mention of the fourth option d , with g being neither a nor b, in which case g contains one or more features not present in either a or b.
And this is an option grammar cannot do without. One should bear in mind that in all four cases we have a mathematical function—either a function a from b to g, or a function b from a to g in terms of constituency trees; in dependency trees the function notation is different.
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Functions are the central mathematical tool for carrying out compositional computations through tree structures. They have a high degree of conceptual necessity in view of the semantic problem of computing complex meanings from simple ones. From this angle, option d is at least as good as c —in fact, it is indispensable, since it is common in language for two or more elements to combine into a new constituent whose category differs from those of its constituents. A propositional structure, for example, consists of a predicate and one or more terms, none of which has to be a propositional structure itself, and it is not hard to argue that this is a conceptual necessity see sections 3.
Move applies within one syntactic object O, and only if O is the result of several applications of Merge and, possibly, Move. It involves the transportation of a bundle of features, usually a whole lexical item or phrase, from one position in the tree to another, leaving behind a trace t. The movement is obligatory and unidirectional. The obligatory character is expressed by the condition of Last Resort, which says that the movement, though it may be carried out at any moment in the derivation, has to take place and can take place only when driven by the relevant features.
Unidirectionality means that movement is possible only from a lower to a higher position in the tree that constitutes O. That is, only raising is allowed always leaving behind a trace t , never lowering. Thus, if the tree is right-branching, the raising movement is from right to left. The element raised is somehow attached to its target, which has to be a head of a higher construction. There appear to be various modes of attachment, whose inconclusive and cryptic descriptions take up many pages in The Minimalist Program for some greater clarity, see Uriagereka — However, since our critique of the system transcends such details and concerns higher levels of generality, it seems unnecessary to engage in the demanding exercise of sorting out all the possibilities that are investigated and their consequences for the limited amount of data that are taken into account.
The feature values of the heads of the functional categories will then have to be matched with those of the corresponding phrases with lexical heads. If the features match, the derivation may proceed; otherwise, it will crash. But this does not necessarily mean that the phonological manifestations of the corresponding lexical items words must also be in the position assigned to their semantic and grammatical features. In other words, the position of a word or phrase in the phonetically realized sentence need not correspond with its position in LF.
However, SO does not prevent nonphonological features to be raised by Move. The only difference is that raising after SO is covert—that is, without any perceptible result. Given the extreme opacity of the text of chapter 4 in The Minimalist Program, it is hard to make out what the actual structures are meant to look like.
Marr’s levels and the minimalist program
A good guess is made in Johnson and Lappin for the LF of the sentence John saw Mary, which would be something like figure 2. The subscripts indicate the chains linking the actual items with their traces. There is a considerable amount of leapfrogging going on, as one sees from figure 2. The movements are both restricted and enhanced by the Minimal Link Condition MLC , which restricts raising to the shortest 1.
What this could mean in formal or computational terms is left unclear. Projected structures implied in The Minimalist Program, chapter 4 distance and thus prevents the passing by of any intermediate possible targets. Separate leaps are required for each shortest distance. That there should be such a heavy traffic of constituents, even for such a simple sentence as John saw Mary, is not in itself a point of criticism. Surface simplicity often conceals an intricate underlying system. It becomes a criticism, however, when the movements are not or insufficiently motivated, and that does seem to be the case here.
One should realize that figure 2. In more ordinary language one would say that figure 2. The problem is, however, that LF is never properly defined, from neither a semantic nor a syntactic point of view. Yet no such criterion is ever mentioned. All that is found in the way of a formal specification is that LF may contain arguments in argument A- position, adjuncts in A-bar position, lexical elements in zero-bar position, predicates position unspecified , and operator-variable constructions, the operator in A-bar and the variable in A-position; the source of each chain of traces indicates the semantically proper position of the element concerned — Yet on p.
But then why have the elements in question moved at all from their original position?
Why does Merge not put them straight away in their proper position? The answer will presumably be that the higher part of the LF tree contains the functional elements of case, gender, number, person, tense, modality, and probably also quantifiers, and that the predicate and argument terms must be united with them for proper interpretation.
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Yet semanticists will object that this is not so for tense, modalities, and quantifiers. Elementary knowledge of modern Predicate Calculus tells one that tense and modality are operators over propositions, while quantifiers are operators over pairs of propositional functions.
Gender, number, and person, moreover, do not belong in the functional upper part of the LF tree at all but are inherent features of argument terms. In the MP there is hardly any comment on the status of the formal language of Predicate Calculus LPC , devised by Russell and Whitehead a century ago, although semanticists and philosophers of language largely agree that LPC, extended with a lexicon and a few additional expressive devices, is by far the most effective and well-founded language available for the systematic representation of meanings, and thus a serious a priori candidate for any claim to psychological reality.
The result is a dilettante and offhand treatment of central semantic notions such as operator scope. The syntax and semantics of such primary scope-bearing elements as negation and the quantifiers is badly neglected. Furthermore, no indication is given of what the semantic interpretation envisaged might be taken to consist in, though there are hints that standard model-theoretic methods of semantic interpretation are not looked upon favorably.
In short, the notion of LF is left without any empirical or formal criteria and without anything approaching a definition. This means, for one thing, that the computation from N to LF is subject to clear criteria only insofar as it is determined by phenomena recoverable from the overt phonological form of the sentences concerned, which in itself should suffice to consider the MP with the greatest possible suspicion.
The chances are that the relation of the MP to natural language is like that of the game of Monopoly to the real estate market. But we must press on. Unless inhibited by special stipulation, all operations in CHL are applicable at any stage in the derivation D. This is called the requirement of uniformity It means that selections can be made from N and that movements are allowed even after SO, during the covert phase of D on its way to LF. To ensure that no undue selection is made after SO, it is stipulated that only lexical items without any phonological features such as certain covert complementizers can be introduced by Select and Merge after SO.
This principle says that raising should be postponed for as long as possible, in any case till after SO, if that is permitted. The permission is made dependent, in principle at least we skip details that are irrelevant in this context , on a distinction between strong and weak grammatical features. Strong grammatical features want to be checked before SO and carry the phonological features with them while they are raised.
Weak grammatical features will wait till after SO, inhibited as they are by Procrastinate.
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For them, the question of whether to bring along the phonological features does not arise, since the phonological features have already been siphoned off into the phonological component and are on their way to PF. Languages differ as to the assignment of strength to grammatical features. The principle of Procrastinate, combined with the stipulation that no phonologically endowed items must be selected after SO, effectively ensures that LF will not contain any phonological features. It should be mentioned, in this context, that the desired effect of herding all phonological material into the phonological component and thus keeping the covert part of D free from phonological blemishes is achieved more simply by defining SO as a station of D—as a proper level of representation, at which N must have been depleted all its items must have been used up , and all phonological features must be isolated and directed toward the A-P interface.
However, Chomsky seems to set great store by the avoidance of levels of representation beyond N, PF, and LF, any further levels being considered conceptually unnecessary. This question will be pursued in a moment but see also the discussion in section 5. In a general sense, the operation Move is seen as an unwanted concession forced on the theory by the facts of language. That they must be taken to do so results from the obvious fact, recognized by all professional linguists, that the surface form of sentences is, generally speaking, unfit for direct semantic interpretation.
In the generative framework, this means that a transformational procedure is required relating surface structures with corresponding semantic representations formulated in terms of a properly regimented language of semantic representation that should be either universal or at least much less language-specific than the surface sentences of individual languages.
Since the period of generative semantics, which lasted from about to , it has been generally accepted, in most formal theories of grammar, that this mapping procedure should be considered the central part of the grammar of the language in question. This notion of grammar deviates from an earlier notion, developed in the context of American structuralism, where a grammar was taken to be merely the set of rules that define well-formed structures built up of morphemes.
The MP has now implicitly adopted this generative semantic notion of grammar, though it applies it in a random-generator way, which not only goes against the spirit of generative semantics and of most other schools of grammar, whether formal or traditional, but is also internally incoherent, as appears from the analyses presented in chapter 7.
follow Moreover, since the Chomskyan notion of semantic representation is both formally and semantically undefined, it must remain unclear what the relation between surface forms and semantic representations must be taken to look like, even though the formal disparity between the two levels of representation is recognized. Moreover, many languages have grammatically defined forms of copying, or spread, examples of which are given in section 8. What these facts show is that the transformational machinery relating surface forms to semantic representations makes use of all the mathematically possible devices of a transformational system.
The grammar will, therefore, have to belong to a mathematically unrestricted form of rewrite procedures, its restrictions coming from other than mathematical sources. For it is easily conceivable in the otherwise repellent terms of a random-generator language system that a language L should be defined merely by the operations Select and Merge, these two jointly constituting the grammar of L. The features that are semantically or phonologically irrelevant would then not be needed in the grammar see section 5.
No exclusivity is implied, however. As there is no statement to the contrary, the possibility is left open for more than one admissible derivation to be assigned equal ranking on the scale set by the economy metric. The cost values are not properly specified, however. However, given the doubtful status of the notions concerned, it is highly 2.
They show that, to the extent that this notion can be given a precise content, it is computationally intractable, and they conclude that it should be dispensed with altogether, as it can be replaced, without loss of empirical coverage, by local constraints on Move—a point further elaborated in their later work They also observe that the notion of reference set as suggested by Chomsky is acutely problematic in the context of his view of language as a nearperfect product of evolution.
They might have added that one wonders about the fate of those sentences that would be the product of less economical derivations than others, given the same N, and are blocked by the economy metric. One of two things. Either such sentences are grammatical but are unhappily blocked by the economy metric, which would make the grammar empirically inadequate, or they are ungrammatical, in which case this mysterious metric will have taken over the function of the grammar.
This being so, it seems unnecessary to spend any further time on the issue. It is implied Chomsky that the selection N made from the lexicon by the operation Numeration of CHL is arbitrary or random.