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Q  (#(#   #@PxP7@P#` `  %Minimal Projection ` `  %Heads ` `  % & ` `  %Optimality  , ` `  %#xP7 P#Jane Grimshaw  [ # xP7aJP#` `  %Center for Cognitive Science ` `  %Department of Linguistics ` `  %Rutgers University ` `  %grimshaw@ruccs.rutgers.edu .#xP7aJP#Technical Report #4, September 1993 (Rutgers University Center for Cognitive Science 6Rutgers University 9PO Box 1179 5Piscataway, NJ 088550_'0*0*0* Q !0  u #Xt\  PJC[hXP#X` hp x (#%'0*,.8135@8:"(#m 1 ,1.The Basics!p>"(#m 4 ,2.Constraint Conflict: Obligatory Heads and the Projection Principle!p>"(#m 6 ,3.The Optimality Theoretic Account!p>"(#m 8 ,,3.1 Matrix Declaratives!p>"(#m 9 ,,3.2 Matrix Interrogatives!p>"(#m 9 ,,3.3 Subordinate Interrogatives!p"(#m 10 ,,3.4 Some Alternatives!p"(#m 13 ,4.Inversion into Unselected Projections!p"(#m 15  Y ,,4.1 Inversion in Complements to functional heads: Negative Preposing!p"(#m 15 ,,4.2 Inversion in Adjuncts and Lexically Filled Heads!p"(#m 19 ,,4.3 Verb Second: Inversion in matrix declaratives!p"(#m 21 ,5. Adjunction!p"(#m 22 ,,5.1 Topicalization!p"(#m 22 ,,5.2 A Mixed Specifier and Adjunction System!p"(#m 26  Y ,6. DoSupport!p"(#m 28  Y ,,6.1 The Occurrence of do!p"(#m 28 ,,6.2 Main Verbs!p"(#m 30 ,,6.3 Cooccurrences!p"(#m 30  Y ,,6.4 Wh Subjects!p"(#m 32  Y ,,6.4 do with negation!p"(#m 33  Y` ,7.The Obligatoriness of that!p"(#m 35 ,8.Competition!p"(#m 40 ,9.Conclusion!p"(#m 42 ,References!p"(#m 45 %=0*0*0*        =+Minimal Projection, Heads, and Optimalityă  r .9Jane Grimshawă  u 0. Introduction The goal of this paper is to show that inversion of the subject and auxiliary verb in English follows from the interaction of four principles, given the notion of Extended Projection proposed in Grimshaw (1991). The principles are these: ,Projection Principle (ProjP)(# ,Selected complements must be the same at dstructure and sstructure(# ,OperatorsinSpecifier (OpSpec)(# ,Syntactic operators must be in Specifier position(# Obligatory Heads (ObHd) ,Heads must be filled at sstructure(# ,Minimal Projection (MinProj)(# ,A functional projection must be functionally interpreted (# There is no theory of inversion per se, rather the patterns of inversion follow from the  Y# interactions among these principles. Moreover, because of the generality of the principles the  Y theory extends automatically to the distribution of do and to the occasional obligatoriness of the  Y that complementizer. ProjP is a generalized version of the principle proposed in Chomsky (1981), which constrains head movement as in Rizzi and Roberts (1989), and adjunction (McCloskey 1992). ProjP prohibits these movements in a selected projection. OpSpec is based on the insight of Rizzi (1991) and related work, that there is a special relationship between the Specifier position and a certain kind of operator. I define a syntactic operator as a scopebearing expression which takes its scope by virtue of its syntactic (as oppposed to LF) position. OpSpec requires that such an expression be a Specifier. ObHd requires a head to be filled: it can be filled by lexical material, by a trace, or by phifeatures, as in the English I. '=0*0*0* MinProj requires that a functional projection make a contribution to the functional representation of the extended projection that it is part of; it is a relative of the principle of "Full Interpretaton". It is violated by empty projections, by projections which contain only functionally unspecified material and by projections which contain redundant functional information. The nature and distribution of inversion follows from the interaction of these principles, which are related in a special way: they have the potential to conflict with each other. For example, ObHd requires X0 movement to fill the head of a projection, but ProjP will prohibit such movement if the projection is selected. Such conflicts prove essential to explaining the empirical generalizations at issue, and can be straightforwardly understood under the assumptions of Optimality Theory, as developed by Prince and Smolensky (1993) (see Legendre et al (1993) for another instance of the application of Optimality Theory to syntactic representations). The core of Optimality is these three ideas: ,Constraints can be violated(# ,Constraints are ranked (# ,The optimal form is grammatical (# To preview a central case from the present work, a clause in which ObHd is violated can be grammatical, but only where ObHd conflicts with ProjP, and where there is no other form available which satisfies both principles. In this situation, the form that violates ObHd is optimal, hence grammatical. This is the key to the distribution of inversion. Several of the principles have appeared in the literature, either in the form of concrete proposals incorporated into the theory here, or in the form of background assumptions which are recognised as partial truths and occasionally appealed to as part of an explanation. This is the case for ObHd, for example. In order to recruit them in an explanation for inversion, however, we must take several theoretically important steps. First, the principles are not "surfacetrue", i.e. it is easy to find examples of clauses that violate them. Thus one might be led to believe that they are not in fact correct. Under Optimality Theory, however, this is exactly what we expect: the only principle which will always be surfacetrue is one which never conflicts with any other principle, or which is victorious in any conflict because it is higher ranked than any principle that it conflicts with. Second, the assumption that clauses are not structurally uniform (the result of MinProj) interacts in crucial ways with the rest of the system. This contradicts a background position which, though rarely stated, seems quite pervasive, and which leads to conclusions such as these: if any matrix clause must be a CP, then every matrix clause must be a CP; if a verb ever takes a CP complement then it always takes a CP complement; if a projection is ever possible it is always present. The background assumption of structural uniformity is explicitly denied by MinProj. This principle has an obvious affinity with recent proposals concerning economy and minimalism (Chomsky (1991, 1992)). #'0*((ԌFinally, we will make essential use of the notion of extended projection (see Grimshaw 1991, Van Riemsdijk (1990), also Haider (1989) for a related proposal). The fundamental claim is that the functional projections erected over a lexical projection are projections not only of their own structural head but also of the head of the lexical projection. A CP is thus an extended projection of V (also in fact of I). A match in syntactic category is a prerequisite for an extended projection: C, I, and V are all verbal in category, P (or at least some Ps), D, and N are all nominal. The smallest verbal projection, then, is VP. IP is intermediate in size between VP and CP. This plays a critical role in the argument of the present paper in two respects. First, the proper understanding of the ProjP depends on the theory of selection, and it is crucial that extended projections be regulated by principles of projection and not of selection. Second, an essential component of OT concerns the definition of the set of competitors: the best form will be grammatical, but which forms must be considered in deciding which is best? The competition set is defined as the class of extended projections with identical lexical projections, and nondistinct LF representations. Competition is therefore between bigger and smaller extended projections with the same lexical projection at the base. An inevitable outcome of the line of research developed here is a reevaluation of the status of functional projections. I will argue that labels like "CP", "IP" etc. are merely notational conveniences. They play no role in the theory, which just requires that an extended projection be composed of a series of projections of matching category, its size and organization determined by a set of general wellformedness principles. 0*((  u 1.The Basics First, consider an English matrix declarative sentence. Here, inversion is neither required nor allowed. (1)a.44They will read some books b.44*Will they read some books Under Minimal Projection, these are IPs, not CPs. Wellformedness requirements require the V in a matrix declarative to be finite, hence the extended projection must be an IP rather than a VP for this reason at least, perhaps also for reasons having to do with the Extended Projection Principle (Chomsky 1981). Crucially, no wellformedness requirements motivate Spec of CP, or C. Hence a CP representation for these clauses violates MinProj, and the clauses must be represented as IPs. Thus the only heads are V and I, both of which are filled: V by lexical material and I by phifeatures. There is no empty head and inversion is both unnecessary and impossible.  Y (2)[IP They will [VP read some books]] The second basic example is that of English matrix wh questions. Wh questions are operator variable constructions and the wh phrase is subject to OpSpec, hence it must be in Specifier position. Specifier of VP is filled by the underlying subject, specifier of IP by the surface subject, hence the operator must be in specifier of a higher projection. Matrix questions will  YS have to be CPs in order not to violate OpSpec. In questions introduced by how come there is  Y> no empty C because how come itself is a C (Collins 1991). But in other wh questions, the CP has an empty C head, which must be filled, otherwise ObHd will be violated. C cannot be  Y filled by the complementizer that because that is a subordinator, and cannot occur in main clauses. So the only way for C to be filled is by head movement. Thus in English wh questions, inversion is both possible and necessary, in order to satisfy ObHd. (3)a.44Which books will they t read t? b.44*Which books they will read t?  Ys (4) [CP Which booksi willj [IP They ej [VP read ei]] In English matrix yesno questions, inversion is again required. (5)a.44Will they read some books? b.44*They will read some books? If matrix yesno questions are CPs this effect will be explained. The C position will be empty, and ObHd will induce inversion. Why is a CP consistent with MinProj here? Yesno questions, like wh questions, involve an operator, which must be in Spec of CP, to satisfy OpSpec. This is a crucial assumption (for interrogative complements at least) under Relativized'0*(( Minimality (Rizzi 1990a), since embedded yesno questions induce minimality effects like those induced by overt wh interrogative operators. Moreover, polarity items can occur in yesno questions, as illustrated by the polarity interpretation of any in (6), again motivating the presence of an operator to license them: (6)Will they read any books? So a matrix yesno question is a CP with an empty C, hence inversion is predicted.  The fact that inversion is obligatory in yesno questions is obscured by the existence of the use of declaratives with interrogative intonation to function as questions. Given the assumptions made here, these cannot be true interrogatives, since they are not CPs, and indeed we find that  Y these sentences do not allow polarity items, so any in (7) has only the free choice reading: (7)They will read any books? Polarity items are licensed by an operator: the operator is present in (6) but not in (7); if it were present in (7) then CP would be motivated and inversion would have occurred. This illustrates the idea. A clause is only as big as it needs to be. It is an IP unless it has to be a CP (a VP unless it has to be an IP, cf. Safir (1993)). A clause always has the minimal structure consistent with its wellformedness. There is no fixed structure for either matrix or subordinate clauses; no unique answer to the question of whether they are IPs or CPs. Sometimes they are one, sometimes the other, depending on what wellformedness conditions are relevant. However, every projection that is present has a head position which must be filled and inversion results when head movement applies to satisfy ObHd. The head which moves is simply the one that is in the right structural position for movement (given ECP), and it moves just to fill a structural position. Later we will develop the picture further by looking at a range of constructions in which inversion takes place: matrix yesno questions, negative preposing contexts, conditionals, and verb second clauses. In each case we see the same basic paradigm: an "extra" projection is motivated by some wellformedness principle, and inversion fills an otherwise empty head. 0*((  u 2.Constraint Conflict:  uM Obligatory Heads and the Projection Principle As is well known, inversion in interrogatives is limited to main clauses in most varieties of English (see McCloskey (1992) for analysis of inversion in Hibernian English). (8)I wonder when I will see such a sight again *I wonder when will I see such a sight again This simple fact turns out to provide key information about the system of principles involved in inversion, and explaining it will be a central result of the theory. Initially it is quite puzzling. OpSpec will require that the wh phrase be in Specifier of CP in subordinate interrogatives, for just the same reason as in matrix interrogatives. Wh phrases show polarity licensing behavior in both. (9)How many students have done any homework? I wonder how many students have done any homework They asked how many students had done any homework Thus we cannot reasonably assimilate subordinate interrogatives to the case of topicalization, which I will argue in Section 5 are adjunctions (although adjunction seems to be a possibility in French, see 5.2 and D)prez (1991)). The CP projection must be present, yet its head is apparently empty. Why then doesn't ObHd require filling of the head position here as in matrix clauses? This is where the ideas of constraint domination developed in Prince and Smolensky (1993) come into play. What I propose is that ObHd is violated in subordinate interrogatives because it conflicts with a higherranked constraint in exactly this instance. This higherranked constraint is the Projection Principle. The constraints conflict because filling the head position would violate ProjP. Since ProjP is the dominant constraint, and since it is not possible to satisfy both ProjP and ObHd, the structure with the head position empty is wellformed. It is the optimal structure, hence it is the only one possible. There are two crucial steps involved in recruiting ProjP to interact with ObHd in the right way. The first is to accept the idea proposed in Rizzi and Roberts (1989) that ProjP rules out movement into the head of a selected phrase. The second is to incorporate into ProjP the Extended Projection theory of selection: this will be postponed to 4.1. Rizzi and Roberts' proposal is that the root nature of certain head movements (see Emonds 1975) follows from the ProjP. Head movement which is direct substitution is disallowed in selected contexts. When (10b) is derived from (10a), for example, (their (39a,b), the sstructure head will be both a C and an I. A verb which selected this head would have a different complement after movement than it had before movement. ' 0*((Ԍ(10a)44` `  ! % )-(10b) 44` ` CP % )-<<0hh4CP< 44` `   ! % )-<<0hh4  44` ` C- ! % )-<<0hh4C-  ! 44   % )-<<0   44C` `  !IP % )-<<0Chh48IP 44 ` `  !  % )-<<0 hh48   Y 44e` `  !I- % )-<<0Ihh48I- 44` `  !  % )-<<0hh48   YT 44` `  !I % )-<<0hh48t The ProjP proposed here in fact generalizes even further, so that it excludes adjunction to arguments, which would have the result that the complement at dstructure is not the complement at sstructure. Selection will then prevent both inversion and adjunction. Thus we can derive the general finding that adjunction to arguments is impossible (Chomsky 1986, McCloskey 1992), and the observation made by Rochemont (1989) that topicalization adjoins to either CP or IP in a matrix, but only to IP in a subordinate clause. ProjP will disallow head movement in complements to lexical heads, but it will allow head movement in matrix clauses and adjuncts. Ultimately we will see also (section 4.1) that it will allow movement in complements to functional heads, since they are not selected in the Extended Projection view of headcomplement relations (Grimshaw 1991)). From this plus the Optimality Theory idea of constraint interaction, we derive the full pattern of inversion. ObHd will be satisfied except where it conflicts with ProjP. s 0*((  u 3.The Optimality Theoretic Account We can now lay out a precise version of the analysis in terms of optimality. In fact, even before investigating subordinate interrogatives we had already appealed implicitly to the notion that a constraint can be violated if the violation leads to satisfaction of another constraint. MinProj says that empty projections are not possible, because they have no functional content.. However, in order to satisfy OpSpec we posited exactly such projections in the form of empty CPs, with Spec positions filled at sstructure by a wh operator. (Examples with negative operators will arise later). Thus it is clear that MinProj should be viewed as a violable constraint, which can conflict with OpSpec, and lose. In other words it is ranked lower than OpSpec. The theory must specify the constraints and their ranking. So far, then, we have determined that OpSpec outranks MinProj and that ProjP outranks ObHd. The correct ranking will ultimately prove to have OpSpec higher ranked than ObHd, as we will see below, so I will always represent them in this way, where the left to right arrangement reflects ranking: ,ProjP OpSpec ObHd MinProj(# The theory will be successful if the grammatical sentences are those which are optimal. The optimal form is selected from among the class of competitors in the following way: the form which satisfies the highestranking constraint on which the competitors conflict, is optimal. For example, consider a situation where constraint A outranks B and B outranks C. Suppose there are two competing forms, one which satisfies A, violates B, and satisfies C; and a second form which satisfies A and B and violates C. We can represent this as follows: ,A *B C(# ,A B *C(# The optimal form is the second one, since the highest ranked constraint on which they differ is B, and the second form satisfies B. I refer the reader to Prince and Smolensky (1993) for further details. An essential component of the theory is the set of principles by which the class of competitors, Prince and Smolensky's "candidate set", is chosen. In order to determine which form is optimal we need to know which forms to compare. As I mentioned in the Introduction, the class of competitors is the set of extended projections which shares a lexical projection and has a nondistinct logical form. (I will postpone a more precise treatment until Section 8.) In a matrix declarative such as (1), then, it is the set of extended projections which include will and have the same underlying VP. We can now see how these principles and their ranking work out in the cases discussed so far. In order to simplify the presentation, I will assume that the possibility of a VP as a matrix' 0*(( or complement clause is ruled out, so I will not consider VP as one of the possible structures to be evaluated by the principles. I adopt a notational convention for extended projections which can be illustrated in this way: a CP in which the C takes an IP complement in which the I takes a VP complement is written as: CPIPVP. A "$" indicates the optimal, i.e. grammatical version of the extended projection. I will present the constraints in accordance with their final ranking, and will point out the crucial evidence as we proceed. I will provide labelled bracketings, but to make them readable I will not show movement of the subject from inside VP to Specifier of IP.  u 3.1Matrix Declaratives  YP [IPDPI 44[VP  !V .. ]]-<<0hh48ProjP OpSpec ObHd MinProj LL]xxa$  Y" [CPe 44[IPDP !I  %[VP V .. ]]]hh4 8ProjP OpSpec *ObHd *MinProjLL]xxa i  Y [CPIi44[IPDP !ei %[VP V .. ]]]hh48ProjP OpSpec ObHd *MinProj LL]xxa i When the matrix is an IP, every principle is respected. (It follows from this that the corresponding sentence must be grammatical.) ObHd is satisfied by phi features in I and by a lexical head in V. MinProj is respected since there is no empty projection, and ProjP and OpSpec are not relevant. When the matrix is a CP, MinProj will always be violated, since the CP is empty. In addition, if nothing inverts to C, ObHd will be violated. Thus of the three competing possibilities, the best is the IP. It is crucial that IP and CP compete, otherwise the optimal CP variant would be grammatical and inverted declarative CPs would be grammatical, alongside declarative IPs. Matrix declaratives provide no grounds for ranking: the constraints never conflict hence any ranking will give the same result.  u 3.2 Matrix Interrogatives  Y [IPDPI 44[VP V wh]]  )-<<0hh48<ProjP *OpSpec ObHd MinProjxxa  Y [CPe 44[IPDP I  %[VP V wh]]] hh48<ProjP *OpSpec *ObHd *MinProj  Y! [CPwhe 44[IPDP I  %[VP V t]]]hh48<ProjP OpSpec *ObHd *MinProjxxa i  Y^# [CPwhIi 44[IPDP ei %[VP V t]]]hh48<ProjP OpSpec ObHd *MinProj $ 44` `  If the matrix is an IP, OpSpec will be violated, since the wh operator will not be in a Specifier position. (See 6.4 for the case where the Spec of IP is a wh operator). When the' 0*(( matrix is a CP, MinProj is violated because the CP is empty at dstructure. If wh movement does not apply OpSpec will be violated here too. OpSpec can be satisfied by movement to Spec of CP, and ObHd will be satisfied if I inverts to C, violated otherwise. Hence the optimal form is CPIPVP with inversion: it satisfies all constraints except MinProj. Matrix interrogatives, as noted previously, provide crucial evidence that OpSpec outranks MinProj.  uH 3.3 Subordinate Interrogatives The crucial point of contrast between a matrix interrogative and a subordinate interrogative lies in the fact that the matrix CP is unselected, so ProjP is irrelevant. The subordinate interrogative is selected, however. Let us for now consider just the CP version of the complement.  Y  [CPwh e44[IPDP I [VP V t]]]<<0hh48ProjP OpSpec *ObHd *MinProj $  Y [CP e 44[IPDP I [VP V wh]]]hh48ProjP *OpSpec *ObHd *MinProj  Y [CPwh Ii 44[IPDP ei [VP V t]]]<<0hh48*ProjP OpSpec ObHd *MinProj  Y [CP Ii 44[IPDP ei [VP V wh]]]hh48*ProjP *OpSpec ObHd *MinProj The CP complement will violate MinProj. If wh preposing does not occur, OpSpec will be violated. With respect to the other principles there are two possibilities: if inversion occurs ObHd will be satisfied, but ProjP will be violated, since this is a selected complement. If inversion does not occur ObHd will be violated but ProjP will be satisfied. The optimal form is one which satisfies ProjP and OpSpec but violates ObHd, hence the clause with no inversion is grammatical, and the clause with inversion is not. Ranking ProjP above ObHd derives the absence of inversion in subordinate interrogatives, since the optimal form violates ObHd. Thus here we have critical evidence that ProjP outranks ObHd. The presence of an additional projection above CP would eliminate the ProjP violation for subordinate interrogatives with inversion, so why is this not possible? The answer is that such an extra projection will always result in a situation which is less favored than the one with no inversion: the extra projection will violate both MinProj and ObHd. For subordinate interrogatives with wh movement and no inversion the analysis is: ProjP OpSpec *ObHd *MinProj. With the extra projection and inversion in CP the analysis is: ProjP OpSpec *ObHd **MinProj. Hence the noninverted structure is optimal. $ 0*(( So far we have examined only the CP form: if the clause is just an IP then OpSpec will necessarily be violated: it turns out that by examining this case we determine that OpSpec is crucially ranked higher than ObHd. With this ranking we correctly predict that the best CP structure is better than IP, since OpSpec is more important than ObHd:  Y [IPDP I [VP V wh]] -<<0hh48ProjP *OpSpec ObHd MinProjLL]  Y_ [CPwh e [IPDP I [VP V t]]]<<0hh48ProjP OpSpec *ObHd *MinProj $ If ObHd were ranked higher than OpSpec the IP complement would be the optimal one, since it would now be better than the best CP, and we would predict no wh movement in complements at all:  Y [IPDP I 44[VP V wh]] -<<0hh48ProjP ObHd *OpSpec MinProjLL]$  Y [CPe 44[IPDP I [VP V wh]]] hh48ProjP *ObHd *OpSpec *MinProjxxa  Yy [CPwh e44[IPDP I [VP V t]]]<<0hh48ProjP *ObHd OpSpec *MinProj  i(#(#p  YK [CPwh Ii44[IPDP ei [VP V t]]]<<0hh48*ProjP ObHd OpSpec *MinProj xxa The IP complement violates OpSpec only. The best CP complement, however, violates ObHd, and no higher ranked principle. If, then, ObHd is ranked higher than OpSpec, the form which respects ObHd will be optimal, giving us the indicated winner, with the result that there is no wh movement in complement clauses. Hence the ranking must have OpSpec above ObHd. We can now see how the system works in subordinate yesno questions, which will be CPs  Y by the reasoning just applied in wh questions. The if version will respect all four principles:  Y~ presumably if has a functional specification so its presence will satisfy MinProj, although this  Yi is not actually crucial here. Certainly if fills C so ObHd is satisfied, OpSpec is satisfied if the null operator is in Spec of CP, and ProjP is satisfied since nothing has changed in the derivation.   Y [CPOp if [IPDP I [VP V ..]]] <<0hh48<?ProjP OpSpec ObHd MinProj i  Y Under the proposal in Kayne (1991), whether is a Spec of CP, unlike if, so it occurs with an empty C. In order to fill C, movement would have to take place into the head of a selected complement. Here, as in the other kinds of subordinate interrogatives, ProjP and ObHd  Y" conflict, and ProjP is dominant, so we find no inversion in whether clauses. (I have marked MinProj as violated here but nothing depends on this interpretation.)  Y[% [CPwhether e  ![IPDP I [VP V t]]]8<?ProjP *ObHd OpSpec *MinProj $(#(#p44  Y-' [CPwhether Ii ![IPDP ei-[VP V t]]]<?*ProjP ObHd OpSpec *MinProj  i-'0*((ԌThis case is informative for the principles which govern competition, to be taken up in  Y Section 8. Assuming Kayne's proposal, the indirect question introduced by if and the indirect  Y question introduced by whether must not compete. If they did compete then the if form would  Y be the only grammatical one, since it violates no constraints while the best whether version violates ObHd. So far, then, we have evidence for the following pair rankings: ProjP >  > ObHd;  %OpSpec > { > ObHd; ?OpSpec >  > MinProj Subsequently we will find evidence that ObHd outranks MinProj. Evidence for ranking comes, of course, from the instances where there is a conflict between two principles. It is the resolution of the conflict that tells us which of the two constraints is dominant. There is one more respect in which the pattern of subordinate interrogatives could be the result of constraint conflict. The maximally general formulation of ProjP given in Section 1 is violated by wh movement in a subordinate clause, as well as by head movement. So we need either to take a more specific version of ProjP, which will allow movement to Specifier, or to consider the possibility that OpSpec is ranked above ProjP. The result of the ranking would be that movement to Specifier is freely available in subordinate clauses, while the other movements are not. Adding OpSpec into the constraint evaluation we would arrive at this analysis, which correctly predicts that wh preposing with no inversion is optimal, since it beats absence of wh preposing on OpSpec, and preposing with inversion on ProjP, the highest ranking, where inversion adds a second violation.  Y [CPwhe 44[IPDP I  %[VP V t]]]hh48<OpSpec *ProjP *ObHd *MinProj $  Y [CPe 44[IPDP I  %[VP V wh]]]hh48<*OpSpec ProjP *ObHd *MinProj  Yk [CPwhIi44[IPDP ei %[VP V t]]]hh48<OpSpec **ProjP ObHd *MinProj I will leave open the question of whether this further generalization of ProjP is correct, and continue to assume that ProjP and OpSpec are not crucially ranked. Nothing in this paper depends on this assumption. Thus we have answered three questions: why there is no inversion in matrix declaratives, why there is inversion in matrix interrogatives and why matrix and subordinate interrogative clauses should show different inversion patterns. Heads are obligatory except where ProjP makes them impossible. The fact that an empty head is possible is a side effect of the fact that movement is not. Since ProjP does not affect matrix clauses or adjuncts, a head can be empty only in a selected complement. )'0*((ԌThe essential property of the solution is that each component principle is fully general: none of the principles is specific to interrogatives or to inversion, for example. In fact, there is no theory of inversion here, inversion is just the result of ObHd, whose effects are seen whenever the effects of ProjP do not obscure them.  uv 3.4Some Alternatives Consider an alternative to the constraint conflict proposal for the absence of preposing in subordinate interrogatives, which might have some initial appeal, namely that there is a null C, or a C filled by +wh, in subordinate interrogatives. Now it is necessary to distinguish in a principled way between the empty head in this case, which by hypothesis would be filled by a null element, and other empty heads, such as the one in a matrix interrogative (and others to be analyzed in Section 4), which cannot be filled by a null complementizer. In order to make this distinction, it is necessary to state that only selected heads can be null. What is revealing about this idea is that it builds into the principle governing empty heads exactly the effects of ProjP. The situation is that heads can be empty in exactly the case where ProjP will not allow them to be filled: this is a direct consequence of constraint conflict but not of an empty heads solution, where a condition reflecting the effects of conflict must be stipulated. The highly specific character of this kind of solution entails that it cannot extend over the range of cases which follow from the present proposal: this will be particularly clear in the case of obligatory complementizers (Section 7). A particularly telling example is the following condition from Plunkett (1990): Specifier Licensing Condition (Plunkett 1990, 128) ,If a maximal projection is in a nonsubcategorized position, its specifier may not be filled at sstructure unless its head position has also been filled by that time. (# This is a description of an empirical situation, not the explanation for it. It is certainly not the principle governing inversion. Examining each part of the condition reveals that it is a statement concerning the effects of the interaction of the relevant principles in the particular case at hand. A recent proposal for inversion has been developed by Rizzi (1991) Haegeman (1992). It uses the idea that a head with a certain feature has to raise in cases of inversion in order to get into a Specifierhead relationship with a Specifier with the same feature, to meet a wellformedness principle, called the "Wh Criterion" for the interrogative cases. The matrixsubordinate contrast results from the initial distribution of the feature: it is on I at dstructure in matrix clauses, hence it must raise to C, and it is on C already in subordinate clauses, hence inversion is not required to put it in the right relationship to Specifier of CP. The insight that the relationship of Specifiers and heads lies behind inversion is incorporated into the present proposal. The central difference between the two proposals lies in the role of constraint conflict. What is the result of constraint interaction in the present paper is instead the'0*(( result of feature distribution in RizziHaegeman approach. The dstructure position of the features is determined by selection: selected +wh goes in C, unselected in I. In this way the Wh Criterion builds into the account of feature distribution the effects of the independently existing ProjP.  Maximally general principles will inevitably conflict. The alternative is to formulate more specific principles which are designed never to conflict, and the price is generality. In the remainder of this paper we will see the effect of the generality of ObHd, in predicting the  YH distribution of do, and of that as a obligatory element. Only by allowing constraints to conflict can we avoid building the effects of every principle into all of the others that it potentially conflicts with.  0*((  u 4.Inversion into Unselected Projections Inversion into the head of a selected projection violates ProjP. Matrix CPs are one kind of unselected projection, and there inversion does occur. The prediction is of course that other unselected projections will also admit inversion. In this section I investigate the other projections where inversion takes place, and show that this is indeed because ProjP is not operative there.  u 4.1 Inversion in Complements to functional heads:  r Negative Preposing  If a negative operator is preposed inversion is required, as illustrated in (11) (Klima 1964, Liberman (1974)). In the absence of preposing, inversion is not allowed (see (12)). (11)a.44Never in her life will she work this hard again(#4 ,b.44*Never in her life she will work this hard again(# (12)Xa.,44She will never (in her life) work this hard(#4 ,b.44*Will she never (in her life) work this hard(# As expected, a moved negative takes scope over the entire IP: (13)*Anyone will never work this hard again Never will anyone work this hard again This paradigm follows under the assumption that negative operators occur in specifier position, so a projection is present when preposing occurs, which is otherwise absent. The head of this projection is empty. Hence head movement must occur to fill the head, and inversion follows. (Several other operators prepose and induce inversion, just like the negatives, but I will not illustrate them here.) What projection is involved? It cannot be CP since the negative element follows C in subordinate clauses, where the entire paradigm can be replicated, a point which I take up shortly.  ! (14)a.44She said that never in her life would she work this hard again b.44*She said that never in her life she would work this hard again c.44She said that she would never (in her life) work this hard again(#4 ,d.X44*She said that would she never (in her life) work this hard again(#4  G$  Nor can the projection be IP since the Specifier of IP is already filled by the subject. Thus the projection must be a further member of the verbal extended projection, which intervenes between IP and CP. I label it "XP" and postpone further discussion of its analysis until the final section of the paper.'0*((Ԍ Y ԙ(15)[CP` `  C ![XP X [IPDP I [VP V Adv]]] When negative preposing occurs in a matrix clause, the possibility of having a CP projection is ruled out in just the same way as for matrix declaratives; the CP projection will violate MinProj and ObHd, and otherwise have the same constraint profile as the XP, so it can never be optimal. I will therefore demonstrate the operation of the principles only for XP and IP.  Y_ [IPDP44I` `  ![VP V Adv]]] hh48<?CProjP *OpSpec ObHd MinProj i(#(#p  YH [XP 44e ` `  ![IP DP I-[VP V Adv]]] ?CProjP *OpSpec *ObHd *MinProj(#(#p  Y [XPnever 44e` `  ![IP DP I -[VP V t]]]<?CProjP OpSpec *ObHd *MinProj i(#(#p  Y [XP 44Ii  ![IP DP ei -[VP V Adv]]]?CProjP *OpSpec ObHd *MinProj   Y [XPnever 44Ii ` `  ![IP DP ei -[VP V t]]]<?CProjP OpSpec ObHd *MinProj i$  If the matrix is an IP then there will be no possibility for preposing in the first place, so Op Yy Spec will be violated.7yr T ԍI have simplified the discussion here by proceeding as if all negative phrase operators are subject  T to OpSpec. This is a translation into the present terms of the position taken in Rizzi (1991, class lectures LSA Linguistic Institute): a negative phrase cannot be a syntactic operator unless it is in Specifier position. This leaves open the analysis of negative expressions that are not moved to Spec of XP, such as never in (i): they are scopetaking even if they are not operators, so what wellformedness conditions are relevant for them?   (i) She has never read anything in my class  ( The position occupied by never here seems to be a phrasal rather than a head position: it can be occupied by expressions like quite often, almost always, although not by PPs like on Tuesdays. There are two likely analyses. The phrase is a Specifier, of a projection intermediate between VP and the projection of the auxiliary verb, the head position being unfilled because there is nothing available to fill it (or perhaps being filled by the main verb). Alternatively it is an adjunct, in which case it takes scope by virtue of its LF position, ie. it is not a syntactic operator. It is then necessary to explain why it cannot then adjoin to IP and take scope from there. If this were possible, there would be a wellformed structure without inversion, with the same structural analysis as topicalization (see Section 5). To exclude this possibility, we might hypothesize that LF operators, as opposed to syntactic operators, take scope only from their dstructure positions. It then follows that an operator either undergoes movement to Specifier and takes scope from there, or stays in place and takes scope only at LF.7 If the matrix is an XP, MinProj will always be violated because the XP will be empty. There are four possibilities for the XP: no inversion and no preposing will violate ObHd and OpSpec, preposing without inversion will violate ObHd, inversion without preposing will violate OpSpec, but preposing with inversion will violate nothing other than MinProj. Hence it is optimal, and grammatical. In this way the principles predict that preposing "induces" inversion, and inversion is impossible without preposing. 0*((ԌWhen we turn to negative preposing in subordinate clauses, we confront the revealing fact that inversion to X is not limited to main clauses. We have seen why inversion is not possible in subordinate interrogatives, but why isn't the same true here? Why should inversion in interrogatives be sensitive to the main/subordinate distinction, but inversion with negative preposing not show a matrixsubordinate contrast? Here it becomes important to accept the basic premise of Extended Projection (Grimshaw 1991), that the wellformedness of an extended projection is governed by projection, and not selection. In this view, functional heads do not select their complements, only lexical heads do. The principles which determine what complements functional heads take are principles of projection such as categorial consistency, and principles of functional composition. The XP projection motivated by operator movement is part of the verbal extended projection: more specifically it is a complement to C. But it is not selected by C, since C is a functional head. In fact, the behavior of XPs illustrates the argument developed in Grimshaw (1991) for the absence of selectional effects with functional heads. If C did select it would be necessary to complicate the description of C in order to allow it to take either an IP or an XP complement. Once we abandon the idea that selection regulates the relationship between C and the lower part of the extended projection, the optionality of XP is no longer a complication, it is simply the result of the fact that no principles require that XP always be present. (See the final section for an extended version of this argument.) We now derive the consequence that ProjP will be violated by head movement into the complement of a lexical head, but not by movement into the complement of a functional head; it follows from the fact that lexical heads are selectors and functional heads are not. The CP of a subordinate interrogative is a complement to a lexical head. The XP of preposed negatives is a complement to a C. XP is like a matrix clause in the critical respect: both are unselected, and therefore both allow inversion. In demonstrating that the principles do give the right results here, I will simplify the  Ye presentation at this point, and consider only the case where the complement is a CP with that filling C. In Section 7 I will show that this is indeed the only possibility allowed, since all the other possibilities are less than optimal.  Y  [CP that [IP DP !I %[VP V Adv]]] 8<?CProjP *OpSpec ObHd MinProj i(#(#p  Y [CP that [XP  !e %[IP DP I <<0[VP V Adv]]] CProjP *OpSpec *ObHd *MinProj(#(#p  Y [CP that [XPnever !e  %[IP DP I <<0[VP V t]]]?CProjP OpSpec *ObHd *MinProj i(#(#p  Y! [CP that [XP  !Ii %[IP DP ei <<0[VP V Adv]]]CProjP *OpSpec ObHd *MinProj i(#(#p  Y" [CP that [XPnever !Ii %[IP DP ei <<0[VP V t]]]?CProjP OpSpec ObHd *MinProj i$ If the CP dominates just IP, then OpSpec will be violated. If XP is present MinProj is always violated, since XP is empty at dstructure. With no preposing and no inversion OpSpec and ObHd are violated; with negative preposing but no inversion ObHd is violated; with inversion but no preposing OpSpec is violated, and with both preposing and inversion nothing%'0*(( but MinProj is violated. Hence the version with preposing and inversion is the grammatical one. As discussed above, ObHd does not conflict with ProjP here since the XP is not a selected complement, being the complement of a functional head, C, and not of a lexical head. This is why inversion with negative preposing is unaffected by the matrix/subordinate distinction. MinProj requires that the XP intermediate verbal projection be omitted unless its presence leads to satisfaction of a higher ranked principle. As a consequence the structure of a subordinate clause with a preposed negative is different from that of one with no preposing. One has the extra XP and the other does not. This is crucial to inversion of course: when the XP is present inversion must occur, when the XP is absent inversion is not possible. In order to understand inversion in this way it is essential to view it as the result of an interaction between OpSpec, MinProj and ObHd. It is ObHd which requires that a head be filled, but it is OpSpec and MinProj that determine what head positions are present in the first place.  y0*((  u 4.2 Inversion in Adjuncts and Lexically Filled Heads Inversion should be possible in adjunct clauses since they too are unselected. This we can see in conditional adjuncts. We can also see another effect here. In the present proposal, the only reason the X0 moves is to fill an empty head position. The properties of the X0 itself are really quite irrelevant it merely happens to be in the right place at the right time. We expect, then, that if the language can fill the head lexically, ObHd will be equally well satisfied. Moreover, there should be a complementary relationship between inversion and the lexical item, since only one head position will be available, given MinProj. The pattern in conditionals, illustrated in (16)(18) and (20), and similar paradigms, have been pointed out in Rizzi and Roberts (1989). (16)a.44Had I been on time I would have caught the train b.44Were he to be asked, he would probably say no. c.44Should it ever happen, you will be sorry. (17)a.44*I had been on time I would have caught the train b.44*He were to be asked, he would probably say no. c.44*It should ever happen, you will be sorry. The analysis is that conditional adjuncts are operator constructions, and the conditional operator, like the others discussed, is subject to OpSpec. The operator thus motivates a projection which has no head and X0 movement fills the head position, resulting in inversion.  YS However, if can fill the head instead. (18)a.44If I had been on time I would have caught the train b.44If he were to be asked, he would probably say no. c.44If it should ever happen, you will be sorry. When the structure is an IP, OpSpec will always be violated, as there is no Specifier position available for the conditional operator. I will set this possibility aside as it is easy to see that it will never lead to the optimal representation.  Yo [CP Op e44[IPDP !I %[VP V ..]]] hh48ProjP OpSpec *ObHd MinProj  YA [CP Op  Ii44[IPDP !ei %[VP V ..]]]hh48ProjP OpSpec ObHd MinProjLL]$  Y" [CP Op  if` ` [IPDP %I  )[VP V ..]]]8<ProjP OpSpec ObHd MinProjxxa$ i Provided we take the basegenerated operator in Spec of CP to result in satisfaction of MinProj we will get the right result. Since the adjunct CP is not selected, no conflict between ProjP and ObHd and movement can occur. Both the candidate with inversion and the candidate with  Y' if respect all of the constraints, hence both are grammatical. Conditionals thus illustrate a'0*(( further point about the optimality theoretic account: in conditionals there are two variants, one  Y with if and one with inversion. Both are possible because both satisfy the same constraints.8r Tb ԍThis does depend on the assumption that MP is not violated by the conditional with inversion, which is not obviously correct. Alternatively, the inversion and if conditional may not compete, in which case both will be grammatical. See Section 8 for relevant discussion of competitors. Another alternative is that MP should be reformulated so that it is never violated when a projection contains an operator or contentful head. I leave this open for now. Alternative competing forms will be possible only if they have exactly the same status with respect to all the constraints (Prince and Smolensky 1993). This pattern of alternation between a lexical head and inversion is never possible in complements to lexical heads, because of the effects of ProjP, so only (19a) is possible (in standard English): (19)Xa.44I wonder if he will do ithh4(ProjP OpSpec ObHd MinProj)(# b.44*I wonder will he do ithh48(*ProjP OpSpec ObHd *MinProj)  Y Similarly, in declarative complements there is no alternation between that and inverted structures: ProjP will be violated if the C is filled by inversion.  Y Inversion is not merely unnecessary but also impossible when if occurs: (20)*If had I been on time I would have caught the train   Y: [CPOpif [XP Ii [IP DP ei<<0[VP V ..]]]?CProjP OpSpec ObHd *MinProj i  Y  [CP  if [XPOp Ii [IP DP ei<<0[VP V ..]]]?CProjP OpSpec ObHd *MinProj i One projection violates MinProj but obeys OpSpec, providing the necessary specifier position.  Y But in order to have both if and inversion as in (20), it is necessary to have two head positions and hence two projections. The second will violate MinProj with no compensating improvement on any higher ranked constraint, hence the configuration is not legitimate. This structure competes with those in (16) and (18), and loses. ?0*((  u 4.3Verb Second: Inversion in matrix declaratives  6 Verb second languages show a paradigm in which inversion is found in matrix declaratives, as illustrated in (21), with examples from Weerman (1989).   (21) a. De man heeft een boek gezien the man has a book seen b.Een boek heeft de man gezien a book has the man seen c.Gistern heeft de man een boek gezien yesterday has the man a book seen  While there are a number of different accounts of V2, they have in common that they view the typological property that distinguishes the V2 languages from the others as a property of the C position. Such accounts leave open, however, the question of why these languages are V2 and not V1: why do they have a filled Spec of CP position?   In the present terms we can look at V2 from another angle: suppose that the typological property of a V2 language is that it requires the topic to occur in Specifier for a matrix clause, i.e. it shows the effects of a "Topic in Specifier" constraint (TopSpec), which outranks MinProj. (Or perhaps V2 languages treat topics as syntactic operators, subject to OpSpec.) It will now follow that in a V2 language a matrix declarative must have an extra projection, and inversion will be required to fill the otherwise empty head position. Another characteristic difference between English and V2 languages is the ability of a main verb to move to C; this is addressed in 6.2.  Y~  ~ [IPDP 44I ` ` [VP V ..]] -<<0hh48<ProjP OpSpec *TopSpec ObHd MinProj(#(#p  Y   [CPtopic 44e` ` [IPDP I  )[VP V t]]]8<ProjP OpSpec TopSpec *ObHd *MinProj(#(#p  YZ  Z [CPtopic 44Ii` ` [IPDP ei )[VP V t]]]8<ProjP OpSpec TopSpec ObHd *MinProj(#(#p$  Y   [CP 44e ` ` [IPDP I  )[VP V ..]]] 8<ProjP OpSpec *TopSpec *ObHd *MinProj For the sake of convenience only I have designated the extra projection here as "CP"; see Section 9. TopSpec is either absent in non V2 languages, or ranked below MinProj where it can have no effect (Prince and Smolensky (1993)).  Matrix V2 structures fall in with the inversion pattern of negative preposing, inversion in adjuncts, and inversion in matrix interrogatives, as cases of inversion into an unselected projection. Since matrix clauses are unselected, here we see the effects of ObHd without the  Y! obscuring effects of ProjP.8!r T%$ ԍThe distribution of V2 in subordinate clauses is a complex issue. It will be governed by interactions among ProjPrin, TopSpec and ObHd, and perhaps other wellformedness conditions. See McCloskey (1993) and Grimshaw (in prep.) for discussion of related questions concerning English inversion in subordinate clauses. '0*((Ԍ!h0*((  u 5. Adjunction Not every case of preposing induces inversion: in terms of the present system of constraints inversion will not be induced when preposing does not motivate a projection by satisfying a constraint which is higher ranked than MinProj. This will be the situation when the preposing is an adjunction rather than a movement to Spec. Adjunction does not increase the number of projections present in the representation: (22)a.  % )-<<0hh4b.  X  44` `  XP % )-<<0hh48< XP  ~ 2 44  !  )-<<0hh48 ?   X  44 Spec ! %X- )-<<0hh48 ZP?CXP  2 44` `  !  -<<0hh48<?  ppKN  X  44` `  !X % YP <<0hh48<?SpecDDGX-  2 44` `  ! % )-<<0hh48<?C  N  X  44` `  ! % )-<<0hh48<?C XDDG YP The moved phrase simply adjoins to an existing projection, hence there are no more heads to  YE be filled in an adjoined structure than in a structure with no adjunction at all. ObHd will be satisfied in exactly the same way in the adjoined structure as it is in the structure involving no adjunction. Inversion will therefore never be necessary and never be possible.  u 5.1Topicalization  Y I will argue that this is the analysis of topicalization.hr T8 ԍ(Lasnik and Saito (1992) also crucially take topicalization to be adjunction. Baltin (1982) argues that topicalization is adjunction to S (=IP), however his arguments are not helpful in the present context as they cannot distinguish between topicalization as adjunction to IP and topicalization as movement to Spec of a projection between IP and CP, a difference which is crucial here.  What then distinguishes a topic, which merely adjoins, from a phrase which occurs in Specifier? The difference is that topics have a particular discourse status but not a special LF status. To put it another way, operators move for reasons of scope, topics move for discourse reasons. Topicalization is not an operatorvariable structure, but a topicpredication structure; see ErteschikShir (1992, in prep.) for a recent theory of topic and focus. (Relative clauses seem to line up with topicalization in most respects, behaving as predicates rather than as operatorvariable configurations. Presumably this lies behind the absence of inversion even in wh relatives, although I will not explore this here.)~@0*((ԌSeveral differences between topicalization and the operatorvariable constructions fall into place under this hypothesis, including differences with respect to resumptive pronouns, weak  Y crossover, and island effects.`r TK ԍIt is surely not an accident also that interrogative operators must be overt, while in topicalization no wh element can appear. Again this suggests that there is a fundamental difference between the two. Topicalizations can involve a resumptive pronoun (in a "Left Dislocation" configuration), while true operator variable constructions, such as interrogatives, or the Negative Preposings cannot: (23)a.44That man, I can't stand. b.44That man, I can't stand him. (24)a. Which man/who do you hate? b.44*Which man/who do you hate him? (25)a.44None of those men/no men can I stand b.44*None of those men/no men can I stand them/him Lasnik and Stowell (1991) observe that weak crossover effects are absent in topicalizations. The point is illustrated by (26a), based on Lasnik and Stowell's (20c), and (27a). They contrast with (26b) and (27b) where the preposed phrase is a syntactic operator.  Y (26)a.44?This booki, I would expect itsi author to buy t (#4  Y b.44*Which booki would you expect itsi author to buy t?(#4  Y (27)a.44?Johni, only hisi mother loves t(#4  Y Xb.,44*Whoi does (only, even) hisi mother love t(#4 Similar results obtain with other operators:  Ye (28)a.44*No booki would I expect itsi author to buy t(#4  YN b.44*Only a very good booki would I expect itsi author to autograph t publicly(#4 This suggests that weak crossover constrains operatorvariable constructions and that topictrace constructions do not count as such. Relativized Minimality (Rizzi 1990a) gives us further insight into this difference. Syntactic operators should all act as intervening Abar operators/specifiers for relativized minimality. Topics, on the other hand, should not do so if they are not operators. There are two respects in which we can compare topics to operators. Is the relationship between a topic"0*(( and its trace blocked by an intervening operator? Is the relationship between an operator and its trace blocked by an intervening topic? Although the data is complicated there seems to be a consistent pattern: the examples in which topics extract over operators, or in which operators extract over topics, are consistently better than those involving two operators. For instance, extraction of a topic from a wh island is considerably better than extraction of a wh phrase: in (29) a topic PP or DP has been extracted from a wh island note the absence of inversion. In (30) the PP or DP is a wh operator note the inversion. The pair of examples in (30) is considerably worse than the pair in (29). (29)a.44?With that kind of job, even the government must wonder who could be happy b.44?That kind of job, even the government must wonder who could be happy with (30)a.44*With what kind of job must even the government wonder who could be happy b.44*What kind of job must even the government wonder who could be happy with? Contrasts of this type have been mentioned in the literature: Rizzi (1990a, 1056) notes that PP Preposing from a wh island is possible in Italian if the PP is [wh], but not if the PP is [+wh]. In the present terms, this would suggest that the [+wh] PP is an operator, but the [wh] PP is simply a topic, essentially as proposed by Cinque (1990). Then the presence of the operator in Spec of CP of the interrogative complement does not affect the relationship between the topic and its trace. The second relevant configuration is extraction of an operator over a topic, versus extraction  Y of an operator over an operator. Does topicalization create an island for operator movement?r Th ԍRochemont (1989) claims that topic constructions are islands to further extraction: citing examples like (i). However such examples involve crossing dependencies and probably processing difficulties, so the fact that they do indeed seem ungrammatical is probably not very informative: (i),*What does John think that Bill, Mary gave t to t(#  Comparison of adjunct extraction over a topic and adjunct extraction over an operator shows a significant difference: (31)a.44??Under which/what circumstances did you say [that children they would give those books t to t]?(#4  Xb.,44*Under which/what circumstances did you ask [which children they would give those books to t]?(#4 (32)a.44??Under which/what circumstances did you say [that those books they would ,,44give t to children t]?(# b.44*Under which/what circumstances did you ask [which books they would give ,,44t to children t]?(#  0*((ԌWhile I have not presented a complete paradigm and analysis, I hope this is sufficient to show that extraction patterns of topics are quite unlike those of operatorvariable constructions. This conclusion coheres in an interesting way with observations concerning relativization: both in Swedish (Engdahl 1980) and in Italian (Rizzi 1982), it is possible to relativize into a wh island, however in both languages there appears to be a significant difference between relativization into a wh island and operator movement from a wh island, which is probably properly treated as ungrammatical. Again, this suggests that relativization and topicalization do not involve operatorvariable binding, but are predication structures. Despite the important similarities in extraction patterns among all of these different cases, there are fundamental differences in the way in which the longdistance relationship is represented, which leads to the conclusion that while they all exemplify the same movement process they are otherwise not uniform. Differences may be due to the nature of the gap, and or to differences in the nature of the antecedent for the gap: see Cinque (1990) Lasnik and Stowell (1991), Postal (1992) , Dwivedi (1993) for recent discussion. The evidence from inversion strongly supports the view that there is indeed an important difference in the analysis of the antecedent: topics are adjoined, operators move to Specifier. In the system of principles developed here, then, we predict that a group of effects will cluster together: movement to specifier will cluster with inversion, weak crossover effects, polarity item licensing when the operator is of the right kind, and operatorbased relativized minimality effects. Topicalization shows none of these, because it is not operator movement, hence it is adjunction, not movement to specifier. Why does the topic adjoin to IP? Under the assumptions about phrase structure which are emerging here, and which will be elaborated in Section 9, it is impossible to stipulate that IP is the adjunction site. Indeed, it would also be incorrect. Rochemont (1989) argues that topicalization can adjoin to CP in matrix, but not subordinate, clauses, on the basis of examples like (32): (32)a.44Tom, why would anyone want to meet? b.44*I wonder Tom, why would anyone want to meet? We must conclude from this that topicalization can in principle adjoin to any projection, and that any restrictions on its appearance must be independently explicable; of course the matrix/subordinate asymmetry observed by Rochemont is expected under the present system of principles, since adjunction to a subordinate CP violates ProjP. Of the other possible adjunction sites, it appears that topicalization can adjoin to XP, although adjunction to the IP inside XP is ungrammatical: (33)a.44(He said that) Beans, never in his life had he been able to stand (#4 Xb.,44*(He said that) Never in his life had beans, he been able to stand (#4 #'0*((ԌNote that the ungrammaticality of (33b) again shows that it is not correct to analyze topicalization as adjunction to IP: here the topic adjoins to IP but the result is ungrammatical.  Y VP adjunction for topics, and adjunction to the projection headed by do (see Section 6), both seem impossible, although either is possible for an adverb like usually. (34)a.44*(He said that) he beans, couldn't stand (#4 b.44*He said that be couldn't beans, stand c.44He said that he (usually) couldn't (usually) stand beans It seems that the topic has to be the subject of a predication relation and that in the illformed sentences the topic is adjoined to a subpart of the predicate rather than to the predicate itself. Thus the VPadjoined position is a possible position for a VP adjunct but not for a topic, since part of the predicate is not included in the VP. Similarly IP adjunction is possible for a topic, but not if it is included in an XP, since then again part of the predicate is outside IP. The topic can adjoin only to a phrase which corresponds to the predicate of the topicpredicate relation. If this is correct, then topicalization can adjoin to any verbal projection in principle. Phrase structure labels such as "IP" play no role in the theory of topics. This provides one piece of evidence that they are notational conveniences but not theoretical entities, a point to be further taken up in Section 9.  u 5.2A Mixed Specifier and Adjunction System French shows a mixture of a system respecting OpSpec, like English, and one using adjunction, like English topicalization. Observationally, wh movement is optional, but inversion occurs only with wh movement (Rizzi 1991). The optionality of movement indicates, in the present terms, that French wh phrases are ambiguous between quantifiers (see Kim (1990) on Korean) and true wh operators. On their quantifier analysis, they are not subject to OpSpec. The presence of a CP projection with the inverted form will violate MinProj with no compensating satisfaction of OpSpec, hence the uninverted version will be optimal: (35)a.44Elle a rencontr) qui? 44She has met who b.44*Atelle t rencontr) qui? 44Has she met who  Y" [CP Ii44[IPDP !ei  %[VP V qui]]]hh48ProjP OpSpec ObHd *MinProjLL]xxa  Y$ [IPDPI 44[VP  !V qui]] -<<0hh48ProjP OpSpec ObHd MinProj $ '0*((ԌIn their operator incarnation, however, the wh phrases are subject to OpSpec and move to Spec of CP, inducing inversion in the usual way: (36)Qui atelle t rencontr) t? Who has she met  Yv [CPquiIi44[IPDP !ei %[VP V t]]]hh48ProjP OpSpec ObHd *MinProjLL]$  YH [CPquie 44[IPDP !I  %[VP V t]]] hh48ProjP OpSpec *ObHd *MinProj The final piece of the paradigm, (37), is explained if the wh phrase, though clause initial, is not a wh operator, but is adjoined (cf D)prez 1991). (37)Qui elle a rencontr) t? Who she has met  Yy [IPqui [IPDP I [VP V t]]] -<<0hh48ProjP OpSpec ObHd MinProj $ Under this analysis, (37) violates no constraints, so it is inevitably grammatical. The adjoined wh phrase should be distinguishable from the operator wh phrase, however. It should not license an unmoved wh element, as pointed out by R. Zanuttini (p.c.). Nor should it license polarity items, or induce weak crossover. According to this analysis, the difference between French and English is in the nature of the wh phrases, (not in the presence or absence of dynamic agreement as in Rizzi (1991), Haegeman (1992)). French interrogative phrases are not always syntactic operators, while the English counterparts are. |0*((  u 6. DoSupport  Y9 The generalization governing do in English is simple to state but has proved challenging to  Y$ formalize: that do is possible only when it is necessary (Chomsky 1957, 1991).  Y The theory developed so far formalizes exactly this conceptualization of do, given two  Y assumptions. First, do is a semantically and functionally empty verbal head: this seems to be  Y the minimal specification we can give to do. As a result a projection headed by do violates MinProj. Second, ObHd outranks MinProj, i.e. an empty (MinProjviolating) functional projection is possible when it results in satisfaction of ObHd. From these two assumptions,  Y plus the constraints proposed here, the distribution of do follows.  u_ 6.1The Occurrence of do I will first show how the analysis works out for the contrast between matrix declaratives and matrix interrogatives, starting with declaratives. I will not show the VP and CP options since it is clear that they could never be optimal. I will assume throughout this section that the first auxiliary verb in a clause always raises to I, although I will not discuss the motivation for this movement, see Grimshaw (in prep.). (38)a.44She said that )-<<0 b.44*She did say that-<<0   Y [IPDP I 44[XP e [VP V .. ]]]<<0hh4ProjP OpSpec *ObHd *MinProj LL]xxa  Y [IPDP doi44[XP ei [VP V .. ]]]<<0hh4ProjP OpSpec ObHd *MinProj LL]xxa  Ym [IPDP I  44[VP V .. ]] )-<<0hh4ProjP OpSpec ObHd MinProj  ZLL]$ Here then, the IP form of the clause, with no auxiliary verb projection, is the optimal one, since  Y( it involves no violations, while the alternative with do involves violation of MinProj, and the  Y alternative which has an extra projection but no do, indicated by "YP", violates both ObHd and  Y MinProj. Thus auxiliary do cannot occur in a declarative.  Y Other auxiliaries can, however. They differ from do in having semantic content, hence the structure with the auxiliary will not compete with the structure without the auxiliary. See Section 9. " 0*(( In interrogatives the result is different. I simplify by considering only those forms which do not violate OpSpec, i.e. where wh movement has occurred, and by not treating the case of an extra projection (XP) with an empty head, which we have already seen in the previous case. (39)a.44What did she say?<<0hh4 b.44*What she said?-<<0 c.44*What she did say? X4` <hDp Lx (#%'0*,.8135@8: