Notes on Assignment 5

1 Derivation

Stay tuned for details.

2 Long-distance Movement in Relative Clauses

Note: I'm going to use the 'trace' symbol 't' to indicate copies of movement, rather than the strikeout notation, because it's a bit easier to deal with when writing up these notes.

The easiest way to see where things go wrong in (3), repeated below using labelled brackets, is to focus on the most embedded CP.

• the book [_CP which₁ [_S I think [_CP t₁ that [_SLee said [_CP t₁ that [_SKim likes t₁]]]]]]

According to our assumptions, the S node is going to be type t. Function Application will handle compositon of the verb and direct object trace, and the VP and the subject, giving us a proposition that is true just in case Kim likes g(1), where g(1) is the value that the assignment function (whatever it is) assigns to the index 1. I told you to assume that complementizers are semantically vacuous, which would mean that a CP of the form [_CP that [Kim likes t₁]] is also type t. If this constituent were supplied as the argument to the sentence embedding verb said, which by hypothesis is type [t, et], we would be all set: this is presumably what happens in a simple embedded clause construction like Lee said that Kim likes artichokes. However, this is not what is going on in (4); instead, that Kim likes t₁ must first combine with the intermediate trace in SpecCP.

This is where the problem arises. According to our rule for interpreting variable-denoting expressions (Heim and Kratzer's Pronouns and Traces Rule), [[t₁]]^g = g(1) for any assignment g, which means that a trace is of type e. But if [[that Kim likes t₁]]^g is type t, and [[t₁]]^g is type e, then we have no rule that derives a denotation for [[CP]]^g: we have a type mismatch. The same problem is going to arise at the next intermediate trace, and more generally, for any intermediate trace.

Worse, even if we could somehow fix the type mismatch, we have no way of integrating the variable introduced by the intermediate trace into the meaning. For example, if we were to apply our Predicate Abraction Rule at the highest CP node (the one that has the relative operator as one of its daughters), then all of the traces indexed 1 in the relative clause are going to be bound by the lambda operator introduced at the top. But this gives us a completely incoherent meaning:

• [^x in D_e.I think x that Lee said x that Kim likes x]

This is not a coherent function, precisely because the first and second occurrences of the variable x are not integrated compositionally into the truth conditions: there is nothing for them to serve as the argument of.

What we really want is for these 'extra' variables to be eliminated at the end of the day, so that all we are left with is the variable in the 'theta position', giving us the following meaning for the relative clause (the complementizers really are optional here):

• [^x in D_e.I think (that) Lee said (that) Kim likes x]

The question is how to do this. A number of options present themselves, the first of which is purely syntactic: assume that intermediate traces are required only for the purpose of licensing movement, but have no semantic effect. That is: intermediate traces are deleted from the representation that feeds interpretation. On this view, the semantics does not 'see' the structure in (4), but rather the one below:

• the book [_CP which₁ [_S I think [_CP that [_SLee said [_CP that [_SKim likes t₁]]]]]]

The type mismatch engendered by the intermediate traces is gone; given our assumption that that is semantically vacuous, we now have type t embedded clauses being supplied as the first arguments to the type [t,et] sentence embedding verbs. Moreover, it should be fairly easy to convince yourselves that this structure will map onto the function we want for the relative clause, since there is only one occurrence of t₁, and it is in the theta position.

The problem with this approach, of course, is that it necessesitates a weaker link between the syntax and the semantics than the one we have (mostly) been assuming: some expressions that are generated by the syntax have no meaning, and must crucially be eliminated from the syntactic representation before it can be interpreted. We have made similar assumptions before for e.g. predicative BE and the indefinite article A in predicate nominals, but these were mainly for convenience. Here we have to assume deletion, or the semantic computation fails.

Alternatively, we could take the other route we considered for BE and A, as well as for that, and treat intermediate traces as semantically vacuous. On this view, the trace in theta position is interpreted normally according to our rule for interpreting variables (H&K's Pronouns and Traces Rule), but they have a special vacuous (type [t,t]) meaning when they're in SpecCP. The details are spelled out in the context sensitive rule below:

• Trace Interpretation Rule
  For any assignment g, [[t_i]]^g =
  • g(i) if t_i is in a theta position, else
  • [^lambda p in D_t.p]

This would do the trick; the ugly part is that we no longer have a uniform interpretation rule for traces. We also have to ensure that we have a clear definition of 'theta positon', something that Assignment 3 called into question. While this point can probably be worked out, the necessity of a context-dependent interpretation rule remains. Usually when we have to posit a rule of the form 'Do either X or Y, depending on Z', it means that we haven't looked hard enough for a more general explanation.

This brings us to the third option, which involves refining our semantic analysis of movement a little bit. The problem with (4) is that we have several instances of movement (the movement that takes which from an origin point to the next-highest SpecCP position), and so several traces, but only one point at which Predicate Abstraction applies; this is why there are several variables but only one lambda, which is the root of the problem. What if we assumed instead that every instance of movement not only left a trace (interpreted in the normal way --- as a variable), but also created a structure that was subject to Predicate Abstraction? That is, what if every instance of movement introduced both a variable and a lambda to bind it? The result for (4), going bottom up, would give us something like the following, where I have computed the meaning for the structure generated by each instance of successive-cyclic movement, and then plugged that into the next biggest constituent:

• [_CP which₁ that Kim likes t₁]
  = [^x in D_e.Kim likes x]
• [_CP which₁ that Lee said t₁ [^x in D_e.Kim likes x]]
  = [^y in D_e.Lee said that [^x in D_e.Kim likes x](y)]
• [_CP which₁ I think that t₁ [^y in D_e.Lee said that [^x in D_e.Kim likes x](y)]]
  = [^z in D_e.I think that [^y in D_e.Lee said that [^x in D_e.Kim likes x](y)](z)]
  = [^z in D_e.I think that [^y in D_e.Lee said that Kim likes y](z)] (by lambda conversion on ^x)
  = [^z in D_e.I think that Lee said that Kim likes z] (by lambda conversion on ^y)

This gets us what we want; the trick is making precise exactly how this works. That's what we'll be doing in class this week.