Hitherto, we have assumed that the main motivation for phases is to reduce the complexity of the computational operations which the syntax has to perform by ensuring that probes only have a limited search space within which to locate matching goals – and hence that all syntactic operations are local. However, Chomsky (1998) suggests that phases also have an important role to play in respect of lexical selection. We can illustrate this second role in relation to the following sentence (adapted from Chomsky 1998, p. 17, ex. (7ii)):

Suppose that we have reached the stage of derivation represented informally below:

Since the lexical array for sentence (62) – i.e. the set of items we take out of the lexicon in order to form the sentence – includes expletive there, preference of Merge over Move will mean that we must select there at this point in order to satisfy the [EPP] requirement of [T will], so deriving:

But this in turn means that we have no way of deriving (62), since (62) requires the nominal proofsto become the subject of will at the stage of derivation represented in (63). What are we to do at this point?

Chomsky (1998, pp. 19–20) suggests that the problem can be overcome in the following way. Suppose (as we have done throughout) that the first step in deriving a given expression is to take a set of items out of the lexicon, and that these constitute the lexical array out of which the expression will be composed. But suppose, in addition, that only a specific subarray of the items taken out of the lexicon can be accessed at any phase of derivation: in particular, suppose that the subarray out of which a given phase is built can comprise only a single occurrence of a phase head (e.g. C or a transitive light verb, v∗) – cf. Chomsky’s (1999, p. 9) claim that ‘a subarray contains exactly one C or v∗’. The subarray chosen is then ‘placed in active memory (the “work space”)’ (Chomsky 1998, p. 19). Once a given lexical subarray is exhausted (i.e. all the items it contains have been merged in the relevant structure) and the derivation of the corresponding phase has been completed, the computation then selects another lexical subarray to build the next phase with ... and so on. Returning now to (62) There must be a possibility that proofs will be discovered, let’s suppose that our initial subarray of items comprises the set in (65) below:

Suppose furthermore that we have reached the stage of derivation in (63) above. [T will] has an [EPP] feature requiring it to project a specifier. Preference of Merge over Move will mean that if the lexical subarray contains an expletive, this will be merged in spec-TP. But the subarray in (65) contains no expletive. Hence, the only way of deleting the [EPP] feature of [T will] in (63) is by movement of proofs to spec-TP, deriving:

Merger of the complementizer that with the TP in (66) will in turn derive the CP (67) below:

The bracketed TP will undergo transfer at this point, and the italicized trace of proofs will be deleted from the structure transferred to the phonological component. Since we have now exhausted the lexical subarray in (65) and completed the derivation of the CP phase, the syntactic computation can now access a further subarray. Let’s suppose that this comprises the set below (where ø is a null declarative complementizer):

Successive merger operations introducing possibility, a, be, must, there and ø into the derivation will generate the structure (69) below:

At this point, TP1 will undergo transfer in accordance with (7i), and subsequently CP1 will undergo transfer in accordance with (7ii) – so eventually deriving the structure associated with (62) There must be a possibility that proofs will be discovered.