shown in (10) (where λ = the label of Σ).14,15 This set is read as “Σ is headed
by λ” at the interfaces.
(10) M 0 ◦S 0 (Σ) = {Σ, λ}
For example, in the labeling of the SO {love, himself}, Search 0 applies to this
SO and picks out the SO itself and love, and Merge 0 applies to these objects
and forms the set of them, as in (11). As a result of this application of M 0 ◦S 0 (Σ),
love will be interpreted as the label of the relevant constituent.
(11) M 0 ◦S 0 ({love, himself}) = {{love, himself}, love}
If the discussion so far is on the right track, labeling is unifi ed with other opera-
tions such as Agree, binding and chain-formation, and we now have a very general
unifying mechanism. This is one of the most notable results obtained here. Chomsky
has suggested in his various writings that (minimal) search is involved in labeling
(see, for example, Chomsky 2005, 2007, 2008). Although it is safe to bet that
some search mechanism is also involved in operations like Agree (see, for example,
Chomsky 2015b), it is not clear how to unify these operations with labeling under
the standard probe-goal system. This is because under the latter system, the two
items to be related (that is, the probe and the goal) must be located in such a
way that one c-commands the other, but in the case of labeling, an SO and its
label are not in such a positional relationship.^16 In contrast, under the current
proposal, in which the traditional notion of probe/goal is abandoned, we can
unify labeling and other operations such as Agree in a very natural way under a
single operation M 0 ◦S 0 (Σ) (see note 7 for relevant discussion).
3 Decomposing Merge
According to Chomsky, Merge is an operation that takes n objects and combines
them by forming the set of these objects (cf. Chomsky 2005, 2007, 2008,
among others). Given these two functions of Merge, it can be also regarded as
a composite operation. Recall from the discussion in the preceding section that
Search is decomposed into two more primitive operations Search 0 and Merge 0.
The former picks out n objects and the latter applies to these objects and forms
the set of them. In this section, we propose that Merge is also an instance of the
composition of Search 0 and Merge 0 , M 0 ◦S 0.^17 In the preceding section, we for-
mulated Search 0 in such a way that it applies to SOs. Below, we argue that this
formulation of Search 0 should be modifi ed, thereby allowing M 0 ◦S 0 to cover the
cases of Merge, particularly the cases of External Merge (EM).
Let us begin our discussion with IM. Under our proposal, IM involves an
application of M 0 ◦S 0 as shown below:
(12) Internal Merge (IM)
M 0 ◦S 0 (Σ) = {α, Σ} (where α is contained in Σ)^18
On the primitive operations of syntax 33