structures in (9b) and (10b) are classified as symmetric in this sense, because
they form a φ-equilibrium and a Q-equilibrium, respectively. In contrast, cases
like (15a,b) do not count as symmetric under the definition in (17), given the
lack of matching features shared by XP and YP. In this approach, then, the {XP,
YP} structures in (15) cease to be exceptional in the face of Fukui’s (2011)
generalization in (11).
Note that the notion of featural symmetry is defined in (17) relative to some
feature F present in {α, β}. If a relevant feature does not exist in the SO, F-
(a)symmetry is not even defined and the notion simply becomes irrelevant.
Therefore, the XP-YP structure in (9b) does count as φ-symmetric, but it is
neither symmetric nor asymmetric with respect to, say, [Q], given the lack of
[Q] in the SO.
Recall that we still want to classify cases of {H, XP} structures like (7) as
asymmetric SOs, typical of EM. How does our new concept of featural sym-
metry achieve this result? It is not clear whether H and XP share any matching
feature in these cases. Observationally, there are various sorts of dependencies
between H and the head of XP in these structures: C assigns finiteness to T in
(7a); T determines tense and aspectual properties of v in (7b); v/n/a/p assign
their categorial features to V/N/A/P in SOs like (7c) (which may originally
be uncategorized root LIs); V and P select/subcategorize n in (7d-e); and so
on. A variety of linguistic theories hypothesize abstract features and mechanisms
of feature-checking to capture these dependencies. Quite independently of the
nature of these dependencies and any analyses we may give them, it is clear
that SOs of the form {H, XP} are “unbalanced” with respect to the size of
their two constituents, or the “depth” of features embedded in H and XP:
H is an LI, which is the smallest possible syntactic element, immediately pre-
senting its features, but XP is a phrasal composite whose featural content can
be determined only by further inspection of its LI terms. Building on this
observation (see also Chomsky 2013), we define the notion of feature-
equilibrium in (16) in such a way as to require that the matching feature F
must be “equally prominent” in α and β. Here we characterize structural
prominence inductively as in (18).^5
(18) Structural Prominence (see Kato et al. 2016; see also Ohta et al. 2013
for a related notion of “Degree of Merger”):
Suppose that Depth(α) = m (m ≥ 0) is the order of depth – the inverse
relation of prominence – associated with an SO α, with lower prominence
indicated by a higher value of depth. Then, we can say:
a. Depth(α) = 0 if there is no SO β such that α ∈ β (i.e., α is a root SO
dominated by no other SO).
b.If Depth(α) = m, then, Depth(β) = m + 1 for any β such that β ∈ α
(i.e., β is a daughter of α).
(18a) says that every root SO within a given workspace is of the highest order
of prominence (0), and (18b) says that the prominence of an SO decreases as
Feature-equilibria in syntax 17