Here, our mother-based solution to chains can be applied to the cases of feature-
chains as well. Suppose that feature-chains are defi ned in terms of the “mothers”
of relevant feature-occurrences. Note that LIs have been traditionally understood
as bundles (i.e., sets) of features. Thus, each LI counts as the “mother” of the
features it contains, if we assume that a set in the set-theoretic notation of
phrase structure is regarded as the “mother” of its members. Then, we might
say that what M 0 ◦S 0 creates, when applying in the case of feature-chain forma-
tion, is in fact a set of two LIs, {T, n} in the case of (25) (assuming that n is
the LI that contains φ-features within a nominal). The two LIs each defi ne an
occurrence of the relevant agreement feature.
(27) M 0 ◦S 0 (WS) = {T, n}
Given these considerations, we propose that chains are uniformly character-
ized as sets of the mothers of the relevant elements. This approach not only
eliminates the problem of extensional equivalence, but also has a broader empiri-
cal application, unifying chains of movement and feature-chains created by
Agree(ment).^22
5 Minimizing Search 0
We saw that M 0 ◦S 0 not only derives recursive structure-generation via Merge,
which constantly extends and rearranges the elements within WS, but also
provides a unifi ed account of various relation-forming computations, such as
chain-formation, Agree(ment), binding and labeling. In this section, we will
provide arguments that M 0 ◦S 0 in service of relation-formation obeys certain
locality conditions.
To begin, let us discuss the case of M 0 ◦S 0 in service of labeling, which takes
the following form.
(28) M 0 ◦S 0 (WS) = {Σ, λ}
It has been proposed in various forms that labeling obeys a strong locality
condition, or what Chomsky (2012, 2013, 2015a) calls a “minimal search”
requirement (see also Narita 2014). For example, consider the case of labeling
in (29), which yields (30a).
(29) vP = {v, {read, {n, books}}} ∈ WS
(30) M 0 ◦S 0 (WS) = a. {vP, v}
b. ∗{vP, read}
c. ∗{vP, n}
Whenever labeling targets an SO Σ within WS, it must select the highest pos-
sible element λ within Σ as the label of Σ. Thus, only (30a) among (30a-c)
counts as a legitimate instance of labeling.
On the primitive operations of syntax 37