binding. As a concrete example, consider again the vP structure in (21), and
specifi cally the instance of M 0 ◦S 0 that serves to generate a chain with two copies
of what in (22).^21
(21) vP = {what, {John, {v, {buy, what}}}}
(22) M 0 ◦S 0 (WS) = {what (at the edge of vP), what (within VP)}
In (22), the two copies of what are identical and indistinguishable from each
other, assuming that there are no indices or other representational tricks that
differentiate the two tokens (cf. the Inclusiveness Condition of Chomsky 1995
et seq.). Then, readers may wonder if chain-notations like (22) cause a problem
from the perspective of set theory. The reason is that the output of (22) should
be equivalent to that of (23) in terms of extension.
(23) M 0 ◦S 0 (WS) = {what}
(23) can be achieved when Search 0 (vP) picks out only one instance of what within
vP. The two sets in (22) and (23) contain exactly the same (in fact unique) ele-
ment, and hence count as identical, if we follow the basic principle of set theory
that a set is determined uniquely by its members (the Zermelo-Fraenkel axiom
of extensionality). This is problematic because the conception that (22) = (23)
fails to capture the chain relation between the two occurrences of what in (21).
One way to circumvent this problem is to adopt Chomsky’s (2001) idea,
namely that each occurrence of an SO is in fact defi ned in terms of its “mother”
node SO. According to this hypothesis, the chain corresponding to (22) is
represented as in (24).
(24) M 0 ◦S 0 (WS) = {{what, {John, {v, {buy, what}}}}, {buy, what}}
This approach nicely resolves the problem of extensional equivalence, since the
non-distinguishable copies of what in (22) are successfully replaced with their
“mother” SOs, which are distinguishable from each other.
Moreover, the mother-based defi nition of chains can also offer a unifi ed
analysis of the notion of “feature-chain” (that is, the agreement relation estab-
lished between features of LIs). Recall that we defi ned the output of M 0 ◦S 0 in
service of φ-agreement informally as in (25):
(25) M 0 ◦S 0 (WS) = {[φ] (of T), [φ] (of the subject nP)}
If a valued feature and its unvalued counterpart count as identical to each other
(cf. Chomsky’s (2000:124) remark, “We therefore understand “feature-identity”
[.. .] to be identity of choice of feature, not of value.”), then the two sets of
φ-features may yield another case of extensional equivalence as shown in (26).
(26) M 0 ◦S 0 (WS) = {[φ], [φ]} = {[φ]}
36 Takaomi Kato et al.