D. La jurisprudencia
IV. Intentos de nueva regulación
In §2.2, we observed that Mandarin unconditionals and∀-FC constructions share very close structures, both of which are embedded in the ‘wúlùn...dou’ construction. We repeat examples (3a) and (42c) below as illustrations:
(3a) (Wúlùn) (no-matter) [shenme] what shuiguo fruit Yuehan John *(dou) dou keyi may chi. eat. ‘John may eat any fruit.’
(42c) (Wúlùn) No-matter paidui party zai at shui who jia, house, Yuehan John *(dou) *(dou) keyi may qu. go. ‘No matter whose house the party will be, John may go.’
In both cases, the presence of dou is obligatory, and the unconditional headwúlùn
is optional. The only difference is while the unconditional antecedent in (42c) is a full question, the ∀-FC construction in (3a) contains only a wh-phrase ‘shenme (what)
shuiguo(fruit)’. Further, we justified in §2.2.1.3 that douindeed associates with thewh- question/phrase, and gave the following interpretation (49) (repeated from the same section) ofdouin the ‘wúlùn...dou’ constructions, written asdouQ, based onInqB.
(49) ⟦douQ⟧c=λPTλQTλsst. |alt(Qc)|>1 | {z } plurality . ∀α∈alt(Qc) :s⊆[α⇒info(Pc)] | {z } distributivity effect
The entry spells out exactly how the plurality requirement and distributivity effect are instantiated. The former is imposed on the antecedent question and ensures its contextual inquisitiveness, and the latter is given in the form of alifted conditional(see 2.11 for the definition) indicating that any resolution of the antecedent questionQwill result in the same situation specified by the (non-inquisitive) consequentP. In particular, the distributivity effect imposed on eachalternativeofQechoes the Hamblin-style analysis of unconditionals proposed by Rawlins (2013), and is able to derive the orthogonality
between the antecedent and the corresponding consequent, which, according to Rawlins, is the key semantic contribution of an unconditional utterance.
Inspired by the above structural similarity, as well as Rawlin’s hypothesis that FC effects can also be characterized as conveyingorthogonality, we applied the unconditional analysis in the derivation of Mandarin∀-FC constructions. In particular, we assumed that thewh-phrase headed by ‘wúlùn’ functions as raising anidentityquestion. Moreover, we made a conceptual modification regarding the location of orthogonality—we claim that instead of between the antecedent and the consequent, theorthogonality(conveyed by unconditionals) is actually between the antecedent and the whole proposition. These modifications help extend the coverage of orthogonality to ‘donkey unconditionals’ as in (51), and make it possible to formally define the orthogonality conveyed by FC constructions.
In §3.2.3.2, we introduced into the logical vocabulary anidentification operator?urais- ing the issue about the identity of thedrefu. Functioning as an update function, it takes the input contextcand returns those information statess∈cwhose possibilitiespfeature the same assignment toufrom all the assignment functions inGp(see Definition 97 and
Fig. 3.4 for illustration). It should be clear at this point that the previous assumption ofwh-phrase as an identity question was in fact inspired by the identification operator. Moreover, as discussed in the same section and exemplified in (98) and Fig. 3.4, it is in effect the identification operator?u(and ?uonly) that introduces the inquisitiveness into a wh-question. This observation is quite interesting, as it indicates that at least in the framework of InqD, the plurality requirement of douQ is imposed on the same
object, whether it’s used in an unconditional or a∀-FC construction (withwh-phrases). Moreover, as we will see in the discussion ofdouassociating with definite plurals, the plurality requirement can be captured with a counterpart of the identity question at the possibility-level. But before that, let’s finish the section by extending the semantics of
douQ to the language ofInqD. First we give the semantic sentence of lifted conditionals
(implicationsin Dotlaˇcil and Roelofsen, 2019) inInqD. The notation ‘>’ is overloaded here from Definition 2.11.
(110) A(kk) >B(kk) :=λckλsi.s∈c∧ ∀t⊆s: ∀t′ ∈A(c) [t≼t′ →t≼B(A(c))] =λckλsi.s∈c∧ ∀α∈alt(A({s}↓)) :α≼B(A({s}↓)),where
- {s}↓ :={t|t⊆s}denotes the downward-closure ofs.
Note that here the notationaltfollows the Definition 3.10 inInqD, whereas the one in (49)
is itsInqBcounterpart defined in Definition 2.2. The first line of the definition shows that
A(kk) >B(kk) updates an arbitrary contextc to the (downward-closed) set of information
states s ∈ c where for any t ⊆ s (thus t is also in the set), if t subsists in/supports the updateA(c), then it subsists in/supports the further updateB(A(c)) as well. The second line rewrites the first line in terms of alternatives, namely, the update function A > B
takes those information statess ∈ cwhose ‘local’ update byA, i.e.A({s}↓), supports the further update B(A({s}↓)), where the downward closure {s}↓ of s is taken as the local context to be tested. Now we can give the semantic interpretation ofdouQ inInqD, as
shown in (111)24: (111) ⟦douQ⟧:=λPTλQTλckλsi. |alt(Q(c))|>1 | {z } plurality .s∈c∧ ∀α∈alt(A({s}↓)) : α≼B(A({s}↓)) | {z } distributivity effect
This (dynamic) interpretation ofdouQderives the unconditional reading and∀-FC read-
ing of corresponding Mandarin constructions in almost the same way as (54), which is illustrated by the diagrams shown in Fig. (2.3). The only two differences are as follows. First, whereas the contextc is a relativized notion based on which the antecedent and consequent propositions are evaluated, here it enters into the semantic composition di- rectly. Second, whereas in the static system the identity ofuis treated as a piece of world information that contributes to the identification of the actual world, in the dynamic sys- temInqD, it is attributed to the discourse information. Therefore, the two-dimensional
representation in Fig. (2.3) can be easily adapted to the dynamic setting where each black dot stands for a possibility and each row corresponds to an information state resolving the question?u.