User:Magnap/Completeness Proposal

Depends on: Inquisitive Semantics Proposal

What does it mean to be an answer to a question? Take the following examples:

• Ma shê, ꝡä bu dua jí, mä reutoaı gú rá sáq rá jó, nä dua jí, ꝡä reutoaı hí mea gú róı sáq róı jó móq? (if I don't know whether 2 nor 3 nor 4 are primes, do I know which among 2, 3, and 4 is/are prime?)
• Ma shê, ꝡä dua jí, ꝡä reutoaı jó, rú bu dua jí, mä reutoaı gú rá sáq ,nä dua jí, ꝡä reutoaı hí mea gú róı sáq róı jó móq? (if I know that 4 is a prime and I don't know whether 2 nor 3 are primes, do I know which among 2, 3, and 4 is a prime / are prime?)
• Ma shê, ꝡä dua jí, ꝡä reutoaı gú rú sáq, rú bu dua jí, mä reutoaı jó, nä dua jí, ꝡä reutoaı hí mea gú róı sáq róı jó móq? (if I know that 2 and 3 are primes and I don't know whether 4 is a prime, do I know which among 2, 3, and 4 is a prime / are prime?)
• Ma shê, ꝡä dua jí, ꝡä reutoaı gú rú sáq, rú dua jí, ꝡä bu reutoaı jó, nä dua jí, ꝡä reutoaı hí mea gú róı sáq róı jó móq? (if I know that 2 and 3 are primes and I know that 4 is not a prime, do I know which among 2, 3, and 4 is a prime / are prime?)
• Ma shê, ꝡä dua jí, ꝡä reutoaı gú, rú dua jí, ꝡä bu reutoaı jó, rú bu dua jí, mä reutoaı sáq, nä dua jí, ꝡä reutoaı hí mea gú róı sáq róı jó móq? (if I know that 2 is a prime, and that 4 is not a prime, and I don't know whether 3 is a prime, do I know which among 2, 3, and 4 is a prime / are prime?)

This proposal aims to clear up such questions.

Note that we cannot rely solely on our intuitions to disambiguate! Take the following scenario, in which German-speakers and English-speakers have different intuitions for the exhaustivity of "to correctly predict"/"korrekt vorhersagen" (adapted from this paper):

We have a string of letters, "XXXX", and I predict that the two middle letters will change. Then, the string becomes "XOOO".

• Was my prediction correct? No.
• War meine Vorhersage korrekt? Ja. ("Was my prediction correct? Yes.")
• Ma due shíudua jıbo móq? ("Was my prediction correct?")

TODO Background

• Roelofsen, F., Theiler, N., & Aloni, M. (2014). Embedded interrogatives : the role of false answers. Presented at the 7th questions in discourse workshop, Göttingen, Sept 2014.
• Theiler, N. (2014). A multitude of answers: Embedded questions in typed inquisitive semantics. MSc thesis, University of Amsterdam, supervised by M. Aloni and F. Roelofsen.

TODO paint the rest of the owl

We will need to add a new phrase to the grammar, the completeness phrase, which will have a completeness operator as its head, and we'll have to pick exactly one of the following as its complement: a $\Sigma {\text{P}}$, a ${\text{CP}}$, or a ${\text{DP}}$. Completeness operators map a proposition to the (not necessarily downwards closed! thus, not necessarily a proposition) set of suitable answers to it in some world (each of which is a truth-conditional proposition). TODO describe the completeness operators. However, it will usually have a null head. Alternatively, we could have completeness be lexical for clause-embedding words, which would avoid building a concept of a "suitable answer" into the semantics (as long as we don't attempt lexicosemantics on predicates).