## 1. Preliminaries



R.G. Collingwood (1939) was an early advocate of taking questions
seriously. In the decades since the publication of Collingwood's
autobiography the topic of questions has regularly received attention
from linguists, logicians, and philosophers of language, but few have
joined Collingwood (1939, 36-37) in suggesting that
propositional logic be replaced by a logic of question and answer in
which neither question nor proposition is more basic. Instead, most
work on questions in the philosophy of language and in formal
semantics fits squarely within a reductive paradigm inspired 
by (if not perfectly reflective of) Frege in which
propositions, declarative sentences, and assertion have primacy. The
primacy of the assertoric is especially evident in the work of many
who write on the semantics of what Belnap and Steel (1976) call
elementary questions and who regard any such question as being
identifiable with a set or function involving the propositions that
are the question's answers. Only relatively recently, an
alternative to this reductive paradigm, taking up
Collingwood's suggestion to replace classical logic with a logic
of questions and propositions in which neither question nor
proposition is seen as more basic, has gained traction under the
heading of *inquisitive semantics* (Ciardelli *et al*.
2018).


### 1.1 Questions, answers, and presuppositions



Familiar considerations from the philosophy of language make it clear
that one should distinguish interrogative sentences from their
contents and distinguish both of these from the speech acts that can
be performed via the utterance of interrogative sentences. For
example, Belnap and Steel (1976, 3) understand a question to be an
abstract thing for which an interrogative sentence is a piece of
notation. This parallels the distinction between propositions and the
declarative sentences that express them. The structure and composition
of a question (understood as the abstract content of an interrogative
sentence) vary from theory to theory. The speech act of asking a
question is standardly regarded, e.g., by Searle (1969, 69), as a
special case of the illocutionary act of requesting. Searle
distinguishes requesting information (asking a real question) from
requesting that the hearer display knowledge (asking an exam
question). Aqvist (1965) connects questions with speaker
knowledge rather than hearer knowledge by proposing that to ask a
question is to command the hearer to cause the speaker to know the
question's answer.



As is already clear, an important concept in many theories of
questions is that of an answer, sometimes called a *direct
answer*. Many theorists agree that an answer is a piece of
language or semantic object that, as Belnap and Steel (1976, 3) put
it, "completely, but just completely, answers the
question." A sentence or proposition need not be true to be a
direct answer. Whether each question can be associated with a definite
set of direct answers is a controversial matter, however. Most authors
require answers to be sentences or propositions, so that answers to a
question are the kind of thing that is true or false. Tichy (1978) is
a striking exception and argues that answers can be of any logical
type. Consider this example:


* (1) Who was the
President of the USA in 1978?
* a.
Jimmy Carter was the
President of the USA in 1978.
* b.
Gerald Ford was the
President of the USA in 1978.
* c.
Jimmy Carter
* d.
Gerald Ford
* e.
Someone over three
inches tall was the President of the USA in 1978.



Most theorists would say that (1a) is the correct answer to (1), that
(1b) is an answer but not the correct answer, and that (1c-e)
are not answers to (1) at all. Tichy would say that, among
(1a-e), only (1c-d) are answers, and (1c) is the correct
answer. Braun (2006) would count (1a-b) as answers and include
(1e) as both an answer and a correct answer. What these different
theoretical interpretations of the notion of an answer show is there
is no univocal pre-theoretical notion of an answer. The notion should
rather be seen as a technical one, which can differ from one theory to
another. Some theorists make explicit what they understand answers to
be, but some leave this implicit. This can be problematic: without
explication of which pre-theoretical construct the technical notion of
an answer in a given theory is intended to capture, the theory cannot
be evaluated empirically.



A second important basic concept connected with questions is that of a
*presupposition*. Belnap and Steel (1976, 5) define a question
as presupposing a statement if and only if the truth of the statement
is a logically necessary condition for there being a true (i.e.,
correct) answer to the question. For example, (1a) presupposes the
following:


* (2) The USA had exactly
one President in 1978.



To deny a presupposition of a question is to give a *corrective
answer* to the question, but most theorists join Belnap and Steel
in not counting corrective answers as direct answers.


### 1.2 Kinds of questions



Several kinds of questions have been distinguished in the
literature.



*Whether-questions* are questions like 'Was there a
quorum at the meeting?' and 'Does Jones live in Italy, in
Spain, or in Germany?'. These examples illustrate that
whether-questions come in two varieties: a whether-question may be of
the yes-or-no variety, or it may present two or more alternative
direct answers other than yes and no. In either case, a
whether-question explicitly presents a finite number of direct
answers. Consider the first example:


* (3)Was there a quorum
at the meeting?
* a.
There was a quorum at the meeting.
* b.
There was no quorum at the meeting.



The answers to (3) are (3a-b), and (3) presupposes that the
meeting occurred. Thus (4) is a corrective answer to (3):


* (4)
The meeting did not take place.



Question (5) is ambiguous:


* (5)Does Jones live in
Italy, in Spain, or in Germany?
* a.
Jones lives in Italy.
* b.
Jones lives in Spain.
* c.
Jones lives in Germany.



Question (5) can be read as a yes-no question having two direct
answers, but it also has a reading on which it presents exactly three
direct answers, namely (5a-c). On the latter reading, (5)
presupposes that Jones lives in Italy, in Spain, or in Germany; thus
(6) is a corrective answer to (5):


* (6)Jones does not live
in Italy, in Spain, or in Germany.



*Which*-questions are questions like 'What is the
smallest prime number greater than 12?', 'Which cardinal
was elected Pope in 2013?', and 'Who shot J.R.?'
Unlike a whether-question, a which-question may have an indefinite or
infinite number of direct answers.



Belnap and Steel (1976) refer to whether- and which-questions as
*elementary questions*. We consider these kinds of questions in
detail in section 2.



Another major category of questions are *why*-questions. It has
long been recognized that why-questions are intimately linked with the
concept of explanation. For example, Hempel and Oppenheim (1948, 334)
write as follows:



> 
> A scientific explanation may be regarded as an answer to a
> why-question, such as "Why do the planets move in elliptical
> orbits with the sun at one focus?"
> 



We consider why-questions in detail in section 3.



Yet another major category of questions are *embedded* or
*indirect* questions, which occur as complements of
clause-embedding predicates such as 'know' and 'wonder':


* (7) John knows /
wonders *who spoke to Mary*.



The issue of how to understand embedded questions lies at the
intersection of the philosophy of language and epistemology and will
be treated in section 4.


## 2. The semantics of elementary questions



This section provides an overview of some of the most prominent
treatments of elementary questions at the intersection of philosophy
of language and formal semantics.


### 2.1 Classical semantic theories of questions


#### 2.1.1 Hamblin semantics



A common starting point for many formal semantic treatments of
questions is the idea that "questions set up a choice-situation
between a set of propositions, namely those propositions that count as
answers to it" (Hamblin 1973, 48). One way to implement this
idea is to take a question to denote, in a world \(w\), the set of
propositions that correspond to a possible answer to the question
(Hamblin 1973). Another way to implement the same idea is to let a
question denote, in a world \(w\), the set of propositions that
correspond to its *true* answers in \(w\) (Karttunen 1977). In
both systems, the *meaning* of a question is a function from
worlds to sets of propositions. In Hamblin's system, this
function maps every possible world to the same set of propositions,
corresponding to the set of all possible answers; in Karttunen's
system, every world is mapped to a subset of all possible answers,
namely those that are true in the given world. As acknowledged by
Karttunen (1977, 10), the difference is inessential. In both cases,
the meaning of a question is fully determined by--and could be
identified with--the set of all propositions that correspond to a
possible answer.



A fundamental problem with these accounts is that they do not specify
in more detail what "possible answers" are supposed to be.
Of course, they do provide a compositional semantics for a fragment of
English, and thereby specify what they take to be the possible answers
to the questions in that fragment. But in order for these theories to
be evaluated, we first need to know what the notion of a
"possible answer" is intended to capture. To illustrate
this point, consider the following example:


* (8) Who is coming for
dinner tonight?
* a.
Paul is coming.
* b.
Only Paul and Nina are
coming.
* c.
Some girls from my class
are coming.
* d.
I don't
know.



In principle, all the responses in (8a-d) could be seen as
possible answers to (8). For Hamblin and Karttunen, only (8a) counts
as such. However, it is not clear what the precise criteria are for
being considered a possible answer, and on which grounds (8a) is to be
distinguished from (8b-d).


#### 2.1.2 Partition semantics



Groenendijk and Stokhof (1984) take a question to denote, in each
world, a single proposition embodying the *true exhaustive*
answer to the question in that world. For instance, if \(w\) is a
world in which Paul and Nina are coming for dinner, and nobody else is
coming, then the denotation of (8) in \(w\) is the proposition
expressed by (8b).



The *meaning* of a question, then, is a function from worlds to
propositions. These propositions have two special properties: they are
*mutually exclusive* (since two different exhaustive answers
are always incompatible), and together they form a *cover* of
the entire logical space (since every world is compatible with at
least one exhaustive answer). So the meaning of a question can be
identified with a set of propositions which form a *partition*
of the logical space.



In many cases, it is intuitively clear what the "true exhaustive
answer" to a question in a given world is, at least much clearer
than what all the "possible answers" to that question are.
This means that a partition semantics can in many cases be tested
against clear intuitions, unlike a Hamblin semantics.



However, in some cases it is not so clear what the "true
exhaustive answer" to a question in a given world is. Consider
the following examples (in (10) we use \(\uparrow\) and \(\downarrow\)
to indicate rising and falling intonation, respectively):


* (9) If Ann is coming,
will Bill come as well? [conditional question]
* (10) Is
Ann\(\uparrow\) coming, or Bill\(\downarrow\)? [alternative
question]



What is the true exhaustive answer to (9) in a world where Ann is
coming and Bill is coming as well? One option is the proposition
\(\{w\): Ann and Bill are both coming in \(w\}\), but another option
is the proposition \(\{w\): if Ann is coming in \(w\) then Bill is
also coming in \(w\}\). It is not quite clear pre-theoretically which
of these two options is more suitable. Notice that if we pick the
second option, then we must assume that the true exhaustive answer to
(9) in a world where Ann is coming but Bill is not coming is \(\{w\):
if Ann is coming in \(w\) then Bill is not coming in \(w\}\). And this
would mean that these two 'exhaustive' answers actually
overlap (they both contain all worlds where Ann is not coming) and
thus do not form a partition. This may be considered a reason to pick
the first option instead. However, this line of reasoning is purely
theory-internal; it seems impossible to decide on theory-external
grounds what the true exhaustive answers to a conditional question
should be taken to be. 



Conditional questions like (9) also present another challenge for a
partition semantics, concerning answers that deny the antecedent of
the conditional (in this case the answer that Ann is not coming).
Intuitively, such answers dispel the issue raised by the question, but
do not resolve the issue as intended. Their status differs from
answers that do resolve the issue as intended (in this case the answer
that Bill is coming if Ann is coming, and the answer that Bill is not
coming if Ann is coming). In a basic partition semantics it is
impossible to capture this. In worlds where Ann is not coming, the
answer that Ann is not coming presumably is the true exhaustive
answer. Its special status, however, cannot be captured.



A similar problem arises with alternative questions like (10). In this
case, the answer that neither Ann nor Bill is coming and the answer
that Ann and Bill are both coming have a different status than the
answer that only Ann is coming and the answer that only Bill is
coming. Again, this difference in status cannot be captured in a
simple partition semantics.


### 2.2 Questions in dynamic semantics


#### 2.2.1 Updating equivalence relations



We now turn our attention to a line of work that aims to capture the
semantics of questions in a *dynamic* framework. The first
theories in this line of work were developed by Jager (1996),
Hulstijn (1997), and Groenendijk (1999). Aloni *et al*. (2007b)
contains a collection of papers elaborating on these early proposals.
All these theories essentially reformulate the partition theory of
questions in the format of an update semantics (Veltman 1996). This
means that they explicitly identify meanings with *context change
potentials*, i.e., functions over discourse contexts. However,
unlike a simple update semantics where discourse contexts are modeled
as sets of worlds--embodying the information established in the
discourse so far--these theories provide a more refined model of
discourse contexts, one that also embodies the issues that have been
raised so far. More specifically, a discourse context is modeled as an
*equivalence relation* \(R\) over a set of worlds \(C\). The
set of worlds \(C\), i.e., the domain of \(R\), can be thought of as
the *context set*, i.e., the set of all worlds that are
compatible with the information established in the discourse so far.
\(R\) itself induces a partition on \(C\), and can thus be taken to
encode the issues that have been raised so far. More specifically, we
can think of \(R\) as relating two worlds \(w\) and \(v\) just in case
the difference between \(w\) and \(v\) is not (yet) at issue, i.e.,
the discourse participants have not yet expressed an interest in
information that would distinguish between \(w\) and \(v\). In other
words, \(R\) can be conceived of as a relation encoding
*indifference* (Hulstijn 1997).



Both assertions and questions can then be taken to have the potential
to change the context in which they are uttered. Assertions restrict
the context set \(C\) to those worlds in which the asserted sentence
is true (strictly speaking, they remove all pairs of worlds \(\langle
w,v\rangle\) from \(R\) such that the asserted sentence is false in at
least one of the two worlds). Questions *disconnect* worlds,
i.e., they remove a pair \(\langle w,v\rangle\) from \(R\) just in
case the true exhaustive answer to the question in \(w\) differs from
the true exhaustive answer to the question in \(v\).



Thus, the dynamic framework of Jager (1996), Hulstijn (1997), and
Groenendijk (1999) provides a notion of context and meaning that
embodies both informative and inquisitive content in a uniform way.
However, the framework inherits several issues from the classical
partition theory of questions, in particular those discussed above
concerning conditional and alternative questions.



Moreover, there is a conceptual issue concerning the equivalence
relation \(R\). Namely, if \(R\) is primarily thought of as a relation
encoding *indifference*, then it is not clear why it should
always be an *equivalence relation*. In particular, it is not
clear why \(R\) should always be *transitive*. The discourse
participants could very well be interested in information that
distinguishes \(w\) from \(v\), while they are not interested in
information that distinguishes either \(w\) or \(v\) from a third
world \(u\). To model such a situation, we would need an indifference
relation \(R\) such that \(\langle w,u\rangle \in R\) and \(\langle
u,v\rangle \in R\) but \(\langle w,v\rangle \not\in R\). This is
impossible if we require \(R\) to be transitive.


#### 2.2.2 Giving up transitivity



These concerns have been addressed by Groenendijk (2009) and
Mascarenhas (2009). The overall architecture of their system is very
much like that of the early dynamic systems discussed above, only
indifference relations are no longer defined as equivalence relations,
but rather as reflexive and symmetric (not necessarily transitive)
relations.



Groenendijk and Mascarenhas argued that this adjustment, besides
addressing the conceptual issue concerning indifference relations
discussed above, also allows for a better analysis of conditional
questions and alternative questions. However, Ciardelli (2009) and
Ciardelli and Roelofsen (2011) show that, although the proposed system
indeed behaves better for simple cases, it does not scale up to more
complex cases in a suitable way. In particular, whereas alternative
questions with two disjuncts, like (10) above, are dealt with
satisfactorily, or at least more satisfactorily than in a partition
semantics, alternative questions with three or more disjuncts are
still problematic.



The gist of the problem can be illustrated with a simple example.
Consider a language with three atomic sentences, \(p, q\), and \(r\),
and an information state consisting of three worlds, \(w\_{pq},
w\_{qr}\), and \(w\_{pr}\), where the subscripts of each world indicate
which atomic sentences are true at that world. Note that in this
information state none of the atomic sentences is known to hold. Now
consider an issue which is resolved just in case at least one of the
atomic sentences is established, i.e., just in case we know that the
actual world is located within one of the ovals depicted in figure
1.



![an alternative question with three disjuncts](figure-1-three-ovals.png)

Figure 1: An issue that cannot be
represented in the pair-semantics.




The problem with the system of Groenendijk (2009) and Mascarenhas
(2009) is manifested by the fact that this issue cannot be represented
by means of an indifference relation. An indifference relation over
the information state \(\{w\_{pq},w\_{qr},w\_{pr}\}\) necessarily
contains all reflexive world-pairs, and possibly one, two, or three
non-reflexive pairs. In either case, however, the resulting issue does
not correspond to the one depicted in Figure 1.



The general conclusion that has been drawn from this problem, as
discussed in detail by Ciardelli and Roelofsen (2011), is that
question meanings cannot be suitably modeled in terms of indifference
relations, even if these indifference relations are allowed to be
non-transitive. This insight has led to the development of an
alternative logical notion of question meanings, which forms the
cornerstone of the framework of *inquisitive semantics*, to be
discussed below.


### 2.3 Inquisitive semantics


#### 2.3.1 The basic system



Recall from section 2.1.1 that a fundamental problem with the
classical semantic theories of Hamblin (1973) and Karttunen (1977) is
that they do not specify clear criteria for when a response should
count as a "possible answer". Partition semantics
(Groenendijk and Stokhof 1984) does specify explicitly which responses
should count as possible answers, namely only those that are true and
exhaustive. In many cases, it is clear what the true and exhaustive
responses to a given question are. However, this is not always the
case, as witnessed by conditional and alternative questions. A natural
way to proceed, then, is to consider another criterion for what should
count as a possible answer.



One natural criterion is the following. We could say that a response
to a question counts as a proper answer just in case it
*resolves* the issue that the question raises. If we adopt this
criterion then we also have to impose a certain structural condition
on question-meanings. That is, question-meanings cannot just be
defined as arbitrary sets of propositions, as in the theories of
Hamblin (1973) and Karttunen (1977). Rather, they should be defined as
*downward closed* sets of propositions. That is, if a question
meaning contains a certain proposition \(\alpha\), then it must also
contain all stronger propositions \(\beta \subseteq \alpha\). After
all, suppose that \(\alpha\) is an element of the meaning of a
question \(Q\). Given our answerhood criterion, this means that
\(\alpha\) corresponds to an issue-resolving response to \(Q\). But
then every \(\beta \subseteq \alpha\) corresponds to an even more
informative, and therefore also issue-resolving response. So, given
our answerhood criterion, \(\beta\) must also be an element of the
meaning of \(Q\).



This conception of question meanings forms the cornerstone of the most
basic implementation of *inquisitive semantics*, the system
\(\Inq\_B\) (Groenendijk and Roelofsen 2009, Ciardelli 2009, Ciardelli
and Roelofsen 2011, Roelofsen 2013, Ciardelli 2016, Ciardelli *et
al.* 2018). In this system, question meanings are defined as
downward closed sets of propositions that together cover the entire
logical
 space.[1]
 We will refer to such sets as *inquisitive* *question*
*meanings*.[2]



Partitions correspond to a specific kind of inquisitive question
meanings. That is, for every partition \(\rP\), there is a
corresponding inquisitive question meaning \(I\_{\rP}\), consisting of
all propositions that are contained in one of the blocks in
\(\rP\):



\(I\_{\rP} : = \{\alpha \subseteq \beta \mid \beta \in \rP\}\) 



However, not every inquisitive question meaning corresponds to a
partition. In fact, an inquisitive question meaning \(I\) corresponds
to a partition if and only if for every subset \(I'\subseteq I\) such
that \(\cap I'\ne \varnothing\), \(\cup I'\) is also in \(I\). There
are many inquisitive question meanings that do not have this special
property. Thus, the notion of question meanings in \(\Inq\_B\) is more
general than the notion of question meanings in partition
semantics.



The set of all meanings in \(\Inq\_B\), together with a suitable notion
of entailment, form a Heyting algebra, just like the set of all
meanings in classical logic ordered by classical entailment (Roelofsen
2013). Thus, the basic connectives (disjunction, conjunction,
implication, and negation) can be associated with the basic algebraic
operations on meanings (join, meet, and (relative)
pseudo-complementation), just as in classical logic. This is indeed
how the connectives are treated in \(\Inq\_B\), although other
treatments of the connectives are also conceivable in this setting
(see, e.g., Ciardelli *et al*. 2015).


#### 2.3.2 Some extensions



In recent work, the basic system sketched above has been extended in
several directions. Below are pointers to some of these
extensions.



Ciardelli *et al*. (2012) consider a notion of meaning that is
very much like the one adopted in \(\Inq\_B\), but also has a
*presuppositional* component. Such a notion of meaning is
needed to suitably deal with alternative questions and
*which*-questions.



Ciardelli *et al*. (2017) develop a type-theoretic inquisitive
semantics, which is needed for a compositional semantic analysis of
questions.



Roelofsen and Farkas (2015) develop an inquisitive semantics in which
the meaning of a question does not only capture what is needed to
resolve the issue raised by that question, but also which propositions
are made available by the question for subsequent anaphoric reference.
These propositions may serve as antecedents for polarity particles
(e.g. *Is Paul coming? Yes/No* ) and other anaphoric
expressions (e.g. *Is Paul coming? Then/otherwise I'll make
pasta* ).



Farkas and Roelofsen (2017) integrate inquisitive semantics with a
commitment-based model of discourse, in order to capture the special
discourse effects of non-canonical types of questions, such as
tag-questions (*Paul is coming, isn't he?* ) and
declarative questions (*Paul is coming?* ).



Finally, Ciardelli and Roelofsen (2015), Ciardelli (2016), and van
Gessel (2016) develop a system that integrates inquisitive semantics
with *dynamic epistemic logic* (van Ditmarsch *et al*.
2007), in order to formally model the information states and
inquisitive states of the participants of a discourse, and how these
states change when a question is asked or a statement is made. It also
provides a semantics for question-embedding predicates like
'know' and 'wonder' (see also section 4).


### 2.4 Structured question meanings



The theories discussed above all construe question meanings as sets of
propositions, and are therefore referred to as *proposition
set* theories. It has been argued that question meanings as
construed by proposition set theories are all too coarse-grained to
account for certain linguistic phenomena. In order to address this
issue, several theories have been developed that adopt more
fine-grained, *structured* notions of question meanings. Such
theories have been couched in different semantic frameworks, which are
all more fine-grained than the standard possible world framework. For
instance, the proposal of Krifka (2001) is couched in a structured
meanings framework, that of Ginzburg and Sag (2000) in situation
semantics, that of Ginzburg (2005), Cooper and Ginzburg (2012) in type
theory with records, that of Aloni *et al.* (2007a) in dynamic
semantics, and that of Blutner (2012) in ortho-algebraic semantics. We
will illustrate the general approach here by focusing on the proposal
of Krifka (2001), which in turn has its roots in earlier work of Hull
(1975), Tichy (1978), Hausser (1978), von Stechow and Zimmermann
(1984), von Stechow (1991), and Ginzburg (1992).



The central idea is that question meanings are pairs \(\langle
B,R\rangle\), where \(B\) is called the *background* and \(R\)
the *restriction*. \(B\) is a function that, when applied to
the semantic value of an appropriate term answer to the question,
yields a proposition. \(R\) specifies what appropriate term answers
are, i.e., what the semantic entities are that \(B\) can be applied
to.



For instance, the meaning assigned to (11a) is
 (11b):[3]


* (11)  a.
Which student
called?
* b.
\(\langle \lambda
x.\lambda w.called(x)(w),\text{ students}\rangle\)



In this case, \(B\) is a function that maps every individual \(x\) to
the proposition \(\{w: x\) called in \(w\}\), and \(R\) is the set of
students. In the case of a polar question, \(R\) is taken to be a set
consisting of two functions on propositions, the identity function and
the function that maps every proposition to its complement, which are
assumed to be expressed by *yes* and *no*, respectively.
For instance:


* (12)  a.
Did Mary call?
* b.
\(\langle \lambda
f.f(\lambda w.called(m)(w)),\{\lambda p.p,\lambda p.\neg
p\}\rangle\)



From a structured question meaning it is always possible to obtain the
corresponding proposition set meaning, by applying \(B\) to all the
elements of \(R\) (and taking the downward closure of the resulting
set of propositions in case we want an inquisitive question meaning in
the sense of \(\Inq\_B\). It is not possible to go in the other
direction, which means that structured question meanings have strictly
more expressive power than proposition set meanings (e.g., von Stechow
1991, Krifka 2001). 



This additional expressive power is needed to account for certain
phenomena. For instance, the questions in (13) and (14) have exactly
the same set of exhaustive/resolving answers, which means that they
receive exactly the same semantic value in any of the proposition set
accounts discussed above.


* (13)Is the door open?
Yes. / No.
* (14)Is the door open or
closed? \*Yes. / \*No.



Yet, the two questions differ in that the first licenses answer
particles like 'yes' and 'no' while the second
doesn't. In a structured-meanings approach, the two questions
are semantically distinguishable. This additional semantic
fine-grainedness forms the basis for an account of polarity particle
responses.



Note that some of the extended implementations of inquisitive
semantics (e.g., Roelofsen and Farkas 2015) are also fine-grained
enough to account for answer particles. As mentioned above, in these
implementations the meaning of a question does not only capture what
is needed to resolve the issue that the question raises, but also
which propositions are made available by the question for subsequent
anaphoric reference, for instance by answer particles. In effect,
capturing anaphoric potential also adds structure to question
meanings. Thus, these implementations maintain a proposition set
perspective, but at the same time address the need for richer semantic
structures as well. Such a synthesis is also achieved in Aloni *et
al.* (2007a).


### 2.5 Pointers to further reading



The overview provided here of semantic theories of elementary
questions is of course not exhaustive. There are a number of excellent
recent handbook articles, each focusing on different aspects.
Groenendijk and Stokhof (1997) provide a thorough review of the
literature up to 1997, focusing on the partition theory, but also
supplying an in-depth discussion of the epistemic-imperative approach
(Aqvist 1965, Hintikka 1976, Hintikka 1983) and the treatment of
questions in speech act theory (Searle 1969, Vanderveeken 1990).



Ginzburg (2010) provides a concise overview of several more recent
analyses of questions, including, besides the ones discussed here, the
*inferential erotetic logic* of Wisniewski (2001), the
treatment of questions in modal logic by Nelken and Francez (2002) and
Nelken and Shan (2006), the dialogue-based approach of Ginzburg
(1996), Ginzburg (2012), Roberts (1996), Larsson (2002), among others,
the SDRT based approach of Asher and Lascarides (1998), and the
treatment of questions in *dynamic epistemic logic* developed
by van Benthem and Minica (2012). For comparison of the latter
approach with inquisitive semantics, see Ciardelli and Roelofsen
(2015) and Ciardelli (2016).



Finally, Krifka (2011) provides an overview of the classical
proposition set accounts, early implementations of inquisitive
semantics, and the structured meanings approach, taking a more
linguistic perspective than other overview articles. Krifka does not
only discuss the semantics of questions, but also their possible
syntactic configurations and intonation patterns, supplying examples
from a wide range of languages.


## 3. Why-questions



For whether-questions (indeed, for all elementary questions in the
view of some), the question-answer relationship can be defined in
purely formal terms. One approach to why-questions is to try to make
the question-answer relationship formal in that case, too, or at least
as formal as possible. The main proponent of this approach is
Bromberger (1966), whose account is also the first influential account
of why-questions. Van Fraassen (1980) takes an opposite view,
theorizing that the question-answer relationship is almost purely
pragmatic. Skow (2016) proposes a theory that is neither formal nor
pragmatic but is instead metaphysical, claiming that answers to
lower-level why-questions always identify causes or grounds. We
consider all three theories in some detail below.


### 3.1 A formal approach: abnormic laws



If we follow Hempel in regarding an explanation as an answer to a
why-question, Bromberger's theory of why-questions can be seen
also as a theory of explanation, indeed, one that incorporates
Hempel's deductive-nomological model while aiming to improve on
it.



Bromberger introduces several concepts for use in his account: the
*presupposition* of a why-question, *abnormic laws* and
their *antonymic predicates*, and *general rules*,
focusing especially on general rules that are *completed by*
abnormic laws.



Bromberger supposes that (15) is the general form of a
why-question:


* (15)Why is it the case
that \(p\)?



The presupposition of (15) is \(p\), and this agrees with the usual
concept of presupposition for questions, since if \(p\) is not the
case then (15) has no correct answer. A *general rule* is a
(true or false) law-like statement of the form:


* \(\forall x(Fx
\rightarrow G\)x),



where \(Fx\) and \(Gx\) may, in the general case, be conjunctions. A
*special abnormic law* is a true, law-like statement of the
form:


* \(\forall x(Fx
\rightarrow(Ex \leftrightarrow(A\_1 x \vee \ldots \vee
A\_n\)x))).



Special abnormic laws satisfy five additional conditions of
non-triviality and non-redundancy that we need not get into, and
Bromberger (1966, 98) introduces the more complicated notion of a
general abnormic law, which we may also ignore for present purposes.
The predicate \(E\) appearing in a special abnormic law and
\(E\)'s negation are the *antonymic predicates* of the
abnormic law. Bromberger (1966, 98) illustrates the concept of an
abnormic law with the following example:



> 
> No sample of gas expands unless its temperature is kept constant but
> its pressure decreases, or its pressure is kept constant but its
> temperature increases, or its absolute temperature increases by a
> larger factor than its pressure, or its pressure decreases by a larger
> factor than its absolute temperature.
> 



The antonymic predicates of this special abnormic law are
'expands' and 'does not expand', and the
logical form that Bromberger's theory postulates for this
abnormic law is as
 follows:[4]


* (16)  \(\forall x(Gx
\rightarrow(Ex \leftrightarrow (Tx \vee Px \vee Ax \vee Dx)))\)



Bromberger (1966, 99) defines the completion of a general rule by an
abnormic law as follows:



> 
> An abnormic law is the completion of a general rule if and only if the
> general rule is false and is obtainable by dropping the
> "unless" qualifications. ([...] this requires
> negating the predicate substituted for \(E\)--or dropping the
> negation if it is already negated--deleting the biconditional
> connective, and making the obvious bracketing adjustments.)
> 



Abnormic law (16) is the completion of the (false) general rule
'No gas expands':


* (17)  \(\forall x(Gx
\rightarrow \neg Ex)\)



Bromberger (1966, 100) goes on to define the correct answer to a why
question as follows: \(q\) is the correct answer to (15) if and only
if (i) there is an abnormic law \(L\) (which may be general or
special) and \(p\) is the proposition that results from predicating of
some individual one of the antonymic predicates of \(L\); and (ii)
\(q\) together with \(L\) and other premises \(r\_1 ,\ldots ,r\_j\)
constitute a deductive-nomological explanation with conclusion \(p\);
and (iii) there is a false proposition \(s\) such that \(s\) and \(p\)
are contraries and, were it not for the falsity of \(s\) and \(L\),
premises \(r\_1 ,\ldots ,r\_j\) and the general rule completed by \(L\)
would count as a deductive-nomological explanation of \(s\); and (iv)
the general rule completed by \(L\) is such that if one of the
conjuncts of its antecedent is removed, the resulting general rule
cannot be completed by an abnormic law.



Here is an illustration of Bromberger's theory based on abnormic
law (16). Suppose \(a\) is a sample of gas that expanded, and suppose
its pressure was kept constant but its temperature increased, i.e.,
\(Ga\), \(Ea\), and \(Pa\) are all true. Now consider the
question:


* (18) Why did \(a\)
expand?



On Bromberger's theory, the correct answer is \(Pa\), i.e., 


* (19) The pressure of \(a\) was
kept constant while the temperature of \(a\) increased.



This is the correct answer because \(Pa\), along with \(Ga\) and
abnormic law (16) form the premises of a deductive-nomological
explanation with conclusion \(Ea\), but when \(Pa\) is deleted as a
premise (leaving \(Ga\) as a premise) and general rule (17) is
substituted for abnormic law (16) as a premise, we obtain argument
(20), which would count as a deductive-nomological explanation of
\(\neg Ea\), were it not for the fact that (17) and \(\neg Ea\) are
not true: 


* (20)  \(a\) is a
sample of gas; no sample of gas expands; therefore \(a\) did not
expand, i.e., \(Ga\); \(\forall x(Gx\rightarrow \neg Ex)\); therefore
\(\neg Ea\).



So, in this application of Bromberger's theory, \(p\) is \(Ea\),
\(q\) is \(Pa\), \(L\) is (16), the general rule completed by \(L\) is
(17), \(r\_1\) is \(Ga\), and \(s\) is \(\neg Ea\).



Intuitively, Bromberger's account makes \(Pa\) the correct
answer to (18) in virtue of the idea that \(Pa\) is a full
specification of the special (or "abnormal") circumstances
triggering the expansion of \(a\). Notice that one of the premises of
the deductive-nomological explanation of \(Ea\), namely \(Ga\), is not
part of the triggering package and is not part of the correct answer
to (18). Two factors in Bromberger's account jointly keep \(Ga\)
from being included. The first is that \(Ga\) is a premise not only in
the actual deductive-nomological explanation of \(Ea\) but also in the
fictitious deductive-nomological explanation (20) of \(\neg Ea\). So
relative to (16) and (17), \(Ga\) is not a special or abnormal
circumstance. Is there another abnormic law/general rule pair relative
to which \(Ga\) would be included in the correct answer to (18)?
Apparently not, which brings us to the second factor excluding \(Ga\)
from the correct answer to (18): if \(Gx\) is dropped from (17) we
obtain the general rule 'Nothing expands', which it seems
that no abnormic law
 completes.[5].



Bromberger's theory was aimed at saving certain intuitions about
what should and should not count as correct answers to why-questions.
For example, consider a straight, 40-foot high utility pole standing
perpendicular to the ground. A taut 50-foot wire is fastened to the
top of the pole and to a point on the ground 30 feet from the base of
the pole. Now consider the question:


* (21) Why is the height
of the pole 40 feet?



and the intuitively incorrect answer 


* (22)  Because there is
a 50 foot wire that is tautly stretched between the top of the pole
and a point 30 feet from the base of the pole.



Bromberger (1966, 105) argues that (22) does not count as a correct
answer to (21) on his theory in part because the following is not an
abnormic law:


* (23)  No pole that is
straight and perpendicular to the ground is 40 feet high unless there
is a 50 foot wire that is tautly stretched between the top of the pole
and a point 30 feet from the base of the pole.



Nor would (23) become an abnormic law if additional disjuncts were
added after 'unless'.



Teller (1974) argues that while (22) may not count as a correct answer
to (21) on Bromberger's theory, other answers that are as
objectionable as (22) do get counted as correct answers, such as this
"dispositional" answer to (21):


* (24)  Because if a 50
foot wire were tautly stretched from the top of the pole to the
ground, it would touch the ground at a point 30 feet from the base of
the pole.



Teller (1974, 375) argues that Bromberger's theory requires that
(24) count as a correct answer in virtue of the following abnormic
law:


* (25)  No pole that is
straight and perpendicular to the ground is 40 feet high unless it is
such that if a 50 foot wire were tautly stretched from the top of the
pole to the ground, it would touch the ground at a point 30 feet from
the base of the pole.



Teller proposes other counterexamples by devising a method for turning
examples showing that Hempel's deductive-nomological theory of
explanation is too permissive into examples showing that
Bromberger's theory of why-questions is also too permissive.
Teller's method exploits the fact that when abnormic laws are
rewritten in certain logically equivalent ways, the resulting
statements must then also count as abnormic laws.


### 3.2 A pragmatic approach: explanatory contrast



A second major development in the theory of why-questions is the
account of van Fraassen (1980, ch. 5). Van Fraassen's theory is
motivated by the idea that explanation is not a special relationship
between theory and reality. Rather, an explanation is just a
*description* of reality that serves a contextually determined
purpose, namely that of answering a why-question. Van Fraassen's
theory is thus an erotetic (i.e., question-theoretic) theory of
explanation, as opposed to an account of why-questions in terms of
explanation. He offers this theory in the context of developing his
account of Constructive Empiricism. 



For van Fraassen, a why-question \(Q\) can be identified with a triple
\(\langle P,X,R\rangle\), where \(P\) is a true proposition (the
*topic* of the question); \(X\) is a set of propositions to
which \(P\) belongs and of which \(P\) is the only member that is true
(*the contrast class* of \(Q)\); and \(R\) is a contextually
determined relation of explanatory relevance, which holds between a
proposition and the topic/contrast-class pair \(\langle P,X\rangle\).
The standard linguistic expression of \(Q\) is:


* (26)  Why \(P\) in
contrast to the rest of \(X\)?



For example, consider 'Why do birds in the northern hemisphere
go south for the winter, whereas mammals and reptiles do not?'
In this case, \(P\) is the proposition that birds in the northern
hemisphere go south for the winter, and \(X\) is the set containing
\(P\) along with the proposition that mammals in the northern
hemisphere go south for the winter and the proposition that reptiles
in the northern hemisphere go south for the winter. The contrast class
parameter allows one to distinguish different why-questions that have
the same topic. Thus one can ask why northern hemisphere
*birds* (rather than mammals or reptiles) go south for the
winter, and this is different from asking why northern hemisphere
birds go *south* (rather than north or west) for the winter.
Until one specifies a contrast class, van Fraassen argues, a
particular why-question has not been identified or posed. Like van
Fraassen, Garfinkel (1981) advances a view on which explanatory
contrast takes center stage, but we will focus here on the details of
van Fraassen's account. See Temple 1988 for a comparison of van
Fraassen's and Garfinkel's respective treatments of
explanatory contrast.



Suppose that \(X=\{P,P\_1 ,\ldots ,P\_k,(\ldots)\}\), and that \(P\) is
not one of the \(P\_k\)s. (Note that \(X\) may be finite or infinite.)
Then, where \(A\) is any proposition, van Fraassen (1980, 144) defines
a direct answer to \(Q\) to be any proposition having the following
truth conditions:


* (27)\(P\) and, for all
\(k\ge 1\), \(\neg P\_k\), and \(A\).



The standard wording of a direct answer (28) to \(Q\) uses the word
'because' in place of the second 'and' in
(27):


* (28)\(P\), in contrast
to the rest of \(X\), because \(A\).



On van Fraassen's view, the contribution of
'because' to the truth conditions of (28) is simply
boolean conjunction, as reflected in (27). The role of
'because' in (28) is to perform the pragmatic function of
indicating that (27) is being used for an explanatory purpose, not to
give a non-truth-functional dimension to the truth conditions of (28).
Proposition \(A\) (the core of answer (27)/(28)) is said to be
relevant to \(Q\) iff \(A\) bears the relevance relation \(R\) to
\(\langle P,X\rangle\). In general, to ask why is to ask for a reason,
and \(R\) varies according to the kind of reason that is being
requested in a given context. One can ask why in order to request
causal factors, to request a justification, to request a purpose, to
request a motive, to request a function, and so on.



A why-question, according to van Fraassen (1980, 144-145)
presupposes (i) that its topic is true, (ii) that, in its contrast
class, only its topic is true, and (iii) that at least one proposition
bearing the explanatory relevance relation to the topic/contrast-class
pair is true. When the first or second presupposition fails (because
the contextually determined body of background knowledge in play does
not entail both (i) and (ii)), the why-question *does not
arise*. When the third presupposition fails, the why-question has
no answer even if it arises. For example, suppose that paresis
indeterministically strikes some people who have untreated syphilis.
Then, if ten people have untreated syphilis, and exactly one of them,
John, goes on to contract paresis, there may be no answer to the
question 'Why did John, in contrast to the other nine, contract
paresis?' Since paresis develops indeterministically from
syphilis, nothing favors John (in contrast to the other nine syphilis
patients) as being likely to develop paresis. On the other hand, if
Bill and Sarah never had syphilis, the question 'Why did John,
in contrast to Bill and Sarah, develop paresis?' does have an
answer: 'John developed paresis, in contrast to Bill and Sarah,
because John had syphilis but Bill and Sarah did not.' In this
case, as in the first, the why-question requests causal factors that
led to John's getting paresis while the others mentioned in the
contrast class did not. In both cases, then, the same relevance
relation \(R\) is in play because the same kind of information is
requested, namely causal factors leading to the truth of the topic in
contrast to the other members of the contrast class. If there are no
such causal factors, as in the first version of the paresis case, the
question is to be rejected. If, as in the second version of the
paresis case, there are such factors, so that at least one proposition
bears the relevance relation to the topic/contrast-class pair, then a
candidate answer \(A\) is evaluated according to three criteria: how
acceptable or likely \(A\) is, the degree to which \(A\) favors \(P\)
over other members of \(X\), and whether \(A\) is made irrelevant by
other answers.


#### 3.2.1 How-questions and explanatory contrast



Van Fraassen's theory of why-questions is intended as a theory
of explanation, but why-explanation seems not to be the only kind of
explanation there is. Cross (1991) argues that answers to
how-questions are explanations, too, and, building on van
Fraassen's theory of why-questions, Cross offers a theory of
how-questions that ultimately unifies why- and how-explanation in a
single theory of explanatory questions.



Firstly, it must be noted that not every how-question requests an
explanation. For example, 'How far is it to Cleveland?'
asks for a distance, not an explanation. In general, according to
Cross (1991, 248), a how-question is explanation-seeking whenever
'how' can be paraphrased as 'in what way'.



Secondly, ways, like reasons, come in a variety of kinds (Cross 1991,
248-9):


* (29)a.By
what road (How did you
get here?)
* b.In
what manner (How did
you behave at the party?)
* c.By
what argument (How
will you justify this?)
* d.By
what method (How do
you perform an appendectomy?)
* e.By
what means (How did
you get that money?)
* f.In
what respect (How do
these differ?)
* g.By
what process (How do
DNA molecules replicate?)



Thirdly, Cross argues that one can see phenomena of explanatory
contrast in how-questions in such examples as the following: 


* (30)a.How
do DNA molecules (in
contrast to molecules of benzene and hexane)
replicate?
* b.How
do reptiles (in
contrast to mammals and birds) reproduce?



The linguistic form (31) of a how-question and its answer (32),
according to Cross, are as follows, where, as in van Fraassen's
theory, the contrast class \(X\) is a set of propositions containing
\(P\): 


* (31) How is \(P\) (in
contrast to the rest of \(X)\) the case?
* (32) \(P\) (as
contrasted with the rest of \(X)\) in this way: \(A\).



Notice, however, that whereas in (30a) the propositions in \(X\) other
than \(P\) are false, in (30b) all three members of \(X\) are true:
birds, mammals, and reptiles reproduce. This, Cross argues, reflects
the fact that how-questions can exhibit two different kinds of
explanatory contrast. By asking (30a) one requests an answer that
highlights those special qualities of DNA that enable it to replicate
and that benzene and hexane do not possess. By asking (30b), on the
other hand, one requests an answer that highlights the differences
between the way in which reptiles reproduce and the ways in which
mammals and birds reproduce. The latter kind of explanatory contrast
also appears to be at play when (30b) is re-worded this way:


* (33) I know how
mammals and birds reproduce, but how do *reptiles*
reproduce?



In view of this, Cross introduces a contextual parameter in his
account of how-questions to indicate whether a given how-question
presupposes that all members of the contrast class are true or whether
it presupposes that all members of the contrast class other than \(P\)
are false. In the resulting account, a how-question is an ordered
quadruple \(\langle P,X,R,n\rangle\), where \(P\) is the topic of the
question; \(X\) is the contrast class, which is a set of propositions
to which \(P\) belongs; \(R\) is a contextually determined relation of
explanatory relevance, which holds between a proposition and the
topic/contrast-class pair \(\langle P,X\rangle\), and \(n\) is the
contrast value 0 or 1. If \(n = 0\), the question presupposes that in
\(X\) only \(P\) is true; if \(n = 1\), the question presupposes that
all of the members of \(X\) are true. The explanatory relevance
relation \(R\) is to be understood as varying from context to context
depending on what kind of way is being requested in that context.
Finally, Cross (1991, 252) defines a direct answer to a how-question
as follows:


* (34) A proposition
\(B\) is a direct answer to \(\langle P,X,R,n\rangle\) iff there is
some proposition \(A\) such that \(A\) is relevant to \(\langle
P,X,n\rangle\) and if \(n = 0\), then \(B\) is the proposition which
is true iff \(A\) and \(P\) are true and every \(C\) such that \(C\in
X\)\\(\{P\}\) is false, and if \(n= 1\), then \(B\) is the proposition
which is true iff \(A\) and all members of \(X\) are true.



Having found examples in which how-questions have contrast value 1,
Cross argues that why-questions, too, can presuppose that the other
members of their contrast classes are true. Consider a therapy meeting
for alcoholics in which each member of the group is asked the
following question:


* (35) Why did
*you* (in contrast to the other members of the group) start
drinking too much?



In this case it appears that the asker is requesting an answer that
highlights factors that distinguish the alcoholism of the person to
whom the question is addressed from that of the others in the group.
This and other evidence leads Cross to conclude that how- and
why-questions are the same kind of question--both are
*explanatory* questions--and both can be represented as
having the structure \(\langle P,X,R,n\rangle\). If a proposition
\(A\) must be a *reason* for \(P\) (in contrast to the rest of
\(X)\) in order to bear relation \(R\) to \(\langle P,X,n\rangle\),
then the question is worded with 'why' and the answer with
'because'; if \(A\) must be a *way* for \(P\) to be
the case (in contrast to the rest of \(X)\) in order to bear relation
\(R\) to \(\langle P,X,n\rangle\), then the question is worded with
'how' and the answer with 'by', 'in this
way', or similar wording. 



It is possible to accept Cross's theory as a theory of
how-questions only and to resist the final move of unifying how- and
why-questions into a single species of question. The unification that
Cross proposes assumes that why-questions can have contrast value 1,
but Risjord (2000, 73-4) argues that instead of accepting that
(35) is a why-question with contrast value 1, one can instead analyze
it as a why-question with contrast value 0 that makes reference to the
topics of other why-questions (also having contrast value 0) that have
been or could be raised in the given context.


#### 3.2.2 Criticisms of the pragmatic/contrastivist approach



Kitcher and Salmon (1987) were early critics of van Fraassen's
theory of why-questions as a theory of explanation. They object (1987,
319) that the lack of constraints on the relevance relation \(R\)
"allows just about anything to count as the answer to just about
any [why-]question." Other critics of van Fraassen's
theory include Ruben (1987) and Temple (1988), who argue that
explanatory contrast is an unnecessary complication because any
contrastive why-question 'why \(P\) (in contrast to
\(Q)\)?' is equivalent to the non-contrastive why-question
'why P&\(\neg\)Q?'. Risjord (2000, 70) rebuts this
reduction of the contrastive to the non-contrastive by arguing that it
leads to the untenable result that whenever \(P\) entails both
\(\neg\)Q and \(\neg\)R, 'why \(P\) (in contrast to
\(Q)\)?' must then be logically equivalent to 'why \(P\)
(in contrast to \(R)\)?', since \(P \amp \neg Q\) is logically
equivalent to \(P \amp \neg R\) if \(P\) entails \(\neg Q\) and \(\neg
R\). But questions of these forms need not be equivalent, since they
may call for different answers. For example, if Art is a vegan and is
allergic to chocolate, a correct answer to 'Why did Art eat
fruit for dessert (rather than eating ice cream and skipping the
fruit)?' will cite his being a vegan and not his chocolate
allergy, whereas a correct answer to 'Why did Art eat fruit for
dessert (rather than eating chocolate and skipping the fruit)?'
will cite his chocolate allergy but not his being a vegan.


#### 3.2.3 Other versions of the contrastivist approach



Where van Fraassen's theory places few restrictions on the
contrast class or *foils* of a why-question, some authors have
argued that the set of possible foils is constrained in various ways.
One example is Sober (1986), who contends that the presuppositions of
'Why \(P\) rather than \(Q\)?' include a two-part common
cause presupposition, namely that (1) the truth of \(P\) and the
falsity of \(Q\) trace back to a common cause, and (2) the common
cause discriminates \(P\) from \(Q\) in the sense that it makes \(P\)
more likely than \(Q\). Both presuppositions fail for Sober's
(1986, 145) example of the unanswerable question, 'Why is Kodaly
a Hungarian rather than a vegetarian?' Another author who argues
for additional constraints on foils is Lipton (1990), who aims in part
to improve on Lewis's (1986) account of causal explanation.
Lipton contends that a causal answer to 'Why \(P\) rather than
\(Q\)?' must cite a cause of \(P\) and the absence of a
corresponding event in the history of \(\neg Q\), i.e., a causal
difference between \(P\) and \(\neg Q\). Lipton (1990, 256) calls this
The Difference Condition. The central requirement for a sensible
contrastive question is that fact and (negated) foil have a similar
causal history against which the differences stand out (Lipton 1990,
258). According to Barnes (1994), Lipton is correct that fact and
(negated) foil must have a similar causal history, but Barnes goes
further and claims that a why-question presupposes that the fact and
foil can be viewed as culminating outcomes of some single type of
natural causal process (Barnes 1994, 50).


### 3.3 A metaphysical approach: answers as reasons-why



A notable recent development in the discussion of why-questions is
Skow 2016, which begins with two key ideas: first, that a theory of
explanation ought to be a theory of answers to why-questions, and,
second, that a theory of answers to why-questions is a theory of
reasons-why. Skow goes on to defend the view that all reasons-why are
causes or grounds, and he argues that reasons-why come in levels. At
one level there are reasons why \(P\), and at a higher level there are
reasons why \(Q\) is a reason why \(P\). For example, if I strike a
match and the match lights, my striking the match is a reason why the
match lit, and the relevant physical laws are reasons why striking the
match is a reason why it lit. These physical laws are not lower-level
reasons (i.e., reasons why the match lit); thus the higher and lower
levels are distinct. The levels are not strictly disjoint, however, as
the presence of oxygen in the air is both a reason why the match lit
and a reason why striking the match is a reason why it lit.



In the history of theorizing about explanation, Skow argues, the
higher and lower levels of reasons-why have been conflated as far back
as the Deductive-Nomological theory of Hempel and Oppenheim (1948).
According to the D-N model, an answer to the question of why an event
occurred must cite both prior conditions and a law of nature, and the
occurrence of the explanandum event must be deducible from the latter
jointly. For example, certain physical laws are involved in the
lighting of a match when it is struck. According to the D-N model, but
not according to the account of reasons-why in Skow 2016, those laws
are part of the explanation of why the match lit.



While acknowledging the distinction between first- and second-level
reasons-why, Lawler (2019) argues that second-level reasons (in
particular, the laws of nature that mediate cause and effect) are
properly included in answers to why-questions. If Lawler is right,
then, contrary to the account in Skow 2016, an answer to a
why-question need not be a cause or ground.



Another critic of Skow 2016 is Vayrynen (2019), who argues that
while Skow's theory ought to apply to normative explanation as
well as to empirical explanation, the theory does not account for
reason-enablers that are important in normative explanation. Consider
the question of why I ought to shovel the snow from my neighbor's
sidewalk. That I can do it, Vayrynen argues, enables other facts
to be reasons why I ought to, but that I can do it may be neither a
reason why I ought to do it nor a reason why some other fact is a
reason why I ought to do it.


### 3.4 Pointers to further reading



Aside from the the formal, pragmatic, and metaphysical approaches, the
topic of why-questions has been somewhat neglected by philosophers, at
least compared to other topics in the theory of questions. A notable
exception is Hintikka and Halonen 1995, which develops a theory of
why-questions in the context of Hintikka's interrogative model
of inquiry.


## 4. Embedded (or indirect) questions



Interrogative expressions can serve as the argument of certain
clause-embedding predicates, as when someone is said to know, tell,
care, or wonder who, what, whether, how, or why. Where the attitude
predicate is knowledge, these sorts of examples are called cases of
*knowledge-wh*. Knowledge-how in the sense of skill-possession,
as in 'Smith knows how to ride a bicycle', has generated a
literature of its own and is treated elsewhere (see the entry on
 knowledge how).
 



The discussion of knowledge-wh has focused mostly on whether-, what-,
which-, and who-complements, as in these examples:


* (36) John knows
whether the closet is empty.
* (37) John knows what
is in the closet.
* (38) John knows who
came to the meeting.
* (39) John knows where the meeting
was held.



Groenendijk and Stokhof (1982) provide a rich source of examples of
intuitively valid and invalid inferences involving wh-complements,
such as the following intuitively valid inference (179):


* (40) John believes
that Bill and Suzy walk; only Bill walks; hence, John doesn't
know who walks.


### 4.1 Knowledge-wh and the imperative-epistemic theory of wh-questions



Knowledge-wh figures explicitly in the *imperative-epistemic theory
of wh-questions* developed by Aqvist (1965). The
imperative-epistemic account is further developed by Hintikka (1975,
1976) and has been influential among philosophers of science
interested in models of inquiry and discovery, such as Kleiner
(1993).



According to the imperative-epistemic account, to ask a question is to
issue an imperative requiring the addressee to bring it about that the
speaker knows the answer to the question. Knowledge-wh comes into it
because to know the answer is to be in a state that can be described
using a knowledge-wh sentence. For example, according to the
imperative-epistemic account, question (41) is to be understood as
imperative (42):


* (41) Is the cat on the
mat?
* (42) Bring it about
that I know whether the cat is on the mat!



and question (43) is to be understood as imperative (44):


* (43) When does the
meeting begin?
* (44) Bring it about
that I know when the meeting begins!


### 4.2 Wh-complements as meaningful units



If a wh-complement is part of a longer sentence, then what is its
contribution to the semantic value of that sentence? Formal semantic
theories of wh-complements can be organized around answers to this
question.



One option (Groenendijk and Stokhof 1982) is to take a wh-complement
to denote a proposition, just like a that-complement. A second option
(Karttunen 1977) is to take wh-complements to denote sets of
propositions. In either case, John's knowing who walks consists
in the obtaining of a relation between John and the denotation of the
expression 'who walks'. On the view that wh-complements
denote single propositions, wh-complements and that-complements are
treated uniformly, and Groenendijk and Stokhof (1982) contend that
this uniform treatment is a virtue of their theory. Lewis (1982)
favors the same sort of account, but he applies it only to
whether-complements. Theiler *et al.* (2018) propose a uniform
analysis of that- and wh-complements in the inquisitive semantics
framework, overcoming certain limitations of Groenendijk and Stokhof's
partition semantics.



Karttunen, a proponent of the second option, takes wh-complements to
denote sets of true propositions, so that 'what John
reads' denotes (Karttunen 1977, 20) "a set which contains,
for each thing that John reads, the proposition that he reads
it." On Groenendijk and Stokhof's account, by contrast,
'what John reads' denotes the proposition that is true in
a possible world if and only if the set of things that John reads in
that world equals the set of things John in fact reads. That is,
'what John reads' denotes a proposition that entails for
each thing John reads that he reads it and for each thing John does
not read that he does not read it. Thus if one knows what John reads,
it follows on Groenendijk and Stokhof's account (but not on
Karttunen's) that one knows what John does not read. Also, on
Groenendijk and Stokhof's account, the difference between
knowing-that and knowing-wh amounts to a difference in what we might
call the *rigidity* of the complement. Consider the claim that
I know that John reads *Moby Dick* and the claim that I know
what John reads. The term 'that John reads *Moby Dick*
' refers to the same proposition at every possible world; the
term 'what John reads' refers to different propositions at
worlds at which John reads different things (and refers to the
proposition that John reads *Moby Dick* at those worlds at
which *Moby Dick* is the one and only thing that John reads).



### 4.3 Wh-complements contextually defined



If wh-complements are not meaningful units of the sentences in which
they occur, one option is to interpret wh-complements
"contextually", as Russell interpreted definite
descriptions. Indeed, Hintikka (1976, Chapter 4) argues that
knowledge-wh sentences like (37)-(39) are ambiguous between two
readings: a universal reading and an existential reading. In the case
of (37), Hintikka's two readings are as follows: 


* (45)  a.
\(\exists x(x\) is in
the closet & John knows that \(x\) is in the closet)
* b.
\(\forall x(x\) is in
the closet \(\rightarrow\) John knows that \(x\) is in the
closet)



Karttunen (1977, 7) disputes the existence of Hintikka's
ambiguity, but a version of this ambiguity that sets aside the details
of Hintikka's analysis of (37) has gained acceptance, namely,
the distinction between *mention-some* and *mention-all*
readings of a question or wh-complement. For example, under a
mention-some reading of 'What is in the closet?', an
answer must mention at least one item, whereas under a mention-all
reading an answer must mention all items. A perhaps clearer example of
a question for which a mention-some reading is natural is (51), which
is discussed below in section
 4.7
 in connection with false-belief sensitivity.


### 4.4 Information provision versus contextualism



Braun (2006) offers a very different account of knowledge-wh on which
the question-answer relationship underlying knowledge-wh is much less
formal, and this makes it very easy to have knowledge-wh on
Braun's account.



Consider this example:


* (46) Who is Hong Oak
Yun?



Examples like (46) are *identity questions*, which seem
intuitively to call for a dimension of context-dependence that
standard theories of the question-answer relationship do not
accommodate. The idea is that different ways of identifying Hong Oak
Yun are relevant in different contexts; accordingly, different
propositions count as answers (or as correct answers) to (46) in
different contexts. Aloni (2005) provides a recent example of a theory
designed to accommodate this idea.



Braun (2006), however, rejects the idea entirely. According to
Braun's (2006, 26) *information provision* account of
questions, "to answer a question is simply to provide
information about the subject matter of the question." That is,
(46) is answered by any proposition that provides information about
Hong Oak Yun, even the proposition expressed by 'Hong Oak Yun is
a person who is over three inches tall'. This answer may not
satisfy or be useful to or be informative for the speaker who poses
(46), but it counts as an answer despite these purely pragmatic
failings, according to Braun's theory. To *know who Hong Oak
Yun is*, according to Braun, is simply to know the truth of a
proposition that answers (46), which is to say, to know the truth of
any proposition that provides information about Hong Oak Yun.
Braun's view contrasts with the contextualism of Boer and
Lycan (1986) according to which knowing who Hong Oak Yun is requires
knowing a proposition that provides contextually relevant information
about Hong Oak Yun. Another contextualist alternative to Braun's
view is the view of Masto (2010), according to which (46) denotes a
contextually determined set of possible answers, and knowing who Hong
Oak Yun is consists in being able to choose or recognize the correct
answer from that contextually determined set.


### 4.5 Question-relativity



Where Boer and Lycan view knowing-wh as context-relative,
Schaffer (2007) views it as question-relative. The problem, according
to Schaffer, is that if knowledge-wh is reduced to knowledge-that and
is not question-relative, then cases of knowledge-wh that should be
distinguished will not be distinguished. Schaffer calls this the
Problem of Convergent Knowledge. For example, suppose that (47) is
true:


* (47) John knows that
the cat is on the mat.



On a non-question-relative account of knowledge-wh that reduces
knowledge-wh to knowledge-that, all three of the following will be
equivalent because all three can be reduced to (47): 


* (48)  a.
John knows whether the
cat is on the mat or in the garage.
* b.
John knows where the cat
is.
* c.
John knows what is on
the mat.



Schaffer argues that sentences like (48a-c) are not equivalent.
According to Schaffer's account, assuming the cat is indeed on
the mat, to know where the cat is is to know that the cat is on the
mat relative to the question 'Where is the cat?', whereas
to know what is on the mat is to know that the cat is on the mat
relative to the question 'What is on the mat?'. Schaffer
argues, in the end, that all knowledge, including knowledge-that, is
question-relative. Aloni and Egre (2010) offer a
different take on Schaffer's Problem of Convergent Knowledge,
arguing that it reveals a pragmatic ambiguity concerning what it means
to know the answer to a wh-question. 


### 4.6 Wh-complements as predicates



Brogaard (2009) rejects both reductionist views (which, like
Hintikka's, reduce knowledge-wh to knowledge-that) and
anti-reductionist views (which, like Schaffer's, analyze
knowledge-wh as question-relative knowledge-that), arguing instead
that wh-complements are predicates and knowledge-wh is a special kind
of de re knowledge. For example, on Brogaard's view, the logical
form of (48c) is:


* (49) \(\exists x\)
(John knows that \(x\) is what is on the mat)



A disadvantage of Brogaard's de re approach, Masto (2016)
argues, is that the de re approach does not generalize to certain
other attitude verbs that take wh-clauses as complements. For example,
there is no de re reading of (50):


* (50) John wonders what
is on the mat.



That is, (50) cannot be read as meaning that there is a particular x
about which John has some relevant de re attitude of wonder. Part of
the problem is that whereas 'know' takes both
propositional and interrogative complements, 'wonder'
takes interrogative complements but not propositional complements.
This difference between 'know' and 'wonder' is
the distinction between responsive and rogative predicates, which will
be discussed in detail in section
 4.8,
 below.


### 4.7 False-belief sensitivity



Another basis for rejecting the reducibility of knowledge-wh to
knowledge-that is the view that knowledge-wh is sensitive to false
beliefs. On this view, it is possible for there to be two subjects who
know the truth of exactly the same answer-propositions but exhibit a
difference in knowledge-wh because one subject has a false belief that
the other subject lacks. George (2013) argues for this possibility
using an example in which there are two shops: Newstopia and
PaperWorld. Newstopia sells newspapers, including ones from Italy,
whereas PaperWorld is a stationery shop and does not sell newspapers.
Consider the following question:


* (51) Where can one buy
an Italian newspaper?



(51) is to be read as a "mention-some" question, so that a
less-than-exhaustive answer is considered appropriate. That is, to
answer (51) it suffices to name one place where one can buy an Italian
newspaper. Suppose, next, that the epistemic and doxastic states of
two individuals, Janna and Rupert, are as follows:


* (52)  a.
Janna and Rupert know
that one can buy an Italian newspaper at Newstopia.
* b.
Rupert believes
(falsely) that one can buy an Italian newspaper at PaperWorld.
* c.
Neither Rupert nor Janna
has any other beliefs or knowledge concerning the availability of
Italian newspapers.



In the scenario described in (52), George (2013) argues, we can fix
the relevant contextual parameters and standards governing
knowledge-wh in such a way that (53a) is true, yet, relative to the
same contextual parameters and standards, (53b) is false, and its
falsity is a consequence of Rupert's false belief about
PaperWorld:


* (53)  a.
Janna knows where one
can buy an Italian newspaper.
* b.
Rupert knows where one
can buy an Italian newspaper.



The difference between Janna and Rupert can be described this way:
whereas Janna knows the truth of each answer to (51) that she
believes, the same cannot be said of Rupert.



Phillips and George (2018) present experimental empirical evidence
supporting the false-belief sensitivity of knowledge-wh. There is also
a substantial discussion of false-belief sensitivity in Theiler *et
al.* 2018, where it is referred to as false answer
sensitivity.


### 4.8 Responsive, rogative, and anti-rogative predicates



Knowledge is only one of a broader category of attitudes corresponding
to what Lahiri (2002) calls *responsive predicates*. It is
characteristic of responsive predicates that they accept both
interrogative and declarative complements, as in 'Mary
knows/remembers/forgets who runs' and 'Mary
knows/remembers/forgets that John runs'. Responsive predicates
contrast with what Lahiri (2002) calls *rogative* predicates,
such as 'wonder', 'be curious', and
'inquire', and with what Theiler *et al.* (2019)
call *anti-rogative* predicates, such as 'suspect'
and 'hope'. Rogative predicates accept interrogative
complements but do not accept declarative complements. For example,
one can inquire who ate the last doughnut, but one cannot inquire that
John ate the last doughnut. Anti-rogative predicates on the other
hand, accept declarative complements but not interrogative
complements. For instance, one can suspect that John ate the last
doughnut but one cannot suspect who ate the last doughnut. 



The distinction between rogative and responsive predicates has
epistemological significance, as it underlies Friedman's (2013)
argument that there is a category of attitudes that have
*questions*, not propositions, as their contents. Friedman
calls these the *interrogative* attitudes, and they are
precisely the attitudes denoted by rogative predicates. 



Within the category of responsive predicates Lahiri (2002, 287)
distinguishes the *veridical* from the *non-veridical*.
Veridical-responsive predicates include 'know',
'remember', and 'forget';
non-veridical-responsive predicates include 'be certain',
'agree (about)', and 'conjecture (about)'.
Whereas a veridical-responsive predicate expresses a relation to the
correct answer to its interrogative complement, a
non-veridical-responsive predicate expresses a relation to a possible
(but not necessarily the correct) answer. For example, 'Jane
remembers who won the lottery' entails that Jane has knowledge
that correctly answers the question 'Who won the
lottery?', whereas 'Jane is certain about who won the
lottery' entails that Jane is certain of the truth of a
proposition that may or may not correctly answer that same question.




Recent work in formal semantics has attempted to derive the fact that
rogative predicates do not accept declarative complements and the fact
that anti-rogative predicates do not accept interrogative complements
from independently observable semantic properties of such predicates
(see, e.g., Theiler *et al.* 2019, Uegaki 2019, Roelofsen
2019). 


### 4.9 Pointers to further reading



A detailed uniform treatment of declarative and interrogative
complements of responsive predicates in the context of inquisitive
semantics can be found in Theiler *et al.* 2018. On this
theory, declarative and interrogative complements are of the same
semantic type, which allows each responsive verb to have a single
lexical entry.



For a detailed critique of the recent literature on knowledge-wh, see
Chapter 2 of Stanley 2011. Parent (2014) provides a survey of the
recent literature about knowledge-wh organized around three issues:
the reducibility of knowledge-wh to knowledge-that, the relativity of
knowledge-wh to a contrast proposition, and the issue of whether the
context-sensitivity of knowing-wh is to be understood as a semantic or
a pragmatic phenomenon. Uegaki (2019) provides an overview of recent
work on the semantics of responsive predicates generally and is
organized around four approaches: the reduction of questions to
propositions, the reduction of propositions to questions, the
uniformity approach (on which declarative and interrogative
complements of a responsive predicate are of the same semantic type),
and the ambiguity approach (which postulates distinct
proposition-taking and question-taking readings of a given responsive
predicate).