The philosophy of language since Frege has emphasized propositions anddeclarative sentences, but it is clear that questions andinterrogative sentences are just as important. Scientificinvestigation and explanation proceed in part through the posing andanswering of questions, and human dialogues as well as human-computerinteractions are often structured in terms of questions andanswers.

After going over some preliminaries we will focus on three lines ofwork on questions: one located at the intersection of philosophy oflanguage and formal semantics, focusing on the semantics of whatBelnap and Steel (1976) callelementary questions; a secondlocated at the intersection of philosophy of language and philosophyof science, focusing on why-questions and the notion of explanation;and a third located at the intersection of philosophy of language andepistemology, focusing on embedded questions.

• 1. Preliminaries
  • 1.1 Questions, answers, and presuppositions
  • 1.2 Kinds of questions
• 2. The semantics of elementary questions
  • 2.1 Classical semantic theories of questions
  • 2.2 Questions in dynamic semantics
  • 2.3 Inquisitive semantics
  • 2.4 Structured question meanings
  • 2.5 Pointers to further reading
• 3. Why-questions
  • 3.1 A formal approach: abnormic laws
  • 3.2 A pragmatic approach: explanatory contrast
  • 3.3 A metaphysical approach: answers as reasons-why
  • 3.4 Pointers to further reading
• 4. Embedded (or indirect) questions
  • 4.1 Knowledge-wh and the imperative-epistemic theory of wh-questions
  • 4.2 Wh-complements as meaningful units
  • 4.3 Wh-complements contextually defined
  • 4.4 Information provision versus contextualism
  • 4.5 Question-relativity
  • 4.6 Wh-complements as predicates
  • 4.7 False-belief sensitivity
  • 4.8 Responsive, rogative, and anti-rogative predicates
  • 4.9 Pointers to further reading
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Preliminaries

R.G. Collingwood (1939) was an early advocate of taking questionsseriously. In the decades since the publication of Collingwood’sautobiography the topic of questions has regularly received attentionfrom linguists, logicians, and philosophers of language, but few havejoined Collingwood (1939, 36–37) in suggesting thatpropositional logic be replaced by a logic of question and answer inwhich neither question nor proposition is more basic. Instead, mostwork on questions in the philosophy of language and in formalsemantics fits squarely within a reductive paradigm inspired by (if not perfectly reflective of) Frege in whichpropositions, declarative sentences, and assertion have primacy. Theprimacy of the assertoric is especially evident in the work of manywho write on the semantics of what Belnap and Steel (1976) callelementary questions and who regard any such question as beingidentifiable with a set or function involving the propositions thatare the question’s answers. Only relatively recently, analternative to this reductive paradigm, taking upCollingwood’s suggestion to replace classical logic with a logicof questions and propositions in which neither question norproposition is seen as more basic, has gained traction under theheading ofinquisitive semantics (Ciardelliet al.2018).

1.1 Questions, answers, and presuppositions

Familiar considerations from the philosophy of language make it clearthat one should distinguish interrogative sentences from theircontents and distinguish both of these from the speech acts that canbe performed via the utterance of interrogative sentences. Forexample, Belnap and Steel (1976, 3) understand a question to be anabstract thing for which an interrogative sentence is a piece ofnotation. This parallels the distinction between propositions and thedeclarative sentences that express them. The structure and compositionof a question (understood as the abstract content of an interrogativesentence) vary from theory to theory. The speech act of asking aquestion is standardly regarded, e.g., by Searle (1969, 69), as aspecial case of the illocutionary act of requesting. Searledistinguishes requesting information (asking a real question) fromrequesting that the hearer display knowledge (asking an examquestion). Åqvist (1965) connects questions with speakerknowledge rather than hearer knowledge by proposing that to ask aquestion is to command the hearer to cause the speaker to know thequestion’s answer.

As is already clear, an important concept in many theories ofquestions is that of an answer, sometimes called adirectanswer. Many theorists agree that an answer is a piece oflanguage or semantic object that, as Belnap and Steel (1976, 3) putit, “completely, but just completely, answers thequestion.” A sentence or proposition need not be true to be adirect answer. Whether each question can be associated with a definiteset of direct answers is a controversial matter, however. Most authorsrequire answers to be sentences or propositions, so that answers to aquestion are the kind of thing that is true or false. Tichy (1978) isa striking exception and argues that answers can be of any logicaltype. Consider this example:

• (1)Who was thePresident of the USA in 1978?
• a.Jimmy Carter was thePresident of the USA in 1978.
• b.Gerald Ford was thePresident of the USA in 1978.
• c.Jimmy Carter
• d.Gerald Ford
• e.Someone over threeinches 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 correctanswer. Braun (2006) would count (1a–b) as answers and include(1e) as both an answer and a correct answer. What these differenttheoretical interpretations of the notion of an answer show is thereis no univocal pre-theoretical notion of an answer. The notion shouldrather be seen as a technical one, which can differ from one theory toanother. Some theorists make explicit what they understand answers tobe, but some leave this implicit. This can be problematic: withoutexplication of which pre-theoretical construct the technical notion ofan answer in a given theory is intended to capture, the theory cannotbe evaluated empirically.

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

• (2)The USA had exactlyone President in 1978.

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

1.2 Kinds of questions

Several kinds of questions have been distinguished in theliterature.

Whether-questions are questions like ‘Was there aquorum at the meeting?’ and ‘Does Jones live in Italy, inSpain, or in Germany?’. These examples illustrate thatwhether-questions come in two varieties: a whether-question may be ofthe yes-or-no variety, or it may present two or more alternativedirect answers other than yes and no. In either case, awhether-question explicitly presents a finite number of directanswers. Consider the first example:

• (3)Was there a quorumat 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 themeeting occurred. Thus (4) is a corrective answer to (3):

• (4)The meeting did not take place.

Question (5) is ambiguous:

• (5)Does Jones live inItaly, 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 directanswers, but it also has a reading on which it presents exactly threedirect 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 livein Italy, in Spain, or in Germany.

Which-questions are questions like ‘What is thesmallest prime number greater than 12?’, ‘Which cardinalwas elected Pope in 2013?’, and ‘Who shot J.R.?’Unlike a whether-question, a which-question may have an indefinite orinfinite number of direct answers.

Belnap and Steel (1976) refer to whether- and which-questions aselementary questions. We consider these kinds of questions indetail in section 2.

Another major category of questions arewhy-questions. It haslong been recognized that why-questions are intimately linked with theconcept of explanation. For example, Hempel and Oppenheim (1948, 334)write as follows:

A scientific explanation may be regarded as an answer to awhy-question, such as “Why do the planets move in ellipticalorbits with the sun at one focus?”

We consider why-questions in detail in section 3.

Yet another major category of questions areembedded orindirect questions, which occur as complements ofclause-embedding predicates such as ‘know’ and ‘wonder’:

• (7)John knows /wonderswho spoke to Mary.

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

2. The semantics of elementary questions

This section provides an overview of some of the most prominenttreatments of elementary questions at the intersection of philosophyof 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 ofquestions is the idea that “questions set up a choice-situationbetween a set of propositions, namely those propositions that count asanswers to it” (Hamblin 1973, 48). One way to implement thisidea is to take a question to denote, in a world \(w\), the set ofpropositions that correspond to a possible answer to the question(Hamblin 1973). Another way to implement the same idea is to let aquestion denote, in a world \(w\), the set of propositions thatcorrespond to itstrue answers in \(w\) (Karttunen 1977). Inboth systems, themeaning of a question is a function fromworlds to sets of propositions. In Hamblin’s system, thisfunction maps every possible world to the same set of propositions,corresponding to the set of all possible answers; in Karttunen’ssystem, every world is mapped to a subset of all possible answers,namely those that are true in the given world. As acknowledged byKarttunen (1977, 10), the difference is inessential. In both cases,the meaning of a question is fully determined by—and could beidentified with—the set of all propositions that correspond to apossible answer.

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

• (8)Who is coming fordinner tonight?
• a.Paul is coming.
• b.Only Paul and Nina arecoming.
• c.Some girls from my classare coming.
• d.I don’tknow.

In principle, all the responses in (8a–d) could be seen aspossible answers to (8). For Hamblin and Karttunen, only (8a) countsas such. However, it is not clear what the precise criteria are forbeing considered a possible answer, and on which grounds (8a) is to bedistinguished from (8b–d).

2.1.2 Partition semantics

Groenendijk and Stokhof (1984) take a question to denote, in eachworld, a single proposition embodying thetrue exhaustiveanswer to the question in that world. For instance, if \(w\) is aworld in which Paul and Nina are coming for dinner, and nobody else iscoming, then the denotation of (8) in \(w\) is the propositionexpressed by (8b).

Themeaning of a question, then, is a function from worlds topropositions. These propositions have two special properties: they aremutually exclusive (since two different exhaustive answersare always incompatible), and together they form acover ofthe entire logical space (since every world is compatible with atleast one exhaustive answer). So the meaning of a question can beidentified with a set of propositions which form apartitionof the logical space.

In many cases, it is intuitively clear what the “true exhaustiveanswer” to a question in a given world is, at least much clearerthan what all the “possible answers” to that question are.This means that a partition semantics can in many cases be testedagainst clear intuitions, unlike a Hamblin semantics.

However, in some cases it is not so clear what the “trueexhaustive answer” to a question in a given world is. Considerthe 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)IsAnn\(\uparrow\) coming, or Bill\(\downarrow\)? [alternativequestion]

What is the true exhaustive answer to (9) in a world where Ann iscoming and Bill is coming as well? One option is the proposition\(\{w\): Ann and Bill are both coming in \(w\}\), but another optionis the proposition \(\{w\): if Ann is coming in \(w\) then Bill isalso coming in \(w\}\). It is not quite clear pre-theoretically whichof these two options is more suitable. Notice that if we pick thesecond 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 thiswould mean that these two ‘exhaustive’ answers actuallyoverlap (they both contain all worlds where Ann is not coming) andthus do not form a partition. This may be considered a reason to pickthe first option instead. However, this line of reasoning is purelytheory-internal; it seems impossible to decide on theory-externalgrounds what the true exhaustive answers to a conditional questionshould be taken to be.

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

A similar problem arises with alternative questions like (10). In thiscase, the answer that neither Ann nor Bill is coming and the answerthat Ann and Bill are both coming have a different status than theanswer that only Ann is coming and the answer that only Bill iscoming. Again, this difference in status cannot be captured in asimple 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 thesemantics of questions in adynamic framework. The firsttheories in this line of work were developed by Jäger (1996),Hulstijn (1997), and Groenendijk (1999). Aloniet al. (2007b)contains a collection of papers elaborating on these early proposals.All these theories essentially reformulate the partition theory ofquestions in the format of an update semantics (Veltman 1996). Thismeans that they explicitly identify meanings withcontext changepotentials, i.e., functions over discourse contexts. However,unlike a simple update semantics where discourse contexts are modeledas sets of worlds—embodying the information established in thediscourse so far—these theories provide a more refined model ofdiscourse contexts, one that also embodies the issues that have beenraised so far. More specifically, a discourse context is modeled as anequivalence relation \(R\) over a set of worlds \(C\). Theset of worlds \(C\), i.e., the domain of \(R\), can be thought of asthecontext set, i.e., the set of all worlds that arecompatible with the information established in the discourse so far.\(R\) itself induces a partition on \(C\), and can thus be taken toencode the issues that have been raised so far. More specifically, wecan think of \(R\) as relating two worlds \(w\) and \(v\) just in casethe difference between \(w\) and \(v\) is not (yet) at issue, i.e.,the discourse participants have not yet expressed an interest ininformation that would distinguish between \(w\) and \(v\). In otherwords, \(R\) can be conceived of as a relation encodingindifference (Hulstijn 1997).

Both assertions and questions can then be taken to have the potentialto change the context in which they are uttered. Assertions restrictthe context set \(C\) to those worlds in which the asserted sentenceis true (strictly speaking, they remove all pairs of worlds \(\langlew,v\rangle\) from \(R\) such that the asserted sentence is false in atleast one of the two worlds). Questionsdisconnect worlds,i.e., they remove a pair \(\langle w,v\rangle\) from \(R\) just incase the true exhaustive answer to the question in \(w\) differs fromthe true exhaustive answer to the question in \(v\).

Thus, the dynamic framework of Jäger (1996), Hulstijn (1997), andGroenendijk (1999) provides a notion of context and meaning thatembodies both informative and inquisitive content in a uniform way.However, the framework inherits several issues from the classicalpartition theory of questions, in particular those discussed aboveconcerning conditional and alternative questions.

Moreover, there is a conceptual issue concerning the equivalencerelation \(R\). Namely, if \(R\) is primarily thought of as a relationencodingindifference, then it is not clear why it shouldalways be anequivalence relation. In particular, it is notclear why \(R\) should always betransitive. The discourseparticipants could very well be interested in information thatdistinguishes \(w\) from \(v\), while they are not interested ininformation that distinguishes either \(w\) or \(v\) from a thirdworld \(u\). To model such a situation, we would need an indifferencerelation \(R\) such that \(\langle w,u\rangle \in R\) and \(\langleu,v\rangle \in R\) but \(\langle w,v\rangle \not\in R\). This isimpossible if we require \(R\) to be transitive.

2.2.2 Giving up transitivity

These concerns have been addressed by Groenendijk (2009) andMascarenhas (2009). The overall architecture of their system is verymuch like that of the early dynamic systems discussed above, onlyindifference 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, besidesaddressing the conceptual issue concerning indifference relationsdiscussed above, also allows for a better analysis of conditionalquestions and alternative questions. However, Ciardelli (2009) andCiardelli and Roelofsen (2011) show that, although the proposed systemindeed behaves better for simple cases, it does not scale up to morecomplex cases in a suitable way. In particular, whereas alternativequestions with two disjuncts, like (10) above, are dealt withsatisfactorily, or at least more satisfactorily than in a partitionsemantics, alternative questions with three or more disjuncts arestill 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 indicatewhich atomic sentences are true at that world. Note that in thisinformation state none of the atomic sentences is known to hold. Nowconsider an issue which is resolved just in case at least one of theatomic sentences is established, i.e., just in case we know that theactual world is located within one of the ovals depicted in figure1.

Figure 1: An issue that cannot berepresented 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 representedby means of an indifference relation. An indifference relation overthe information state \(\{w_{pq},w_{qr},w_{pr}\}\) necessarilycontains all reflexive world-pairs, and possibly one, two, or threenon-reflexive pairs. In either case, however, the resulting issue doesnot correspond to the one depicted in Figure 1.

The general conclusion that has been drawn from this problem, asdiscussed in detail by Ciardelli and Roelofsen (2011), is thatquestion meanings cannot be suitably modeled in terms of indifferencerelations, even if these indifference relations are allowed to benon-transitive. This insight has led to the development of analternative logical notion of question meanings, which forms thecornerstone of the framework ofinquisitive semantics, to bediscussed below.

2.3 Inquisitive semantics

2.3.1 The basic system

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

One natural criterion is the following. We could say that a responseto a question counts as a proper answer just in case itresolves the issue that the question raises. If we adopt thiscriterion then we also have to impose a certain structural conditionon question-meanings. That is, question-meanings cannot just bedefined as arbitrary sets of propositions, as in the theories ofHamblin (1973) and Karttunen (1977). Rather, they should be defined asdownward closed sets of propositions. That is, if a questionmeaning contains a certain proposition \(\alpha\), then it must alsocontain all stronger propositions \(\beta \subseteq \alpha\). Afterall, suppose that \(\alpha\) is an element of the meaning of aquestion \(Q\). Given our answerhood criterion, this means that\(\alpha\) corresponds to an issue-resolving response to \(Q\). Butthen every \(\beta \subseteq \alpha\) corresponds to an even moreinformative, and therefore also issue-resolving response. So, givenour answerhood criterion, \(\beta\) must also be an element of themeaning of \(Q\).

This conception of question meanings forms the cornerstone of the mostbasic implementation ofinquisitive semantics, the system\(\Inq_B\) (Groenendijk and Roelofsen 2009, Ciardelli 2009, Ciardelliand Roelofsen 2011, Roelofsen 2013, Ciardelli 2016, Ciardellietal. 2018). In this system, question meanings are defined asdownward closed sets of propositions that together cover the entirelogical space.^[1] We will refer to such sets asinquisitivequestionmeanings.^[2]

Partitions correspond to a specific kind of inquisitive questionmeanings. That is, for every partition \(\rP\), there is acorresponding inquisitive question meaning \(I_{\rP}\), consisting ofall 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 apartition. In fact, an inquisitive question meaning \(I\) correspondsto a partition if and only if for every subset \(I'\subseteq I\) suchthat \(\cap I'\ne \varnothing\), \(\cup I'\) is also in \(I\). Thereare many inquisitive question meanings that do not have this specialproperty. Thus, the notion of question meanings in \(\Inq_B\) is moregeneral than the notion of question meanings in partitionsemantics.

The set of all meanings in \(\Inq_B\), together with a suitable notionof entailment, form a Heyting algebra, just like the set of allmeanings in classical logic ordered by classical entailment (Roelofsen2013). Thus, the basic connectives (disjunction, conjunction,implication, and negation) can be associated with the basic algebraicoperations on meanings (join, meet, and (relative)pseudo-complementation), just as in classical logic. This is indeedhow the connectives are treated in \(\Inq_B\), although othertreatments of the connectives are also conceivable in this setting(see, e.g., Ciardelliet al. 2015).

2.3.2 Some extensions

In recent work, the basic system sketched above has been extended inseveral directions. Below are pointers to some of theseextensions.

Ciardelliet al. (2012) consider a notion of meaning that isvery much like the one adopted in \(\Inq_B\), but also has apresuppositional component. Such a notion of meaning isneeded to suitably deal with alternative questions andwhich-questions.

Ciardelliet al. (2017) develop a type-theoretic inquisitivesemantics, which is needed for a compositional semantic analysis ofquestions.

Roelofsen and Farkas (2015) develop an inquisitive semantics in whichthe meaning of a question does not only capture what is needed toresolve the issue raised by that question, but also which propositionsare 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 anaphoricexpressions (e.g.Is Paul coming? Then/otherwise I’ll makepasta ).

Farkas and Roelofsen (2017) integrate inquisitive semantics with acommitment-based model of discourse, in order to capture the specialdiscourse effects of non-canonical types of questions, such astag-questions (Paul is coming, isn’t he? ) anddeclarative questions (Paul is coming? ).

Finally, Ciardelli and Roelofsen (2015), Ciardelli (2016), and vanGessel (2016) develop a system that integrates inquisitive semanticswithdynamic epistemic logic (van Ditmarschet al.2007), in order to formally model the information states andinquisitive states of the participants of a discourse, and how thesestates change when a question is asked or a statement is made. It alsoprovides 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 ofpropositions, and are therefore referred to aspropositionset theories. It has been argued that question meanings asconstrued by proposition set theories are all too coarse-grained toaccount for certain linguistic phenomena. In order to address thisissue, several theories have been developed that adopt morefine-grained,structured notions of question meanings. Suchtheories have been couched in different semantic frameworks, which areall more fine-grained than the standard possible world framework. Forinstance, the proposal of Krifka (2001) is couched in a structuredmeanings framework, that of Ginzburg and Sag (2000) in situationsemantics, that of Ginzburg (2005), Cooper and Ginzburg (2012) in typetheory with records, that of Aloniet al. (2007a) in dynamicsemantics, and that of Blutner (2012) in ortho-algebraic semantics. Wewill illustrate the general approach here by focusing on the proposalof 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 \(\langleB,R\rangle\), where \(B\) is called thebackground and \(R\)therestriction. \(B\) is a function that, when applied tothe semantic value of an appropriate term answer to the question,yields a proposition. \(R\) specifies what appropriate term answersare, i.e., what the semantic entities are that \(B\) can be appliedto.

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

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

In this case, \(B\) is a function that maps every individual \(x\) tothe proposition \(\{w: x\) called in \(w\}\), and \(R\) is the set ofstudents. In the case of a polar question, \(R\) is taken to be a setconsisting of two functions on propositions, the identity function andthe function that maps every proposition to its complement, which areassumed to be expressed byyes andno, respectively.For instance:

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

From a structured question meaning it is always possible to obtain thecorresponding proposition set meaning, by applying \(B\) to all theelements of \(R\) (and taking the downward closure of the resultingset of propositions in case we want an inquisitive question meaning inthe sense of \(\Inq_B\). It is not possible to go in the otherdirection, which means that structured question meanings have strictlymore expressive power than proposition set meanings (e.g., von Stechow1991, Krifka 2001).

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

• (13)Is the door open?Yes. / No.
• (14)Is the door open orclosed? *Yes. / *No.

Yet, the two questions differ in that the first licenses answerparticles like ‘yes’ and ‘no’ while the seconddoesn’t. In a structured-meanings approach, the two questionsare semantically distinguishable. This additional semanticfine-grainedness forms the basis for an account of polarity particleresponses.

Note that some of the extended implementations of inquisitivesemantics (e.g., Roelofsen and Farkas 2015) are also fine-grainedenough to account for answer particles. As mentioned above, in theseimplementations the meaning of a question does not only capture whatis needed to resolve the issue that the question raises, but alsowhich propositions are made available by the question for subsequentanaphoric reference, for instance by answer particles. In effect,capturing anaphoric potential also adds structure to questionmeanings. Thus, these implementations maintain a proposition setperspective, but at the same time address the need for richer semanticstructures as well. Such a synthesis is also achieved in Alonietal. (2007a).

2.5 Pointers to further reading

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

Ginzburg (2010) provides a concise overview of several more recentanalyses of questions, including, besides the ones discussed here, theinferential erotetic logic of Wisniewski (2001), thetreatment of questions in modal logic by Nelken and Francez (2002) andNelken 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 thetreatment of questions indynamic epistemic logic developedby van Benthem and Minică (2012). For comparison of the latterapproach with inquisitive semantics, see Ciardelli and Roelofsen(2015) and Ciardelli (2016).

Finally, Krifka (2011) provides an overview of the classicalproposition set accounts, early implementations of inquisitivesemantics, and the structured meanings approach, taking a morelinguistic perspective than other overview articles. Krifka does notonly discuss the semantics of questions, but also their possiblesyntactic configurations and intonation patterns, supplying examplesfrom a wide range of languages.

3. Why-questions

For whether-questions (indeed, for all elementary questions in theview of some), the question-answer relationship can be defined inpurely formal terms. One approach to why-questions is to try to makethe question-answer relationship formal in that case, too, or at leastas formal as possible. The main proponent of this approach isBromberger (1966), whose account is also the first influential accountof why-questions. Van Fraassen (1980) takes an opposite view,theorizing that the question-answer relationship is almost purelypragmatic. Skow (2016) proposes a theory that is neither formal norpragmatic but is instead metaphysical, claiming that answers tolower-level why-questions always identify causes or grounds. Weconsider 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 awhy-question, Bromberger’s theory of why-questions can be seenalso as a theory of explanation, indeed, one that incorporatesHempel’s deductive-nomological model while aiming to improve onit.

Bromberger introduces several concepts for use in his account: thepresupposition of a why-question,abnormic laws andtheirantonymic predicates, andgeneral rules,focusing especially on general rules that arecompleted byabnormic laws.

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

• (15)Why is it the casethat \(p\)?

The presupposition of (15) is \(p\), and this agrees with the usualconcept of presupposition for questions, since if \(p\) is not thecase then (15) has no correct answer. Ageneral 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. Aspecial abnormic law is a true, law-like statement of theform:

• \(\forall x(Fx\rightarrow(Ex \leftrightarrow(A_1 x \vee \ldots \veeA_n\)x))).

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

No sample of gas expands unless its temperature is kept constant butits pressure decreases, or its pressure is kept constant but itstemperature increases, or its absolute temperature increases by alarger factor than its pressure, or its pressure decreases by a largerfactor than its absolute temperature.

The antonymic predicates of this special abnormic law are‘expands’ and ‘does not expand’, and thelogical form that Bromberger’s theory postulates for thisabnormic 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 anabnormic law as follows:

An abnormic law is the completion of a general rule if and only if thegeneral rule is false and is obtainable by dropping the“unless” qualifications. ([…] this requiresnegating the predicate substituted for \(E\)—or dropping thenegation if it is already negated—deleting the biconditionalconnective, 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 whyquestion as follows: \(q\) is the correct answer to (15) if and onlyif (i) there is an abnormic law \(L\) (which may be general orspecial) and \(p\) is the proposition that results from predicating ofsome 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 theconjuncts of its antecedent is removed, the resulting general rulecannot be completed by an abnormic law.

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

• (18)Why did \(a\)expand?

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

• (19)The pressure of \(a\) waskept constant while the temperature of \(a\) increased.

This is the correct answer because \(Pa\), along with \(Ga\) andabnormic law (16) form the premises of a deductive-nomologicalexplanation with conclusion \(Ea\), but when \(Pa\) is deleted as apremise (leaving \(Ga\) as a premise) and general rule (17) issubstituted 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 \(\neg Ea\) arenot true:

• (20) \(a\) is asample of gas; no sample of gas expands; therefore \(a\) did notexpand, 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 correctanswer to (18) in virtue of the idea that \(Pa\) is a fullspecification of the special (or “abnormal”) circumstancestriggering the expansion of \(a\). Notice that one of the premises ofthe deductive-nomological explanation of \(Ea\), namely \(Ga\), is notpart of the triggering package and is not part of the correct answerto (18). Two factors in Bromberger’s account jointly keep \(Ga\)from being included. The first is that \(Ga\) is a premise not only inthe actual deductive-nomological explanation of \(Ea\) but also in thefictitious deductive-nomological explanation (20) of \(\neg Ea\). Sorelative to (16) and (17), \(Ga\) is not a special or abnormalcircumstance. Is there another abnormic law/general rule pair relativeto 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) weobtain the general rule ‘Nothing expands’, which it seemsthat no abnormic law completes.^[5].

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

• (21)Why is the heightof the pole 40 feet?

and the intuitively incorrect answer

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

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

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

Nor would (23) become an abnormic law if additional disjuncts wereadded after ‘unless’.

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

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

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

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

Teller proposes other counterexamples by devising a method for turningexamples showing that Hempel’s deductive-nomological theory ofexplanation is too permissive into examples showing thatBromberger’s theory of why-questions is also too permissive.Teller’s method exploits the fact that when abnormic laws arerewritten in certain logically equivalent ways, the resultingstatements 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 theaccount of van Fraassen (1980, ch. 5). Van Fraassen’s theory ismotivated by the idea that explanation is not a special relationshipbetween theory and reality. Rather, an explanation is just adescription of reality that serves a contextually determinedpurpose, namely that of answering a why-question. Van Fraassen’stheory is thus an erotetic (i.e., question-theoretic) theory ofexplanation, as opposed to an account of why-questions in terms ofexplanation. He offers this theory in the context of developing hisaccount 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 (thetopic of the question); \(X\) is a set of propositions towhich \(P\) belongs and of which \(P\) is the only member that is true(the contrast class of \(Q)\); and \(R\) is a contextuallydetermined relation of explanatory relevance, which holds between aproposition and the topic/contrast-class pair \(\langle P,X\rangle\).The standard linguistic expression of \(Q\) is:

• (26) Why \(P\) incontrast to the rest of \(X\)?

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

Suppose that \(X=\{P,P_1 ,\ldots ,P_k,(\ldots)\}\), and that \(P\) isnot one of the \(P_k\)s. (Note that \(X\) may be finite or infinite.)Then, where \(A\) is any proposition, van Fraassen (1980, 144) definesa direct answer to \(Q\) to be any proposition having the followingtruth 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 contrastto the rest of \(X\), because \(A\).

On van Fraassen’s view, the contribution of‘because’ to the truth conditions of (28) is simplyboolean conjunction, as reflected in (27). The role of‘because’ in (28) is to perform the pragmatic function ofindicating that (27) is being used for an explanatory purpose, not togive a non-truth-functional dimension to the truth conditions of (28).Proposition \(A\) (the core of answer (27)/(28)) is said to berelevant 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 beingrequested in a given context. One can ask why in order to requestcausal factors, to request a justification, to request a purpose, torequest 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 contrastclass, only its topic is true, and (iii) that at least one propositionbearing the explanatory relevance relation to the topic/contrast-classpair is true. When the first or second presupposition fails (becausethe contextually determined body of background knowledge in play doesnot entail both (i) and (ii)), the why-questiondoes notarise. When the third presupposition fails, the why-question hasno answer even if it arises. For example, suppose that paresisindeterministically 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 thequestion ‘Why did John, in contrast to the other nine, contractparesis?’ Since paresis develops indeterministically fromsyphilis, nothing favors John (in contrast to the other nine syphilispatients) as being likely to develop paresis. On the other hand, ifBill and Sarah never had syphilis, the question ‘Why did John,in contrast to Bill and Sarah, develop paresis?’ does have ananswer: ‘John developed paresis, in contrast to Bill and Sarah,because John had syphilis but Bill and Sarah did not.’ In thiscase, as in the first, the why-question requests causal factors thatled to John’s getting paresis while the others mentioned in thecontrast class did not. In both cases, then, the same relevancerelation \(R\) is in play because the same kind of information isrequested, namely causal factors leading to the truth of the topic incontrast to the other members of the contrast class. If there are nosuch causal factors, as in the first version of the paresis case, thequestion is to be rejected. If, as in the second version of theparesis case, there are such factors, so that at least one propositionbears the relevance relation to the topic/contrast-class pair, then acandidate answer \(A\) is evaluated according to three criteria: howacceptable or likely \(A\) is, the degree to which \(A\) favors \(P\)over other members of \(X\), and whether \(A\) is made irrelevant byother answers.

3.2.1 How-questions and explanatory contrast

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

Firstly, it must be noted that not every how-question requests anexplanation. For example, ‘How far is it to Cleveland?’asks for a distance, not an explanation. In general, according toCross (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.Bywhat road (How did youget here?)
• b.Inwhat manner (How didyou behave at the party?)
• c.Bywhat argument (Howwill you justify this?)
• d.Bywhat method (How doyou perform an appendectomy?)
• e.Bywhat means (How didyou get that money?)
• f.Inwhat respect (How dothese differ?)
• g.Bywhat process (How doDNA molecules replicate?)

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

• (30)a.Howdo DNA molecules (incontrast to molecules of benzene and hexane)replicate?
• b.Howdo reptiles (incontrast 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’stheory, the contrast class \(X\) is a set of propositions containing\(P\):

• (31)How is \(P\) (incontrast to the rest of \(X)\) the case?
• (32)\(P\) (ascontrasted with the rest of \(X)\) in this way: \(A\).

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

• (33)I know howmammals and birds reproduce, but how doreptilesreproduce?

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

• (34)A proposition\(B\) is a direct answer to \(\langle P,X,R,n\rangle\) iff there issome proposition \(A\) such that \(A\) is relevant to \(\langleP,X,n\rangle\) and if \(n = 0\), then \(B\) is the proposition whichis true iff \(A\) and \(P\) are true and every \(C\) such that \(C\inX\)\\(\{P\}\) is false, and if \(n= 1\), then \(B\) is the propositionwhich 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 othermembers of their contrast classes are true. Consider a therapy meetingfor alcoholics in which each member of the group is asked thefollowing question:

• (35)Why didyou (in contrast to the other members of the group) startdrinking too much?

In this case it appears that the asker is requesting an answer thathighlights factors that distinguish the alcoholism of the person towhom the question is addressed from that of the others in the group.This and other evidence leads Cross to conclude that how- andwhy-questions are the same kind of question—both areexplanatory questions—and both can be represented ashaving the structure \(\langle P,X,R,n\rangle\). If a proposition\(A\) must be areason 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 away for \(P\) to bethe 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 thisway’, or similar wording.

It is possible to accept Cross’s theory as a theory ofhow-questions only and to resist the final move of unifying how- andwhy-questions into a single species of question. The unification thatCross 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 analyzeit as a why-question with contrast value 0 that makes reference to thetopics of other why-questions (also having contrast value 0) that havebeen 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’stheory 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 aboutany [why-]question.” Other critics of van Fraassen’stheory include Ruben (1987) and Temple (1988), who argue thatexplanatory contrast is an unnecessary complication because anycontrastive why-question ‘why \(P\) (in contrast to\(Q)\)?’ is equivalent to the non-contrastive why-question‘why P&\(\neg\)Q?’. Risjord (2000, 70) rebuts thisreduction of the contrastive to the non-contrastive by arguing that itleads 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 logicallyequivalent to \(P \amp \neg R\) if \(P\) entails \(\neg Q\) and \(\negR\). But questions of these forms need not be equivalent, since theymay call for different answers. For example, if Art is a vegan and isallergic to chocolate, a correct answer to ‘Why did Art eatfruit for dessert (rather than eating ice cream and skipping thefruit)?’ will cite his being a vegan and not his chocolateallergy, whereas a correct answer to ‘Why did Art eat fruit fordessert (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 thecontrast class orfoils of a why-question, some authors haveargued 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 commoncause presupposition, namely that (1) the truth of \(P\) and thefalsity of \(Q\) trace back to a common cause, and (2) the commoncause 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 Kodalya Hungarian rather than a vegetarian?’ Another author who arguesfor additional constraints on foils is Lipton (1990), who aims in partto 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 acorresponding event in the history of \(\neg Q\), i.e., a causaldifference between \(P\) and \(\neg Q\). Lipton (1990, 256) calls thisThe Difference Condition. The central requirement for a sensiblecontrastive question is that fact and (negated) foil have a similarcausal 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 goesfurther and claims that a why-question presupposes that the fact andfoil can be viewed as culminating outcomes of some single type ofnatural causal process (Barnes 1994, 50).

3.3 A metaphysical approach: answers as reasons-why

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

In the history of theorizing about explanation, Skow argues, thehigher and lower levels of reasons-why have been conflated as far backas the Deductive-Nomological theory of Hempel and Oppenheim (1948).According to the D-N model, an answer to the question of why an eventoccurred must cite both prior conditions and a law of nature, and theoccurrence of the explanandum event must be deducible from the latterjointly. For example, certain physical laws are involved in thelighting of a match when it is struck. According to the D-N model, butnot according to the account of reasons-why in Skow 2016, those lawsare part of the explanation of why the match lit.

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

Another critic of Skow 2016 is Väyrynen (2019), who argues thatwhile Skow’s theory ought to apply to normative explanation aswell as to empirical explanation, the theory does not account forreason-enablers that are important in normative explanation. Considerthe question of why I ought to shovel the snow from my neighbor’ssidewalk. That I can do it, Väyrynen argues, enables other factsto be reasons why I ought to, but that I can do it may be neither areason why I ought to do it nor a reason why some other fact is areason why I ought to do it.

3.4 Pointers to further reading

Aside from the formal, pragmatic, and metaphysical approaches, thetopic of why-questions has been somewhat neglected by philosophers, atleast compared to other topics in the theory of questions. A notableexception is Hintikka and Halonen 1995, which develops a theory ofwhy-questions in the context of Hintikka’s interrogative modelof inquiry.

4. Embedded (or indirect) questions

Interrogative expressions can serve as the argument of certainclause-embedding predicates, as when someone is said to know, tell,care, or wonder who, what, whether, how, or why. Where the attitudepredicate is knowledge, these sorts of examples are called cases ofknowledge-wh. Knowledge-how in the sense of skill-possession,as in ‘Smith knows how to ride a bicycle’, has generated aliterature of its own and is treated elsewhere (see the entry onknowledge how).

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

• (36)John knowswhether the closet is empty.
• (37)John knows whatis in the closet.
• (38)John knows whocame to the meeting.
• (39)John knows where the meetingwas held.

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

• (40)John believesthat Bill and Suzy walk; only Bill walks; hence, John doesn’tknow who walks.

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

Knowledge-wh figures explicitly in theimperative-epistemic theoryof wh-questions developed by Åqvist (1965). Theimperative-epistemic account is further developed by Hintikka (1975,1976) and has been influential among philosophers of scienceinterested in models of inquiry and discovery, such as Kleiner(1993).

According to the imperative-epistemic account, to ask a question is toissue an imperative requiring the addressee to bring it about that thespeaker knows the answer to the question. Knowledge-wh comes into itbecause to know the answer is to be in a state that can be describedusing a knowledge-wh sentence. For example, according to theimperative-epistemic account, question (41) is to be understood asimperative (42):

• (41)Is the cat on themat?
• (42)Bring it aboutthat I know whether the cat is on the mat!

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

• (43)When does themeeting begin?
• (44)Bring it aboutthat 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 itscontribution to the semantic value of that sentence? Formal semantictheories of wh-complements can be organized around answers to thisquestion.

One option (Groenendijk and Stokhof 1982) is to take a wh-complementto denote a proposition, just like a that-complement. A second option(Karttunen 1977) is to take wh-complements to denote sets ofpropositions. In either case, John’s knowing who walks consistsin the obtaining of a relation between John and the denotation of theexpression ‘who walks’. On the view that wh-complementsdenote single propositions, wh-complements and that-complements aretreated uniformly, and Groenendijk and Stokhof (1982) contend thatthis uniform treatment is a virtue of their theory. Lewis (1982)favors the same sort of account, but he applies it only towhether-complements. Theileret al. (2018) propose a uniformanalysis of that- and wh-complements in the inquisitive semanticsframework, overcoming certain limitations of Groenendijk and Stokhof’spartition semantics.

Karttunen, a proponent of the second option, takes wh-complements todenote sets of true propositions, so that ‘what Johnreads’ denotes (Karttunen 1977, 20) “a set which contains,for each thing that John reads, the proposition that he readsit.” On Groenendijk and Stokhof’s account, by contrast,‘what John reads’ denotes the proposition that is true ina possible world if and only if the set of things that John reads inthat world equals the set of things John in fact reads. That is,‘what John reads’ denotes a proposition that entails foreach thing John reads that he reads it and for each thing John doesnot read that he does not read it. Thus if one knows what John reads,it follows on Groenendijk and Stokhof’s account (but not onKarttunen’s) that one knows what John does not read. Also, onGroenendijk and Stokhof’s account, the difference betweenknowing-that and knowing-wh amounts to a difference in what we mightcall therigidity of the complement. Consider the claim thatI know that John readsMoby Dick and the claim that I knowwhat John reads. The term ‘that John readsMoby Dick’ refers to the same proposition at every possible world; theterm ‘what John reads’ refers to different propositions atworlds at which John reads different things (and refers to theproposition that John readsMoby Dick at those worlds atwhichMoby 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 whichthey occur, one option is to interpret wh-complements“contextually”, as Russell interpreted definitedescriptions. Indeed, Hintikka (1976, Chapter 4) argues thatknowledge-wh sentences like (37)-(39) are ambiguous between tworeadings: a universal reading and an existential reading. In the caseof (37), Hintikka’s two readings are as follows:

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

Karttunen (1977, 7) disputes the existence of Hintikka’sambiguity, but a version of this ambiguity that sets aside the detailsof Hintikka’s analysis of (37) has gained acceptance, namely,the distinction betweenmention-some andmention-allreadings of a question or wh-complement. For example, under amention-some reading of ‘What is in the closet?’, ananswer must mention at least one item, whereas under a mention-allreading an answer must mention all items. A perhaps clearer example ofa question for which a mention-some reading is natural is (51), whichis discussed below in section4.7 in connection with false-belief sensitivity.

4.4 Information provision versus contextualism

Braun (2006) offers a very different account of knowledge-wh on whichthe question-answer relationship underlying knowledge-wh is much lessformal, and this makes it very easy to have knowledge-wh onBraun’s account.

Consider this example:

• (46)Who is Hong OakYun?

Examples like (46) areidentity questions, which seemintuitively to call for a dimension of context-dependence thatstandard theories of the question-answer relationship do notaccommodate. The idea is that different ways of identifying Hong OakYun are relevant in different contexts; accordingly, differentpropositions count as answers (or as correct answers) to (46) indifferent contexts. Aloni (2005) provides a recent example of a theorydesigned to accommodate this idea.

Braun (2006), however, rejects the idea entirely. According toBraun’s (2006, 26)information provision account ofquestions, “to answer a question is simply to provideinformation about the subject matter of the question.” That is,(46) is answered by any proposition that provides information aboutHong Oak Yun, even the proposition expressed by ‘Hong Oak Yun isa person who is over three inches tall’. This answer may notsatisfy or be useful to or be informative for the speaker who poses(46), but it counts as an answer despite these purely pragmaticfailings, according to Braun’s theory. Toknow who Hong OakYun is, according to Braun, is simply to know the truth of aproposition that answers (46), which is to say, to know the truth ofany proposition that provides information about Hong Oak Yun.Braun’s view contrasts with the contextualism of Boër andLycan (1986) according to which knowing who Hong Oak Yun is requiresknowing a proposition that provides contextually relevant informationabout Hong Oak Yun. Another contextualist alternative to Braun’sview is the view of Masto (2010), according to which (46) denotes acontextually determined set of possible answers, and knowing who HongOak Yun is consists in being able to choose or recognize the correctanswer from that contextually determined set.

4.5 Question-relativity

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

• (47)John knows thatthe cat is on the mat.

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

• (48)a.John knows whether thecat is on the mat or in the garage.
• b.John knows where the catis.
• c.John knows what is onthe mat.

Schaffer argues that sentences like (48a–c) are not equivalent.According to Schaffer’s account, assuming the cat is indeed onthe mat, to know where the cat is is to know that the cat is on themat relative to the question ‘Where is the cat?’, whereasto know what is on the mat is to know that the cat is on the matrelative to the question ‘What is on the mat?’. Schafferargues, in the end, that all knowledge, including knowledge-that, isquestion-relative. Aloni and Égré (2010) offer adifferent take on Schaffer’s Problem of Convergent Knowledge,arguing that it reveals a pragmatic ambiguity concerning what it meansto know the answer to a wh-question.

4.6 Wh-complements as predicates

Brogaard (2009) rejects both reductionist views (which, likeHintikka’s, reduce knowledge-wh to knowledge-that) andanti-reductionist views (which, like Schaffer’s, analyzeknowledge-wh as question-relative knowledge-that), arguing insteadthat wh-complements are predicates and knowledge-wh is a special kindof de re knowledge. For example, on Brogaard’s view, the logicalform 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 certainother attitude verbs that take wh-clauses as complements. For example,there is no de re reading of (50):

• (50)John wonders whatis on the mat.

That is, (50) cannot be read as meaning that there is a particular xabout which John has some relevant de re attitude of wonder. Part ofthe problem is that whereas ‘know’ takes bothpropositional and interrogative complements, ‘wonder’takes interrogative complements but not propositional complements.This difference between ‘know’ and ‘wonder’ isthe distinction between responsive and rogative predicates, which willbe discussed in detail in section4.8, below.

4.7 False-belief sensitivity

Another basis for rejecting the reducibility of knowledge-wh toknowledge-that is the view that knowledge-wh is sensitive to falsebeliefs. On this view, it is possible for there to be two subjects whoknow the truth of exactly the same answer-propositions but exhibit adifference in knowledge-wh because one subject has a false belief thatthe other subject lacks. George (2013) argues for this possibilityusing an example in which there are two shops: Newstopia andPaperWorld. 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 buyan Italian newspaper?

(51) is to be read as a “mention-some” question, so that aless-than-exhaustive answer is considered appropriate. That is, toanswer (51) it suffices to name one place where one can buy an Italiannewspaper. Suppose, next, that the epistemic and doxastic states oftwo individuals, Janna and Rupert, are as follows:

• (52)a.Janna and Rupert knowthat 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 Jannahas any other beliefs or knowledge concerning the availability ofItalian newspapers.

In the scenario described in (52), George (2013) argues, we can fixthe relevant contextual parameters and standards governingknowledge-wh in such a way that (53a) is true, yet, relative to thesame contextual parameters and standards, (53b) is false, and itsfalsity is a consequence of Rupert’s false belief aboutPaperWorld:

• (53)a.Janna knows where onecan buy an Italian newspaper.
• b.Rupert knows where onecan 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 shebelieves, the same cannot be said of Rupert.

Phillips and George (2018) present experimental empirical evidencesupporting the false-belief sensitivity of knowledge-wh. There is alsoa substantial discussion of false-belief sensitivity in Theileretal. 2018, where it is referred to as false answersensitivity.

4.8 Responsive, rogative, and anti-rogative predicates

Knowledge is only one of a broader category of attitudes correspondingto what Lahiri (2002) callsresponsive predicates. It ischaracteristic of responsive predicates that they accept bothinterrogative and declarative complements, as in ‘Maryknows/remembers/forgets who runs’ and ‘Maryknows/remembers/forgets that John runs’. Responsive predicatescontrast with what Lahiri (2002) callsrogative predicates,such as ‘wonder’, ‘be curious’, and‘inquire’, and with what Theileret al. (2019)callanti-rogative predicates, such as ‘suspect’and ‘hope’. Rogative predicates accept interrogativecomplements but do not accept declarative complements. For example,one can inquire who ate the last doughnut, but one cannot inquire thatJohn ate the last doughnut. Anti-rogative predicates on the otherhand, accept declarative complements but not interrogativecomplements. For instance, one can suspect that John ate the lastdoughnut but one cannot suspect who ate the last doughnut.

The distinction between rogative and responsive predicates hasepistemological significance, as it underlies Friedman’s (2013)argument that there is a category of attitudes that havequestions, not propositions, as their contents. Friedmancalls these theinterrogative attitudes, and they areprecisely the attitudes denoted by rogative predicates.

Within the category of responsive predicates Lahiri (2002, 287)distinguishes theveridical from thenon-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 thecorrect answer to its interrogative complement, anon-veridical-responsive predicate expresses a relation to a possible(but not necessarily the correct) answer. For example, ‘Janeremembers who won the lottery’ entails that Jane has knowledgethat correctly answers the question ‘Who won thelottery?’, whereas ‘Jane is certain about who won thelottery’ entails that Jane is certain of the truth of aproposition that may or may not correctly answer that same question.

Recent work in formal semantics has attempted to derive the fact thatrogative predicates do not accept declarative complements and the factthat anti-rogative predicates do not accept interrogative complementsfrom independently observable semantic properties of such predicates(see, e.g., Theileret al. 2019, Uegaki 2019, Roelofsen2019).

4.9 Pointers to further reading

A detailed uniform treatment of declarative and interrogativecomplements of responsive predicates in the context of inquisitivesemantics can be found in Theileret al. 2018. On thistheory, declarative and interrogative complements are of the samesemantic type, which allows each responsive verb to have a singlelexical entry.

For a detailed critique of the recent literature on knowledge-wh, seeChapter 2 of Stanley 2011. Parent (2014) provides a survey of therecent literature about knowledge-wh organized around three issues:the reducibility of knowledge-wh to knowledge-that, the relativity ofknowledge-wh to a contrast proposition, and the issue of whether thecontext-sensitivity of knowing-wh is to be understood as a semantic ora pragmatic phenomenon. Uegaki (2019) provides an overview of recentwork on the semantics of responsive predicates generally and isorganized around four approaches: the reduction of questions topropositions, the reduction of propositions to questions, theuniformity approach (on which declarative and interrogativecomplements of a responsive predicate are of the same semantic type),and the ambiguity approach (which postulates distinctproposition-taking and question-taking readings of a given responsivepredicate).

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Acknowledgments

The authors are listed alphabetically. Cross wrote sections 1, 3, and4; Roelofsen wrote section 2.