Categorial nouns and questions

Richard Lawrence

November 18, 2016

1 Categorial nouns

Here is a list of nouns:

person reasonthing waytime amountplace number

They are examples of what I will call categorial nouns, because they expresssome of the most basic and abstract categories we use to understand and de-scribe the world. This essay is about what categorial nouns mean.

We usually describe the meanings of nouns in terms of the things they applyto, or stand for, or denote. We say that a noun like ‘horse’, for example, denotesthe horses, or the class of horses, or a function defined by its relationship tohorses. So this essay is also about whether there are such things as persons,numbers, reasons, or ways—things which categorial nouns stand for or denote.Most of what I have to say will be in the formal mode, but my goal is to shedlight on this material issue.

Each case has its defenders and detractors. It seems perfectly obvious tosome philosophers, for example, that there are such things as reasons: we sayand do things for reasons; we explain those reasons to others; and in doing so,we can use ‘reason’ to make true claims. The reason I began this paragraphwith a capital ‘E’ was that the rules of English grammar required it. That isa true statement! It follows that there are reasons, such as the one I just men-tioned: the reason I began this paragraph with a capital ‘E’.

To other philosophers, this sort of argument sounds like pure sophistry.How could it possibly be so easy to establish that there are things called ‘rea-sons’, and that they affect our actions? Reasons are a bit more difficult to findin the world than things like horses. These philosophers will be inclined toparaphrase my statement to get rid of the categorial noun it contains. Whileit is true that the reason I began the previous paragraph with a capital ‘E’ wasthat the rules required it, this just means that I began that paragraph with acapital ‘E’ because the rules required it. The apparent reference to a reason is

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a linguistic trick, and the statement’s truth does not reveal much about whatthere is, or what moves us to act.

Debates like this one seem to reach a stalemate pretty quickly. I think wecan avoid the stalemate by rejecting an assumption that is common to bothsides, namely, the usual model of what nouns mean. In this case, both sidesaccept that ‘reason’ denotes the reasons, and they picture this relationship asa relationship between the word and some things in the world. That is whythe first camp thinks that the truth of sentences containing ‘reason’ reveals thatthere are reasons, the things denoted by the noun. It is also why the secondcamp, doubting that there are any such things for the noun to denote, wantsto paraphrase it away. They both accept the usual model, but they apply it inopposite directions. If we can reach a better understanding of what categorialnouns mean, we can avoid the opposition.

My thesis is that the meanings of categorial nouns should be described interms of their role in practices of asking and answering questions. You mighthave noticed that each of the nouns in the list above corresponds to a kind ofquestion we can ask using one of the basic question words of English: ‘who’,‘what’, ‘when’, ‘where’, ‘why’, and ‘how’ (including ‘how much’ and ‘howmany’). A categorial noun signifies a kind of question. Semantically, a questiondistinguishes its possible answers from non-answers. Thus, a categorial noundetermines a range of answers, or a kind of answer. Its job is to make explicitwhat would and would not count as giving the answer to a certain question.

Here is a simple example. Suppose I say, “Today I met the person I willmarry”. How should we describe what the noun phrase ‘the person I willmarry’ means in this sentence? ‘Person’ corresponds to ‘who’; this noun phrasecorresponds to the question you might ask by saying, “Who will you marry?”I have not answered this question, and you don’t need to know the answerto understand my assertion. But you do need to know what would count asanswering this question. The answer could be that I will marry Amelie, orBeatrice, or Charlotte. The answer could not be that I will marry soon, or thatI will marry in my home town; if someone responded to the question that way,she would be making a category mistake. It is this distinction, between theanswers expressed by ‘Amelie’, ‘Beatrice’, and ‘Charlotte’ on the one hand,and the non-answers expressed by ‘soon’ and ‘in my home town’ on the other,that the categorial noun ‘person’ expresses. What I said means that today I metAmelie, or Beatrice, or Charlotte, or some other person, whom I will marry.My statement cannot mean that today I met soon, or today I met in my hometown. If you took it that way, you would be misinterpreting me.

In fact, I think a much wider class of nouns should be understood this way,including other nouns that signify abstract things, like ‘month’ or ‘ratio’, andeven nouns that signify very concrete things, like ‘horse’. We should describewhat almost all nouns mean in terms of their relationship to questions. What’sdistinctive about categorial nouns is their relationship to question words, andtherefore to our most basic kinds of questions. This relationship has some puz-zling features which the usual model cannot explain. Describing the meaningof categorial nouns in terms of questions accounts for those features, so these

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features motivate a question-based approach to categorial nouns. But once wesee how to describe the meanings of categorial nouns in terms of questions,we will see that this approach applies equally well to other nouns, so thereis no reason to treat categorial nouns as a special case.1 The question-basedapproach is ultimately attractive because it generalizes the usual model, in away that clarifies what both realists and anti-realists get right in debates aboutreasons, numbers, persons, or ways of appearing or acting.

2 Two approaches to categorial nouns

My question, then, is: how should we describe what categorial nouns mean?In this section, I want to examine two natural approaches to answering thisquestion. These approaches are natural because they are conservative: they tryto preserve the usual model of noun meaning, in two different ways. They areboth ultimately unsatisfying, though, and it is instructive to see why.

The first approach is just the usual one: categorial nouns denote classes ofobjects. ‘Person’ denotes the persons, ‘reason’ denotes the reasons, and ‘num-ber’ denotes the numbers, just as ‘horse’ denotes the horses. This answer isnot necessarily false, but it is incomplete, because it fails to explain the specialrelationship between categorial nouns and question words. Categorial nounphrases are intersubstitutable with question-word phrases in a way that mostnoun phrases are not, and a description of their meaning should explain whythat is. The usual model can’t do that, so it is incomplete at best.

The second approach is a kind of null hypothesis: categorial nouns don’treally mean anything. That is, they don’t perform the same semantic functionas nouns like ‘horse’; they are semantically idle, and perform only a syntacticfunction. This answer tries to preserve the usual model of noun meaning in thegeneral case by making an exception for categorial nouns. It is suggested bythe kind of move that I sketched in the debate about ‘reason’ above: categorialnouns are often eliminable via paraphrase. But this answer is also incorrect.Categorial nouns do perform a semantic function, as we can see by looking attheir behavior more closely. I will say how we should describe that semanticfunction in Section 3.

2.1 The usual model of noun meaning

Let’s first see why the usual approach does not adequately describe the mean-ings of categorial nouns. Our usual model for understanding the semantics ofnouns says that nouns denote classes of objects. ‘Horse’ denotes the class of

1There are a few kinds of noun that I will ignore here. These include mass nouns, like ‘water’or ‘rice’, and nouns which are derived from other parts of speech, like ‘redness’ from ‘red’ or‘rejection’ from ‘reject’. I think these nouns can ultimately be accommodated on the question-based approach I describe, but explaining how to do so would take me too far afield. I focus onjust the nouns that the usual model aims to describe: count nouns which seem to denote or signifya class of things.

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horses, ‘potato’ the class of potatoes, and ‘silicate’ the class of silicates. Does itmake sense to say the same thing about categorial nouns? Should we say that‘reason’ denotes the class of reasons, ‘way’ denotes the class of ways, ‘amount’denotes the class of amounts, and so on?

There are some intuitive reasons not to say so. Part of the point of sayingthat nouns denote classes of objects is to indicate what we are talking aboutwhen we use those nouns. By saying that ‘horse’ denotes the class of horses,we indicate that sentences containing ‘horse’ are about horses, and that wemust look to the horses to determine whether such sentences are true. But itis not so clear that sentences containing ‘way’, for example, are about ways,or that we must somehow ‘look to the ways’ to determine if they are true. Sowe might think that categorial nouns like ‘way’ should be given a differentsemantic treatment from nouns like ‘horse’.

These intuitive considerations are not strong enough to show that the usualmodel does not apply to categorial nouns, though. For one thing, they do nothold equally well for all the nouns that appear in the list above. It is just asobvious that there are persons as that there are horses, for example, and thatwe use ‘person’ to talk about them. For another, there might be good reasons toassimilate ‘way’ and ‘horse’ for the purposes of semantic theorizing. Whateverintuitive differences we feel there are between ways and horses, it may be thatthose differences are better represented elsewhere, outside of a semantic theoryfor natural language.

Still, there is one serious challenge for any semantic theory that assimilatescategorial nouns and other nouns, which I would now like to explain. Catego-rial nouns are semantically related to question words in a way that most nounsare not. I’ll describe the relationship, and then explain why it’s a problem forthe usual model.

2.1.1 Categorial noun phrases and nominal interrogatives

The special relationship between categorial nouns and question words is ondisplay in pairs of sentences like these:

(1) a. What Amelie did was truly amazing.b. The thing Amelie did was truly amazing.

(2) a. I learned how Amelie escaped.b. I learned the way Amelie escaped.

The sentences in such pairs are truth-conditionally equivalent. How could itbe true that what Amelie did was truly amazing, but false that the thing shedid was truly amazing? Or true that I learned the way Amelie escaped, butfalse that I learned how she escaped? It doesn’t seem to be possible to believeone but doubt the other, or to coherently adopt any other opposing attitudestoward them.

Some terminology will be useful to describe this relationship. In the sen-tences above, ‘what Amelie did’ and ‘how Amelie escaped’ are examples of

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what I will call nominal interrogatives.2 Nominal interrogatives are completephrases that begin with a question word. They are nominal in the sense thatthey occupy grammatically nominal positions, such as the subject or directobject of a transitive verb. (This distinguishes them from clauses that beginwith question words, such as relative clauses and complete interrogative sen-tences.) Nominal interrogatives can be replaced by descriptions, such as ‘thething Amelie did’ or ‘the way Amelie escaped’. Such a description is a nounphrase or determiner phrase, in which the first noun is a categorial noun. I willcall this sort of description a categorial noun phrase.

A nominal interrogative can (almost) always be traded in for a categorialnoun phrase without changing the truth conditions of the sentence as a whole.This is the relationship exemplified in the pairs above. Here are some otherexamples:

(3) a. Beatrice was [who you met that day].b. Beatrice was [the person you met that day].

(4) a. Ten p.m. is [when I go to bed].b. Ten p.m. is [the time I go to bed].

(5) a. Charlotte went back to [where she first saw the lion].b. Charlotte went back to [the place she first saw the lion].

(6) a. We’ll never know [why Dieter fled the country].b. We’ll never know [the reason Dieter fled the country].

(7) a. The flavor depends on [how much vodka you add].b. The flavor depends on [the amount of vodka you add].

(8) a. Ernest counted [how many birds he’d seen so far].b. Ernest counted [the number of birds he’d seen so far].

Again, in each case, the two sentences are truth-conditionally equivalent. Andit would be easy to multiply these examples. An appropriate categorial nounphrase can be substituted for a nominal interrogative in a wide variety of con-texts and syntactic environments, without changing the truth conditions.

There are some exceptions to this general pattern, of course. Sometimes,a nominal interrogative cannot be replaced by any categorial noun phrase be-cause the resulting sentence would be ungrammatical. This is generally truefor nominal interrogatives beginning with ‘which’ and ‘whether’; I will havemore to say about these question words below. It is also true for nominal in-terrogatives that appear after certain verbs, such as ‘wonder’: you can wonderwhere I went, but you cannot wonder the place I went. Sometimes, main-taining grammaticality requires adding a preposition to the categorial nounphrase, or modifying the containing sentence slightly. These exceptions are

2I am using this terminology to encompass two kinds of question-word phrases that linguiststypically distinguish: interrogatives and free relatives. They are distinct because they have differ-ent syntactic distributions, and in some languages (though not in English), they differ morpholog-ically. The syntactic differences are not important for my purposes here, and distinguishing themwould obscure the semantic parallel between them that I want to focus on.

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important from a syntactic perspective, but they shouldn’t distract us from thegeneral semantic pattern. Where grammar permits it, a nominal interrogativewill be intersubstitutable with some appropriate categorial noun phrase, andthe resulting sentence will be truth-conditionally equivalent.

This relationship to nominal interrogatives is unique to categorial nouns. Anominal interrogative can often be replaced by a non-categorial noun phrase,too, but the result is not truth-conditionally equivalent:

(9) a. [What Werner cooked] was inedible.b. [The food Werner cooked] was inedible.

These two sentences are not equivalent, because what Werner cooked mightnot have been food. Suppose, for example, that the only thing he cooked was ashoe: then it’s true that what he cooked was inedible, but it’s not true that thefood he cooked was inedible, because he didn’t cook any food.

In fact, the intersubstitutability of nominal interrogatives and categorialnoun phrases is distinctive enough that I will take it to define the class of catego-rial nouns.3 A categorial noun is a noun associated with a particular questionword, such that noun phrases headed by that noun can in general replace nom-inal interrogatives beginning with that question word, without changing thetruth conditions of the containing sentence. The sentences in (1)–(8) are meantto vindicate my original list of categorial nouns. But I am focused on this gen-eral pattern, not any particular list of nouns. Depending on our judgmentsabout equivalence, and how much grammatical ‘fudging’ we allow, we’ll endup with different lists of the categorial nouns in English; some of the nouns Ilisted might have to go. That does not matter, for my purposes. The pattern isclear enough for philosophically-interesting nouns like ‘reason’, ‘number’, and‘way’. Noun phrases with ‘reason’ can be substituted for interrogatives with‘why’; those with ‘number’ for interrogatives with ‘how many’; those with‘way’ for interrogatives with ‘how’; and so on.

2.1.2 The usual model is incomplete

This relationship between categorial noun phrases and nominal interrogativesraises a puzzle about categorial nouns. In the version of the sentence con-taining the nominal interrogative, the categorial noun does not appear. Butin many cases, that is the only significant difference between the two versionsof the sentence. The only difference between (6-a) and (6-b), for example, isthat ‘why’ has been replaced by ‘the reason’; the rest of the sentence is string-identical. The same goes for the other examples. The other words in the sen-tence are the same, and are arranged in the same way. Now, semantic ortho-doxy has it that the truth conditions of a sentence are determined by the se-mantic contributions of each of its parts, together with their arrangement. Sohere’s the puzzle: if the truth conditions of the whole sentence are the same,

3Compare Caponigro (2003), who uses the intersubstitutability of free relatives with descrip-tions as part of a definition of the category of free relatives.

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whether or not the categorial noun is present, what does that noun contributeto the truth conditions of the whole? If categorial nouns make a semantic con-tribution, it doesn’t seem to be an essential one, since the same truth conditionscan be had in their absence. Whatever the semantic contribution of ‘reason’ is,‘why’ can make the same contribution without it. We need to describe the se-mantics of categorial nouns in a way that accounts for this fact. So how shouldwe do it?

The usual model can’t resolve this puzzle, even for nouns like ‘person’ towhich it uncontroversially applies. This is because it applies equally well tonon-categorial nouns, so if we use it to describe the semantic contribution ofcategorial nouns, we will be left without an explanation of their special rela-tionship to question words. To see this, consider again the sentences in (3):

(3) a. Beatrice was [who you met that day].b. Beatrice was [the person you met that day].

Suppose we follow the usual model, and grant that ‘person’ denotes the classof persons. Even granting this, the problem remains: how do we explain why(3-a) and (3-b) are equivalent, given that the latter employs ‘person’ and theformer employs ‘who’?

In fact, applying the usual model makes the problem more acute, becausesaying that ‘person’ denotes the class of persons assimilates our semantic ex-planation of (3-b) to our explanations of sentences where another noun occursin the place of ‘person’:

(10) a. Beatrice was the woman you met that day.b. Beatrice was the queen you met that day.c. Beatrice was the relative you met that day.d. Beatrice was the Canadian you met that day.e. . . .

A typical semantic explanation of, say, (10-b) would compositionally derive astatement of its truth conditions using a lexical clause that says ‘queen’ denotesthe class of queens. This explanation could be carried over to any of the othersentences in the family in (10) simply by replacing this clause with a clausefor another noun. Likewise, it could be carried over to (3-b) simply by replac-ing the clause for ‘queen’ with a clause that says ‘person’ denotes the class ofpersons.

The trouble is that none of the sentences in (10) is equivalent to (3-a), andany reasonable explanation of their semantics will predict this. Each of thesentences in (10) could be false while (3-a) is true. Intuitively, the reason ineach case is that the italicized noun restricts which objects the description ‘theNOUN you met that day’ might denote, while ‘who you met that day’ is notsimilarly restricted: it might have been true of someone that she was who youmet that day, yet false that she was a woman, a queen, a relative, or a Canadian.This restricting effect of nouns will typically be represented in a semantic the-ory in the way that clauses for nouns compose in larger expressions. But ‘per-

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son’ differs from ‘queen’, ‘woman’, ‘relative’ and so on precisely in that it doesnot impose a similar restriction in this context, or most other contexts wherea categorial noun phrase can occupy the same position as a ‘who’-nominal.Thus, saying that ‘person’ denotes the class of persons just as ‘queen’ denotesthe class of queens makes the need for an explanation of this difference all themore pressing.

The problem is clearly that a disquotational lexical clause that says

(11) ‘Person’ denotes the class of persons

does not say anything about the relationship of ‘person’ to ‘who’. A naturalthought to have at this point is that we could solve this problem by sayingsomething about the relationship in our lexical clause for ‘who’, perhaps byusing a clause like

(12) ‘Who . . . ’ denotes the person that . . .

An approach like this would allow us to maintain the usual disquotationalclause for ‘person’ while capturing its special relationship to ‘who’, by adopt-ing a non-disquotational clause for the question word. This ensures the rightconnection between the question word and the noun.

Unfortunately, this approach won’t save the usual model, because the rela-tionship between question words and nouns is sometimes more complicatedthan the relationship between ‘who’ and ‘person’. Consider ‘when’, for exam-ple. ‘When’ is associated with the categorial noun ‘time’, but in certain con-texts, another noun is needed to replace nominal ‘when’-interrogatives:

(13) a. Wednesday is when I do my shopping.b. Wednesday is the {day/??time} I do my shopping.

In (13-b), the non-categorial noun ‘day’ seems like a better choice than the cat-egorial noun ‘time’ for producing a sentence equivalent to (13-a). In other con-texts, nouns like ‘month’ or ‘year’ are needed to replace ‘when’-nominals, forsimilar reasons. Now, the usual model tells us that ‘day’ denotes the days,‘month’ denotes the months, ‘year’ denotes the years, and so on. But combin-ing the usual model with a non-disquotational lexical clause for ‘when’ wouldonly aggravate the problem of explaining patterns like the one in (13): the re-sulting theory would say that ‘when I do my shopping’ denotes the time I domy shopping, not the day I do my shopping; but that is exactly the opposite ofwhat’s observed in (13-b). Instead, we should say that ‘day’ denotes a certainkind of time, so it too says something about when things happen; ‘day’ is moreappropriate in (13-b) just because it is more specific than ‘time’, and thus morerelevant. But we can’t say this unless we go beyond what the usual model tellsus about ‘day’ and ‘time’.

Thus, the usual model will still not suffice to describe the meaning of cate-gorial nouns, or explain the special relationship between categorial nouns andquestion words. The conclusion is not that we cannot apply our usual modelto the semantics of categorial nouns. I am claiming only that if we apply it,

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we will not have made any progress toward understanding their unique se-mantic behavior. When a nominal interrogative is replaced by an appropriatecategorial noun phrase, the resulting sentence is truth-conditionally equiva-lent. When the same interrogative is replaced by a non-categorial noun phrase,the result is not equivalent—except in cases where a non-categorial noun hasa derivative semantic relationship to a categorial noun, like ‘day’ has to ‘time’.Since the usual model simply says that nouns denote classes of objects, it pro-vides no resources for explaining this difference. Thus, the usual model is in-complete. We have to look beyond it if we want to understand the relationshipbetween categorial nouns and question words.

2.2 A syntactic approach to categorial nouns

Now that we have seen the trouble that the usual model has with categorialnouns, a second approach to describing their meaning may look more appeal-ing. Perhaps categorial nouns don’t mean anything at all—at least not in thesense that they contribute to a sentence’s truth conditions. Instead, they servesome other linguistic function.

An approach like this can be motivated by observing that categorial nounsare often eliminable via paraphrase. We have just looked at one way to do so:substitute a nominal interrogative for a categorial noun phrase. This is oftenpossible, and it eliminates a categorial noun from a sentence without changingits truth conditions. But this is not the only strategy for paraphrasing categorialnouns away, or even the most significant one. Here’s another example. We canparaphrase a sentence like (14-a) as (14-b):

(14) a. The reason Harry fell off his horse was that he was drunk.b. Harry fell off his horse because he was drunk.

That eliminates ‘reason’ from the sentence, in favor of ‘because’. Again, thesentences in this pair seem to be truth-conditionally equivalent; it seems im-possible for one to be true while the other false, to suppose one without sup-posing the other, and so on. Similarly, we can eliminate ‘way’ from (15-a):

(15) a. The way Harry got drunk was by downing a bottle all at once.b. Harry got drunk by downing a bottle all at once.

In this case, we don’t even need to introduce a word like ‘because’; the syntaxof adverbial modification in (15-b) seems to be enough to express what ‘way’expresses in (15-a).

What’s interesting about examples like (14) and (15) is that the concept ex-pressed by the categorial noun can be equivalently expressed without using anoun. This, we might think, is a hint that categorial nouns like ‘reason’ and‘way’ are importantly different from more ordinary nouns like ‘horse’, and sowe shouldn’t describe what they mean by saying that they denote a class of ob-jects. They play some other role in sentences like (14-a) and (15-a), and perhapsin the language as a whole.

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I would now like to consider one way of developing this idea, based ona recent proposal by Thomas Hofweber (Hofweber, 2007; Hofweber, 2005).Hofweber discusses a third example, of the same type as (14) and (15):4

(16) a. The number of Jupiter’s moons is four.b. Jupiter has four moons.

To explain the truth-conditional equivalence of pairs like these, Hofweber pro-poses that the two sentences are merely syntactic variants of each other. Thesyntactic differences between them affect their communicative import, but nottheir truth conditions. I want to see whether we can leverage this proposalto obtain a general account of the linguistic role of categorial nouns. Perhapscategorial nouns occur for purely syntactic and communicative reasons, anddo not contribute anything to the truth conditions of sentences in which theyoccur. I think Hofweber is right to look at the different effects that (16-a) and(16-b) have in communication, but as we will see, those effects cannot be en-tirely explained by syntax. Thus, Hofweber’s proposal will not give us an ex-planation of the role of categorial nouns like ‘number’ on its own. We cannotavoid giving a semantic description of categorial nouns.

2.2.1 Categorial nouns as products of syntactic variation

The central idea in Hofweber’s proposal is that the relationship between (16-a)and (16-b) is much like the relationship in the following pairs of sentences:

(17) a. It is soccer that Johan likes.b. Johan likes soccer.

(18) a. Quietly was how Mary entered.b. Mary entered quietly.

The distinction here is between focused sentences, like (17-a) and (18-a), andneutral sentences, like (17-b) and (18-b). Intuitively, a focused sentence placesstress or emphasis on some part of what’s said, where the neutral sentence doesnot. Hofweber’s idea is that (16-a) is a focused variant of the neutral sentence(16-b); he calls it a focus construction.

Like the other examples we have seen, the focused sentences in these pairsare truth-conditionally equivalent to their neutral counterparts.5 For how couldit be true that Johan likes soccer, but false that it is soccer that Johan likes? Ortrue that Mary entered quietly, but false that quietly is how she entered? Ineach case, the focused sentence communicates just the same information asits neutral variant. How, then, should we account for the differences betweenthem?

Hofweber’s answer is that the neutral and focused versions of a sentencehave different communicative uses, and these different communicative uses

4The pair of sentences in this example originates from Frege (1980, §57).5As Hofweber points out, this is not true in general. Focus can affect truth conditions. But it

doesn’t seem to do so in the examples above, including (16).

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explain the differences in their syntax. The most important communicativedifference is that neutral sentences can be used to answer more questions thantheir focused variants. For example, the neutral sentence (17-b) can answereither “Who likes soccer?” or “What does Johan like?” The focused sentence(17-a), on the other hand, is only an appropriate answer to “What does Johanlike?”. It exhibits a focus on some aspect of the information being communi-cated. When that aspect of the information is not in question, or when someother aspect of the information was asked for, this focus is communicatively in-appropriate. Hofweber claims that (16-a) communicates the same informationas (16-b), but focuses on the ‘how many’ aspect of that information. Both (16-a)and (16-b) can answer a question like “How many moons does Jupiter have?”.But due to its focus, (16-a) is not an appropriate answer to other questions, like“Which planet has four moons?”.

This is a good time to point out that (16-a), as well as the parallel examplesin (14-a) and (15-a), all belong to a class of copular sentences known to linguistsas specificational sentences. I will have more to say about them below. At themoment, I just want to point out that one of the distinctive properties of spec-ificational sentences is that they exhibit focus on the phrase after the copula.6

So Hofweber is right that these sentences, like the (non-specificational) focusconstructions (17-a) and (18-a), are not neutral, and as a result, they can be usedto answer fewer questions in discourse.

The fact that specificational sentences exhibit focus suggests a hypothesisabout why categorial nouns can often be eliminated via paraphrase, as we sawin examples (14), (15), and (16) above. Following the analogy with other typesof focus constructions, like the ‘it’-cleft construction in (17), we can supposethat a specificational sentence and its neutral counterpart are merely syntacticvariants of each other. If that is right, it tells us that ‘reason’, ‘way’, and ‘num-ber’ occur in these sentences for purely syntactic reasons, as byproducts of thevariation that produces the focus in a specificational sentence. Perhaps, then,categorial nouns are merely byproducts of syntactic variation in general, evenoutside of specificational sentences. We make use of such variation to producecertain effects in communication, such as focus effects, but these effects do notinfluence the truth conditions of the sentence. Accordingly, when this syntac-tic variation introduces a categorial noun into a sentence, that noun occurs forpurely syntactic reasons. It is just a ‘dummy’ noun, required by grammar, likethe ‘it’ in an ‘it’-cleft. It is not interpreted, and makes no contribution to thesentence’s truth conditions or the information it expresses.

This hypothesis explains why we can often paraphrase categorial nounsaway, and offers a deflationary answer to the question of what they mean. Ac-cording to the hypothesis, they don’t really mean anything, in the sense of mak-ing a semantic contribution to sentences in which they occur. At the same time,it explains why we have such nouns: they are needed to package informationin certain ways in syntax, in order to achieve certain effects in discourse, such

6There is consensus among linguists on this point; see Mikkelsen (2005, p. 133) and referencesthere.

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as focus effects. This hypothesis will seem attractive to a philosopher who hastrouble believing that there are such things as reasons, ways, or numbers. If thehypothesis is true, it means that we do not need to admit that ‘way’ denotesthe ways, or ‘number’ denotes the numbers, but neither do we need to say thatthese words serve no expressive purpose. They have an important role in thelanguage; but it’s not the same role that a noun like ‘horse’ plays.

2.2.2 Against the syntactic hypothesis

Nevertheless, the hypothesis is highly implausible. Categorial nouns really domean something—something that should be captured and represented in a se-mantic theory, and that we cannot plausibly account for just by pointing to theextra-semantic effects of constructions where they appear. This is intuitivelyobvious, and should be our default position; but I will offer a few observationsto support it, since they help motivate the semantic approach I describe below.

The first observation is simply that we have more than one categorial noun,and different categorial nouns are not interchangeable. This is not what we’dexpect, if categorial nouns were only ‘dummy’ words that occur because they’rerequired by grammar. One such noun would suffice, and two or more thatserve the same purpose would be interchangeable. That is clearly not so, how-ever:

(19) a. #The way of Jupiter’s moons is four.b. #The number Harry got drunk was by downing a bottle all at once.

These sentences, it seems, are syntactically well-formed but semantically bad.It is not clear why this should be so, if both ‘number’ and ‘way’ are merelyuninterpreted bits of syntax that only occur because they help achieve focusand other discourse effects. Intuitively, the problem with these sentences is thatthere is some kind of semantic disagreement between the focused expressionand the noun: four is not a way you can have moons, and downing a bottle allat once is not a number of getting drunk. This suggests that ‘number’ and ‘way’have semantic features which can agree or disagree with the semantic featuresof focused expressions.

A second observation further supports this thought. Categorial nouns arenot interchangeable in focus constructions because they are sensitive to thesemantic contribution of the focused expression, and not merely its syntax. Forexample, ‘number’ cannot be used as part of a focus construction when thefocused expression is not a number word. We can see this as follows. Recallthe sentences in (16):

(16) a. The number of Jupiter’s moons is four.b. Jupiter has four moons.

Hofweber’s idea was that (16-a) is a syntactic variant of (16-b), which serves tofocus on the ‘how many’ aspect of the information communicated by (16-b). In(16-b), the number word ‘four’ expresses this aspect of the information.

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Syntactically, ‘four’ is either an adjective or a determiner, so if the sentencesin (16) are merely syntactic variants of each other, then we should be able toform analogous pairs of variants using expressions from one of these cate-gories. But we can’t. First, suppose ‘four’ is an adjective, like ‘yellow’. Theneutral version of the sentence with ‘yellow’ is fine, but the focused, specifica-tional version is not:

(20) a. #The number of Jupiter’s moons is yellow.b. Jupiter has yellow moons.

(20-a) does have a (bizarre) reading on which ‘yellow’ is predicated of the num-ber of Jupiter’s moons, like ‘even’ or ‘larger than 10’ could be. But it cannotbe interpreted as a specificational sentence: ‘yellow’ cannot specify the numberof Jupiter’s moons in the same sense in which ‘four’ specifies that number in(16-a).

Maybe the problem here is that ‘yellow’ is an adjective but ‘four’ is a deter-miner, and so (20-a) is not an analogous variant of (16-a). But things don’t goany better if we use a determiner instead:

(21) a. */# The number of Jupiter’s moons is some.b. Jupiter has some moons.

Again, the neutral version is fine. Moreover, ‘some’ is not just any determiner,but a quantifier; so like (16-b) (and unlike (20-b)), (21-b) says something abouthow many moons Jupiter has. Still, we cannot use (21-a) in order to focus onthat ‘how many’ aspect of what (21-b) says. The specificational version of thesentence is not even obviously grammatical. Even if it is, it is semanticallyincongruous, just like (20-a): ‘some’ cannot specify a number.

Whether we treat ‘four’ as an adjective or a determiner, the examples areeasy to multiply. ‘Number’ only seems to allow the focused expression to be anumber word. Other expressions with the same syntax, even those that pro-vide ‘how many’ information, cannot be the focused expression in a specifica-tional sentence analogous to (16-a). If that is right, then ‘number’ is sensitive tothe semantic features of the focused expression, and not merely its syntax. Theonly plausible way of distinguishing number words from both quantifiers like‘some’ and non-numerical adjectives like ‘yellow’ is along semantic lines: num-ber words express definite quantities, while these other expressions do not. Theuse of ‘number’ in focus constructions is sensitive to these semantic distinc-tions, which means that it has some semantic features. These semantic featuresare the best explanation of why ‘number’ is not intersubstitutable with ‘way’or other categorial nouns, and why it can only be used in a specificational sen-tence that focuses on an expression for a definite quantity. Thus, we cannotplausibly claim that ‘number’ is simply an uninterpreted piece of syntax insentences like (16-a).

The analogy between specificational sentences and other focus construc-tions, like ‘it’-clefts, is therefore misleading. Both types of sentence exhibitfocus. But unlike the ‘it’ in an ‘it’-cleft, the role of ‘number’ in (16-a) is not ex-

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hausted by its syntactic role in creating focus or other discourse effects. Whileit is true that (16-a) exhibits a focus effect, we are not justified in regarding it asmerely a syntactic variant of (16-b).

A further observation about ‘number’ underscores this point. ‘Number’also distinguishes ‘four’ from ‘yellow’ when it occurs outside specificationalsentences, as a simple predicate:

(22) a. Four is a number. (>)b. Yellow is a number. (⊥)

(22-a) is obviously true, while (22-b) is obviously false, and the only explana-tion for this is that ‘number’ makes a genuine contribution to the truth condi-tions of these sentences. It is useful to compare this example with one in whichthe non-categorial noun ‘color’ appears as the predicate:

(23) a. Four is a color. (⊥)b. Yellow is a color. (>)

Switching the nouns flips the truth values, and there is every reason to thinkthat these pairs of sentences are semantically parallel. ‘Number’ makes thesame kind of semantic contribution as non-categorial nouns like ‘color’.

These observations all generalize to categorial nouns other than ‘number’,too. Categorial nouns are not interchangeable with each other or with othernouns; they can only be used in specificational sentences where the focusedexpression belongs to a certain semantically-distinguished class; and they canoccur as significant predicates. The best explanation for these facts is the sim-plest one: categorial nouns make a semantic contribution, of the same kind asother nouns. The problem is simply that we must somehow describe that con-tribution in a way which explains the special features of categorial nouns. Iwould now like to explain how I think we should do so.

3 Meanings via questions

We saw above that we cannot adequately describe the semantics of categorialnouns in the usual way, by saying that they denote classes of objects. Cate-gorial nouns have a special relationship to question words, which cannot becaptured by simply disquoting them to describe the classes of objects they de-note. We also saw that when a categorial noun appears in a focused sentencesuch as a specificational sentence, it can often be eliminated in an equivalentneutral sentence, and that the distinction between focused and neutral sen-tences concerns their different relationships to questions. These facts suggesta different approach to describing the meaning of categorial nouns, and nounsmore generally. We should describe their meanings in terms of questions.

In this section, I’ll explain one approach to doing this. The idea is that anoun phrase expresses a question, and a noun expresses a certain part or aspectof that question—namely, the range of a variable whose values determine its

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possible answers. This approach generalizes the usual model of noun meaningwhile capturing the special features of categorial nouns. In order to describethis idea in detail, I first need to explain how I am thinking about questions. Iwill then explain how to describe the semantics of nouns in terms of questions,and show how this account accommodates the observations above.

3.1 A primer on questions and answers

As I will understand it, a question is different from the phrases which expressit, which can include both noun phrases and nominal interrogatives. Likewise,the act of asking a question is different from the question itself: a question maybe expressed without being asked. These distinctions parallel more familiardistinctions between a proposition and the sentence which expresses it, on theone hand, and the act of asserting it on the other. Just as we can think of propo-sitions as defined by their role in acts of asserting, we can think of questions asdefined by their role in practices of asking and answering them. In speaking ofquestions, I am describing the details of that role in practice.

Questions have answers, and we ask them in order to find their answers. Ofcourse, sometimes things turn out badly: a question can be confused, or haveno answer, or have no good answer so far as anyone knows. But these excep-tions prove the rule. Questions are asked in expectation of getting an answer. Inthe normal case, an answer can be supplied, though perhaps only after someinvestigation or thought.

One of the most important features of questions is the epistemological gapbetween a question and its answer. To understand a question, you need not al-ready know how to answer it. Indeed, that is the whole point: questions are auseful means of acquiring knowledge precisely because we can ask and under-stand them without already possessing that knowledge. On the other hand,understanding a particular question still requires knowing something. Other-wise, all questions would be the same, which is clearly not so. The questionsasked by, say, “Where did you eat?” and “What did you eat?” are different. Weunderstand them differently because we know they require different answers.

In literature on the logic and semantics of questions, these facts are stan-dardly represented by saying that a question admits of a range of possible an-swers.7 To understand a question, you do not need to know what its specificanswer is, but you do need to know what would count as an acceptable answer,or what the general range of answers is like. That is, you must be able to dis-tinguish between claims which can provide an answer and claims which can’t.If you ask me where I ate, and I say that I ate a sandwich, I have misinterpretedyour question.8 If I had interpreted it correctly, then I would understand that Icould only answer it by saying that I ate at the park, or at Pat’s Steakhouse, or

7See, for example, Hamblin (1958).8Probably, anyway. I could also be giving an indirect answer: by saying I ate a sandwich, I

may be inviting you to infer that I ate at the sandwich shop, or to draw on your other backgroundknowledge about where I usually eat sandwiches. But giving indirect answers like this depends onthe possibility of giving direct answers. When I speak of answers, I am focusing on direct answers.

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in my living room, and so on. So semantically, a question distinguishes possi-ble answers from non-answers. We may say that it delimits, or presents, a set ofpossible answers. Answering a question involves selecting among these pos-sible answers. To answer a question is to say which of its possible answers areactually true.

It is helpful to draw a distinction between two basic kinds of questions,which concerns two different ways that questions can present their possibleanswers. Following Belnap and Steel (1976), I will call the two types of ques-tions whether-questions and which-questions. A whether-question presents anexplicit, finite list of possible answers. Yes-no questions are typical whether-questions: a question like “Is Alec in Germany?” presents just the two possibleanswers that Alec is in Germany, and that he isn’t. A which-question, on theother hand, presents an indefinitely large class of possible answers. In general,the possible answers to a which-question cannot be exhaustively and explicitlylisted, even by someone who understands the question.

A which-question presents its possible answers by giving their commonform, as a statement containing an ‘unknown’. In natural language, such anunknown is expressed by a question word; in formal analyses, it is typicallyrepresented with an algebraic variable. Here are some examples of which-questions, together with some examples of the possible answers they presentand a statement giving their common form by means of a variable:

(24) Who is in Germany?a. {Alec is in Germany, Fiedler is in Germany, Liz is in Germany, . . . }b. x is in Germany.

(25) Where is Alec?a. {Alec is in Germany, Alec is in France, Alec is in Spain, . . . }b. Alec is in x.

In a which-question, what’s unknown is which value, or values, of the vari-able will make the statement-form true. A which-question thus asks, whichstatements of this form are true? To understand it, you must understand therange of the variable, because the range of the variable determines the range ofpossible answers.

The distinction between whether- and which-questions is useful here be-cause categorial nouns are related to words that express which-questions, ratherthan whether-questions. These are the question words ‘who’, ‘what’, ‘when’,‘where’, ‘why’ and ‘how’. For example, ‘who’ means something like ‘whichperson’ in English; it is a word for a which-question where the variable rangesover persons. Similarly, ‘where’ means something like ‘which place’, ‘how’means something like ‘which way’, and so on. We may therefore leave whether-questions aside, and focus on which-questions and their relationship to nouns.

Because a which-question presents its possible answers by giving their gen-eral form, rather than listing them explicitly, the answer to a which-questioncan be viewed from two perspectives, or levels. At a high level, an answer

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to a which-question is the same as for a whether-question: it selects some ofthe possible answers and puts them forward as true. But at a lower level,because the possible answers of a which-question differ only by the valuesthat they assign to a variable, giving values for that variable suffices to answera which-question. Giving values for a variable is the means of answering awhich-question. For example, saying “Alec and Fiedler” in response to (24) isa means of claiming that Alec is in Germany and Fiedler is in Germany. Thesetwo names select two of the possible answers to this question, by giving twodifferent values for the variable it introduces, which ranges over persons.

Let’s reflect in more detail on what it means to ‘give’ the value of a vari-able, since that is the crucial step in answering a which-question. We shoulddistinguish giving a value of a variable from merely describing or constrainingit. The distinction is easiest to illustrate in an algebraic setting. Consider thesetwo equations:

x3 − 4 = 23x = 3

Both equations are true if and only if the value of x is 3, but there is an impor-tant difference between them. The first equation does not say which value xhas; it merely describes or constrains that value. The second equation actuallygives the value. The difference is crucial in algebraic practice. It is possible tounderstand the first equation, but not the second, without knowing the valueof x. That is why the first equation states a problem, while the second equationprovides its solution.

I will say that the second equation specifies the value of x, in contrast tothe first, and that ‘3’ is a specifier for this value. A specifier is a special sortof subsentential expression. It is distinguished from other expressions for thesame value by the fact that no question can arise about which value it standsfor. ‘3’ contrasts with expressions like ‘ 3

√23 + 4’ in this respect: even though

both stand for the number 3, it is generally appropriate to ask which numberthe latter stands for, so it generally cannot be used to specify this number. ‘3’is a specifier for 3 because no such question is appropriate. It is importantthat we distinguish specifiers from non-specifiers in practice, because it is byrecognizing an expression for a value as a specifier that we recognize that thevariable has been given a value, and an answer to the problem has been offered.

These same distinctions apply to answers to which-questions in natural lan-guage. We distinguish between giving an answer and merely describing oradverting to it. Consider the question asked by

(26) Who stole the documents?

If you were to ask someone this question, it would obviously be unsatisfyingto be told, in reply, that it was ‘the person who stole the documents’ or ‘thedocument thief’, even though these replies are in a sense perfectly true. Thesereplies merely repeat the question; they are unsatisfying because they invitethe rejoinder, “But which person is that? That’s what I wanted to know.” They

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do not specify a person, or say which person it was that stole the documents.In contrast, a reply like ‘Alec’ does say which person it was. In most contexts, arejoinder of “Which person is that?” to this reply would indicate a misunder-standing on the part of the questioner, either about how proper names workin general, or about how ‘Alec’ is used in this particular case. When a propername is used unambiguously, it specifies a person, and can be used to give theanswer to a ‘who’-question. A definite description, on the other hand, gener-ally only constrains the answer, and is subject to a possible rejoinder.

Of course, we sometimes accept expressions other than a proper name inanswer to a ‘who’-question. This can happen because one of the conversationalparticipants does not know the name, or because some other way of specifyingthe person is clearer. A description like ‘the last person to open the file cabinet’may or may not be accepted as specifying a person in response to (26), depend-ing on what else is known. This shows that the criteria we use to distinguishspecifiers from non-specifiers can depend on the context, but not that there isno such distinction. In every context where a which-question can be answered,some such criteria are operating, because it is by applying such criteria that werecognize when an answer to the question has been given.

Since the distinction between specifiers and non-specifiers is a distinctionbetween kinds of expressions, it might seem like these criteria must be syntacticcriteria. But while syntax can certainly help, syntactic criteria are generally notsufficient to distinguish expressions which can specify a value for a variablefrom expressions which cannot. For example, consider a ‘where’-question anda ‘when’-question about the same event:

(27) Where will the drop take place?a. At Waterloo Station.b. #At noon.

(28) When will the drop take place?a. At noon.b. #At Waterloo Station.

Here, ‘at Waterloo Station’ and ‘at noon’ are prepositional phrases, consistingof the preposition ‘at’ together with a name. Each can be used to answer onequestion but not the other: ‘at Waterloo Station’ can specify where the drop willtake place, and ‘at noon’ can specify when it will take place, but not vice versa.This pattern cannot be explained by any syntactic differences between the ex-pressions. Instead, the explanation is clearly that ‘Waterloo Station’ namesa place, so it is suitable to specify a value for the variable introduced by a‘where’-question. ‘Noon’ names a time, so it is suitable to specify a value forthe variable introduced by a ‘when’-question. The distinction between placesand times is a semantic one, not a syntactic one. So in general, the distinctionbetween expressions which can and cannot specify a value for a variable mustbe drawn along semantic lines.

To sum up: semantically, a question distinguishes its possible answers from

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non-answers. Understanding a question requires understanding this distinc-tion, and answering it requires selecting among its possible answers. In thecase of a which-question, where the possible answers share a common form,selecting among those possible answers is done by specifying values for a vari-able. Only certain expressions can be used to specify a variable’s values, andthey are distinguished from other expressions at a semantic, rather than syn-tactic, level.

3.2 Meanings for nouns

With these basic facts about questions and answers in hand, I now want toexplain how to use them to describe the meanings of categorial nouns, andnouns more generally.

Here is my proposal. Complete noun phrases, including categorial nounphrases, express which-questions. The different parts of the noun phrase playdifferent roles in expressing that question. The noun itself expresses the rangeof the question’s variable, while the rest of the phrase presents the commonform of its possible answers. The semantic role of a noun is therefore to dis-tinguish values that occur in a which-question’s possible answers from valuesthat do not. The values in this range can be given by a certain class of spec-ifiers. The noun abstracts over this class of specifiers; its content determinesa distinction between expressions which count as specifying values in that se-mantic range, and expressions which do not.

To see how this works in detail, let’s apply it to the example I began with:

(29) Today I met the person I will marry.

What is the semantic contribution of ‘the person I will marry’ in this sentence?According to my proposal, we should describe it as follows. ‘The person I willmarry’ here expresses a which-question. The which-question is one that thespeaker could normally ask with an interrogative like “Who will I marry?”. Itis a question whose possible answers have the common form

(30) I will marry x

The variable x here represents the unknown expressed by ‘who’ in English,and it ranges over a certain set of values. To answer this question is to selectamong the possible answers with this form by specifying a value in its range.

Suppose now that you already knew the answer to this question. Sup-pose, for example, that you already knew that the speaker of (29) would marryAmelie. You would then interpret the speaker’s claim as saying that today hemet Amelie, since Amelie is who he will marry. Similarly, if you already knewhe would marry Beatrice or Charlotte, then you would interpret him as sayingthat he met Beatrice or Charlotte, and so on. But of course, you do not al-ready need to know how to answer the question to interpret what the speakersays. To move from understanding (29) to attributing one of these more specificclaims to the speaker is to cross an additional epistemological gap, the same

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gap you would cross by asking and answering the question explicitly. All thatis required to understand (29) is that you take the speaker to be asserting thattoday he met whoever it is that should be specified in answer to the question ofwho he will marry. Thus, we might represent what a speaker asserts with (29)like this:

(31) Today I met x, and I will marry x.

This representation depicts the idea that in (29), ‘the person I will marry’ ex-presses a which-question whose answers have the common form in (30), andthat with (29), the speaker asserts that he met whoever answers this question.9

To understand this question, and therefore to understand what the speakersays with (29), you also have to know the range of the variable. You have toknow that the question could be answered by means of names like ‘Amelie’or ‘Beatrice’ or ‘Charlotte’, but not by means of other kinds of expressions,such as ‘Waterloo Station’, ‘for only one hour’, or ‘in my home town’. That iswhat distinguishes different which-questions whose possible answers have thecommon form in (30), such as the question of who the speaker will marry fromthe question of when he will marry, the question of which French citizen he willmarry, and so on. ‘Person’ is our word for expressing this requirement on yoursemantic knowledge. If you interpret the variable in the question as havingvalues which can be specified with expressions like ‘Waterloo Station’, or ifyou interpret it as not having values which can be specified with expressionslike ‘Charlotte’, then you are misinterpreting what (29) says. In that sense,‘person’ expresses the range of a variable in a which-question.

‘Person’ is a categorial noun, but exactly the same explanation will workfor non-categorial nouns. Almost all nouns can be viewed as expressing therange of a which-question’s variable. The only difference will be in the rangeof values that the noun expresses, and the corresponding class of specifiers thatit abstracts over. Suppose, for example, that instead of ‘the person I will marry’,the noun phrase in (29) was ‘the horse that won on Saturday’. This changes therange of values from persons to horses, and the class of specifiers to namesfor horses. The sentence then says that the speaker met whatever answers thequestion of which horse won on Saturday. You need not already know theanswer to this question to interpret the sentence, but you can learn the answerthrough further inquiry. ‘Horse’, like ‘person’, is a word that distinguisheswhat can happen in such inquiry from what cannot. By learning Saturday’swinner, you might learn that the speaker met American Pharaoh, or Big Brown,or California Chrome. But you could not learn that she met in a secluded location,or that she met the Prime Minister of Canada, for those are not possible answersto the question which ‘the horse that won on Saturday’ expresses.

This, then, is how I propose to describe the meaning of nouns: nouns ex-

9There are other aspects of the question that this representation does not depict, such as thepresupposition that the answer will select a unique value. I leave aside issues about how theseother aspects of the question should be represented, because they do not affect my proposal thatnouns express ranges of variables introduced by a which-question.

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press ranges for the variables in which-questions. Let’s see now how this ap-proach accounts for the observations we made above.

3.2.1 Categorial nouns and question words

In Section 2, we saw that categorial nouns have a special relationship to ques-tion words. We also saw that we could not account for this relationship by de-scribing their semantic contribution using the usual model, or by thinking ofcategorial nouns as making a different kind of contribution from non-categorialnouns (namely, none at all). By thinking of noun phrases as expressing ques-tions, we can give a better explanation of the relationship between categorialnouns and question words, without saying that categorial and non-categorialnouns make different sorts of semantic contributions. This is an importantadvantage for the question-based approach over the more conservative ap-proaches we looked at above.

According to the question-based approach, both ‘person’ and ‘horse’ ex-press ranges for which-questions, and mark the distinction between correctand incorrect responses to these questions. The difference is simply that wehave a question word (‘who’) which introduces a variable over one of theseranges, but not the other. We do not have a question word that introducesa variable over the range expressed by ‘horse’, so we have no independentmeans of identifying this range, as we do in the case of ‘person’. That is justa contingent fact about the question words we have in English, though, nota deep difference between the semantic contributions of ‘person’ and ‘horse’.We could have had a question word ‘whorse’ that expresses a variable overthis range, so that ‘whorse’-interrogatives would express which-horse ques-tions just as ‘who’-interrogatives express which-person questions. If we added‘whorse’ to English, the meaning of ‘horse’ would not change; neither wouldthe meaning of ‘person’ if we dropped ‘who’.

This is the key to understanding what makes categorial nouns special. Bothcategorial and non-categorial nouns are related to questions, but categorialnouns have a unique relationship to question words. A categorial noun ex-presses the normal range for the variable introduced by a question word. Theseare certain very general ranges that have become lexicalized, perhaps becauseof their cognitive or evolutionary importance. But they are not essentially dif-ferent from the other ranges that we do not have question words for, and thatare expressed by non-categorial nouns.

The unique relationship between categorial nouns and questions words ex-plains why categorial noun phrases can replace nominal interrogatives withoutaffecting the truth conditions of the containing sentence. When a nominal inter-rogative is replaced by a categorial noun phrase, the result is equivalent simplybecause the two phrases express the same question. ‘The person I will marry’can replace ‘who I will marry’, for example, because ‘person’ expresses the nor-mal range of the variable that ‘who’ introduces. (In ‘the person’, the variable isinstead introduced by ‘the’.) ‘The horse that won on Saturday’ cannot replaceany nominal interrogatives, but that is just because we have no question word

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with which to form the interrogatives it would be able to replace.This explanation may sound similar to the one I rejected earlier, in which we

treat ‘who’ non-disquotationally. The difference is subtle, but important. Ear-lier, we tried to explain the equivalence between ‘who’-nominals and ‘person’-noun phrases by defining the meaning of ‘who’ in terms of the meaning of ‘per-son’, as described by the usual model. We are now proceeding in the oppositedirection, describing the meaning of ‘person’ in terms of the type of questionexpressed by ‘who’. In effect, ‘the person’ expresses how we normally inter-pret ‘who’, as the variable in a which-question that is answered by specifyingsomeone like Amelie or Beatrice or Charlotte. The important point is that thedistinction between answers and non-answers to this type of question shouldbe taken as explanatorily prior to the meaning of ‘person’. We demonstrateour understanding of this distinction in practice by accepting responses like‘Amelie’ as answers to these questions, and rejecting responses like ‘at noon’ or‘in Philadelphia’ as non-answers. ‘Person’ expresses this aspect of our under-standing of these questions: it is our word for marking the distinction betweencorrect and incorrect responses to a certain type of which-question.

When we use different nouns corresponding to the same question word, weexpress different understandings of the range of possible answers to the type ofwhich-question it signifies. To see this, consider two different ways you couldanswer a ‘when’-question:

(32) When did you get married?a. The year I got married was 1982.b. The month I got married was May.

Either response can be appropriate, depending on how you interpret the ques-tion. By using different nouns in your answer, you express your interpretationof the question, and thus the range of answers that it admits. For example, sup-pose you think the questioner wants to know what to buy for your anniversary.Then you will probably answer in the first way, expressing your understand-ing of the question as having answers in the range allowed by ‘year’, such as1982 or 2014. Expressing your understanding this way helps you coordinatewith the questioner. If your understanding does not agree with hers, she canrephrase (“Ah, no, I meant to ask, which month. . . ”).

This makes it clear why different nouns may be needed to replace the samequestion word in different contexts, as we saw in the case of ‘when’-nominalsabove. The variable introduced by a question word can be interpreted as hav-ing different ranges in different contexts, even when we associate these rangeswith the same basic type of question. Different nouns are needed to expressthose different ranges, and it is often communicatively useful to do so.

3.2.2 Specificational sentences and focus

The idea that noun phrases express questions also explains what’s happeningin specificational sentences. As I noted above, specificational sentences are a

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kind of copular sentence. Like all copular sentences, they have two significantparts: the subject phrase, which appears before the copula, and the complementphrase, which appears after it.

A good way to get a handle on the class of specificational sentences is tocontrast them with predicational sentences, which are another familiar speciesof copular sentence.10 In a predicational sentence, the complement phrase ispredicated of what the subject phrase denotes. For example,

(33) Dieter is paranoid.

predicates ‘paranoid’ of Dieter. By contrast, in a specificational sentence, thecomplement phrase specifies what the subject phrase asks for. For example, in

(34) The paranoid person is Dieter.

‘Dieter’ specifies which person is paranoid. The sentence says that ‘Dieter’answers the question asked by “Who is paranoid?”, which is the question ex-pressed by the subject. In general, a specificational sentence pairs a questionwith an answer. The subject expresses a which-question, and the complementgives one or more values for the variable introduced by that question.

Once we recognize that the noun phrase in the subject of a specificationalsentence expresses a question, it is easy to explain why specificational sen-tences exhibit focus on the complement phrase. Recall that a focused sentencecan be used to answer fewer questions in discourse than its neutral counter-part. We observed earlier that the specificational sentence (16-a), for example,can answer questions like “How many moons does Jupiter have?” but not“Which planet has four moons?”, while the neutral sentence (16-b) can answerboth.

(16) a. The number of Jupiter’s moons is four.b. Jupiter has four moons.

Specificational sentences answer fewer questions than neutral sentences be-cause they already contain expressions of the particular question they address.A specificational sentence says that something is the answer to a particularquestion, and it is incongruous to use a sentence which specifies an answer toone question when answering a different one.

This analysis of specificational sentences also helps to explain why the cat-egorial nouns in them are often eliminable via paraphrase. A specificationalsentence provides the answer to a question. The neutral paraphrase of the sen-tence provides an equivalent answer to this question. But the neutral sentencecan also answer other questions, sometimes of a very different basic type. Thecategorial noun’s disappearance is a symptom of the fact that the neutral sen-tence does not say explicitly which question it addresses.

10The distinction between specificational and predicational sentences is originally due to Akma-jian (1970) and Higgins (1979). For a recent discussion of the taxonomy of copular sentences, seeMikkelsen (2011).

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Finally, there is a straightforward explanation of why ‘number’ can only beused in specificational sentences that focus on number words. ‘Number’, likeall nouns, expresses a certain range of values. These values can be specifiedby number words, but not by quantifiers or color words. Using anything otherthan a number word to specify a value in this range is like replying “Soon”when asked “Who will you marry?”. This reply just doesn’t make sense, be-cause it’s not the sort of expression that can give an answer to the questionbeing asked. For the same reason, ‘yellow’ and ‘some’ cannot occupy the com-plement of a specificational sentence where ‘number’ is the head noun in thesubject. This explanation extends to categorial nouns more generally: they con-strain the expressions that can appear in the complement of a specificationalsentence because they only abstract over the specifiers for values in a certainsemantic range.

So it appears that we can account for the special properties of categorialnouns and the sentences where they occur by adopting a question-based ap-proach to their semantics. This approach explains the equivalence betweennominal interrogatives and categorial noun phrases, the eliminability of cate-gorial nouns via paraphrase, and the focus effect in specificational sentences.At the same time, it doesn’t require us to think of categorial nouns as seman-tically inert, or as making an entirely different kind of semantic contributionthan ordinary nouns make. I conclude that this is a promising and plausi-ble approach to describing the meanings of categorial nouns and nouns moregenerally. Their meanings are best described by saying that a noun expresses arange of values for a which-question’s variable. It abstracts over a class of spec-ifiers for those values, which can be used to answer the question. Its semanticrole is to make the boundary between possible answers and non-answers to acertain kind of question explicit.

4 Do nouns denote objects?

I would like to close by returning to the philosophical debates surroundingcategorial nouns, to see what light the question-based approach can shed onthese debates. Are there such things as numbers, reasons, or ways of appearingor acting?

I have proposed that we should not think of nouns as denoting objects, butas expressing the range of a variable in a which-question. In purely formalterms, these two approaches to describing the meaning of nouns are not sodifferent. A formal semantic theory that follows the usual model will typicallyuse a lexical clause for nouns that looks something like this:

(35) JnumberK = λx.x is a number

In such clauses, the noun is explicitly used in exactly the way I have describedas the normal case, to delimit the range of a variable. Thus, by describing nounsas expressing ranges of variables in questions, I am not recommending a new

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sort of formalism. Instead, the difference between my approach and the usualmodel lies in the informal descriptions of what such clauses say. These differentdescriptions invite different understandings of the significance of these clauses,and of formal semantic theories more generally.

When we follow the usual model, semantics seems to push us toward a pla-tonistic ontology. The usual model describes these clauses as saying that ‘num-ber’ denotes the class of numbers, just as ‘horse’ denotes the class of horses or‘person’ the class of persons. Since we think of denoting as a relationship be-tween words and entities in the world, the usual model invites us to assimilatethe ontology of numbers and horses. Someone who accepts the usual modelwill be pressed to admit that there are reasons, numbers, and other classesof abstract objects; that we speak about these objects when we use categorialnouns; and that because we speak truly of them, it is clear that they are justas real and existent as horses and persons. Conversely, someone who wantsto resist that ontological picture will resist the usual model, or at least resistits application to particular nouns. The usual model thus invites the sort ofontological debate between realists and anti-realists that I sketched in the in-troduction.

In contrast, I am recommending that we think about the relationship be-tween language and things in the world as mediated by practices of inquiry.Rather than picturing noun phrases as denoting or referring to objects, weshould think of them as ‘keeping a place’ for potential specifiers, the wordswe would use to answer the questions they express.11 In some cases, thosespecifiers might refer to things in the world, so that we could think of the nounphrase itself as doing so, albeit indirectly or derivatively. These are the casesthat the usual model handles well. But in other cases, that is probably not theright way to think about what the specifiers would do, and so it is probablynot the right way to think about what the noun phrases that keep a place forthem do. These are the cases where the usual model seems most puzzling.The advantage of the question-based approach is that it applies to both kindsof case. It generalizes the usual model, and thereby avoids the debates whicharise from its controversial applications.

To see this, first consider the kind of case that the usual model handleswell. The examples we looked at with ‘person’ and ‘horse’ are paradigms ofthis kind of case.12 Noun phrases headed by ‘person’ or ‘horse’ keep a place forproper names and other specifiers for persons and horses, and (let’s suppose)proper names refer to individual entities. So if we like, we can think of ‘theperson I will marry’ or ‘the horse that won on Saturday’ as indirectly referringto persons and horses, via their relationship to proper names. Describing thesenouns as denoting classes of objects is appropriate, because we give values inthe ranges they express by specifying such objects, using referring expressions.Thus, when it is obvious that the values in the range expressed by a noun are

11This terminology is from Prior (1971). Prior’s defense of non-nominal quantification was animportant inspiration for my account of noun meaning.

12See the discussion of example (29) above.

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objects we can refer to or denote, the usual model falls out as a special case onthe question-based approach.

On the other hand, ‘way’ noun phrases are an example of the second kindof case, the kind where the usual model seems puzzling. Suppose I say:

(36) George slipped out the way he had come in.

If we follow the usual model in this kind of case, we will think of ‘the way hehad come in’ as picking out an object among a class of abstracta, the ways. Ahost of puzzling questions then seem relevant. What are these objects? Whereare they? How do we know about them, and how do we manage to pick themout when speaking or interpreting others?

The question-based approach sidesteps these puzzles. On the question-based approach, ‘the way he had come in’ here expresses a which-question, onethat we could normally express with an interrogative like “How did Georgecome in?”. Someone who asserts (36) is asserting something we might repre-sent as follows:

(37) George slipped out x, having come in x.

The role of ‘way’ in (36) is to express the range of the variable here. The spec-ifiers for the values in that range are not proper names, but adverbial expres-sions like ‘hastily’, ‘via the rear exit’, ‘without interrupting anyone’, and so on.The question-based approach requires that we think of these expressions asgiving values for the variable in a ‘how’-question, but it does not require thatwe think of those values as objects in any ordinary sense, or the specifiers asdenoting or referring to such objects. So we do not have to say that ‘the wayhe had come in’ refers to an object in (36), any more than we have to say that‘hastily’ would refer to an object in the same position. Thus, the question-basedapproach can avoid the puzzles raised by the usual model in this case, with-out losing track of what ‘the way he had come in’ semantically has in commonwith ‘the person I will marry’.

By generalizing the usual model to account for this second kind of case, wecan see more clearly what’s happening in ontological debates, without favor-ing one camp over the other. Are there reasons? Are there numbers? Yes, ofcourse: the number of words in the previous sentence is 3, and the reason thatnumber is prime is that no smaller positive integers divide it, except 1. Therealist intuition is entirely correct, in that we can not only speak truly of suchthings, but give specific examples of them. But the question-based approach todescribing what ‘reason’ and ‘number’ mean shows us how to think about thisintuition in a way that divests it of much ontological significance, and this willplacate the anti-realist. There are reasons and numbers, but this simply meansthat there are answers to the types of questions we ask with ‘why’ and ‘howmany’. The question-based approach is compatible with saying that these thingsare objects in some thicker sense, but it does not force that conclusion on us,as the usual model seems to do. To support any more substantial conclusion,such as that reasons and numbers are really existing entities in anything like

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the sense that horses and people are, we will have to go beyond the meaningsof the nouns themselves.

The question-based approach is valuable because it offers a new perspec-tive about where such ontological inquiries should begin. To move from thesemantics of ‘reason’ or ‘number’ to the ontology of reasons or numbers, wemust first answer the following question: how is what we can ask for related towhat is? This is a question about the nature of inquiry, and the relationshipbetween the world and the practices by which we come to know about it. Thegeneral answer is surely that some of the things we ask for and specify exist,while others do not. A more specific answer, though, must wait for anotheroccasion.

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Caponigro, Ivano (2003). “Free not to ask: On the semantics of free relativesand Wh-words cross-linguistically”. University of California, Los Angeles.URL: http://idiom.ucsd.edu/%20ivano/Papers/2003_dissertation_revised_7-13-05.pdf.

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