Categorial nouns and questions

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Categorial nouns and questions Richard Lawrence November 18, 2016


Categorial nouns

Here is a list of nouns: person thing time place

reason way amount number

They are examples of what I will call categorial nouns, because they express some of the most basic and abstract categories we use to understand and describe the world. This essay is about what categorial nouns mean. We usually describe the meanings of nouns in terms of the things they apply to, or stand for, or denote. We say that a noun like ‘horse’, for example, denotes the horses, or the class of horses, or a function defined by its relationship to horses. 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 shed light on this material issue. Each case has its defenders and detractors. It seems perfectly obvious to some philosophers, for example, that there are such things as reasons: we say and 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 paragraph with a capital ‘E’ was that the rules of English grammar required it. That is a true statement! It follows that there are reasons, such as the one I just mentioned: 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 ‘reasons’, and that they affect our actions? Reasons are a bit more difficult to find in the world than things like horses. These philosophers will be inclined to paraphrase my statement to get rid of the categorial noun it contains. While it is true that the reason I began the previous paragraph with a capital ‘E’ was that the rules required it, this just means that I began that paragraph with a capital ‘E’ because the rules required it. The apparent reference to a reason is


a linguistic trick, and the statement’s truth does not reveal much about what there is, or what moves us to act. Debates like this one seem to reach a stalemate pretty quickly. I think we can avoid the stalemate by rejecting an assumption that is common to both sides, namely, the usual model of what nouns mean. In this case, both sides accept that ‘reason’ denotes the reasons, and they picture this relationship as a relationship between the word and some things in the world. That is why the first camp thinks that the truth of sentences containing ‘reason’ reveals that there are reasons, the things denoted by the noun. It is also why the second camp, doubting that there are any such things for the noun to denote, wants to paraphrase it away. They both accept the usual model, but they apply it in opposite directions. If we can reach a better understanding of what categorial nouns mean, we can avoid the opposition. My thesis is that the meanings of categorial nouns should be described in terms of their role in practices of asking and answering questions. You might have noticed that each of the nouns in the list above corresponds to a kind of question we can ask using one of the basic question words of English: ‘who’, ‘what’, ‘when’, ‘where’, ‘why’, and ‘how’ (including ‘how much’ and ‘how many’). A categorial noun signifies a kind of question. Semantically, a question distinguishes its possible answers from non-answers. Thus, a categorial noun determines a range of answers, or a kind of answer. Its job is to make explicit what 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 will marry”. How should we describe what the noun phrase ‘the person I will marry’ means in this sentence? ‘Person’ corresponds to ‘who’; this noun phrase corresponds 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 answer to understand my assertion. But you do need to know what would count as answering this question. The answer could be that I will marry Amelie, or Beatrice, or Charlotte. The answer could not be that I will marry soon, or that I 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 the answers 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 met Amelie, 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 home town. 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’, and even nouns that signify very concrete things, like ‘horse’. We should describe what almost all nouns mean in terms of their relationship to questions. What’s distinctive about categorial nouns is their relationship to question words, and therefore to our most basic kinds of questions. This relationship has some puzzling features which the usual model cannot explain. Describing the meaning of categorial nouns in terms of questions accounts for those features, so these 2

features motivate a question-based approach to categorial nouns. But once we see 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 there is no reason to treat categorial nouns as a special case.1 The question-based approach is ultimately attractive because it generalizes the usual model, in a way that clarifies what both realists and anti-realists get right in debates about reasons, numbers, persons, or ways of appearing or acting.


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 this question. These approaches are natural because they are conservative: they try to preserve the usual model of noun meaning, in two different ways. They are both ultimately unsatisfying, though, and it is instructive to see why. The first approach is just the usual one: categorial nouns denote classes of objects. ‘Person’ denotes the persons, ‘reason’ denotes the reasons, and ‘number’ denotes the numbers, just as ‘horse’ denotes the horses. This answer is not necessarily false, but it is incomplete, because it fails to explain the special relationship between categorial nouns and question words. Categorial noun phrases are intersubstitutable with question-word phrases in a way that most noun phrases are not, and a description of their meaning should explain why that 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’t really mean anything. That is, they don’t perform the same semantic function as nouns like ‘horse’; they are semantically idle, and perform only a syntactic function. This answer tries to preserve the usual model of noun meaning in the general case by making an exception for categorial nouns. It is suggested by the kind of move that I sketched in the debate about ‘reason’ above: categorial nouns are often eliminable via paraphrase. But this answer is also incorrect. Categorial nouns do perform a semantic function, as we can see by looking at their behavior more closely. I will say how we should describe that semantic function in Section 3.


The usual model of noun meaning

Let’s first see why the usual approach does not adequately describe the meanings of categorial nouns. Our usual model for understanding the semantics of nouns says that nouns denote classes of objects. ‘Horse’ denotes the class of 1 There 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 questionbased approach I describe, but explaining how to do so would take me too far afield. I focus on just the nouns that the usual model aims to describe: count nouns which seem to denote or signify a class of things.


horses, ‘potato’ the class of potatoes, and ‘silicate’ the class of silicates. Does it make 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 saying that nouns denote classes of objects is to indicate what we are talking about when we use those nouns. By saying that ‘horse’ denotes the class of horses, we indicate that sentences containing ‘horse’ are about horses, and that we must look to the horses to determine whether such sentences are true. But it is 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. So we might think that categorial nouns like ‘way’ should be given a different semantic treatment from nouns like ‘horse’. These intuitive considerations are not strong enough to show that the usual model does not apply to categorial nouns, though. For one thing, they do not hold equally well for all the nouns that appear in the list above. It is just as obvious that there are persons as that there are horses, for example, and that we use ‘person’ to talk about them. For another, there might be good reasons to assimilate ‘way’ and ‘horse’ for the purposes of semantic theorizing. Whatever intuitive differences we feel there are between ways and horses, it may be that those differences are better represented elsewhere, outside of a semantic theory for natural language. Still, there is one serious challenge for any semantic theory that assimilates categorial nouns and other nouns, which I would now like to explain. Categorial nouns are semantically related to question words in a way that most nouns are not. I’ll describe the relationship, and then explain why it’s a problem for the usual model. 2.1.1

Categorial noun phrases and nominal interrogatives

The special relationship between categorial nouns and question words is on display in pairs of sentences like these: (1)

a. b.

What Amelie did was truly amazing. The thing Amelie did was truly amazing.


a. b.

I learned how Amelie escaped. I learned the way Amelie escaped.

The sentences in such pairs are truth-conditionally equivalent. How could it be true that what Amelie did was truly amazing, but false that the thing she did was truly amazing? Or true that I learned the way Amelie escaped, but false that I learned how she escaped? It doesn’t seem to be possible to believe one but doubt the other, or to coherently adopt any other opposing attitudes toward them. Some terminology will be useful to describe this relationship. In the sentences above, ‘what Amelie did’ and ‘how Amelie escaped’ are examples of


what I will call nominal interrogatives.2 Nominal interrogatives are complete phrases that begin with a question word. They are nominal in the sense that they occupy grammatically nominal positions, such as the subject or direct object of a transitive verb. (This distinguishes them from clauses that begin with question words, such as relative clauses and complete interrogative sentences.) Nominal interrogatives can be replaced by descriptions, such as ‘the thing Amelie did’ or ‘the way Amelie escaped’. Such a description is a noun phrase or determiner phrase, in which the first noun is a categorial noun. I will call this sort of description a categorial noun phrase. A nominal interrogative can (almost) always be traded in for a categorial noun phrase without changing the truth conditions of the sentence as a whole. This is the relationship exemplified in the pairs above. Here are some other examples: (3)

a. b.

Beatrice was [who you met that day]. Beatrice was [the person you met that day].


a. b.

Ten p.m. is [when I go to bed]. Ten p.m. is [the time I go to bed].


a. b.

Charlotte went back to [where she first saw the lion]. Charlotte went back to [the place she first saw the lion].


a. b.

We’ll never know [why Dieter fled the country]. We’ll never know [the reason Dieter fled the country].


a. b.

The flavor depends on [how much vodka you add]. The flavor depends on [the amount of vodka you add].


a. b.

Ernest counted [how many birds he’d seen so far]. Ernest counted [the number of birds he’d seen so far].

Again, in each case, the two sentences are truth-conditionally equivalent. And it would be easy to multiply these examples. An appropriate categorial noun phrase can be substituted for a nominal interrogative in a wide variety of contexts 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 because the resulting sentence would be ungrammatical. This is generally true for nominal interrogatives beginning with ‘which’ and ‘whether’; I will have more to say about these question words below. It is also true for nominal interrogatives that appear after certain verbs, such as ‘wonder’: you can wonder where I went, but you cannot wonder the place I went. Sometimes, maintaining grammaticality requires adding a preposition to the categorial noun phrase, or modifying the containing sentence slightly. These exceptions are 2I

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


important from a syntactic perspective, but they shouldn’t distract us from the general semantic pattern. Where grammar permits it, a nominal interrogative will be intersubstitutable with some appropriate categorial noun phrase, and the resulting sentence will be truth-conditionally equivalent. This relationship to nominal interrogatives is unique to categorial nouns. A nominal interrogative can often be replaced by a non-categorial noun phrase, too, but the result is not truth-conditionally equivalent: (9)

a. b.

[What Werner cooked] was inedible. [The food Werner cooked] was inedible.

These two sentences are not equivalent, because what Werner cooked might not have been food. Suppose, for example, that the only thing he cooked was a shoe: then it’s true that what he cooked was inedible, but it’s not true that the food he cooked was inedible, because he didn’t cook any food. In fact, the intersubstitutability of nominal interrogatives and categorial noun phrases is distinctive enough that I will take it to define the class of categorial nouns.3 A categorial noun is a noun associated with a particular question word, such that noun phrases headed by that noun can in general replace nominal interrogatives beginning with that question word, without changing the truth conditions of the containing sentence. The sentences in (1)–(8) are meant to vindicate my original list of categorial nouns. But I am focused on this general pattern, not any particular list of nouns. Depending on our judgments about equivalence, and how much grammatical ‘fudging’ we allow, we’ll end up with different lists of the categorial nouns in English; some of the nouns I listed might have to go. That does not matter, for my purposes. The pattern is clear 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 interrogatives raises a puzzle about categorial nouns. In the version of the sentence containing the nominal interrogative, the categorial noun does not appear. But in many cases, that is the only significant difference between the two versions of the sentence. The only difference between (6-a) and (6-b), for example, is that ‘why’ has been replaced by ‘the reason’; the rest of the sentence is stringidentical. The same goes for the other examples. The other words in the sentence are the same, and are arranged in the same way. Now, semantic orthodoxy has it that the truth conditions of a sentence are determined by the semantic contributions of each of its parts, together with their arrangement. So here’s the puzzle: if the truth conditions of the whole sentence are the same, 3 Compare Caponigro (2003), who uses the intersubstitutability of free relatives with descriptions as part of a definition of the category of free relatives.


whether or not the categorial noun is present, what does that noun contribute to the truth conditions of the whole? If categorial nouns make a semantic contribution, it doesn’t seem to be an essential one, since the same truth conditions can 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 semantics of categorial nouns in a way that accounts for this fact. So how should we do it? The usual model can’t resolve this puzzle, even for nouns like ‘person’ to which it uncontroversially applies. This is because it applies equally well to non-categorial nouns, so if we use it to describe the semantic contribution of categorial nouns, we will be left without an explanation of their special relationship to question words. To see this, consider again the sentences in (3): (3)

a. b.

Beatrice was [who you met that day]. Beatrice was [the person you met that day].

Suppose we follow the usual model, and grant that ‘person’ denotes the class of 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 the former employs ‘who’? In fact, applying the usual model makes the problem more acute, because saying that ‘person’ denotes the class of persons assimilates our semantic explanation of (3-b) to our explanations of sentences where another noun occurs in the place of ‘person’: (10)

a. b. c. d. e.

Beatrice was the woman you met that day. Beatrice was the queen you met that day. Beatrice was the relative you met that day. Beatrice was the Canadian you met that day. ...

A typical semantic explanation of, say, (10-b) would compositionally derive a statement of its truth conditions using a lexical clause that says ‘queen’ denotes the class of queens. This explanation could be carried over to any of the other sentences in the family in (10) simply by replacing this clause with a clause for another noun. Likewise, it could be carried over to (3-b) simply by replacing the clause for ‘queen’ with a clause that says ‘person’ denotes the class of persons. The trouble is that none of the sentences in (10) is equivalent to (3-a), and any reasonable explanation of their semantics will predict this. Each of the sentences in (10) could be false while (3-a) is true. Intuitively, the reason in each case is that the italicized noun restricts which objects the description ‘the N OUN you met that day’ might denote, while ‘who you met that day’ is not similarly restricted: it might have been true of someone that she was who you met 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 theory in the way that clauses for nouns compose in larger expressions. But ‘per7

son’ differs from ‘queen’, ‘woman’, ‘relative’ and so on precisely in that it does not impose a similar restriction in this context, or most other contexts where a categorial noun phrase can occupy the same position as a ‘who’-nominal. Thus, saying that ‘person’ denotes the class of persons just as ‘queen’ denotes the class of queens makes the need for an explanation of this difference all the more 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 natural thought to have at this point is that we could solve this problem by saying something about the relationship in our lexical clause for ‘who’, perhaps by using a clause like (12)

‘Who . . . ’ denotes the person that . . .

An approach like this would allow us to maintain the usual disquotational clause for ‘person’ while capturing its special relationship to ‘who’, by adopting a non-disquotational clause for the question word. This ensures the right connection between the question word and the noun. Unfortunately, this approach won’t save the usual model, because the relationship between question words and nouns is sometimes more complicated than the relationship between ‘who’ and ‘person’. Consider ‘when’, for example. ‘When’ is associated with the categorial noun ‘time’, but in certain contexts, another noun is needed to replace nominal ‘when’-interrogatives: (13)

a. b.

Wednesday is when I do my shopping. Wednesday is the {day/??time} I do my shopping.

In (13-b), the non-categorial noun ‘day’ seems like a better choice than the categorial noun ‘time’ for producing a sentence equivalent to (13-a). In other contexts, nouns like ‘month’ or ‘year’ are needed to replace ‘when’-nominals, for similar reasons. Now, the usual model tells us that ‘day’ denotes the days, ‘month’ denotes the months, ‘year’ denotes the years, and so on. But combining the usual model with a non-disquotational lexical clause for ‘when’ would only aggravate the problem of explaining patterns like the one in (13): the resulting theory would say that ‘when I do my shopping’ denotes the time I do my shopping, not the day I do my shopping; but that is exactly the opposite of what’s observed in (13-b). Instead, we should say that ‘day’ denotes a certain kind of time, so it too says something about when things happen; ‘day’ is more appropriate in (13-b) just because it is more specific than ‘time’, and thus more relevant. But we can’t say this unless we go beyond what the usual model tells us about ‘day’ and ‘time’. Thus, the usual model will still not suffice to describe the meaning of categorial nouns, or explain the special relationship between categorial nouns and question words. The conclusion is not that we cannot apply our usual model to the semantics of categorial nouns. I am claiming only that if we apply it, 8

we will not have made any progress toward understanding their unique semantic behavior. When a nominal interrogative is replaced by an appropriate categorial noun phrase, the resulting sentence is truth-conditionally equivalent. 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 has a 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 provides no resources for explaining this difference. Thus, the usual model is incomplete. We have to look beyond it if we want to understand the relationship between categorial nouns and question words.


A syntactic approach to categorial nouns

Now that we have seen the trouble that the usual model has with categorial nouns, a second approach to describing their meaning may look more appealing. Perhaps categorial nouns don’t mean anything at all—at least not in the sense that they contribute to a sentence’s truth conditions. Instead, they serve some other linguistic function. An approach like this can be motivated by observing that categorial nouns are 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 often possible, and it eliminates a categorial noun from a sentence without changing its truth conditions. But this is not the only strategy for paraphrasing categorial nouns away, or even the most significant one. Here’s another example. We can paraphrase a sentence like (14-a) as (14-b): (14)

a. b.

The reason Harry fell off his horse was that he was drunk. Harry fell off his horse because he was drunk.

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

a. b.

The way Harry got drunk was by downing a bottle all at once. 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 syntax of 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 expressed by the categorial noun can be equivalently expressed without using a noun. This, we might think, is a hint that categorial nouns like ‘reason’ and ‘way’ are importantly different from more ordinary nouns like ‘horse’, and so we shouldn’t describe what they mean by saying that they denote a class of objects. They play some other role in sentences like (14-a) and (15-a), and perhaps in the language as a whole. 9

I would now like to consider one way of developing this idea, based on a 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. b.

The number of Jupiter’s moons is four. Jupiter has four moons.

To explain the truth-conditional equivalence of pairs like these, Hofweber proposes that the two sentences are merely syntactic variants of each other. The syntactic differences between them affect their communicative import, but not their truth conditions. I want to see whether we can leverage this proposal to obtain a general account of the linguistic role of categorial nouns. Perhaps categorial nouns occur for purely syntactic and communicative reasons, and do not contribute anything to the truth conditions of sentences in which they occur. 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 entirely explained by syntax. Thus, Hofweber’s proposal will not give us an explanation of the role of categorial nouns like ‘number’ on its own. We cannot avoid 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. b.

It is soccer that Johan likes. Johan likes soccer.


a. b.

Quietly was how Mary entered. Mary entered quietly.

The distinction here is between focused sentences, like (17-a) and (18-a), and neutral sentences, like (17-b) and (18-b). Intuitively, a focused sentence places stress or emphasis on some part of what’s said, where the neutral sentence does not. 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 pairs are truth-conditionally equivalent to their neutral counterparts.5 For how could it be true that Johan likes soccer, but false that it is soccer that Johan likes? Or true that Mary entered quietly, but false that quietly is how she entered? In each case, the focused sentence communicates just the same information as its neutral variant. How, then, should we account for the differences between them? Hofweber’s answer is that the neutral and focused versions of a sentence have different communicative uses, and these different communicative uses 4 The

pair of sentences in this example originates from Frege (1980, §57). 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). 5 As


explain the differences in their syntax. The most important communicative difference is that neutral sentences can be used to answer more questions than their focused variants. For example, the neutral sentence (17-b) can answer either “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 Johan like?”. It exhibits a focus on some aspect of the information being communicated. When that aspect of the information is not in question, or when some other aspect of the information was asked for, this focus is communicatively inappropriate. Hofweber claims that (16-a) communicates the same information as (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 examples in (14-a) and (15-a), all belong to a class of copular sentences known to linguists as specificational sentences. I will have more to say about them below. At the moment, I just want to point out that one of the distinctive properties of specificational sentences is that they exhibit focus on the phrase after the copula.6 So Hofweber is right that these sentences, like the (non-specificational) focus constructions (17-a) and (18-a), are not neutral, and as a result, they can be used to answer fewer questions in discourse. The fact that specificational sentences exhibit focus suggests a hypothesis about why categorial nouns can often be eliminated via paraphrase, as we saw in examples (14), (15), and (16) above. Following the analogy with other types of focus constructions, like the ‘it’-cleft construction in (17), we can suppose that a specificational sentence and its neutral counterpart are merely syntactic variants of each other. If that is right, it tells us that ‘reason’, ‘way’, and ‘number’ occur in these sentences for purely syntactic reasons, as byproducts of the variation that produces the focus in a specificational sentence. Perhaps, then, categorial nouns are merely byproducts of syntactic variation in general, even outside of specificational sentences. We make use of such variation to produce certain effects in communication, such as focus effects, but these effects do not influence the truth conditions of the sentence. Accordingly, when this syntactic variation introduces a categorial noun into a sentence, that noun occurs for purely syntactic reasons. It is just a ‘dummy’ noun, required by grammar, like the ‘it’ in an ‘it’-cleft. It is not interpreted, and makes no contribution to the sentence’s truth conditions or the information it expresses. This hypothesis explains why we can often paraphrase categorial nouns away, and offers a deflationary answer to the question of what they mean. According to the hypothesis, they don’t really mean anything, in the sense of making 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 information in certain ways in syntax, in order to achieve certain effects in discourse, such 6 There is consensus among linguists on this point; see Mikkelsen (2005, p. 133) and references there.


as focus effects. This hypothesis will seem attractive to a philosopher who has trouble believing that there are such things as reasons, ways, or numbers. If the hypothesis is true, it means that we do not need to admit that ‘way’ denotes the ways, or ‘number’ denotes the numbers, but neither do we need to say that these words serve no expressive purpose. They have an important role in the language; 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 do mean something—something that should be captured and represented in a semantic theory, and that we cannot plausibly account for just by pointing to the extra-semantic effects of constructions where they appear. This is intuitively obvious, and should be our default position; but I will offer a few observations to 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’d expect, if categorial nouns were only ‘dummy’ words that occur because they’re required by grammar. One such noun would suffice, and two or more that serve the same purpose would be interchangeable. That is clearly not so, however: (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 merely uninterpreted bits of syntax that only occur because they help achieve focus and other discourse effects. Intuitively, the problem with these sentences is that there is some kind of semantic disagreement between the focused expression and the noun: four is not a way you can have moons, and downing a bottle all at 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 features of focused expressions. A second observation further supports this thought. Categorial nouns are not interchangeable in focus constructions because they are sensitive to the semantic contribution of the focused expression, and not merely its syntax. For example, ‘number’ cannot be used as part of a focus construction when the focused expression is not a number word. We can see this as follows. Recall the sentences in (16): (16)

a. b.

The number of Jupiter’s moons is four. Jupiter has four moons.

Hofweber’s idea was that (16-a) is a syntactic variant of (16-b), which serves to focus 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.


Syntactically, ‘four’ is either an adjective or a determiner, so if the sentences in (16) are merely syntactic variants of each other, then we should be able to form analogous pairs of variants using expressions from one of these categories. But we can’t. First, suppose ‘four’ is an adjective, like ‘yellow’. The neutral version of the sentence with ‘yellow’ is fine, but the focused, specificational 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 number of Jupiter’s moons, like ‘even’ or ‘larger than 10’ could be. But it cannot be interpreted as a specificational sentence: ‘yellow’ cannot specify the number of 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 determiner, and so (20-a) is not an analogous variant of (16-a). But things don’t go any better if we use a determiner instead: (21)

a. b.

*/# The number of Jupiter’s moons is some. 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 about how many moons Jupiter has. Still, we cannot use (21-a) in order to focus on that ‘how many’ aspect of what (21-b) says. The specificational version of the sentence is not even obviously grammatical. Even if it is, it is semantically incongruous, just like (20-a): ‘some’ cannot specify a number. Whether we treat ‘four’ as an adjective or a determiner, the examples are easy to multiply. ‘Number’ only seems to allow the focused expression to be a number word. Other expressions with the same syntax, even those that provide ‘how many’ information, cannot be the focused expression in a specificational sentence analogous to (16-a). If that is right, then ‘number’ is sensitive to the semantic features of the focused expression, and not merely its syntax. The only plausible way of distinguishing number words from both quantifiers like ‘some’ and non-numerical adjectives like ‘yellow’ is along semantic lines: number words express definite quantities, while these other expressions do not. The use of ‘number’ in focus constructions is sensitive to these semantic distinctions, which means that it has some semantic features. These semantic features are 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 sentence that focuses on an expression for a definite quantity. Thus, we cannot plausibly claim that ‘number’ is simply an uninterpreted piece of syntax in sentences like (16-a). The analogy between specificational sentences and other focus constructions, like ‘it’-clefts, is therefore misleading. Both types of sentence exhibit focus. But unlike the ‘it’ in an ‘it’-cleft, the role of ‘number’ in (16-a) is not ex13

hausted by its syntactic role in creating focus or other discourse effects. While it is true that (16-a) exhibits a focus effect, we are not justified in regarding it as merely a syntactic variant of (16-b). A further observation about ‘number’ underscores this point. ‘Number’ also distinguishes ‘four’ from ‘yellow’ when it occurs outside specificational sentences, as a simple predicate: (22)

a. b.

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

(22-a) is obviously true, while (22-b) is obviously false, and the only explanation for this is that ‘number’ makes a genuine contribution to the truth conditions of these sentences. It is useful to compare this example with one in which the non-categorial noun ‘color’ appears as the predicate: (23)

a. b.

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

Switching the nouns flips the truth values, and there is every reason to think that these pairs of sentences are semantically parallel. ‘Number’ makes the same 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 other nouns; they can only be used in specificational sentences where the focused expression belongs to a certain semantically-distinguished class; and they can occur as significant predicates. The best explanation for these facts is the simplest one: categorial nouns make a semantic contribution, of the same kind as other nouns. The problem is simply that we must somehow describe that contribution in a way which explains the special features of categorial nouns. I would now like to explain how I think we should do so.


Meanings via questions

We saw above that we cannot adequately describe the semantics of categorial nouns in the usual way, by saying that they denote classes of objects. Categorial nouns have a special relationship to question words, which cannot be captured by simply disquoting them to describe the classes of objects they denote. We also saw that when a categorial noun appears in a focused sentence such as a specificational sentence, it can often be eliminated in an equivalent neutral sentence, and that the distinction between focused and neutral sentences concerns their different relationships to questions. These facts suggest a different approach to describing the meaning of categorial nouns, and nouns more 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 a noun phrase expresses a question, and a noun expresses a certain part or aspect of that question—namely, the range of a variable whose values determine its


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


A primer on questions and answers

As I will understand it, a question is different from the phrases which express it, which can include both noun phrases and nominal interrogatives. Likewise, the act of asking a question is different from the question itself: a question may be expressed without being asked. These distinctions parallel more familiar distinctions between a proposition and the sentence which expresses it, on the one hand, and the act of asserting it on the other. Just as we can think of propositions as defined by their role in acts of asserting, we can think of questions as defined by their role in practices of asking and answering them. In speaking of questions, I am describing the details of that role in practice. Questions have answers, and we ask them in order to find their answers. Of course, sometimes things turn out badly: a question can be confused, or have no answer, or have no good answer so far as anyone knows. But these exceptions prove the rule. Questions are asked in expectation of getting an answer. In the normal case, an answer can be supplied, though perhaps only after some investigation or thought. One of the most important features of questions is the epistemological gap between a question and its answer. To understand a question, you need not already know how to answer it. Indeed, that is the whole point: questions are a useful means of acquiring knowledge precisely because we can ask and understand them without already possessing that knowledge. On the other hand, understanding a particular question still requires knowing something. Otherwise, all questions would be the same, which is clearly not so. The questions asked by, say, “Where did you eat?” and “What did you eat?” are different. We understand them differently because we know they require different answers. In literature on the logic and semantics of questions, these facts are standardly represented by saying that a question admits of a range of possible answers.7 To understand a question, you do not need to know what its specific answer 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 distinguish 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 misinterpreted your question.8 If I had interpreted it correctly, then I would understand that I could only answer it by saying that I ate at the park, or at Pat’s Steakhouse, or 7 See,

for example, Hamblin (1958). 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 background knowledge about where I usually eat sandwiches. But giving indirect answers like this depends on the possibility of giving direct answers. When I speak of answers, I am focusing on direct answers. 8 Probably,


in my living room, and so on. So semantically, a question distinguishes possible answers from non-answers. We may say that it delimits, or presents, a set of possible answers. Answering a question involves selecting among these possible answers. To answer a question is to say which of its possible answers are actually true. It is helpful to draw a distinction between two basic kinds of questions, which concerns two different ways that questions can present their possible answers. Following Belnap and Steel (1976), I will call the two types of questions whether-questions and which-questions. A whether-question presents an explicit, finite list of possible answers. Yes-no questions are typical whetherquestions: a question like “Is Alec in Germany?” presents just the two possible answers that Alec is in Germany, and that he isn’t. A which-question, on the other hand, presents an indefinitely large class of possible answers. In general, the possible answers to a which-question cannot be exhaustively and explicitly listed, even by someone who understands the question. A which-question presents its possible answers by giving their common form, as a statement containing an ‘unknown’. In natural language, such an unknown is expressed by a question word; in formal analyses, it is typically represented with an algebraic variable. Here are some examples of whichquestions, together with some examples of the possible answers they present and 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.


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 variable will make the statement-form true. A which-question thus asks, which statements of this form are true? To understand it, you must understand the range of the variable, because the range of the variable determines the range of possible answers. The distinction between whether- and which-questions is useful here because categorial nouns are related to words that express which-questions, rather than whether-questions. These are the question words ‘who’, ‘what’, ‘when’, ‘where’, ‘why’ and ‘how’. For example, ‘who’ means something like ‘which person’ in English; it is a word for a which-question where the variable ranges over persons. Similarly, ‘where’ means something like ‘which place’, ‘how’ means something like ‘which way’, and so on. We may therefore leave whetherquestions aside, and focus on which-questions and their relationship to nouns. Because a which-question presents its possible answers by giving their general form, rather than listing them explicitly, the answer to a which-question can be viewed from two perspectives, or levels. At a high level, an answer


to a which-question is the same as for a whether-question: it selects some of the 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 values that they assign to a variable, giving values for that variable suffices to answer a which-question. Giving values for a variable is the means of answering a which-question. For example, saying “Alec and Fiedler” in response to (24) is a means of claiming that Alec is in Germany and Fiedler is in Germany. These two names select two of the possible answers to this question, by giving two different 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 variable, since that is the crucial step in answering a which-question. We should distinguish giving a value of a variable from merely describing or constraining it. The distinction is easiest to illustrate in an algebraic setting. Consider these two equations: x3 − 4 = 23 x=3 Both equations are true if and only if the value of x is 3, but there is an important difference between them. The first equation does not say which value x has; it merely describes or constrains that value. The second equation actually gives the value. The difference is crucial in algebraic practice. It is possible to understand the first equation, but not the second, without knowing the value of x. That is why the first equation states a problem, while the second equation provides its solution. I will say that the second equation specifies the value of x, in contrast to the first, and that ‘3’ is a specifier for this value. A specifier is a special sort of subsentential expression. It is distinguished from other expressions for the same value by the fact that no question√can arise about which value it stands for. ‘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 number the 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 important that we distinguish specifiers from non-specifiers in practice, because it is by recognizing an expression for a value as a specifier that we recognize that the variable 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 language. We distinguish between giving an answer and merely describing or adverting to it. Consider the question asked by (26)

Who stole the documents?

If you were to ask someone this question, it would obviously be unsatisfying to be told, in reply, that it was ‘the person who stole the documents’ or ‘the document thief’, even though these replies are in a sense perfectly true. These replies merely repeat the question; they are unsatisfying because they invite the rejoinder, “But which person is that? That’s what I wanted to know.” They 17

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, a rejoinder of “Which person is that?” to this reply would indicate a misunderstanding on the part of the questioner, either about how proper names work in general, or about how ‘Alec’ is used in this particular case. When a proper name is used unambiguously, it specifies a person, and can be used to give the answer to a ‘who’-question. A definite description, on the other hand, generally only constrains the answer, and is subject to a possible rejoinder. Of course, we sometimes accept expressions other than a proper name in answer to a ‘who’-question. This can happen because one of the conversational participants does not know the name, or because some other way of specifying the 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), depending on what else is known. This shows that the criteria we use to distinguish specifiers from non-specifiers can depend on the context, but not that there is no 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 we recognize when an answer to the question has been given. Since the distinction between specifiers and non-specifiers is a distinction between kinds of expressions, it might seem like these criteria must be syntactic criteria. But while syntax can certainly help, syntactic criteria are generally not sufficient to distinguish expressions which can specify a value for a variable from expressions which cannot. For example, consider a ‘where’-question and a ‘when’-question about the same event: (27)

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


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

Here, ‘at Waterloo Station’ and ‘at noon’ are prepositional phrases, consisting of the preposition ‘at’ together with a name. Each can be used to answer one question but not the other: ‘at Waterloo Station’ can specify where the drop will take 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 expressions. Instead, the explanation is clearly that ‘Waterloo Station’ names a 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 for the variable introduced by a ‘when’-question. The distinction between places and times is a semantic one, not a syntactic one. So in general, the distinction between expressions which can and cannot specify a value for a variable must be drawn along semantic lines. To sum up: semantically, a question distinguishes its possible answers from


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


Meanings for nouns

With these basic facts about questions and answers in hand, I now want to explain how to use them to describe the meanings of categorial nouns, and nouns more generally. Here is my proposal. Complete noun phrases, including categorial noun phrases, express which-questions. The different parts of the noun phrase play different roles in expressing that question. The noun itself expresses the range of the question’s variable, while the rest of the phrase presents the common form of its possible answers. The semantic role of a noun is therefore to distinguish values that occur in a which-question’s possible answers from values that do not. The values in this range can be given by a certain class of specifiers. The noun abstracts over this class of specifiers; its content determines a distinction between expressions which count as specifying values in that semantic 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 will marry’ here expresses a which-question. The which-question is one that the speaker could normally ask with an interrogative like “Who will I marry?”. It is 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 select among the possible answers with this form by specifying a value in its range. Suppose now that you already knew the answer to this question. Suppose, for example, that you already knew that the speaker of (29) would marry Amelie. You would then interpret the speaker’s claim as saying that today he met Amelie, since Amelie is who he will marry. Similarly, if you already knew he would marry Beatrice or Charlotte, then you would interpret him as saying that he met Beatrice or Charlotte, and so on. But of course, you do not already need to know how to answer the question to interpret what the speaker says. To move from understanding (29) to attributing one of these more specific claims to the speaker is to cross an additional epistemological gap, the same 19

gap you would cross by asking and answering the question explicitly. All that is required to understand (29) is that you take the speaker to be asserting that today he met whoever it is that should be specified in answer to the question of who 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’ expresses a which-question whose answers have the common form in (30), and that with (29), the speaker asserts that he met whoever answers this question.9 To understand this question, and therefore to understand what the speaker says with (29), you also have to know the range of the variable. You have to know 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 is what distinguishes different which-questions whose possible answers have the common form in (30), such as the question of who the speaker will marry from the question of when he will marry, the question of which French citizen he will marry, and so on. ‘Person’ is our word for expressing this requirement on your semantic knowledge. If you interpret the variable in the question as having values which can be specified with expressions like ‘Waterloo Station’, or if you interpret it as not having values which can be specified with expressions like ‘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 work for non-categorial nouns. Almost all nouns can be viewed as expressing the range of a which-question’s variable. The only difference will be in the range of values that the noun expresses, and the corresponding class of specifiers that it 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 the range of values from persons to horses, and the class of specifiers to names for horses. The sentence then says that the speaker met whatever answers the question of which horse won on Saturday. You need not already know the answer to this question to interpret the sentence, but you can learn the answer through further inquiry. ‘Horse’, like ‘person’, is a word that distinguishes what can happen in such inquiry from what cannot. By learning Saturday’s winner, 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 answers to the question which ‘the horse that won on Saturday’ expresses. This, then, is how I propose to describe the meaning of nouns: nouns ex9 There are other aspects of the question that this representation does not depict, such as the presupposition that the answer will select a unique value. I leave aside issues about how these other aspects of the question should be represented, because they do not affect my proposal that nouns express ranges of variables introduced by a which-question.


press ranges for the variables in which-questions. Let’s see now how this approach 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 question words. We also saw that we could not account for this relationship by describing their semantic contribution using the usual model, or by thinking of categorial nouns as making a different kind of contribution from non-categorial nouns (namely, none at all). By thinking of noun phrases as expressing questions, we can give a better explanation of the relationship between categorial nouns and question words, without saying that categorial and non-categorial nouns make different sorts of semantic contributions. This is an important advantage for the question-based approach over the more conservative approaches we looked at above. According to the question-based approach, both ‘person’ and ‘horse’ express ranges for which-questions, and mark the distinction between correct and incorrect responses to these questions. The difference is simply that we have a question word (‘who’) which introduces a variable over one of these ranges, but not the other. We do not have a question word that introduces a variable over the range expressed by ‘horse’, so we have no independent means of identifying this range, as we do in the case of ‘person’. That is just a contingent fact about the question words we have in English, though, not a deep difference between the semantic contributions of ‘person’ and ‘horse’. We could have had a question word ‘whorse’ that expresses a variable over this range, so that ‘whorse’-interrogatives would express which-horse questions just as ‘who’-interrogatives express which-person questions. If we added ‘whorse’ to English, the meaning of ‘horse’ would not change; neither would the meaning of ‘person’ if we dropped ‘who’. This is the key to understanding what makes categorial nouns special. Both categorial and non-categorial nouns are related to questions, but categorial nouns have a unique relationship to question words. A categorial noun expresses the normal range for the variable introduced by a question word. These are certain very general ranges that have become lexicalized, perhaps because of their cognitive or evolutionary importance. But they are not essentially different from the other ranges that we do not have question words for, and that are expressed by non-categorial nouns. The unique relationship between categorial nouns and questions words explains why categorial noun phrases can replace nominal interrogatives without affecting the truth conditions of the containing sentence. When a nominal interrogative is replaced by a categorial noun phrase, the result is equivalent simply because the two phrases express the same question. ‘The person I will marry’ can replace ‘who I will marry’, for example, because ‘person’ expresses the normal range of the variable that ‘who’ introduces. (In ‘the person’, the variable is instead introduced by ‘the’.) ‘The horse that won on Saturday’ cannot replace any nominal interrogatives, but that is just because we have no question word 21

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. Earlier, 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 ‘person’, as described by the usual model. We are now proceeding in the opposite direction, describing the meaning of ‘person’ in terms of the type of question expressed by ‘who’. In effect, ‘the person’ expresses how we normally interpret ‘who’, as the variable in a which-question that is answered by specifying someone like Amelie or Beatrice or Charlotte. The important point is that the distinction between answers and non-answers to this type of question should be taken as explanatorily prior to the meaning of ‘person’. We demonstrate our 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 understanding of these questions: it is our word for marking the distinction between correct and incorrect responses to a certain type of which-question. When we use different nouns corresponding to the same question word, we express different understandings of the range of possible answers to the type of which-question it signifies. To see this, consider two different ways you could answer 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 question. By using different nouns in your answer, you express your interpretation of the question, and thus the range of answers that it admits. For example, suppose you think the questioner wants to know what to buy for your anniversary. Then you will probably answer in the first way, expressing your understanding of the question as having answers in the range allowed by ‘year’, such as 1982 or 2014. Expressing your understanding this way helps you coordinate with the questioner. If your understanding does not agree with hers, she can rephrase (“Ah, no, I meant to ask, which month. . . ”). This makes it clear why different nouns may be needed to replace the same question word in different contexts, as we saw in the case of ‘when’-nominals above. The variable introduced by a question word can be interpreted as having different ranges in different contexts, even when we associate these ranges with the same basic type of question. Different nouns are needed to express those 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 happening in specificational sentences. As I noted above, specificational sentences are a


kind of copular sentence. Like all copular sentences, they have two significant parts: the subject phrase, which appears before the copula, and the complement phrase, which appears after it. A good way to get a handle on the class of specificational sentences is to contrast them with predicational sentences, which are another familiar species of copular sentence.10 In a predicational sentence, the complement phrase is predicated of what the subject phrase denotes. For example, (33)

Dieter is paranoid.

predicates ‘paranoid’ of Dieter. By contrast, in a specificational sentence, the complement 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 expressed by the subject. In general, a specificational sentence pairs a question with an answer. The subject expresses a which-question, and the complement gives one or more values for the variable introduced by that question. Once we recognize that the noun phrase in the subject of a specificational sentence expresses a question, it is easy to explain why specificational sentences exhibit focus on the complement phrase. Recall that a focused sentence can be used to answer fewer questions in discourse than its neutral counterpart. 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 answer both. (16)

a. b.

The number of Jupiter’s moons is four. Jupiter has four moons.

Specificational sentences answer fewer questions than neutral sentences because they already contain expressions of the particular question they address. A specificational sentence says that something is the answer to a particular question, and it is incongruous to use a sentence which specifies an answer to one question when answering a different one. This analysis of specificational sentences also helps to explain why the categorial nouns in them are often eliminable via paraphrase. A specificational sentence provides the answer to a question. The neutral paraphrase of the sentence provides an equivalent answer to this question. But the neutral sentence can also answer other questions, sometimes of a very different basic type. The categorial noun’s disappearance is a symptom of the fact that the neutral sentence does not say explicitly which question it addresses. 10 The distinction between specificational and predicational sentences is originally due to Akmajian (1970) and Higgins (1979). For a recent discussion of the taxonomy of copular sentences, see Mikkelsen (2011).


Finally, there is a straightforward explanation of why ‘number’ can only be used in specificational sentences that focus on number words. ‘Number’, like all nouns, expresses a certain range of values. These values can be specified by number words, but not by quantifiers or color words. Using anything other than 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, because it’s not the sort of expression that can give an answer to the question being asked. For the same reason, ‘yellow’ and ‘some’ cannot occupy the complement of a specificational sentence where ‘number’ is the head noun in the subject. This explanation extends to categorial nouns more generally: they constrain the expressions that can appear in the complement of a specificational sentence because they only abstract over the specifiers for values in a certain semantic range. So it appears that we can account for the special properties of categorial nouns and the sentences where they occur by adopting a question-based approach to their semantics. This approach explains the equivalence between nominal interrogatives and categorial noun phrases, the eliminability of categorial 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 semantically inert, or as making an entirely different kind of semantic contribution than ordinary nouns make. I conclude that this is a promising and plausible approach to describing the meanings of categorial nouns and nouns more generally. Their meanings are best described by saying that a noun expresses a range of values for a which-question’s variable. It abstracts over a class of specifiers for those values, which can be used to answer the question. Its semantic role is to make the boundary between possible answers and non-answers to a certain kind of question explicit.


Do nouns denote objects?

I would like to close by returning to the philosophical debates surrounding categorial nouns, to see what light the question-based approach can shed on these debates. Are there such things as numbers, reasons, or ways of appearing or acting? I have proposed that we should not think of nouns as denoting objects, but as expressing the range of a variable in a which-question. In purely formal terms, these two approaches to describing the meaning of nouns are not so different. A formal semantic theory that follows the usual model will typically use 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 described as the normal case, to delimit the range of a variable. Thus, by describing nouns as expressing ranges of variables in questions, I am not recommending a new


sort of formalism. Instead, the difference between my approach and the usual model lies in the informal descriptions of what such clauses say. These different descriptions 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 platonistic ontology. The usual model describes these clauses as saying that ‘number’ 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 between words and entities in the world, the usual model invites us to assimilate the ontology of numbers and horses. Someone who accepts the usual model will be pressed to admit that there are reasons, numbers, and other classes of abstract objects; that we speak about these objects when we use categorial nouns; and that because we speak truly of them, it is clear that they are just as real and existent as horses and persons. Conversely, someone who wants to resist that ontological picture will resist the usual model, or at least resist its application to particular nouns. The usual model thus invites the sort of ontological debate between realists and anti-realists that I sketched in the introduction. In contrast, I am recommending that we think about the relationship between language and things in the world as mediated by practices of inquiry. Rather than picturing noun phrases as denoting or referring to objects, we should think of them as ‘keeping a place’ for potential specifiers, the words we would use to answer the questions they express.11 In some cases, those specifiers might refer to things in the world, so that we could think of the noun phrase itself as doing so, albeit indirectly or derivatively. These are the cases that the usual model handles well. But in other cases, that is probably not the right way to think about what the specifiers would do, and so it is probably not the right way to think about what the noun phrases that keep a place for them 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 kinds of case. It generalizes the usual model, and thereby avoids the debates which arise from its controversial applications. To see this, first consider the kind of case that the usual model handles well. The examples we looked at with ‘person’ and ‘horse’ are paradigms of this kind of case.12 Noun phrases headed by ‘person’ or ‘horse’ keep a place for proper 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 ‘the person I will marry’ or ‘the horse that won on Saturday’ as indirectly referring to persons and horses, via their relationship to proper names. Describing these nouns as denoting classes of objects is appropriate, because we give values in the 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 11 This terminology is from Prior (1971). Prior’s defense of non-nominal quantification was an important inspiration for my account of noun meaning. 12 See the discussion of example (29) above.


objects we can refer to or denote, the usual model falls out as a special case on the question-based approach. On the other hand, ‘way’ noun phrases are an example of the second kind of 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 he had come in’ as picking out an object among a class of abstracta, the ways. A host of puzzling questions then seem relevant. What are these objects? Where are they? How do we know about them, and how do we manage to pick them out when speaking or interpreting others? The question-based approach sidesteps these puzzles. On the questionbased approach, ‘the way he had come in’ here expresses a which-question, one that we could normally express with an interrogative like “How did George come in?”. Someone who asserts (36) is asserting something we might represent 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 specifiers for the values in that range are not proper names, but adverbial expressions like ‘hastily’, ‘via the rear exit’, ‘without interrupting anyone’, and so on. The question-based approach requires that we think of these expressions as giving values for the variable in a ‘how’-question, but it does not require that we think of those values as objects in any ordinary sense, or the specifiers as denoting or referring to such objects. So we do not have to say that ‘the way he 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-based approach can avoid the puzzles raised by the usual model in this case, without losing track of what ‘the way he had come in’ semantically has in common with ‘the person I will marry’. By generalizing the usual model to account for this second kind of case, we can see more clearly what’s happening in ontological debates, without favoring one camp over the other. Are there reasons? Are there numbers? Yes, of course: the number of words in the previous sentence is 3, and the reason that number is prime is that no smaller positive integers divide it, except 1. The realist intuition is entirely correct, in that we can not only speak truly of such things, but give specific examples of them. But the question-based approach to describing what ‘reason’ and ‘number’ mean shows us how to think about this intuition in a way that divests it of much ontological significance, and this will placate the anti-realist. There are reasons and numbers, but this simply means that there are answers to the types of questions we ask with ‘why’ and ‘how many’. The question-based approach is compatible with saying that these things are 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 26

the sense that horses and people are, we will have to go beyond the meanings of the nouns themselves. The question-based approach is valuable because it offers a new perspective about where such ontological inquiries should begin. To move from the semantics of ‘reason’ or ‘number’ to the ontology of reasons or numbers, we must first answer the following question: how is what we can ask for related to what is? This is a question about the nature of inquiry, and the relationship between the world and the practices by which we come to know about it. The general 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 another occasion.


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