On ‘Average’

uses of ‘average’ differ in several ways from concrete uses. In sentences of the sort we are focusing on, in which ‘average’ is part of a definite description in subject position, the truth conditions of examples with concrete ‘average’ can typically be paraphrased as generic statements. For example, (4a) is true just in case it generally holds that individuals who are New Yorkers and are average relative to the class of New Yorkers (a kind of relativity that may or may not be similar to the familiar comparison class relativity of gradable predicates) are also stressed out. This strategy fails utterly for abstract ‘average’, however. It would be wrong to say that (1a) is true just in case it generally holds that if an individual is American and is average 5 (6a) and (6c) highlight the flexibility in determining what properties can be taken into consideration in particular contexts — in these cases, political blogs — when measuring typicality. On ‘Average’ 593 Mind, Vol. 118 . 471 . July 2009 ! Kennedy and Stanley 2009 at Srials D eartm nt on N ovem er 2, 2011 hp://m ind.oxfjournals.org/ D ow naded rom (relative to other Americans), then that individual has 2.3 children: no American has 2.3 children! Given these considerations, it is not surprising that replacing ‘average’ with ‘typical’ in sentences like (1a) and (1b) results in anomaly: (7a) and (7b) are not paraphrases of (1a) and (1b), but are rather understood as generic statements, and are odd precisely because they entail the existence of individuals who have fractional children and belong to fractional airline programmes. (7) (a) #The typical American has 2.3 children. (b) #The typical Freddie Voter belongs to 3.2 airline programs. The contrast between (8a) and (8b) makes a similar point. (8) (a) The average French woman today is 137.6 pounds, compared to 133.6 pounds in 1970. (www.msnbc.msn.com/ id/11149568/) (b) ??The typical French woman today is 137.6 pounds, compared to 133.6 pounds in 1970. Sentence (8b) does not involve a commitment to impossible individuals (such as people with fractional children); it is odd because it describes a highly unlikely scenario: one in which it is generally the case that contemporary French women have a very specific weight of 137.6 pounds. The use of a specific measurement introduces a high standard of precision, but this clashes with the inherent imprecision of a generic statement. The fact that no comparable anomaly arises in (8a) suggests that the semantics of abstract ‘average’ does not involve generic quantification over individuals, but rather some kind of reference to actual averages, that is, to numbers or amounts which may (or may not) be precise. Finally, unlike concrete ‘average’, abstract ‘average’ is not gradable, as shown by the anomaly of (9a) and by the fact that (9b) entails that there is a Republican member of Congress who has served for 9.2 years (namely, the most average one). (9) (a) #The most average American has 2.3 children. (b) The most average Republican member of Congress has served 9.2 years. 594 Christopher Kennedy and Jason Stanley Mind, Vol. 118 . 471 . July 2009 ! Kennedy and Stanley 2009 at Srials D eartm nt on N ovem er 2, 2011 hp://m ind.oxfjournals.org/ D ow naded rom In what follows, we will take it to be diagnostic of the distinction between concrete and abstract ‘average’ that the former can be replaced without significant change in meaning or acceptability by the term ‘typical’, disprefers precise measurements, and can be modified by degree morphology, while the opposite holds of the latter. 3. Previous proposals We have a number of distinct complaints about each previous approach to the problem of ‘average’ sentences, which fall into three categories: analysis-specific empirical or conceptual shortcomings, non-compositionality, and lack of generality. We will discuss the first two points in the following subsections as they apply to specific accounts; the third point is that any account that is specifically designed to deal with ‘the average American’ will fail to explain the fact that the abstract interpretation of ‘average’ appears in a variety of different constructions. Several additional (and arguably more colloquial) uses of abstract ‘average’ are illustrated in (10). (10) NYU has reported that the 53 teens have lost an average of half of their excess weight over the past year, and that’s truly excellent, considering that their average weight was 297 pounds at the beginning! So, assuming that they should weigh an average of, oh, 125 pounds, they were an average of 175 pounds overweight, which means they’d lost an average of 87 pounds over the year — spectacular weight loss, IMO, even though we are talking about averages here. (From a posting on ) The examples in (11a)–(11e) illustrate the different ways of expressing the content of the underlined part of (10) (with word order variations given in parentheses). (11) (a) The average weight of the teens in the study was 297 lbs. (The teens’ average weight was 297 lbs.) (b) The teens in the study averaged 297 lbs in weight. (c) The teens in the study weighed an average of 297 lbs. On ‘Average’ 595 Mind, Vol. 118 . 471 . July 2009 ! Kennedy and Stanley 2009 at Srials D eartm nt on N ovem er 2, 2011 hp://m ind.oxfjournals.org/ D ow naded rom (d) The teens in the study weighed on average 297 lbs. (The teens in the study weighed 297 lbs on average.) (On average, the teens in the study weighed 297 lbs.) (e) The average teen in the study weighed 297 lbs. That these are all instances of abstract ‘average’ is shown by the fact that the numeral in each example can be felicitously modified by ‘exactly’ and by the fact that each of these examples could be true even if no individual student among the group of 53 weighed 297 lbs. These examples make it quite clear both that we are dealing with numerical averages here, and that such meanings are a part of everyday, colloquial English. The semantic analysis of abstract ‘average’ that we develop in section 4 is unique in that it not only accounts for (11e), it also generalizes to the entire array of ‘average’ constructions in (11a)–(11d). On that count alone, then, it achieves a higher level of explanatory adequacy than the alternatives we discuss below. 3.1 The pretence account Perhaps the most straightforward account of abstract ‘average’ in definite descriptions is the pretence account. According to this analysis, there is no special abstract meaning of ‘average’. Though there is no individual that satisfies the description ‘average American’, we pretend that there is one when we utter sentences such as (1a), and we allow for the possibility that this pretence individual has (otherwise impossible) properties such as having 2.3 children. Whether it is true in the pretence that the average American has 2.3 children depends on the relevant distribution of facts in the real world. On this view, abstract readings are not due to a special semantic content for certain uses of ‘average’; they arise because we can pretend that certain ordinary semantic contents are true. The pretence account of ‘average’ has come in for significant criticism in Stanley 2001; here we reiterate some of those criticisms, and add some additional ones. According to the pretence account, the definite description ‘the average American’ is a genuine singular term, like ‘the young American on the corner’ or ‘the nice boy next door’. It is just that when we utter ‘The nice boy next door is going to college’, we are not pretending that there is a nice boy next door (we are instead presupposing that there is one), whereas when we utter (1a), we are pretending there is an average American. The pretence account accords with 596 Christopher Kennedy and Jason Stanley Mind, Vol. 118 . 471 . July 2009 ! Kennedy and Stanley 2009 at Srials D eartm nt on N ovem er 2, 2011 hp://m ind.oxfjournals.org/ D ow naded rom Chomsky’s view that ‘the average American’, in its abstract use, is no different than other definite descriptions. But there are a host of differences between descriptions containing abstract uses of ‘average’ and ordinary descriptive phrases. First, abstract uses of ‘average’ can only occur with the determiner ‘the’.uses of ‘average’ can only occur with the determiner ‘the’. The following sentences quite clearly involve concrete ‘average’, in that they have meanings that remain the same if ‘average’ is replaced by ‘typical’, and they commit the person who asserts them to the existence of individuals with impossible numbers of children. (12) (a) Every average American has 2.3 children. (b) Most average Americans have 2.3 children. (c) Some average American has 2.3 children. The impossibility of quantification over pretend individuals — which is what would be required to maintain abstract interpretations in (12a)–(12c) — is mysterious if the difference between for example, ‘the average NP ’ and ‘the young NP ’ has nothing to do with the syntactic or semantic behaviour of these phrases, but rather only with whether or not they are being evaluated literally or under a pretence. It is worth emphasizing how serious problem it is for the pretence account of abstract uses of ‘average’ that it only can co-occur with the determiner ‘the’. For example, even the Russellian translation of ‘the average American’ is infelicitous: (13) #There is one and only one average American, and he has 2.3 children. The occurrence of ‘average’ in (13) does not allow an abstract use. This is deeply mysterious if the correct account of an abstract use of ‘the average American’ involves pretence rather than something to do with the semantic content of ‘average’. Perhaps, (12a)–(12c) do not allow abstract uses of ‘average’, because a sufficiently clear context has not been set up. Let us suppose that the following are all true: (14) (a) The average Swede has 1.3 children. (b) The average Norwegian has 1.2 children. (c) The average Dane has 1.4 children. On ‘Average’ 597 Mind, Vol. 118 . 471 . July 2009 ! Kennedy and Stanley 2009 at Srials D eartm nt on N ovem er 2, 2011 hp://m ind.oxfjournals.org/ D ow naded rom According to the pretence account, we pretend that there is an average Swede with 1.3 children, and an average Norwegian with 1.2 children, and an average Dane with 1.4 children. If so, (15) should be both felicitous and true, but it is neither. (15) #Every average Scandinavian has between 1 and 1.5 children. In particular, it does not allow a reading where it simply states the conjunction of (14a)–(14c), as it should if the pretence account were correct. It is possible to convey this information, but only if we replace ‘every’ with ‘the’ in (15), further illustrating the importance of the definite determiner in licensing the abstract interpretation of ‘average’. A further problem for the pretence account of abstract uses of ‘average’, also emphasized in Stanley 2001, is that unlike other adjectives, one cannot place adjectives between ‘the’ and the adverbial use of ‘average’. (16) (a) The old fancy car is parked outside. (b) The fancy old car is parked outside. (17) (a) The average conservative American has 1.2 guns. (b) #The conservative average American has 1.2 guns. (18) (a) The average red car gets 2.3 tickets per year. (b) #The red average car gets 2.3 tickets per year. If the abstract use of ‘average’ simply had to do with a pretence governing the relevant instance of ‘the average NP ’, rather than any fact about the compositional semantics of the phrase, then it would be mysterious why one could not place adjectives between the abstract use of ‘average’ and the determiner ‘the’. In sum, there are a host of distributional facts about ‘average’ that are rendered completely mysterious by the pretence account. These distributional facts strongly suggest that the abstract use of ‘average’ emerges from facts about the meaning and compositional structure of the relevant constructions, rather than an attitude of pretence we have towards ordinary contents. More generally, this type of account provides absolutely no explanation of the similarity in meaning between sentences like those in (11), in which ‘average’ appears in different syntactic contexts. 598 Christopher Kennedy and Jason Stanley Mind, Vol. 118 . 471 . July 2009 ! Kennedy and Stanley 2009 at Srials D eartm nt on N ovem er 2, 2011 hp://m ind.oxfjournals.org/ D ow naded rom 3.2 Stanley 2001 Stanley (2001) proposes a very different kind of theory, according to which instances of ‘the average NP ’, when ‘average’ has an abstract use, denote degrees on a contextually salient scale. According to Stanley, the syntactic structure of an instance of ‘the average NP ’, when it has an abstract use, is as shown in (19), where O denotes a function from properties to measure functions (functions from objects to degrees on a contextually salient scale), whose domains are restricted to the extension of that property.