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...002, and made explicitly in Matushansky & Spector 2005). This is the view I will adopt here. In particular, I will adopt a Kennedy-style understanding of adjectives and gradability (as articulated in =-=Kennedy 1997-=-, 2007, Kennedy & McNally 2005 and elsewhere), and assume gradable nouns work analogously. In such a system, tall denotes a measure function from individuals to their degrees of tallness, as in (48a) ...

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... plays this role. In unmarked (i.e., positive10) forms of adjectives, this role is played instead by an abstract degree head, POS. The structure will look broadly as in (49) (Abney 1987, Corver 1990, =-=Grimshaw 1991-=-, Kennedy 1997, among others): (49) Clyde is [POS tall]. DegP〈e, t〉 Deg〈ed , et〉 POS AP〈e, d〉 tall 9’Yet it appears that nouns too are vague, some of them just as vague as certain adjectives. Why does...

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...ressed, and consequently probably the clearest window available onto how degree modification works. But gradability is not a property of adjectives alone (Bolinger 1972, Sapir 1944, and more recently =-=Abney 1987-=-, Doetjes 1997, Thanks to Ai Matsui, Alan Bale, Alan Munn, Ana Arregui, Angelika Kratzer, Anna Maria di Sciullo, Anne-Michelle Tessier, Artemis Alexiadou, Bernhard Schwarz, Calixto AgueroBautista, Chr...

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...on 4. 3.1 Assumptions About Nominal Gradability One way to conceptualize nominal gradability would be to make use of supervaluations, in which there is no need for degrees as such in the first place (=-=Kamp 1975-=-, Fine 1975, others). Kamp & Partee (1995) explicitly propose that nouns are interpreted in this way.7 This has the advantage of being compatible with the usual assumption that nouns denote properties...

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...ssumptions About Nominal Gradability One way to conceptualize nominal gradability would be to make use of supervaluations, in which there is no need for degrees as such in the first place (Kamp 1975, =-=Fine 1975-=-, others). Kamp & Partee (1995) explicitly propose that nouns are interpreted in this way.7 This has the advantage of being compatible with the usual assumption that nouns denote properties. 6This sen...

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...itly in Matushansky & Spector 2005). This is the view I will adopt here. In particular, I will adopt a Kennedy-style understanding of adjectives and gradability (as articulated in Kennedy 1997, 2007, =-=Kennedy & McNally 2005-=- and elsewhere), and assume gradable nouns work analogously. In such a system, tall denotes a measure function from individuals to their degrees of tallness, as in (48a) (though see Heim 2000 for argu...

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...ause is taken to denote a degree. I leave this as a sketch here, since comparatives as such will not be the primary focus here. (For further discussion, see Bhatt & Pancheva 2004, Kennedy 1997, 2005, =-=Klein 1980-=-, 1982, Larson 1988, Lechner 1999, Ludlow 1989, McConnell-Ginet 1973, Seuren 1973, Stassen 1985, von Stechow 1984a,b, Xiang 2005 among many others, as well as references cited elsewhere in this paper....

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...edy & McNally 2005 and elsewhere), and assume gradable nouns work analogously. In such a system, tall denotes a measure function from individuals to their degrees of tallness, as in (48a) (though see =-=Heim 2000-=- for arguments against this view). I will assume correspondingly that idiot denotes a measure function from individuals to their degree of idiocy, as in (48b): (48) a. J tall K = λx . ιd [x is d -tall...

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...he size of degrees themselves— that is, just as sets can be claimed to be big or small, so too can degrees. Expressions that seem to involve what might be called ‘nominalized’ degrees (in roughly the =-=Chierchia 1984-=-, 1998 sense), such as (69), reflect this, though the results often have the stilted quality of circumlocutions: (69) George’s idiocy Clyde’s enthusiasm for goat cheese Herman’s dorkiness ...

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...that makes (explicit) use of degrees. Another course is be to suppose that nouns—or at least certain nouns— have degree arguments and are associated lexically with scales (an assumption considered in =-=Larson 1998-=-, Matushansky 2001, and Matushansky 2002, and made explicitly in Matushansky & Spector 2005). This is the view I will adopt here. In particular, I will adopt a Kennedy-style understanding of adjective...

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...ves as such will not be the primary focus here. (For further discussion, see Bhatt & Pancheva 2004, Kennedy 1997, 2005, Klein 1980, 1982, Larson 1988, Lechner 1999, Ludlow 1989, McConnell-Ginet 1973, =-=Seuren 1973-=-, Stassen 1985, von Stechow 1984a,b, Xiang 2005 among many others, as well as references cited elsewhere in this paper.) 3.3 The Structure of the Extended Gradable NP Pursuing further the analogy to a...

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... here, since comparatives as such will not be the primary focus here. (For further discussion, see Bhatt & Pancheva 2004, Kennedy 1997, 2005, Klein 1980, 1982, Larson 1988, Lechner 1999, Ludlow 1989, =-=McConnell-Ginet 1973-=-, Seuren 1973, Stassen 1985, von Stechow 1984a,b, Xiang 2005 among many others, as well as references cited elsewhere in this paper.) 3.3 The Structure of the Extended Gradable NP Pursuing further the...

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...which gradable notions are expressed, and consequently probably the clearest window available onto how degree modification works. But gradability is not a property of adjectives alone (Bolinger 1972, =-=Sapir 1944-=-, and more recently Abney 1987, Doetjes 1997, Thanks to Ai Matsui, Alan Bale, Alan Munn, Ana Arregui, Angelika Kratzer, Anna Maria di Sciullo, Anne-Michelle Tessier, Artemis Alexiadou, Bernhard Schwar...

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...a huge problem. SIGNIFICANCE READINGS There is another, more puzzling use of size adjectives that has a non-size flavor. On this use, these adjectives seem to have an expressive role (in the sense of =-=Kratzer 1999-=-, Potts 2003, 2007 and others), and involve some notion of, very roughly, ‘significance’: (43) a. the big political figures of the 20th century b. a huge corporate mucky-muck c. a small little man d. ...

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... same way as measure phrases are—by a nominal counterpart of the Deg MEAS: 15There is actually a connection here to Faller (2000) and Winter (2005)—and Vector Space Semantics more generally (see also =-=Zwarts 1997-=-, Zwarts & Winter 2000)—in that the notion of ‘degree-size’ is rather like VSS’s norm function | · |. 21 (72) DegNP〈e, t〉 DegP big DegN′〈ot , et〉 DegN〈ed , 〈ot , et〉〉 MEASN NP〈e, d〉 idiot The adnomina...

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...of that too emerges from what has already been said, and from the relatively standard assumption that antonymous adjectives measure along 24 scales with opposite orderings (Faller 2000, Kennedy 2001, =-=Rullmann 1995-=-, among others). To illustrate how, consider %small idiot, which does not have a degree reading. If it were to have a degree reading, it would have to be interpreted as big idiot is above. The denotat...

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...e, t〉 DP〈d , t〉 six feet Deg′〈dt , et〉 Deg〈ed , 〈dt , et〉〉 MEAS AP〈e, d〉 tall 18 As (62) reflects, I will interpret the measure phrase as a property (again departing from Svenonius & Kennedy 2006 and =-=Kennedy & Levin 2007-=- and earlier versions of this approach; for a sustained argument for treating measure phrases as predicates, see Schwarzschild 2005). More precisely, MEAS relates an adjective denotation and a measure...

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...enote a degree. I leave this as a sketch here, since comparatives as such will not be the primary focus here. (For further discussion, see Bhatt & Pancheva 2004, Kennedy 1997, 2005, Klein 1980, 1982, =-=Larson 1988-=-, Lechner 1999, Ludlow 1989, McConnell-Ginet 1973, Seuren 1973, Stassen 1985, von Stechow 1984a,b, Xiang 2005 among many others, as well as references cited elsewhere in this paper.) 3.3 The Structure...

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...pical means by which gradable notions are expressed, and consequently probably the clearest window available onto how degree modification works. But gradability is not a property of adjectives alone (=-=Bolinger 1972-=-, Sapir 1944, and more recently Abney 1987, Doetjes 1997, Thanks to Ai Matsui, Alan Bale, Alan Munn, Ana Arregui, Angelika Kratzer, Anna Maria di Sciullo, Anne-Michelle Tessier, Artemis Alexiadou, Ber...

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...ill not be the primary focus here. (For further discussion, see Bhatt & Pancheva 2004, Kennedy 1997, 2005, Klein 1980, 1982, Larson 1988, Lechner 1999, Ludlow 1989, McConnell-Ginet 1973, Seuren 1973, =-=Stassen 1985-=-, von Stechow 1984a,b, Xiang 2005 among many others, as well as references cited elsewhere in this paper.) 3.3 The Structure of the Extended Gradable NP Pursuing further the analogy to adjectives, I w...

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...or very often plays this role. In unmarked (i.e., positive10) forms of adjectives, this role is played instead by an abstract degree head, POS. The structure will look broadly as in (49) (Abney 1987, =-=Corver 1990-=-, Grimshaw 1991, Kennedy 1997, among others): (49) Clyde is [POS tall]. DegP〈e, t〉 Deg〈ed , et〉 POS AP〈e, d〉 tall 9’Yet it appears that nouns too are vague, some of them just as vague as certain adjec...

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...s as a sketch here, since comparatives as such will not be the primary focus here. (For further discussion, see Bhatt & Pancheva 2004, Kennedy 1997, 2005, Klein 1980, 1982, Larson 1988, Lechner 1999, =-=Ludlow 1989-=-, McConnell-Ginet 1973, Seuren 1973, Stassen 1985, von Stechow 1984a,b, Xiang 2005 among many others, as well as references cited elsewhere in this paper.) 3.3 The Structure of the Extended Gradable N...

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...6 for a recent articulation of this view). Analogously, one might expect an adnominal degree head to introduce adnominal measure phrases. Exactly this has been proposed in various forms (Corver 1998, =-=Schwarzschild 2006-=-, Zamparelli 1995)—of may actually spell out such a degree head: (61) six pounds [DegN′ [DegN of ] cheese ] 3.5 Summary Like adjectives, gradable nouns denote measure functions. An adnominal counterpa...

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... selected as the one whose scale is associated the noun. Indeed, one might draw the conclusion from this, as Kennedy (2007) suggests, that what nouns manifest is not so much vagueness as imprecision (=-=Lasersohn 1999-=-, Pinkal 1995). Another way of articulating what I intend by ‘gradable noun’, then, is that gradable nouns are those for which a single criterion can be distinguished from the others as the most salie...

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...at such an abstract scale may play an important semantic role. Any degree can be mapped onto this scale— both positive and negative degrees, in ontologies in which these are distinct (Kennedy 2001 or =-=Faller 2000-=- and Winter 2005).15 Second, to reflect that big can measure both individuals and degrees, I will adopt an ontology with a type o, which includes objects of both types: (70) Do =De ∪Dd The denotation ...

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...& Kennedy 2006 for a recent articulation of this view). Analogously, one might expect an adnominal degree head to introduce adnominal measure phrases. Exactly this has been proposed in various forms (=-=Corver 1998-=-, Schwarzschild 2006, Zamparelli 1995)—of may actually spell out such a degree head: (61) six pounds [DegN′ [DegN of ] cheese ] 3.5 Summary Like adjectives, gradable nouns denote measure functions. An...

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...(45) You’ll be huge in Bolivia! The biggest!6 This odd pattern may correlate with the independent fact that expressive adjectives—whether size adjectives or otherwise—are only possible attributively (=-=Morzycki 2007-=-). The use in (45) appears not to be so clearly expressive, and is largely restricted to characterizations of popularity, as (46) further reflects, and to the adjectives big and huge rather than, say,...

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...al true total complete absolute idiot 12There are other forms of nominal comparatives of less direct relevance here, such as those involving comparative determiners like fewer and more (=-=Hackl 2000-=-, Nerbonne 1995). 15 None of these naturally receives anything other than a degree reading here. It is not possible, for example, to construe true here in the propositional sense. Assigning these morp...

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...act scale may play an important semantic role. Any degree can be mapped onto this scale— both positive and negative degrees, in ontologies in which these are distinct (Kennedy 2001 or Faller 2000 and =-=Winter 2005-=-).15 Second, to reflect that big can measure both individuals and degrees, I will adopt an ontology with a type o, which includes objects of both types: (70) Do =De ∪Dd The denotation of big, then, is...

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...ings of size adjectives in which they are a kind of adnominal counterpart of measure phrases in AP, and restrictions on the construction are brought about in part by the underlying syntax and (contra =-=Morzycki 2005-=-) in part by how the scale structure of the size adjective interacts with the semantics of degree measurement. Section 5 concludes. 2 Two Generalizations and Some More Facts and Complications 2.1 The ...

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... one whose scale is associated the noun. Indeed, one might draw the conclusion from this, as Kennedy (2007) suggests, that what nouns manifest is not so much vagueness as imprecision (Lasersohn 1999, =-=Pinkal 1995-=-). Another way of articulating what I intend by ‘gradable noun’, then, is that gradable nouns are those for which a single criterion can be distinguished from the others as the most salient. For idiot...

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...e as a property (again departing from Svenonius & Kennedy 2006 and Kennedy & Levin 2007 and earlier versions of this approach; for a sustained argument for treating measure phrases as predicates, see =-=Schwarzschild 2005-=-). More precisely, MEAS relates an adjective denotation and a measure phrase by requiring that the minimal degree (on the appropriate scale) that satisfies the measure phrase be smaller than degree to...

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...s. Another course is be to suppose that nouns—or at least certain nouns— have degree arguments and are associated lexically with scales (an assumption considered in Larson 1998, Matushansky 2001, and =-=Matushansky 2002-=-, and made explicitly in Matushansky & Spector 2005). This is the view I will adopt here. In particular, I will adopt a Kennedy-style understanding of adjectives and gradability (as articulated in Ken...

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...(For further discussion, see Bhatt & Pancheva 2004, Kennedy 1997, 2005, Klein 1980, 1982, Larson 1988, Lechner 1999, Ludlow 1989, McConnell-Ginet 1973, Seuren 1973, Stassen 1985, von Stechow 1984a,b, =-=Xiang 2005-=- among many others, as well as references cited elsewhere in this paper.) 3.3 The Structure of the Extended Gradable NP Pursuing further the analogy to adjectives, I will assume that there are degree ...

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...xplicit) use of degrees. Another course is be to suppose that nouns—or at least certain nouns— have degree arguments and are associated lexically with scales (an assumption considered in Larson 1998, =-=Matushansky 2001-=-, and Matushansky 2002, and made explicitly in Matushansky & Spector 2005). This is the view I will adopt here. In particular, I will adopt a Kennedy-style understanding of adjectives and gradability ...

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...l complete absolute idiot 12There are other forms of nominal comparatives of less direct relevance here, such as those involving comparative determiners like fewer and more (Hackl 2000, =-=Nerbonne 1995-=-). 15 None of these naturally receives anything other than a degree reading here. It is not possible, for example, to construe true here in the propositional sense. Assigning these morphemes to DegN i...

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...ulation of this view). Analogously, one might expect an adnominal degree head to introduce adnominal measure phrases. Exactly this has been proposed in various forms (Corver 1998, Schwarzschild 2006, =-=Zamparelli 1995-=-)—of may actually spell out such a degree head: (61) six pounds [DegN′ [DegN of ] cheese ] 3.5 Summary Like adjectives, gradable nouns denote measure functions. An adnominal counterpart of the degree ...

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...consequently probably the clearest window available onto how degree modification works. But gradability is not a property of adjectives alone (Bolinger 1972, Sapir 1944, and more recently Abney 1987, =-=Doetjes 1997-=-, Thanks to Ai Matsui, Alan Bale, Alan Munn, Ana Arregui, Angelika Kratzer, Anna Maria di Sciullo, Anne-Michelle Tessier, Artemis Alexiadou, Bernhard Schwarz, Calixto AgueroBautista, Chris Barker, Chr...