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Degrees as kinds

Abstract

This paper argues that a variety of constructions in a variety of languages suggest a deep connection between kinds, manners, and degrees. We articulate a way of thinking about degrees on which this connection is less surprising, rooted in the idea that degrees are kinds of Davidsonian states. This enables us to provide a cross-categorial compositional semantics for a class of expressions that can serve as anaphors to kinds, manners, and degrees, or introduce clauses that further characterize them. A consequence of this is that equatives emerge as a special case of a more general cross-categorial phenomenon. The analysis is undergirded by independently motivated assumptions about free relatives and type shifting. It provides evidence for a view of degrees on which they are significantly more ontologically complex than is typically thought.

Introduction

It is, one normally assumes, a lexical accident of English that the same wh-word, how, is used for questioning both manners (How did he do it?) and degrees (How tall is he?). Likewise, one normally assumes that it is an accident of English that it uses the same complementizer, as, to build degree modifiers (as tall as Clyde), manner modifiers (die as Clyde did), and adnominal modifiers (such people as Clyde). This is of course all perfectly plausible a priori—languages are routinely guilty of inconsequential coincidences. But these are not accidents of English alone, or even of this corner of English alone. Rather, they are the manifestations of a much broader pattern of cross-categorial correspondences that are present in a large number of languages. The pattern is pervasive enough that, we will argue, it reveals something deep. Minimally, it requires explanation. Providing one requires looking at degrees in a new way.

Our chief aim in this paper is to highlight the theoretical importance of such correspondences, to provide a sufficiently cross-categorial account of at least some of them, and to bring these facts to bear on the question of what degrees are—that is, of how they should be represented in the model. On assumptions that have become the de-facto standard in linguistic semantics, a degree is a relatively impoverished thing. It is simply a representation of measurement, perhaps a point or an interval on an abstract scale. We will argue, building on Landman and Morzycki (2003), that this understanding must be enriched at least enough to construe degrees as a particular species of kind (Carlson 1977b), and that this is part of a larger pattern of parallels between kinds, manners, and degrees.

This project accords with—and in that sense, provides independent evidence for—work that advocates an enriched ontology of degrees, such as Grosu and Landman (1998) and Moltmann (2004, 2009, 2007b). For Grosu and Landman, degrees are structured objects composed of a property, a measure, and an individual. For Moltmann, they are constructed out of particularized property instantiations, or tropes. One might also imagine a role for Kratzerian situations (Kratzer 1989) here. Another option would be to invoke richer elements of the model systematically related to standard degrees (Castroviejo Miró and Schwager 2008; Schwager 2009). The phenomena that will be our principal concern may not be sufficient to adjudicate whether any of these enrichments is the appropriate one, though they certainly bear on the question. We will focus instead on building a compositional semantics for some instantiations of these phenomena, departing from familiar ontological assumptions only to the extent necessary to achieve this goal. This will lead us to model degrees as kinds of Davidsonian states, and manners (following Landman and Morzycki 2003 and Landman 2006) as kinds of events. The truly crucial element, however, is the connection between degrees and kinds. Other considerations may well require a richer ontological foundation than our straightforwardly Davidsonian one.

We explore the basic patterns in Sect. 2. Section 3 puts in place the initial assumptions about kinds, manners, and degrees we will need to get off the ground and discusses how they might make possible an analysis of the most basic constructions. Section 4 turns to the analysis of cross-categorial correspondences in structures that involve kind anaphora. Section 5 provides an analysis of more complicated cases that involve clausal complements to kind modifiers. This entails unifying equatives with constructions previously thought of as a species of relative clause. Section 6 briefly revisits certain ontological and broader conceptual questions that were previously set aside. Section 7 raises some unsolved problems.

The cross-categorial parallels

Polish

Among the languages that most clearly reveal the cross-categorial parallels we will seek to explain are Polish and German. In Polish, a single anaphoric expression, tak, serves as a proform for kinds, manners, and degrees, depending on whether it finds itself in the vicinity of a NP, VP, or AP:

  1. (1)
    figurea

Similar facts obtain in a number of Slavic languages. Polish also uses the same wh-word, jak, across those domains, again depending on its syntactic context:Footnote 1

  1. (2)
    figureb

In the adnominal case, a skeptic might suspect (2a) of simply meaning ‘what dog’. This would be a mistake. The gloss ‘what kind of’ is to be found in e.g. Borsley (1981) and in reference grammars such as Feldstein (2001). Indeed, it’s not clear that what in English isn’t typically used to question kinds, as Heim (1987) has proposed on independent grounds.

When combined, tak and jak are used to abstract over the three domains (though tak can often be omitted):

  1. (3)
    figurec

Strengthening this observation of these parallels is similar cross-categorial behavior with sam (roughly, ‘same’), which can be used to assert similarity across kinds, manners, and degrees:

  1. (4)
    figured

It’s worth contemplating for a moment the least appealing account of these facts possible: that tak happens by chance to have three distinct homophonous forms, and that precisely the same accident has independently befallen jak and sam. Moreover, in each case, it happened to lead to perfectly parallel semantic consequences, leaving each of these words three-ways ambiguous in precisely the same way—between kinds, manners, and degrees. This strains credulity, of course. But, on the most familiar standard assumptions about degrees, what alternative is there? These facts alone are sufficient to suggest that something else must be going on. Yet the outlook for the typical view is more dire still. As we will see, a similar pattern of unexplained coincidences would need to have taken place repeatedly, across many constructions and many languages.

German

The facts so far are not peculiar to Polish. The German anaphor so is also ambiguous between being anaphoric to kinds, to manners, and to degrees (on the degree use, see Umbach and Ebert 2009):

  1. (5)
    figuree

As in Polish, there is a corresponding wh-word, wie, with precisely the same pattern of uses:

  1. (6)
    figuref

English

The Polish and German cases are striking because the parallels manifest themselves especially clearly, but they are only the tip of the iceberg. English manifests one such parallel, as we have already mentioned, in using as in precisely the same way across the three domains:

  1. (7)
    1. a.

      kind: such a dog as this

    2. b.

      manner: Clyde behaved as I did.

    3. c.

      degree: Clyde is as tall as Floyd.

As in Polish and German, (7c) is simply a straightforward equative.

Perhaps an even deeper similarity to the Polish and German facts is to be found in English so. It also has degree and manner uses:

  1. (8)
    1. a.

      degree: so tall (as this)

    2. b.

      manner: stand so as not to block your view

Indeed, English so is probably cognate with the German so (Oxford English Dictionary 1989).

It would seem to lack a kind reading, so that one element of the paradigm would seem to be missing. But in fact, the situation with English so is more complicated, in a way that reflects a deeper underlying connection to kinds. While English does not have a perfect three-way homophony, so does have an adnominal counterpart, such, which has itself been analyzed as a kind anaphor (Carlson 1977b; Landman and Morzycki 2003; Landman 2006; Constantinescu 2011; cf. Siegel 1994). The resemblance is not accidental. The two are cognate (Oxford English Dictionary 1989), and they are sufficiently similar to each other that Bresnan (1973) was driven to derive such from underlying so via transformation. Carlson followed her in this, and Landman decomposes it into so-like.Footnote 2 The chief parallels that originally led Bresnan to this involve a degree-like use of such (apparently first observed by Bolinger 1972, discussed in Carlson 1977b and Landman 2006, and examined most extensively in Constantinescu 2011):

  1. (9)

    Clyde is such \(\left\{\begin{array}{l} \mbox{a tall man}\\ \mbox{an idiot} \end{array}\right\}\).

This constitutes a resemblance to so in two distinct respects. First, it shares its degree meaning. Second, it participates in the fronting operation that moves both of these elements to the left of a (Matushansky 2002):

  1. (10)
    figureg
  1. (11)
    figureh

Third, what would seem to be an AP-modifying use of so is obligatorily pronounced such with mass nouns:

  1. (12)

    \(\left\{\begin{array}{l} \mbox{*so}\\ \phantom{\mbox{*}}\mbox{such} \end{array}\right\}\) fine food

Fourth, both so and such license that phrases (for their semantics, see Meier 2003 and Castroviejo Miró 2011):

  1. (13)
    1. a.

      such a tall man that he might not fit in the car

    2. b.

      so tall a man that he might not fit in the car

    3. c.

      abuse him so much that he might not get in the car

The precise nature of this degree such is somewhat mysterious, and Constantinescu (2011) argues in detail that it shouldn’t be viewed as a genuine degree modifier. Her alternative is a perfect fit for our larger agenda: she suggests that the degree use is essentially parasitic on the kind use. Considering all the facts collectively, though, they suggest that such is a superficial variant of so—and that, by some quirk of linguistic history, English only very narrowly missed overtly manifesting the full three-way parallel as well.

In addition to so and such, English manifests some two-way parallels between the relevant domains. Landman (2006) and Anderson (2010) examine parallels between English like, where like may be used for both kind and manners:

  1. (14)
    1. a.

      kind: a dog like this

    2. b.

      manner: behave like this

And of course English has the already mentioned parallel between degree and manner uses of how:

  1. (15)
    1. a.

      degree: how tall is he?

    2. b.

      manner: how did he behave?

More peripherally, certain degree expressions in an informal register of English—which mean roughly ‘very’—seem to go out of their way to suggest a connection to kinds:

  1. (16)
    1. a.

      He’s some kind of tall.

    2. b.

      Those things are some kind of tasty.

At least one instance of this construction is widely-known: Some Kind of Wonderful has been the title of three distinct songs and a major Hollywood movie. And, of course, English has lexicalized degree words, kinda and sorta—still often spelled kind of and sort of—that also wear their kind-referring origins on their sleeve (for more on these, see Anderson 2013a, 2013b).

So English too provides compelling evidence for the parallel among all the three domains. It doesn’t do it quite so blatantly as some languages, but in one respect, that makes the case stronger. The English evidence is rippling just beneath the surface of a fairly broad swath of the language, manifesting itself in different ways in several different places. Because the evidence is distributed across several morphemes, we can be sure it isn’t a local peculiarity. It shows that these currents run deep.

The broader view

We will not undertake a systematic inventory of evidence from across languages for the larger pattern, but it is worth noting that it reverberates across a number of them—and in one form, across quite a large number.

First, two anecdotal illustrations to provide a flavor of other ways the connections can emerge. French has a three-way parallel in comme ‘like’: (Desmets and Moline 2007; (17b) and (17c) are theirs), though the cases are not perfectly analogous:

  1. (17)
    figurei

The degree exclamative in (17c) is different from the others—it is not an equative—but it is nevertheless a degree reading.

Whereas in English a single wh-word does double-duty for degrees and manners, Japanese has a common wh-expression for kinds and manners, dono-yoo-n{i/a} (where the i/a alternation is present for independent reasons):

  1. (18)
    figurej

As with its Polish counterpart, (18a) is not simply asking about particular books.

The best-documented and most important two-way parallel, however, is in equatives and their manner counterparts (similatives)—in English, the connection between equative and manner as. This connection has been documented extensively from a typological perspective by Haspelmath and Buchholz (1998) and analyzed from a formal-semantic one by Rett (2011). Haspelmath and Buchholz identify a large number of languages spoken in Europe—not all Indo-European—that use the same morpheme to mark their counterpart of an English as clause in both equatives and similatives. The languages in which an identical morpheme used in both cases include those in (19):

  1. (19)
    1. a.

      Romance: Spanish, Portuguese (como); Catalan (com); Occitan (coma); Italian (come)

    2. b.

      Balto-Slavic: Slovene (kot); Russian (kak); Slovak (ako); Lithuanian (kaip)

    3. c.

      Germanic: Dutch (als); Yiddish (vi); Danish, Swedish (som); Icelandic (og); Faroese (sum)

    4. d.

      Northwest Caucasian: Abkhaz (), Kabardian (x o edew)

    5. e.

      Modern Greek (san/ópos)

    6. f.

      Turkish (kadar)

    7. b.

      Romani (kade …sar)

    8. c.

      Finnish (kuin)

    9. d.

      Georgian (rogorc)

    10. e.

      Armenian (inčpes)

    11. f.

      Lezgian (x̂iz)

Of the 43 languages Haspelmath and Buchholz examined, 27 had perfectly identical expressions. Several others used expressions that are clearly cognate.

Independent kind-degree connections: relatives and exclamatives

The facts presented so far focus on overt functional elements whose uses overlap across various combinations of kinds, degrees, and manners. There is, however, another sort of evidence for the kind-degree connection. It comes from constructions that have both kind and degree readings.Footnote 3

The most familiar of these is relative clauses. Carlson (1977a) distinguished a class of amount relatives, which Grosu and Landman (1998) call ‘degree relatives’. They characterize not an individual directly but rather its amount. This is especially clear in examples like (20), due to Heim (1987):

  1. (20)

    degree:

    It will take us the rest of our lives to drink the champagne [that they spilled that evening].

This can be interpreted as an ordinary relative, yielding a reading that involves a life of licking champagne off the floor. But its most natural reading involves drinking the same amount of champagne as was spilled. Amounts are just degrees, so the relative can be construed as denoting a property of degrees: the property of degrees that reflect the amount of spilled champagne.

Alongside these degree readings, there is a class of relatives that characterize kinds (Carlson 1977b; Heim 1987; Grosu and Landman 1998):

  1. (21)

    kind:

    It will take us the rest of our lives to find the champagne [that they had that evening].

As before, this can be interpreted as an ordinary relative, yielding a reading that involves an ill-advised search for liquid that has already been ingested. But the natural reading involves instead a search for champagne of the same kind. The relative, then, denotes a property of kinds instantiated by that evening’s champagne. As Grosu and Landman observe, amount and kind relatives have similarities that distinguish them both from ordinary relatives. First, these readings are generally incompatible with which, though the judgment is easier when the relative contains an existential construction:

  1. (22)
    1. a.

      degree:

      It will take us the rest of our lives to drink the champagne there was at the party that evening.

    2. b.

      kind:

      It will take us the rest of our lives to find the champagne there was at the party that evening.

Second, these readings impose restrictions on the determiner of the head, a fact easier to perceive with count nouns:

  1. (23)
    1. a.

      degree:

      It will take us the rest of our lives to eat chocolates that they ate that evening.

    2. b.

      kind:

      It will take us the rest of our lives to find chocolates that they ate that evening.

So here we again find kinds and degrees patterning together.

A similar sort of evidence arises from nominal exclamatives such as Damn, the things you say! (Zanuttini and Portner 2003; Portner and Zanuttini 2005; Rett 2008). Castroviejo Miró and Schwager (2008) and Schwager (2009) show that, in the presence of a relative clause, these are typically ambiguous between kind and degree readings. This is particularly clear in embedded contexts:

  1. (24)

    It’s amazing the cars he owns.

    1. a.

      kind: It’s amazing what (kinds of) cars he owns.

    2. b.

      degree: It’s amazing how many cars he owns.

The clausal exclamatives in (24a) and (24b) disambiguate the two readings. Castroviejo Miró and Schwager conclude from this that degrees and kinds are two sides of the same coin, and propose an analysis in which the two are systematically related to each other.

Summary

The overall picture that emerges from these facts is clear: the connections between kinds, manners, and degrees are too systematic and too widespread to be accidental, and suggest a profound similarity among these domains. For languages such as Polish and German, the apparent homophonies are simply too unmistakeable to maintain an account based on chance lexical ambiguity. For other languages, a diverse range of other correspondences points to the same conclusion. Relative clauses and exclamatives provide independent evidence for a link between kinds and degrees.

Laying the groundwork

What exactly is a degree?

Over the years, there has been a significant amount of discussion over what exactly a degree is. Some theories of gradability don’t make direct use of degrees as distinguished objects in the model at all (Kamp 1975; Klein 1980, 1982 and others), appealing instead to different ways of delineating the extensions of predicates taken to be inherently vague. These approaches don’t provide the tools we will need. An early alternative to these that does place degrees in the model, but does not treat them as primitives, is a better starting point. This conception, pioneered by Cresswell (1976), is that degrees are equivalence classes of individuals—that is, groups of individuals that are the same with respect to some measure. The degree ‘six feet tall’, for example, consists of the plurality of individuals that are six feet tall. What we will ultimately propose will invoke similar conceptual machinery.

Cresswell’s ontology of degrees, however, has largely—but not entirely—given way to a view of degrees in which they are atomic types, either points or intervals on an abstract scale (Seuren 1973; von Stechow 1984; Kennedy 1997; Schwarzschild and Wilkinson 2002 and countless others). Although the way this is formalized varies, for current purposes most such approaches can be conceptualized as treating degrees as real numbers (or intervals thereof) associated with a scale representing a dimension of measurement. Without further elaboration, this doesn’t encode very much information in a degree. The degree ‘six feet’, for example, simply names a location on a scale of linear extent.

While this conception has proven extremely fruitful—quite possibly precisely because it is concrete and straightforward—it faces a major challenge in facts marshaled most forcefully in Moltmann (2007a, 2009). On the simple conception of degrees, it’s unclear what adjectival nominalizations should denote. For instance, if 〚Clyde’s height〛=6ft, then (25a) and (25b) should be synonymous:

  1. (25)
    1. a.

      Clyde’s height is \(\left\{ \begin{array}{l} \mbox{striking}\\ \mbox{impressive}\end{array}\right\}\).

    2. b.

      ??Six feet is \(\left\{ \begin{array}{l} \mbox{striking}\\ \mbox{impressive}\end{array}\right\}\).

So too for (26a) and (26b):

  1. (26)
    1. a.

      We were amazed at Clyde’s height.

    2. b.

      ??We were amazed at six feet.

Yet the sentences in both (25) and (26) are clearly not synonymous—indeed, the (b) sentences are actually pragmatically odd. It’s possible that the problem here is the premise that Clyde’s height refers to a degree. Perhaps it refers instead to a function from worlds to degrees, the degree analogue of an individual concept like the president.Footnote 4 The failure of substitutability in (25) and (26) would then resemble failure of substitutability of the president and Barack Obama in e.g. The president used to be white. Or perhaps, even more simply, Clyde’s height and six feet simply denote different sorts of degree (say, a point and an interval, respectively, in the spirit of Schwarzschild 2005; Andrea Beltrama and Ryan Bochnak, p.c.).

These are both appealing strategies, but they wouldn’t help with a second challenge to the standard conception of degrees. There are surprisingly many non-degree modifiers of adjectives, as in (27) and (28):

  1. (27)
    1. a.

      Clyde is \(\left\{ \begin{array}{l} \mbox{visibly happy}\\ \mbox{happy in a visible way}\\ \mbox{strangely beautiful}\\ \mbox{beautiful in a strange way}\end{array}\right\}\).

    2. b.

      The talk was \(\left\{ \begin{array}{l} \mbox{oddly unnerving}\\ \mbox{fatally flawed}\end{array}\right\}\).

    3. c.

      These examples might be misleadingly exceptional.

  1. (28)
    1. a.

      Clyde is \(\left\{ \begin{array}{l} \mbox{openly contemptuous}\\ \mbox{youthfully energetic}\\ \mbox{icily competent}\end{array}\right\}\). (based on Ernst 2011)

    2. b.

      Gaudí furniture is bulbously dynamic.

Some of these modifiers may have a degree reading (Katz 2005; Castroviejo Miró 2008; Morzycki 2008; Nouwen 2011). Visibly happy, for example, may mean ‘so happy that it’s visible’, strangely beautiful may (perhaps) mean ‘so very beautiful that it’s strange’, and so on. But that is certainly not the only interpretation of these modifiers, nor indeed the most natural one—and such readings are not available at all for many of the other cases. There has subsequently been some controversy about whether they can be taken at face value as instances of manner modification or are in some respect misleadingly exceptional (Katz 2003; Geuder 2005; Mittwoch 2005; Maienborn 2007; Katz 2008). But as Ernst (2011) demonstrates especially convincingly, the pattern is so extensive that it is difficult to set aside.Footnote 5 Degrees as normally understood don’t encode enough information to reflect this. If a degree is just a location on a scale in the way ‘six feet’ is, it’s hard to see how it can be visible, strange, beautiful, odd, misleading, uncomfortable, or fatal. So these examples suggest either that degrees are more complicated than we usually assume, or else that something other than degrees is at play.

Faced with these problems, one might attempt various enrichments of how degrees are represented. One might, for example, elaborate on Grosu and Landman’s (1998) treatment of degrees, in which they are tuples of an individual, a property, and a measure. This enriches the notion of degrees substantially, certainly enough to provide an analysis of these facts. If a property can always be retrieved from a degree, all the apparently non-degree modifiers in (27) and (28) could be given denotations on which they are actually predicates of properties retrieved from degrees. This would mirror the classical Montagovian analysis of adverbials as predicate modifiers (Montague 1970). The denotations of adjectival nominalizations and measure phrases could be distinguished essentially by type or sort, as already suggested. Perhaps measure phrases denote a sort of degree in which only a property and measure are included, but not an individual. This seems reasonable in general, although the predicate-modifier element of the analysis would seem to represent a step back from the neo-Davidsonian and typically intersective approach we now generally take toward adverbials (Parsons 1990 and many others).

It is Moltmann (2007a, 2009), however, that provides an explicit account of these facts. Her strategy is to enrich the ontology with objects—‘tropes’, also known by the similarly opaque names ‘accidents’ or ‘modes’—rich enough inherently to capture these facts. A trope is a particular instantiation of a property. Moltmann illustrates this using a red box that (she reports) happens to be in front of her. The redness of that box is a trope. Unlike redness in general, this trope involves just the particular shade of redness that her box has. But unlike even redness of that precise shade, this trope has a spaciotemporal location—in her phrase, it is located ‘just where the box is located while it is red’. If she were later to paint her box blue, that trope will then have been located in the past. And of course, no other box has its redness. As the previous sentence itself reflects, we can in fact refer to the trope with a nominalization: the redness of her box. Degrees, Moltmann argues, need to be constructed out of such tropes, and degree modification is really just a species of trope modification.

We are sympathetic to this strategy, and in some respects we will follow a similar path. We too will need a richer conception of degrees than the now-typical off-the-shelf variety. We will, however, not commit to her theory here. In part, this is a rhetorical move. Many linguists find the idea of tropes uncomfortably elusive. We sympathize with this, too, though it’s hard to know how to interpret vague unease as an objection. (What would constitute a counterargument to a vague sense of unease?) Things have a way of seeming more concrete and respectable as they become more familiar. Perhaps tropes are like this, too. They are, moreover, not an innovation of Moltmann’s, but something with an established philosophical pedigree (see Moltmann 2004 for some intellectual history and Loux 2006 for a general introduction). Nevertheless, we think that the safest strategy is to remain on the firmer ground of Davidsonian states, which are better-established and more familiar if not necessarily more clearly defined. This is a conservative take on what Bach (1989) famously called natural-language metaphysics, one that heeds Higginbotham’s (2005) admonition that ‘semantics should … be wary of embracing more in the way of metaphysics’ than absolutely necessary on linguistic grounds (see Maienborn 2005a for further discussion). That said, a reader so inclined can feel free to substitute the notion ‘trope’ for ‘state’ as necessary. Once the analysis has been presented, it will be possible in Sect. 6 to briefly step back from it and reassess these broader questions.

Degrees as kinds and kinds as degrees

To get off the ground in building an analysis, we will need a model that includes kinds, events, and states. Chierchia (1998) provides a way of thinking about kinds that is especially useful for current purposes. The kind rabbit, for example, consists of all possible rabbits—that is, of all the rabbits in every possible world. More precisely, the kind is a function from a world to a (typically plural) individual consisting of all the rabbits in that world. To be a realization of the kind rabbit is simply to be a member of the plurality of rabbits in a world. If that’s what a kind is—the plurality of all possible objects of some type—then for any atomic type in the model, there is a kind counterpart. An event kind can be constructed from any plurality of events across worlds, and likewise for state kinds.

As we have aggressively foreshadowed, we will identify manners with event-kinds (following Landman and Morzycki 2003; Landman 2006 and Gehrke 2011; see also Gehrke 2015, this volume). All possible events performed clumsily, for example, will therefore constitute an event kind, and any particular clumsy event is a realization of the event-kind clumsy. Of course, not just any collection of events across worlds corresponds to a manner. Portner (1991), for example, explicitly pursues a notion of event-kind compatible with this conception on which gerunds like eating green beans and even always eating green beans are taken to denote kinds (in the spirit of Chierchia 1984), as their compatibility with kind-level predicates like is getting popular attests. So the idea of treating events as realizing kinds accords with independent facts about the distribution of gerunds with kind-level predicates, but also shows that there is more to event-kinds than just manners. The most important consideration here, though, is that for anything we might pretheoretically construe as a manner, there will be a corresponding event kind.

For states, the situation is analogous. States could be collected across worlds in numerous ways, and only some of them will correspond to any intelligible notion. In this area, though, language seems to be pointing us in a clear direction: at least one thing state-kinds can represent is degrees.

To see how this might be, it will help to return briefly to the Cresswell (1976) concept of degrees as equivalence classes of individuals. For him, the degree ‘six feet tall’ consists of the plurality of individuals that are precisely six feet tall. Of course, the height of individuals varies across worlds, so ‘six feet tall’ could be thought of as being a function from a world to the plurality of six-foot-tall individuals in that world—in other words, a Chierchia-style kind. This essential insight is in fact behind how Castroviejo Miró and Schwager (2008) and Schwager (2009) propose to relate kinds and degrees in their analysis of nominal exclamatives.

The next step is to put a Davidsonian spin on this. Having a certain height is a state, and states, like ordinary individuals, can be arranged into equivalence classes. All states of being exactly six feet tall, for example, constitute an equivalence class. But just as the plurality of rabbits varies from one world to another, so too the plurality of states of being six feet tall varies from one world to another. We can speak of the plurality of all these states across worlds: all possible ways of being exactly six feet tall. This is a state kind—and it is also a representation of a degree. The degree ‘six feet tall’ picks out the plurality of all possible states of being precisely that tall.

This reduces the notion of ‘measuring’ a state to the question of what degree state-kind it realizes. For a tallness state to have as its measure (along the relevant dimension) ‘six feet’, it must realize the six-feet-tall state-kind. To measure a tallness state, one measures the individual of which it holds, so the appropriate consequence for individuals in such state follows. In a nutshell, then, we are simply combining in a novel way key ideas from Cresswell, Carlson, Chierchia, and Davidson. Simply by intensionalizing equivalence classes, one arrives at a Chierchia-style kind, and it is a small additional step to arrange states rather than only individuals in this way.

As with events, only certain state-kinds are degree state-kinds. One can create pluralities of possible states in many ways, and only some of them will be equivalence classes. This is linguistically important. As already noted in Sect. 3.1, not all modification of states involves degrees: one can be not only six feet tall, but also beautifully tall. A state of being tall can be beautiful or not, so there is a corresponding state-kind beautiful. But this state-kind is not an equivalence class in the relevant sense, so it is not a degree. For this reason too, it is not inherently ordered with respect to a degree state-kind like six-feet-tall.

As it turns out, for events we apparently have no special need to accord equivalence classes any special status. What seems to be grammatically important is just the notion of ‘manner’.

It’s worth pointing out that all this came essentially for free, by simply arranging the usual building blocks of the model in a slightly unusual way. So long as your model includes states, events, worlds, and pluralities thereof, it will necessarily also include state-kinds and event-kinds.

Background assumptions and notational conventions

Although at this point we have not made any particularly unorthodox assumptions about the ontology itself, we will need to talk about combinations of elements of the model in slightly unusual ways. It will therefore help to lay out the following subsets of the domain D, along with the variables we’ll use for each type:

  1. (29)
    1. a.

      D e is the non-kind individuals in D

       variables: x,y,z,…

    2. b.

      D s is the non-kind eventualities (states and events) in D

       variables: s,s′,… for states and e,e′,… for events

    3. c.

      D k is the kinds in D, including state-kinds and event-kinds

       variables: k,k′,…

    4. d.

      D o =D e D s , the non-kind objects (including individuals, states, and  events) in D

       variables: o,o′,…

We will occasionally need to refer to ‘non-kinds’. We will use the term ‘objects’, but it should be understood that we intend for this to include not just individuals but also states and events.

We will of course also need to make frequent use of the notion of realizing a kind. In Chierchia’s system, this is cashed out in terms of the fact that for every kind, there is a corresponding property satisfied by all and only its realizations. In his notation, k is the property counterpart for a kind k, while P is the kind corresponding to a property P. For example, if Bugs realizes the kind rabbit, he satisfies the corresponding property of being a rabbit. This means the operator can represent the realization relation: if Bugs is a rabbit, then rabbit(Bugs). The operator is used the same way for events and states. If e is an elegant event, then elegant(e), and if s is a state of being six feet tall, then six-feet-tall(s).

We will further assume that verbs and adjectives have eventuality arguments and that nouns do not. The latter assumption isn’t absolutely necessary to the analysis, but it will be convenient. The evidence for a state argument for nouns actually seems to be rather limited (see Maienborn 2007 for a review).

The semantics of adjectives in ordinary circumstances

What we have so far suggested is especially unusual for adjectives. To render it initially plausible, we must say something about how adjectives work in the contexts in which we’re most accustomed to finding them. We will reserve our attention here to the positive (i.e., morphologically unmarked) form and to the measure phrase construction.

First, consider a measure-phrase sentence such as (30):

  1. (30)

    Floyd is six feet tall.

Because, by hypothesis, the role of degrees will be played by a particular class of state-kinds, six feet can denote a property of states that realize the state-kind six-feet-tall:Footnote 6

  1. (31)

    six feet〛=λs .  six-feet(s)

On one standard view to which we are normally sympathetic, measure phrases involve a degree head meas that introduces the measure phrase (Svenonius and Kennedy 2006). It would be perfectly natural and unproblematic to implement this under current assumptions. But it will be easier to suppose that the measure phrase is adjoined and interpreted intersectively. To ensure a property denotation for AP, we will assume that the subject begins within the adjectival extended projection (following Bhatt and Pancheva 2004 and others, perhaps in Bhatt and Pancheva’s aP projection). Thus the adjective itself denotes a relation between an individual and a state of having a certain height:

  1. (32)

    tall〛=λxλs . tall(s,x)

Importantly, one shouldn’t read tall(s,x) to indicate that s is a state of x being tall rather than simply having a certain tallness. The computation continues straightforwardly:

  1. (33)
    1. a.

      Floyd tall〛=λs . tall(s,Floyd)

    2. b.

      [six feet] [Floyd tall]〛=λs . tall(s,Floyd)∧ six-feet(s)

The result is that Floyd is in a state of having a certain height, and this state realizes the state-kind six-feet.

On a typical degree theory, the incompatibility of a measure phrase like six feet with an adjective like ugly follows from the fact that six feet and ugly are associated with different scales. Here, the explanation is that no ugliness state can realize the six-feet kind.

Second, consider a simple positive structure as in (34):

  1. (34)

    Floyd is tall.

As before, one standard view to which we are normally sympathetic would have this interpreted with a pos degree head that would introduce the requirement of having exceeded the contextually-provided standard for tallness (von Stechow 1984; Kennedy 1997 and many others). And precisely as before, it would be perfectly natural and unproblematic to implement this under current assumptions. But again, it will be easier here to go down another path, in this instance that of Rett (2008). On the basis of evidence involving a number of degree constructions, she argues that the source of inferences about exceeding a standard is an unpronounced element, eval, whose effect is felt only in structures whose meaning would otherwise be trivial. The positive form is just such a structure. As (33) shows, an unmodified AP has a trivial denotation: it entails only that Floyd has some height. For this reason, only eval can rescue this structure from having fatally weak truth conditions. Given our assumptions, eval would invoke a contextually-provided degree state-kind, standard s,c , the standard in the context c for the scale associated with the state s. It requires that s realize a degree state-kind that exceeds this standard:

  1. (35)

    eval〛=λs . ∃kdegree-state-kinds(s)[ k(s)∧k> s standard s,c ]

This also makes use of the set of degree state-kinds for s, indicated above with degree-state-kinds(s). We will need to reframe this notion slightly later. It also appeals to the ordering associated with the scale for s. That there is such a scale follows from the way equivalence classes work: they are inherently ordered. Each equivalence class corresponds to a particular ordering. In a simple individual-based equivalence class, the set of six foot tall people isn’t ordered with respect to the set of people that weigh 150 pounds. The state-kind approach inherits this property. eval can now be interpreted intersectively with Floyd tall to yield a property of states:

  1. (36)

Once the state argument is existentially closed, this will have the expected truth conditions: Floyd is tall iff he is in a tallness state that realizes a degree state-kind above the standard.

The lesson here is that the familiar compositional machinery used in a degree analysis can be converted to a degrees-as-state-kinds system.

First step: kind anaphoric uses

A simple denotation and an intersective interpretation

In this section, we will build an analysis of kind anaphors without clausal complements (or clausal adjuncts, depending on one’s syntactic assumptions; we will henceforth assume that they are complements). We will provide denotations primarily for Polish, but they should be understood as a convenient placeholder for the broader pattern—including certainly the principal German facts, and, with suitable allowances for the suchso alternation, for English too.

As a starting point, we can begin with roughly the semantics for tak proposed in Landman and Morzycki (2003), which itself is essentially a stripped-down version of what Carlson (1977b) proposed for English such. On this analysis, tak bears an index whose value is a (typically) contextually-supplied kind, and it denotes the property of realizing that kind:Footnote 7

  1. (37)

    tak k 〛=λx .  k(x)

Providing the kind as an index on the anaphor is a natural move, but it will prove advantageous to view it in a slightly different way. In their non-anaphoric uses, tak, such, and their counterparts operate over a kind that is supplied another way: by its complement. To reflect this external dependency, we will assign the index its own branch (i.e., treat it as a null anaphor) so that tak can take as its argument.Footnote 8 Our tak will also need to apply to objects in general (individuals or eventualities). The result:

  1. (38)

    tak〛=λkλo .  k(o)

For the moment, this is all that is required.

The syntax undergirding this will be fairly straightforward. Previous analyses have treated such as either a complex AP (Carlson 1977b; Siegel 1994; Landman 2006) or as essentially a complex degree expression (Bresnan 1973). Either path would be compatible with our broader agenda, but treating it as a degree head has two virtues to recommend it. The first is that is a conveniently straightforward structure. The second is substantive. In its adjective-modifying use, tak (and German so) seems to be in a position normally occupied by degree morphemes. In its other uses, its counterparts are less clear.Footnote 9 There are two mutually incompatible widely-used structures for the extended AP: a newer one in which DegP is a functional projection above A (Abney 1987; Corver 1990; Grimshaw 1991; Kennedy 1997) and an older one in which it is within the specifier of AP (Chomsky 1965; Bresnan 1973; Heim 2000; Bhatt and Pancheva 2004). If tak is to take a complement, as our denotation assumes, it is natural to adopt the older view, because the newer view requires degree heads to have AP as their complement.Footnote 10

The result is (39), a structure in which the DegP is interpreted intersectively (agreement morphology is omitted):

  1. (39)

We assume a rule of intersective interpretation of the same form as Heim and Kratzer’s (1998) Predicate Modification, except that it is generalized cross-categorially in the obvious way to combine any property-denoting expressions.

The intersective interpretation is potentially controversial. Carlson’s semantics for such added a presupposition that the antecedent kind must be a subkind of the kind denoted by the such-modified NP. This was intended to account for the oddness of, for example, introducing the kind animals into the discourse and referring back to it with such mammals. If we were to implement this presupposition, it would preclude an intersective interpretation because such and tak would need access to the NP denotation. It is not clear, however, that there is in fact such a presupposition. Landman (2006, p. 50) provides examples such as Long-haired dogs can be difficult to brush, and such cats are even worse. The oddness of at least some of Carlson’s original examples might be attributed to pragmatic considerations—in these examples, such mammals would have precisely the same denotation as mammals and should be dispreferred on those grounds alone. Nevertheless, nothing we will propose will hinge on an intersective denotation.

Superficially, in extending this to the other uses of tak, it would seem to be smooth sailing from here. The semantics provided above is cross-categorial, and the combinatorics works just as it should. In both the VP and AP uses, tak should be able to combine with a property of eventualities straightforwardly:

  1. (40)
  1. (41)

Sadly, things aren’t so simple.

The problem of missing readings

As already noted in Sect. 2, there is a systematic correspondence across languages noted by Haspelmath and Buchholz (1998) in which the same morphemes are used for equatives (constructions expressing similarity in degree) and similatives (constructions expressing similarity in manner). On the approach we’re pursuing, this is what we would expect, since these would be, respectively, simply kinds of states and events.

There is, however, a problem: there seems to be a gap in what kinds may be constructed for events and states. If one can construct degrees out of states in the way we have suggested, it ought to be possible to construct degrees out of events in the same way. Just as one can order states of tallness according to height, one can order events of running according to distance or duration. So there should be event-kinds such as run-six-miles that can serve as degrees. Kind modifiers of events, including similatives, should therefore be able to get degree readings as well. Yet they don’t seem to. Rett (2011) notes that it seems to be impossible for a similative to have a reading where a degree is equated across events:

  1. (42)
    1. a.

      Floyd ran \(\left\{ \begin{array}{l} \mbox{six miles}\\ \mbox{for two hours}\end{array}\right\}\), and Clyde ran as Floyd did.

    2. b.

      Floyd cooled his coffee 5 degrees, and Clyde cooled his coffee as Floyd did.

In both of these cases, only a manner reading is possible. This is especially notable for (42b) (which closely parallels her examples) because cool is deadjectival. The problem, then, is this: why is it that an event-kind can be constructed for a manner, but that event-kinds for measure of change, temporal intervals, or spatial intervals seem to be inaccessible to kind modifiers?

Berit Gehrke (p.c.) points out that (42a) might be explainable in terms of the fact that event-kinds don’t have spatiotemporal locations. Indeed, it might be possible to tie this fact to distinct levels in the extended verbal projection (Gehrke 2015, this volume). This would be more elegant than the alternative we will be led to below. Nevertheless, we don’t currently see how we could have state-kinds that represent heights like ‘six feet’ without also admitting event-kinds that represent distances like ‘six miles’. But such an explanation would be natural for e.g. Floyd ran in Boston, and Clyde ran as Floyd did, where the similative can’t indicate that Clyde ran in Boston.Footnote 11

This problem has a mirror-image counterpart. If adjectives can support manner modifiers that are predicates of states as suggested in Sect. 3.1, one might expect that these modifiers might correspond to kinds as well. For example, if there are states of being wounded, there are states of being fatally wounded. The set of these states across worlds constitute the state-kind fatally-wounded. So we should expect kind anaphors that attach low to be interpretable as manner anaphors. But this too is impossible:

  1. (43)
    1. a.

      Floyd was fatally wounded, and Clyde was as wounded as Floyd.

    2. b.

      Floyd was contemptuously rude, and Clyde was as rude as Floyd.

Taking the two problems together, what is required is a means to prevent degree readings in eventive contexts and to prevent manner readings in stative contexts.

One might imagine a variety of ways of dealing with this situation by examining more closely the compositional machinery behind these structures. Perhaps what is crucial is how kind modifiers interact with degree heads, for example (this is the direction pursued in earlier incarnations of this work; Morzycki 2011). This still strikes us as a potentially productive analytical avenue, but it is hard to see how it would ensure that only degree readings are possible in one position and only non-degree readings in another. Another approach—an alternative one or a complementary one—would be to treat the unavailability of degree readings in some positions as a consequence of morphological blocking. Degree readings might be unavailable under some circumstances precisely because they are available (unambiguously) under others. For all their appeal, however, in the end such approaches seem to miss a fundamental insight: that degrees simply have some special status with respect to states, and that manners have this special status with respect to events.

Distinguished properties

We don’t have a satisfying answer to why this might be, but it is possible to arrive at a tentative way of thinking about it. The idea that degree state-kinds have a special status with respect to states seems relatively natural. In the case of tallness states, for example, kinds constructed out of states ordered by height seem to have a special status relative to kinds constructed out of different ways of manifesting tallness (beautifully, disconcertingly, etc.). There is a sense that, in the case of states associated with gradable predicates, degrees are a central part of what states are for. The principal reason we talk about such states is to compare them in a scalar fashion to others, or to a standard. Plausibly, this is the case conceptually. But manifestly, it is the case linguistically.

The idea that manner event-kinds have a special status with respect to events may not have the same a-priori naturalness. Nevertheless, it seems reasonable to suppose that a core part of what it is to be an event is to be realized in a certain manner. To be sure, for some events, we care a great deal about their temporal extent, and for others, about their spacial extent. But for virtually any event, we care about how it took place. We don’t talk about events chiefly to measure them. We talk about them chiefly to characterize or explain them. Again, this may be plausible conceptually—or it may not. But again, whatever is the case conceptually, it seems to be the case linguistically.

We will therefore talk about the distinguished properties of an eventuality, which for states are properties associated with degree and which for events are properties associated with manner of realization. This is of course not an explanation of anything. It is simply a way of representing and quarantining the problem, pending a deeper explanation. We could represent it with a relation dist:

  1. (44)

    dist(o,P) is true iff P is among the distinguished properties of o

This amounts to saying that if o is state, dist(o,P) iff P is a degree-related property, and that if o is an event, dist(o,P) iff P is a manner-related property. For individuals, the situation is less clear. So far as we can tell, no aspect of an individual has a distinguished status in the same sense. So if o is an individual, dist(o,P) is true for any P.

What is special about kind modifiers, then, is that they are sensitive to the distinguished properties of an object. This can be implemented as a presupposition:

  1. (45)

    tak〛=λkλo:dist(o, k) .  k(o)

This requires that the property counterpart of the kind associated with the modifier be among the distinguished properties of the modified object.

Of course, for modifiers that do not rely exclusively on distinguished properties, this presupposition is simply absent. The denotations of most manner adverbs will simply lack this requirement, which in turn allows them to achieve manner readings as AP modifiers.

Compositionally, this presupposition changes little. The VP- and AP-modifying cases will, as before, be interpreted intersectively, with a minor change in the resulting denotation:

  1. (46)
    1. a.
    2. b.

For the sake of simplicity, we will omit the distinguished-property presupposition from now on. This will have the rhetorically convenient but intellectually unsavory effect of obscuring that this element is both crucial and mysterious.

Complement clauses and abstracting over kinds

A preview of the big picture, and an initial step

So far, only one element of the compositional system has been put into place: the basic anaphoric uses of kind modifiers. Much of what needs to be explained, however, concerns the complement clauses associated with kind modifiers. These are especially important because in the degree case, they correspond to a familiar degree construction: the ordinary equative. In the adverbial case, there is a somewhat more surprising but nevertheless important connection to free relatives. In the adnominal case, the construction is sometimes characterized as a variety of relative clause (Carlson 1977b). All of these classes of constructions are, on their own terms, relatively well-studied—but not from a unified perspective. So there is a non-trivial compositional challenge in bringing these together.

The path we will take will involve, as might be expected, a syntax that involves wh-movement and lambda abstraction, in our case over a kind-denoting trace. The result is essentially a relative clause. Again, this much is relatively familiar. One issue that needs to be addressed in unifying the constructions is the sense that in the adnominal and adverbial uses, an existential claim is being made about a kind an individual or event realizes—but in the equative use, a claim is being made about a particular height. We will suggest that a key to providing a consistent, independently-motivated semantics for these clauses lies in the analysis of free relatives of Caponigro (2003, 2004), which relies on a uniform semantics and a principled distribution of independently motivated type shifts of a standard variety (Partee 1986). For manner and degree uses, this follows broadly in the footsteps of Rett (2011), who focuses on specifically that connection and provides an explicit account of it, to our knowledge the only existing one. She too takes free relatives as an important analogue.

As before, we will use Polish as our paradigm case, with the assumption that other languages will work similarly. The first step will again be the adnominal use:

  1. (47)
    figurek

One immediate complication is that in this instance, the embedded clause is elided, just as it would normally be in English (Carlson 1977b; Landman 2006).

Following Citko (2000), we treat jak as a wh-element (as our glosses have been presupposing). The similarity between tak and jak is, of course, hard to miss. We will assign it a semantics identical to that of tak:

  1. (48)

    〚 jak〛=λkλx .  k(x)

This will make possible an underlying structure in which jak occupies the same positions as tak, and thereby a relatively simple structure for the embedded clause. In this instance, it would be as in (49):

  1. (49)
    figurel

Chiefly for the sake of simplicity, we will leave jak in situ at LF. The kind variable k is obligatorily abstracted over at the clause level:Footnote 12

  1. (50)

This structure echoes what Landman (2006) proposes for English as complements to such, for which she adduces independent evidence from antecedent-contained deletion. The clause will therefore denote a property of kinds. Superficially, this would seem to be a problem. It is, after all, the complement to tak, which expects an individual, and a type clash should result.

Interlude: Caponigro on free relatives and type shifts

The treatment of the embedded clause proposed here in all relevant respects resembles how Caponigro (2003, 2004) treats free relatives. On its face, this is a good result. Free relatives are, after all, wh-constructions which often find themselves in prototypical argument positions. This is precisely what the clausal complements to kind modifiers do. The connection is in fact deeper: a jak clause can be itself a free relative.

We will follow Caponigro’s analysis one step further. Free relatives, for him, systematically denote properties. They often find themselves in contexts in which a property-denotation is inappropriate, however. The type clash is avoided, Caponigro proposes, by the application of one of a generally available family of type shifts in the style first envisaged by Partee (1986).

The particular case that is most relevant here involves adjoined free relatives, which Caponigro calls ‘PP-like’, such as (51):

  1. (51)

    Captain Kirk went to where no man had gone to before.

One respect in which they are PP-like is that Caponigro analyzes them as PPs—or rather, as embedded in PPs, in this case headed by a null preposition to. In (51), the situation this creates is one in which the preposition expects an individual-denoting argument and receives in its place a property-denoting free relative.

The preferred type shift in his system is Iota, which shifts from properties to individuals. His definition is the standard one, which we have modified here only in generalizing it across types:

  1. (52)

    Iota Shift (from 〈τ,t〉 to τ, where τ is any atomic type):

    shift P to ιx τ [P(x)]

This type shift mirrors the meaning of the (on a Fregean interpretation). It applies to a property and shifts it to the unique individual that satisfies that property. In (51), however, this is of no use—there is no unique location such that no one has gone there before.Footnote 13 So this would take us out of the frying pan and into the fire, from a type clash to a failure of presupposition.

What does rescue this structure is another type shift, which is, by hypothesis, normally dispreferred: the Existential Closure Shift, which shifts from properties to generalized quantifiers. Again, we have modified it only to generalize it across types:

  1. (53)

    Existential Closure Shift (from 〈τ,t〉 to 〈τt,t〉):

    shift P to λQ τ,t . ∃x τ [P(x)∧Q(x)]

This shift will do Captain Kirk some good. The result is that the free relative denotes a generalized quantifier, which will in the normal fashion undergo Quantifier Raising out of the clause and leaves behind an individual-denoting trace. Precisely the same strategy will serve in the jak clause.

Adnominal uses continued

Given the Caponigro semantics for free relatives, the type clash we encountered in the complement of a kind modifier is independently expected—and we should expect that it could be avoided by the same means. As before, the Iota Shift can’t apply, because there is no single kind that any individual realizes. So, as before, the Existential Shift is invoked as a fallback measure. The result is an underlying structure like (54) (in which we leave the copula jest uninterpreted and skip irrelevant levels of structure):

  1. (54)

After the shifted CP QRs to adjoin to the clause and leaves behind a kind-denoting trace, the resulting structure is:

  1. (55)
    figurem

The computation:

  1. (56)
    1. a.
    2. b.
    3. c.

What this requires is that a kind that Floyd realizes also be realized by a dog that barked. This seems an appropriate rendering of the truth conditions.Footnote 14

Manner uses

The construction of primary interest here is the degree use—the equative—but before undertaking that, we should consider how the manner use will work:

  1. (57)
    figuren

The jak clause here is of precisely the sort that Caponigro examined under the rubric of PP-like free relatives, and the assumptions already in place will suffice for it. As before, because it occurs as the complement to tak, the Existential Type Shift applies to avoid a type clash, rendering the jak clause a generalized quantifier. Once it QRs, the resulting structure is as in (58):

  1. (58)
    figureo

The role of Caponigro’s null preposition is here played overtly by tak. The denotation of the type-shifted clause will be similar to the adnominal case. One difference is that, since an event argument comes into play, it has to be quantified off in the usual way. (Nothing hinges here on how this is implemented.) Thus the denotation of the higher VP is as in (59a) and that of the whole clause is as in (59b), which is then shifted into (59c):

  1. (59)
    1. a.
    2. b.
    3. c.

The matrix clause, meanwhile, will involve a similar intersective interpretation of the VP, yielding (60a), and combining the two clauses yields (60b):

  1. (60)
    1. a.
    2. b.

Thus the sentence entails that there is a manner event-kind which both Clyde’s singing and Floyd’s singing instantiate.Footnote 15

Degree uses: the equative

The final piece of this part of the puzzle is the equative use. No further assumptions are necessary at this point, but there is an important twist that follows independently from Caponigro’s approach.

The construction at issue is exemplified, once again, in (61):

  1. (61)
    figurep

Consistent with our earlier assumptions, we will for convenience interpret Clyde in a low, AP-internal subject position, so the structure of the embedded clause will be as in (62):

  1. (62)

    λk jest [AP [DegP jak k] Clyde wysoki]

Also as before, the DegP will be interpreted intersectively, yielding (63a) as the AP denotation and, after the state argument is existentially closed, (63b) as the denotation of the clause:

  1. (63)
    1. a.
    2. b.

This denotes a property of degree state-kinds that are instantiated by a state of Clyde’s tallness. Translating this into more traditional terms, it is a property of degrees of Clyde’s tallness.

This clause is, of course, the complement to tak, which needs a kind as an argument. This is the point at which a type shift is triggered. Unlike in the previous cases, though, the type shift will be Iota, not Existential Closure. Recall that Caponigro’s system assumes that Iota is the default, preferred type shift, and that Existential Closure is resorted to only when Iota would be undefined. In the individual and manner cases, Iota would indeed fail for the reasons already discussed: there is no unique kind or manner that an individual or event instantiates. But for degree state-kinds, Iota would face no such difficulty. There is, in fact, precisely one degree state-kind that a state instantiates: the one that corresponds to the equivalence class of which it is a member.

If the Iota type shift were to be applied to the clausal denotation in (63), the result would be (64):

  1. (64)

This is simply a definite description of the degree state-kind that Clyde’s tallness realizes. It follows in an established tradition of interpreting comparative—and therefore by extension also equative—clauses as definite descriptions that goes back to Russell (1905). Because degrees here are constructed from equivalence classes, the notion of maximality is essentially built-in.

The underlying structure, then, wouldn’t require QR of the embedded clause. It could be interpreted in situ, in the argument position of tak:

  1. (65)

The tak-headed DegP, then, would have as its denotation (66):

  1. (66)

This is more complicated notationally than it is conceptually. It involves shifting the definite description of a kind to its property counterpart. What the ‘ ιk[…](o)’ expression means is that o instantiates the maximal degree state-kind that Clyde’s tallness also instantiates. The situation, if not the formula, becomes clearer at the next step, at which this whole expression is interpreted intersectively with the core AP Floyd wysoki:

  1. (67)
    1. a.

      Floyd wysoki〛=λs′ . tall(s′,Floyd)

    2. b.

This is a property of a state, s′, of Floyd’s tallness. The first conjunct requires that s′ be a realization of the degree state-kind that Clyde’s tallness realizes. So overall, this requires that Floyd’s tallness state realize the same degree state-kind as Clyde’s tallness state.

In a nutshell, then, the interaction of the proposed semantics for tak/jak, our standing assumptions about state-kinds, and Caponigro’s independently-motivated semantics for free relatives—including his assumptions about type-shifts—added up to a semantics for the equative that assigns to it the standard truth conditions.

Comparatives

Given that we are providing a new semantics for degrees, it’s incumbent on us to provide an indication of how other degree constructions work. We have already discussed in Sect. 3.4 the positive (unmarked) form of the adjective and the measure phrase construction, and in the preceding section the equative. There are, of course, many degree constructions, and it would be far beyond the scope of this paper to attempt to reproduce the whole literature in degree semantics in terms of degree state-kinds. But minimally, something should be said about the semantics of the comparative.

We should emphasize, though, that there is a fundamental difference between the comparative and equative that is relevant here: the equative is, as we have shown, a special case of a broader cross-categorial phenomenon: the complements of kind-modifiers. In the comparative, there are no similar mysterious homophonies to explain. Partly because of this, there is no longer any reason to use the Polish data, so we will return to English.

We will assume comparatives parallel equatives structurally: the subject starts low in the AP, and the DegP occupies a specifier position. Standardly, analyses that adopt this syntax assume that the DegP must QR out of its base position. We will leave the DegP in situ for simplicity. The comparative in (68a) will have the structure in (68b):

  1. (68)
    1. a.

      Floyd is taller than Clyde.

    2. b.

      [DegP -er [CP than Clyde is tall]] [Floyd tall]

The basic semantics of the comparative clause itself will be identical to that of the equative. The clause on its own denotes a property of state-kinds, as in (69a), but in order to combine with -er it must undergo the Iota type shift, as in (69b):

  1. (69)
    1. a.

      than Clyde is tall〛=λk . ∃s[ k(s)∧tall(s,Clyde)]

    2. b.

      shift than Clyde is tall〛=ιk[∃s[ k(s)∧tall(s,Clyde)]]

Again, it is Iota that applies rather than the Existential type shift because it is systematically preferred whenever it’s defined. In this case, the result is a definite description of a maximal degree.

The role of the comparative morpheme is to apply to this kind and yield a property of states. In (70), k will wind up being the degree state-kind associated with the than-clause and k′ the degree state-kind associated with the matrix:

  1. (70)

    -er〛=λkλs′ . ∃k′[ k′(s′)∧k′> s k]

The next steps are at least notationally (if not conceptually) complicated, though in a moment the light will hopefully be visible through the trees:

  1. (71)

This is interpreted intersectively with the A′ denotation in (72a), to yield (72b):

  1. (72)
    1. a.

      Floyd tall〛=λs′ . tall(s′,Floyd)

    2. b.

The ‘ιk[…]’ expression picks out the degree state-kind of Clyde’s height. The whole thing will be true of a state of Floyd’s tallness (s′) iff the degree state-kind that his tallness realizes (k′) is greater than the degree state-kind of Clyde’s height.

The most important aspect of this may be that, in a certain precise sense, it isn’t interesting. It mostly echoes a standard degree-semantic approach to comparatives on which they existentially quantify over a degree associated with the matrix clause, which is then required to exceed a degree associated with the than-clause. So the more highly-articulated view of degrees advocated here is compatible with more familiar approaches to degree constructions.

A brief note about ontological considerations

So what have these compositional concerns told us about the ontological assumptions necessary to undergird them? Well, minimally, they have borne out the fundamental hypothesis that degrees can be construed as kinds of states.

We’ve simply presupposed that just as the model includes Davidsonian events, it should include states. Of course, one could deny that states belong in the model at all. The linguistic evidence, though, demonstrates that if they are to be evicted from the model, they will need to be replaced with some analogue. Simply eliminating them entirely would entail arriving at an entirely different explanation of all the parallels we’ve noted and another theory of the compositional machinery we’ve put into place.

Once we accept that something like this belongs in the model, the natural question to ask, though, is what ‘states’ actually means in this context. One choice to be made is between two distinct notions of states, which Maienborn (2005b, 2007) argues has linguistic relevance. Alongside the familiar Davidsonian states, there are what she calls Kimian states (Kim 1976), which are more impoverished. Kimian states are, in Maienborn’s phrase, simply ‘temporally bound property exemplifications’. They consist only of a property, something of which it holds, and a time. Unlike Davidsonian states, they have no location in space, can’t be directly perceived, and can’t be realized in different ways. Various constructions are, she argues, sensitive to the distinction. A state of being tall, for example, would be a Kimian state because of the oddness of # I saw Floyd be tall. If we accept that the distinction is linguistically relevant in the way Maienborn suggests, we might be faced with a difficulty. Kimian states would seem to be too impoverished to suffice for our purposes. Certainly, they aren’t easy to square with the well-formedness of examples such as Parsons’ (1990) coarsely grooved or Mittwoch’s (2005) in the country illegally, which Maienborn considers exceptional. So, to the extent that the point of Kimian states is to provide a pared-down version of their Davidsonian counterparts, it runs counter to our aims here.Footnote 16

On the other hand, one might go in the opposite direction—the one suggested by Moltmann (2004, 2009, 2007b)—and take our talk of states to actually refer to tropes. So far as we can see, everything we have said is at least compatible with such a view. Moltmann explicitly uses tropes to model degrees, so at least that much is to be expected. She doesn’t employ kinds of tropes in her degree semantics, but she does endorse the idea of trope-kinds in Moltmann (2004), where she takes them to be the referents of certain abstract mass nouns like wisdom. Moreover, manner-like modifiers of AP form part of her original motivation for appealing to tropes. The crucial question, then, is whether the facts we examined provide further evidence for a trope-based account, or are merely broadly consistent with it. Moltmann (2009) characterizes states as ‘nothing but the holding of a property of an individual’, with no possibility of being manifested in different ways. This characterization of Davidsonian states rather resembles how Maienborn characterizes Kimian states. Maienborn explicitly proposes that Davidsonian states can vary precisely in how they are manifested. As long as tropes and Davidsonian states à la Maienborn both provide us with a representation rich enough to support this kind of variation, it’s not clear how our facts could bear on the choice.

The possibly-metaphysical puzzle we are most vexed by, however, is the one we’ve quarantined off with the notion of ‘distinguished properties’ of an eventuality. Is there a way of constructing objects in the ontology that would deliver, in an insightful way, the result that states are closely associated with degrees and events to manners? It doesn’t seem out of the question. It seems to us, however, that this question may constitute grounds for soliciting the assistance not just of philosophers, but also cognitive scientists of other descriptions. Some of the answers—or at least some relevant observations—may lie in the psychological representation of eventualities.

One ontological point which we have not resolved is whether degree state-kinds are the only representation of degree in the model, as we have proposed, or whether the model also includes degrees of the more traditional sort in addition. On this view, degree state-kinds would simply be an alternative means of achieving readings that are normally attained via degrees of the more traditional sort. Certainly, it is a more conservative hypothesis, but it is also in light of that a less interesting one. Such a dual analysis may provide a way of coping with phenomena such as differential comparatives (one inch taller) and factor phrases (three times taller), where traditional degrees excel. But it would raise the question of why language might have these two systems existing side-by-side, different means to the essentially same end.

Further directions

Manner modification of adjectives

There are many additional research directions that arise naturally on the view of degrees we have advocated. Before concluding, we will briefly note a few of them.

One difficulty with normal conceptions of degrees is what to do with the manner modifiers of adjectives noted in Sect. 3.1:Footnote 17

  1. (73)
    1. a.

      Floyd is strangely tall.

    2. b.

      ??Floyd is tall to a strange degree.

    3. c.

      Floyd is tall in a strange way.

Our basic assumption is that these modifiers are of type 〈s,t〉, properties of states. They can be thought of as modifying the adjective intersectively:

  1. (74)
    1. a.

      strangely〛=λs .  strange(s)

    2. b.

      Floyd is strangely tall〛=∃s[ strange(s)∧tall(Floyd)(s)]

This makes possible a simple syntax is in line with our assumptions about the syntax of such and as. These modifiers can be placed in the specifier position of an AP, as in (75):

  1. (75)

Two pieces of evidence suggest that this syntax is on the right track.

First, manner modifiers of adjectives appear to be in complementary distribution with degree morphology, including measure phrases, degree adverbs such as completely, and comparative morphology:

  1. (76)
    1. a.

      *Floyd is strangely six feet tall.

    2. b.

      *Floyd is strangely very/really tall.

    3. c.

      ??Floyd is strangely taller than Clyde.

Given that DegP is also inserted into the specifier of AP, this complementary relationship makes sense, as they are competing for the same syntactic slot.

Second, manner adverbs modifying adjectives must appear on the left. When appearing on the right, they get a distinct interpretation on which they express a propositional attitude of the speaker:

  1. (77)
    1. a.

      Floyd is strangely tall.

    2. b.

      Floyd is tall, strangely. (no manner interpretation available)

This pattern also accords with the assumption that these adverbs are inserted in the specifier of AP.

What this analysis doesn’t quite provide in the general case is an account of why such modifiers license entailments to the positive form:

  1. (78)

    Floyd is strangely tall.

    entails: Floyd is tall.

To say that Floyd has a state of having some height, and this state is strange, may reflect on the strangeness of Floyd’s height, but it doesn’t on its own ensure that it is above the contextual standard for tallness. The natural move would be to insert the eval operator here, but in this case, unlike in the simple positive construction, this couldn’t be driven by a need to avoid fatally weak truth conditions.

Nominal degree readings

Another point we have not addressed explicitly is whether this sheds light on the connection between degrees and kinds in the nominal domain. These connections emerged in Sect. 2.5 with relative clauses and with nominal exclamatives. They also emerge in degree readings of such:

  1. (79)

    Floyd is such an idiot.

Constantinescu (2011) provides an extensive discussion of examples like (79), and argues that they can be reduced to a special case of the kind interpretation. If that’s right, not much more needs to be said. But on the current proposal, in some sense the choice need not be made: a kind interpretation and a degree interpretation become inherently rather similar. If, however, one were inclined to grammaticalize the distinction between the two readings more deeply, an interesting consequence might follow. If degrees are a particular variety of state-kind, achieving a degree reading in (79) might require access to states of idiocy. We assumed that nouns have no state argument. Perhaps (79) is an indication that this is misguided, and that somewhere inside the extended NP there is a level at which there are properties of states of idiocy to be modified.

As for the relative clause and nominal exclamative cases, it’s a little unclear whether the proposal has changed the picture. Grosu and Landman (1998) located the connection between amount and kind relatives primarily in the syntax-semantics of the relative clause itself. This is certainly compatible with what we have proposed, but largely independent of it. The degree-kind ambiguity observed in It’s amazing the cars he owns by Castroviejo Miró and Schwager (2008) may be similar. On the one hand, diminishing the conceptual boundary between kinds and degrees may advance their proposal that the nominal in these cases is essentially underspecified with respect to the distinction. On the other, the crucial role played by the relative clause in such examples and the fact that the degree readings necessarily involve amounts (# It’s amazing the idiot he is) suggest maintaining a connection to the relative clause effects.

The so … that construction

As noted in Sect. 2, so and such systematically license that complements:

  1. (80)
    1. a.

      such a tall man that he might not fit in the car

    2. b.

      so tall a man that he might not fit in the car

    3. c.

      abuse him so much that he might not get in the car

Similar data can be found in other languages. Neither the readings involved here nor the syntax underlying them is obviously perfectly parallel. Nevertheless, the pattern seems important, and the present analysis might allow one to make some headway. It would not be easy going, however. The standard assumption about at least the adjectival instances of this construction is that are essentially modal (Meier 2003). This crucial element doesn’t follow straightforwardly from our proposal.

Concluding remarks

We argued that a variety of constructions in a variety of languages point to a fundamental connection between kinds, manners, and degrees, and articulated a way of thinking about degrees as kinds of states (and following previous work, manners as kinds of events). This enabled us to provide a cross-categorial semantics for both for kind modifiers and for their clausal complements, which involve abstraction over degree state-kinds. On this view, equatives emerged as a special case of a cross-categorial phenomenon, one that parallels what have previously been analyzed as kind relatives or free relatives. The analysis we proposed builds on an independently-motivated semantics for free-relatives (Caponigro 2003, 2004). Taking this overall perspective may place several difficult empirical puzzles in a new light. It also converges on a common conclusion with Moltmann (2009) and others, who arrived at it on mostly independent grounds: that the relatively simple ontology of degrees typically assumed should be enriched.

Our focus has been chiefly on the compositional semantics of several specific constructions, and we have tried to be relatively conservative in our metaphysical assumptions. In one respect, we have expanded the ontology: the notion of degree state-kinds is novel. But in another, we have actually streamlined it: if we are on the right track, degrees can actually be derived from an independently-expected interaction of well-established elements in the model. If states and events exist, and if kinds can be constructed in the Chierchia style, it would actually require an independent, extrinsic, and mysterious stipulation to avoid the conclusion that state-kinds and event-kinds should exist as well. Certainly, if one accepts event-kinds, one should accept state-kinds, too. Given all the independent evidence for taking degrees to be primitives and the years of progress in degree semantics that has been achieved based on that idea, it would of course be unwise to cast this idea overboard too readily. But, just as linguistic facts led us all to the usual contemporary conception of degrees, it is linguistic facts—and a robust, crosslinguistic set of them, manifested in a variety of ways—that has lead us away from it here. Over the past several decades, a number of different conceptions of degrees have been proposed, and viewed from that perspective, where we have wound up is not particularly radical. Indeed, it echoes an old and influential idea (Cresswell 1976).

Whatever the merits of these analytical proposals, though, the best-grounded theoretical point here isn’t necessarily about the ontology of degrees. It is, rather, that the correspondences among expressions involving kind, manner, and degree are systematic and deep—and that they cry out for explanation.

Notes

  1. 1.

    Jak also has other uses. Citko (2000) points out that in embedded contexts it has a use as a temporal adverbial and as the antecedent of a conditional, though she argues that these involve a different form of the word that is a wh-complementizer rather than the phrasal wh-expression that gives rise to the readings in (2).

  2. 2.

    Indeed, German solch ‘such’ is in fact historically derived from so and a morpheme similar to like, which suggests construing the like morpheme as a means of deriving adjectival solch from adverbial so (Berit Gehrke, p.c.).

  3. 3.

    Thanks to an anonymous reviewer for pointing out this important connection, which we embarrassingly overlooked in earlier versions of this paper.

  4. 4.

    Thanks to an anonymous reviewer for this suggestion.

  5. 5.

    For some such cases, one might attempt a propositional paraphrase (e.g., for (27a), ‘it’s visible that Clyde is happy’), but even this strategy is unavailable for (28). For a few, one might imagine an intersective property-of-individuals interpretation (e.g., for (28b), ‘Gaudí furniture is bulbous and dynamic’), but this is not possible for most of (27) or openly contemptuous.

  6. 6.

    This yields an exactly-reading for the measure phrase. The at-least reading could be obtained by a denotation closer to what’s suggested for the eval morpheme in (35).

  7. 7.

    We have adapted the denotation to accord with the Chierchia-style conception of kinds and with our other notational conventions.

  8. 8.

    This is precisely what Landman (2006) proposes for like, and she considers such a denotation for such for the same reason.

  9. 9.

    On the other hand, tak is, in its adnominal use, obligatorily inflected, which suggests an adjectival syntax.

  10. 10.

    Again, however, both options are in principle available. On the newer view, one could place the tak phrase in the specifier of DegP, the position occupied by measure phrases.

  11. 11.

    A closely related strategy might be to appeal to the distinction between ordinary and well-established kinds, which Gehrke shows is relevant to the modification possibilities of German adjectival passives. Running any given distance is not a well-established kind of event, but perhaps being any given height is in fact a well-established kind of state—all heights are well-established kinds of tallness, but not all distances are well-established kinds of running.

  12. 12.

    Again, the precise implementation of this is not crucial. Other possibilities include a default binding mechanism or operator movement as in English that relatives in the style of Heim and Kratzer (1998). The most appealing alternative, though, is to suppose that jak actually spells out this relativizing operator. This would entail assuming it occurs as the complement of tak, denotes a function, and therefore must wh-move and leave behind a kind-denoting trace. Because of the identity-function denotation, it would have no effect in its displaced position apart from triggering lambda abstraction.

  13. 13.

    A reviewer points out that this isn’t actually so obvious. We happily refer to discontinuous spatial locations (the territory of the US), so why can’t there be a unique but discontinuous location where no one has gone before? It’s not obvious. But on such an analysis, one might expect where no man has gone before to introduce a discourse referent for this discontinuous region. Yet it would be odd to follow (51) with It is a vast place or What is its area?

  14. 14.

    This interpretation actually predicts potential scope interactions. The judgments rapidly get precarious, but in a sentence such as Every linguist thought she saw a dog such as Floyd, every linguist should scope over the existential contributed by the as-phrase, meaning that the sentence should be true if some linguists think they saw a terrier, others think they saw a male dog, others still a 3-year-old dog, and so on, so long as Floyd actually has all these properties. This seems plausible. Thanks to an audience at Ohio State for discussion on this point.

  15. 15.

    A reviewer points out that it’s not actually obvious that an existential interpretation is appropriate here. Perhaps Floyd and Clyde count as having sung the same way only if their singing was identical in all relevant manners? Indeed, we use a definite description in characterizing the way he sang (not # a way he sang). It’s a delicate question because the individuation criteria for manners are so unclear and the notion of relevance so elastic. But it seems reasonable to say e.g. Floyd died as Clyde did: poor and alone, even if one was stabbed to death and the other died of dysentery. The definiteness requirement in the way he sang may stem from the same slightly mysterious source as in the wrong answer (not # a wrong answer, even though there are almost invariably many; Schwarz 2006).

  16. 16.

    One avenue left unexplored here is the idea that different levels of structure above AP might be properties of different varieties of states.

  17. 17.

    It’s worth noting that (73a) doesn’t naturally get the speaker-oriented reading paraphrasable as Strangely, Floyd is tall.

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Acknowledgements

This paper grows out of work conducted by one of the authors in collaboration with Meredith Landman (Landman and Morzycki 2003). Thanks also to Adam Gobeski, Ai Matsui, Alex Clarke, Ania Łubowicz, Anne-Michelle Tessier, Berit Gehrke, Carlos de Cuba, Chris O’Brien, Elena Castroviejo Miró, Erik Wedin, Gabriel Roisenberg Rodrigues, Geraldine Legendre, Greg Johnson, Jan Anderssen, Judith Tonhauser, Kay Ann Schlang, Kyle Rawlins, Leila Rotschy, Louise McNally, Olga Eremina, Paul Portner, Paul Smolensky, Peter Culicover, Phil Pellino, Tom Ernst, Vesela Simeonova, and audiences at The Ohio State University, Johns Hopkins University, the University of Calgary, and the 2011 Workshop on Modification With and Without Modifiers in Madrid; and to Andrea Beltrama, Ryan Bochnak, and an anonymous NLLT reviewer for very helpful written comments.

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Anderson, C., Morzycki, M. Degrees as kinds. Nat Lang Linguist Theory 33, 791–828 (2015). https://doi.org/10.1007/s11049-015-9290-z

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Keywords

  • Degrees
  • Kinds
  • Manners
  • Equatives
  • Anaphora
  • Relative clauses
  • Cross-categorial phenomena