Affixal rivalry and its purely semantic resolution among English derived adjectives

This paper aims to fill in a long missing piece in the paradigmatic word-formation research: a set of rival affixes whose members are differentiated in meaning. We argue that such a set can be found in English derivational adjectivalization, in the affixal rivalry between the adjectivalizing suffixes -ed and -y. Using the traditional method of doublet comparison (Aronoff 1976, 2020), we reveal that adjectives of the form Xed and those of the form Xy (X standing for the source word) differ in the scale type. Xed adjectives are closed-scale adjectives, but Xy adjectives are totally open-scale adjectives. The scale-type difference explains why Xed adjectives combine with certain degree modifiers, whereas Xy adjectives do not. Furthermore, we show that the rival affixes are doubly differentiated in the deverbal domain in terms of the said output scale type and the input base selection. In this domain, the major sources of the closed-scale -ed adjectives and the open-scale -y adjectives are result and manner verbs, respectively.


INTRODUCTION
In many contemporary theories, derivational affixes tend to be studied vertically or semasiologically, picking up one specific affix and comparing its multiple usages.
[1] I would like to thank Marc van Oostendorp and the anonymous JL referees for their comments and criticisms on the earlier versions and their very valuable suggestions for improvement. My gratitude goes to the Department of Linguistics of The Ohio State University, especially Andrea Sims, for the development of my project during my stay there. I am grateful to Mark Aronoff for sharing his article with me and Kentaro Koga for helping me on French data. I have also benefited from the questions and comments from the audience at the Workshop on Word-Formation and Adjectives (3 March 2021, Osaka University) and the 5th American International Morphology Meeting (28 August 2021, Ohio State University), where I presented parts of this manuscript. The usual disclaimers apply, and no one should be held responsible for any remaining inadequacies. Finally, I acknowledge the financial support from the Japan Society for the Promotion of Science (KAKEN 18KK0324). Abbreviations used in this paper are: Xed/Xy (morphological doublet based on X and suffixed with -ed or -y), Ned/Ny (denominal adjectives suffixed with -ed or -y), Ved/Vy (deverbal adjectives suffixed with -ed or -y), [AEDiv] (the presence or absence of the Division function), HdN (head noun), BseN (base noun). The examples are cited from the Oxford English Dictionary (OED) Online unless otherwise specified.
Studies of affixal rivalry, however, approach the matter horizontally and consider the way each affix is used in terms of its distributional relationships with its rival affixes. Ideally, the vertical and horizontal approaches should complement each other and deepen our understanding of morphology. Aronoff (1976) introduced the concept of rival affixes to address the paradigmatic relationship between -ness and -ity in abstract nominalization in English. Aronoff and his colleagues (Aronoff & Anshen 1981;Anshen & Aronoff 1988;Lindsay & Aronoff 2013) revealed that the two abstract nominalizers have different, if not complementary, base selectional properties, and morphological doublets such as curiousness and curiosity have different grammatical properties. It is easy to see how hard it would be to pin down the lexeme-formation rules of -ness and -ity if these suffixes were studied individually.
This paper also aims to fill in another missing piece in the paradigmatic wordformation research. In reviewing the history of pertinent studies, Aronoff & Lindsay (2014: 72) regretfully remark as follows: (1) In our own work on rival affixes in English over close to forty years, the only robust example of the members of a set of rival affixes becoming differentiated in meaning is the set -dom, -hood, and -ship. Aronoff & Cho (2001) argue that -ship has become specialized to distinguish between stage-level and individuallevel attributes. But Lieber (2010) questions even this case. Based on corpus data she concludes that the three suffixes are frequently interchangeable. This leaves us with no real cases of semantic differentiation in English, the language where this theoretical possibility has been most sought after.
Adopting Gause's principle of mutual exclusion as a central principle, Aronoff's theory of morphological competition looks at affixal rivalry as the struggle for survival among affixes. Two stages should be distinguished: (i) the struggle for existence between competing species and (ii) the outcome of the struggle (Lindsay & Aronoff 2013;Aronoff 2019Aronoff , 2021. The second stage is also called RESOLUTION of the competition if the competing species have successfully found their own ecological niches; in other cases, only one or a few species survive(s), and the others drop out of the race. In the case of language, the struggle between competing constructions can be resolved, in principle, phonetically, phonologically, morphologically, syntactically, semantically, pragmatically, sociolinguistically, or orthographically (for the last case, see Nagano & Shimada 2014;Berg & Aronoff 2017). Lexeme-formation rules working at a particular historical point, if devised richly enough, are different outcomes of the struggle for survival between competing affixes. The research question raised by (1) is to find a pair or set of English affixes whose ecological niches are semantically motivated. Aronoff (2020) claims that the PRIVATIVE adjectivalizers -less and -free in contemporary American English constitute such a pair. Importantly for the research question in (1), pairs such as the following suggest that the earlier rivalry between -less and -free was resolved semantico-pragmatically (examples taken from Dixon 2014: 258-259): (2) (a) parent-less child (an orphan, with no one to look after them) (b) parent-free evening (when teenage children have the house all to themselves, for a party) (3) (a) She fell into a deep dream-less slumber.
(b) He has been suffering from nightmares a lot recently, but last night he experienced a nightmare-free repose.
Both -less and -free express the absence of the base referent (X). However, compared to -less adjectives in (2a) and (3a), -free adjectives in (2b) and (3b) carry the additional assertion that not having X is good. Aronoff maintains that the additional pragmatic implication acquired by -free successfully distinguishes it from its traditional rival -less, which remains neutral on the speaker's evaluation about the absence of X.
We agree with this argument, but the domain of resolution is limited to concrete noun bases, reflecting the once compound-second origin of -free. 2 This matters because if a pair or set of rival adjectivalizers are differentiated PURELY semantically, as is hoped in the passage in (1), the differentiation in question is expected to be observed both in denominal and deverbal adjectivalization. Indeed, we can find such a distribution if we turn our attention to the rivalry between -ed and -y among derived adjectives. We first look at their denominal adjectivalizing usage and then proceed to their deverbal adjectival usage.
First, -ed and -y both produce PROPRIETIVE adjectives from inanimate concrete nouns: (4) (a) well-branched 'having many branches; having a pleasant arrangement of branches' (b) branchy 'full of, covered with, or consisting of branches' [2] For example, helpless and careless do imply the speaker's negative attitude toward the absence of X. However, such instances are not counterexamples to Aronoff's analysis because the rival Xfree is limited to concrete noun bases in the first place. In fact, we need a competition-based analysis to account for the fact that when paired with Xful (helpful, careful ) rather than Xfree, the form Xless (helpless, careless) acquires an additional negative connotation.
(5) (a) well-legged 'having strong or shapely legs' (b) leggy 'having long legs, (sometimes) excessively or disproportionately so' As suggested in (4a) and (5a), the form Xed can be modified by well (Kennedy & McNally 2005;McNally & Kennedy 2013). 3 The combination with this adverbial item confirms that unmodified words of the form Xed, such as branched, are really adjectives. In many cases, adjectives of this form are used in the modified form Mod-Xed, where the Mod slot accommodates not only well but also other morphemes such as ill-, half-, over-, and under-: half-witted, over-witted, under-witted In this paper, we largely focus on well-Xed, but similar observations can be made of ill-Xed, half-Xed, over-Xed, and under-Xed. We believe that these formations constitute a single abstract construction of the form Mod-Xed, and that each modifier (word-internally, see Note 3) functions as a DEGREE MORPHEME that 'modulates the degree to which an adjective holds and, in English, generally occurs to its left' (Morzycki 2016: 287). For example, in (4a), well assigns a 'good' value to the degree argument (d) of the unmodified adjective branched, which simply expresses 'having a branch or branches'. From the interaction between the semantics of well and branched emerge the meanings of the modified construction cited in (4a). Different modifiers have different restrictions on the degree argument of the Xed adjective and yield a series of Mod-Xed constructions (see Figure 1 on the next page). Turning to (4b) and (5b), it seems safe to say that derived adjectives of the form Xy do not occur with the items in Figure 1. As suggested in (7), Xy should be used in the unmodified form, and the contrast between the well-formedness of the form well-Xed and the non-occurrence of the form *well-Xy is striking and demands an explanation: [3] For example, Kennedy & McNally (2005) treat well in a well-loaded truck and a well-known brand as a degree morpheme that saturates the degree argument of the unmodified -ed adjective. While they regard it as a syntactic degree morpheme, it seems to us that we also need to posit well as a word-internal degree morpheme. Thus, well(-)Ved composites can be modified by very, a bona fide syntactic degree morpheme, as in a very well-known brand and this brand is very well known (see McNally & Kennedy 2013: 250). See Miller (2014: 69-70) for an analysis of over-and under-as word-internal degree morphemes.
Another striking thing about (7) is that proprietive adjectives of the form Xy have their degrees fixed without any overt degree morpheme such as well. This is most clearly illustrated by (7e-f). Why can pricey mean 'expensive' or 'high-priced' in an unmodified form, when well-priced 'cheap' depends on well in modulating the degree of priced? Also, why can leggy mean 'long-legged' without any overt degree morpheme? The simplest hypothesis is that Xy adjectives lexically contain a covert degree modifier. Anticipating the upcoming discussion, suppose that Xy covertly contains yet another degree modifier much 'greater than (an average) by a large amount' (Kennedy & McNally 2005: 372-375). In much-deserved rest, for example, much modulates the degree of deserved to be appropriately large. If pricey contains this modifier covertly (i.e. MUCH), then we can explain its 'highpriced' meaning as a result of the setting of the priced-ness degree as appropriately large. The dictionary meanings of branchy and leggy cited in (4b) and (5b) suggest the same. Thus, branchy 'full of branches' can be seen as a reading from 'greatly exceeding an average on the scale associated with having a branch or branches'. In deverbal adjectivalization also, adjectives of the form Xed occur with modifiers in Figure 1, as in (8a)-(10a), but the counterparts of the form Xy occur without such a modifier (8b)-(10b).
In the next section, we consider why Xed accepts well while Xy does not and show that the contrast comes from the scalarity difference between the two adjectivalizers: -ed derives closed-scale adjectives, while -y derives open-scale adjectives. This will be our fundamental answer to the research question raised by (1), but in Section 3, we further probe into the open-scaledness of adjectives of the form Xy. In Section 4, we observe that deverbal Ved/Vy doublets are not so common as denominal Ned/Ny doublets and argue that the fact is related to an independently motivated principle of verb semantics. Section 5 summarizes our findings and clarifies future tasks.

SCALE TYPES OF DERIVED ADJECTIVES
2.1 Affixal rivalry between -y and -ed Bauer, Lieber & Plag's (2013: 305) corpus-based study describes -y as among the most productive suffixes of contemporary English, but, thus far, no major theoretical analysis has been proposed in the literature about this suffix. 4 My observations to be presented greatly benefit from Fradin's (2007Fradin's ( , 2017 research on the French Beard (1995: 220-227), Hamawand (2007), Bauer et al. (2013: Chapter 14), and Sánchez Fajardo (2020) each contain semantic observations on -y, but none of them notes the morphological doublet formation.
adjectivalizer -eux. The English suffix -y exhibits a surprising similarity to -eux in the denominal usage. As summarized in Table 1, French denominal adjectives suffixed with -eux consist of two major groups in terms of base selection, one group derived from abstract nouns and the other group from concrete nouns; and the latter further divides into two types based on the semantic relationship between the derived adjective and the head noun. In addition to this classification, Fradin (2007Fradin ( , 2017 shows that the derivation from concrete nouns is subject to a semantic constraint, which we call the Natural Origin constraint and introduce later in this section. In Table 1, the Concrete Noun Base region is important for us. 5 English -y adjectives are also rich in the types based on concrete nouns, expressing either of the two relationships with respect to the head noun. Proprietive -y adjectives (already introduced in Section 1) correspond to the ciel nuageux type in Table 1, whereas similative -y adjectives (see Section 3.3) correspond to the champignon laiteux type. While -eux and -y clearly differ in the possibility of deverbal adjectivalization (see Section 5), it seems safe to say that they share certain fundamental characters.
[5] In Table 1, we simplified the adjectivalization from abstract nouns because it is not addressed in this paper. See Fradin (2007: 18-21) for French and Nagano (2021) for English. The latter study shows that -y is largely preempted by -ful in this region. As we observed in Section 1, the Ned type in (16) usually accompanies a modifier. The modifier's variety indicates that -ed attaches to two different levels of nouns in Acquaviva's (2016) structural analysis: (i) Number Phrase (many-legged, threelegged) and (ii) Division Phrase (well-legged, a left-handed batsman). In (ii), the unmodified Ned carry a non-individuated sense of the noun, unlike the counterpart in (i). In our lexicalist approach, we assume that Acquaviva's Division-Phrase level correspond to noun lexeme. This is our target type, and 'Ned' in this paper refers to it. Proceeding, similar doublets are widely observable WHEN DERIVED ADJECTIVES OBSERVE THE NATURAL ORIGIN CONSTRAINT: 'the relationship between the HdN's (head noun) referent and the BseN's (base noun) referent must have a natural origin' (Fradin [6] Two notes are in order on the listed items. First, all -ed adjectives have denominal uses according to the OED Online, although colored and shaped can also be deverbal. Second, shapely is exceptional in using the suffix -ly rather than -y. (16) clearly observe this constraint because the base nouns refer to an inherent part/dimension of the head noun referent. As a second instantiation, consider the following doublets:

2007: 22). Denominal adjectives from part and dimension nouns such as
(17) (a) curved curvy fished (lake …) fishy leaved leafy rocked rocky sanded (shore …) sandy stoned stony wooded woody, woodsy (b) aired airy clouded cloudy iced icy misted misty snowed snowy sunned sunny These adjectives all express topographical or mereological existence of the base referent and thus describe naturally occurring phenomena. For example, in clouded sky conditions, the relationship between clouds and sky is a natural occurrence.
Since weather verbs such as to cloud are non-agentive, the natural relation between the cloud and sky is easy to understand, but caution should be taken in that causative verbs can yield an -ed adjective whose semantic relationship to its head noun is internal in the sense of Fradin (2007: 12). Examples include: In (18), denominal verbs of the locatum-or goal-types (Clark & Clark 1979) give rise to resultant-state passive participial adjectives (Kratzer 2000) that are semantically devoid of causality and purely express possession. Such -ed adjectives often have a semantically closely related -y counterpart. In brief, Xed and Xy adjectives are similar in observing the Natural Origin constraint. We return to it in Sections 3.3 and 4. Meanwhile, the morphological doublets exhibit systematic differences also. The most important difference is what we observed in Section 1. Xed adjectives are overtly degree-modified by well or other similar items in Figure 1, while Xy adjectives do not take them.
Second, Xed and Xy adjectives differ in the compatibility with very: (19) (a) ??very dressed very dressy (b) ??very fished (lake) very fishy (c) ??very (left-)handed very handy Fradin also observes that -eux adjectives accept très (Doetjes 2008: 134-138), as follows (Fradin 2007: 4): (20) C'est un champignon très laiteux. 'It's a very milky mushroom.' A third difference is the existence of a morphological antonym. Xed has an antonym sharing the same base and marked with -less or un-, as in legged: legless and dressed: undressed. However, it is hard to find such an antonym for the Xy type.
These differences can be explained if we assume that the affixal rivalry between -ed and -y is resolved along the output adjective's scale type. Below, we first show that Xed adjectives are closed-scale adjectives, while Xy adjectives are open-scale adjectives (Section 2.2). Then, we proceed to the overt and covert degree modification (Section 2.3). Kennedy & McNally (2005) assert that gradable adjectives display a four-way typology of scale structure: (i) TOTALLY OPEN SCALES, (ii) LOWER CLOSED SCALES with minimum values, (iii) UPPER CLOSED SCALES with maximum values, and (iv) TOTALLY CLOSED SCALES with minimum and maximum values. Relative adjectives possessing (i) use a contextually determined relative standard to determine the semantic interpretation of their unmodified positive form, whereas absolute adjectives possessing one of (ii-iv) do not. When the latter take an unmodified form, their standard of comparison defaults to the minimum or maximum value specified on their scale. Since totally closed scales contain both minimum and maximum values, adjectives possessing this type of scale behave either as minimal standard or maximal standard adjectives. Kennedy & McNally (2005) use several tests to prove the presence or absence of scalar endpoints. For example, maximality modifiers such as completely and fully are compatible with adjectives that have a scale with the upper endpoint (Kennedy & McNally 2005: 352-355). If both an adjective and its antonym shun this type of modification, as in (21a), they are associated with a totally open scale. If both accept it, as in (21b), they are associated with a totally closed scale (Doetjes 2008: 150). The scale is partially closed (ii or iii) if only one member of an antonymic pair accepts maximality modification. Expressions whose scale is closed only at the lower endpoint are incompatible with a maximality modifier themselves, but their antonyms should accept it. If so, the following data suggest that the antonymic pairs in (22a-b) and ( unprotected, undocumented, uneducated (b) unneeded, uncriticized, unpraised, unappreciated In (23), we see un-prefixation to the form Ved, an indication that the prefixless Ved is an adjective. As for the scalarity, Kennedy & McNally (2005: 365) observe that 'all deverbal [-ed] adjectives prefixed with un-, which reverses the polarity of the adjectival scale, accept modification by endpoint-oriented modifiers such as completely'. Since un-reverses the polarity of the adjectival scale, this observation means that the prefixless -ed adjectives have a scale that is closed at least at the lower endpoint.

Examining the scale type
As noted in Section 2.1, proprietive -ed adjectives also have a morphological antonym derived by -less or un-, as in: (24) (a) clouded/cloudless/unclouded (b) dressed/undressed (c) legged/legless Each negative antonym naturally accepts maximality modification, as in completely cloudless, totally unclouded, and completely undressed. Therefore, the scale structure of proprietive -ed adjectives is closed (at least) at the lower endpoint. In contrast, -y adjectives have a totally open scale. First, -y adjectives do not accept maximality modifiers, as indicated by ??completely dressy, ??completely cloudy, ??completely leggy. 9 Since many do not have an antonym, the maximality test cannot be employed to check for the presence of an endpoint at the opposite end of the scale. 10 However, the entailment test (Kennedy & McNally [7] Causative psychological predicates behave differently. Additionally, in this paper, we do not concern ourselves with the issue of whether -ed adjectives have an upper endpoint also. [8] Deverbal -ed and denominal -ed are etymologically related (Marchand 1969: 264), but their synchronic commonality has not been seriously investigated. Bauer & Huddleston (2002: 1709 observe that Ned and Ved exhibit the identical phonological alternation between /ɨd/, /t/, and /d/, although the /ɨd/ variant 'occurs exceptionally in a handful of lexicalized words (crooked, dogged, ragged, wicked, wretched) and in forms containing legged (e.g. three-legged, though /legd/ is an alternative pronunciation)'.
[9] The question marks for the maximality reading of completely, excluding its emphatic reading.
[10] When an -y adjective has a morphological antonym, our analysis predicts that both shun maximality modification. This seems to be correct with the pair tasty/untasty.

2005: 358-359) confirms that -y adjectives have a totally open scale. Adjectives
with a totally open scale use a relative standard, so the truth conditions for tall, for example, entail only that the degree of height it attributes to its holder falls above a contextually determined standard of comparison. Hence, the denial x is not tall should not entail that x possesses no amount of height at all. At the same time, an assertion of x is tall should not entail that nothing can be taller than x.
Hence, there are no contradictions in the following sentences (Kennedy & McNally 2005: 359): (25) (a) Sam is not tall, but his height is normal for his age.
(b) That film is interesting, but it could be more interesting.
When this test is applied, -y adjectives behave in the same way, as follows: (26) (a) The sky is not cloudy, but we see some clouds there.
(b) The sky is cloudy, but the weather report says that it will be cloudier in the afternoon.
Since Xed and Xy adjectives differ in the scale type, they differ in the compatibility with very, as observed in (19). As widely assumed in the literature (Doetjes 2008), the modification by very is a hallmark of totally open-scale adjectives.
Compare (27) with (28) Kennedy & McNally (2005: 370); (28cd) from (19) According to their analysis, well is a degree morpheme that combines with a closed-scale gradable predicate. Based on the evaluative scale of goodness, well-Xed composite measures 'the goodness of the event that is related to the degree to which the subject has the property named by the adjective' (Kennedy & McNally 2005: 377). For example, in (29a), well positively evaluates the degree to which Martin becomes acquainted with the facts.
The closed scalarity of Xed is not the only restriction for well modification. Thus, well allows both a degree modifier reading and a manner adverb reading in (30a) The -ed adjectives in (30b) employ maximal standards because they crucially involve incremental theme arguments. Proceeding to (29b), much as a degree morpheme also combines with closedscale minimal standard adjectives. In particular, the denotation of much in (31) contains the restriction d >!! min (S G ), which says that the degree of a gradable adjective G is greater by a large amount than the minimum value of its scale (min (S G )) (Kennedy & McNally 2005: 373).
For example, in (29b), the unmodified needed contains min (S needed ), which is equal to the minimum portion of the relevant event that is large enough to support the statement x needs y. Hence, it can be an input to the modification by much. Now, the selectional properties of well and much summarized above predict that denominal proprietive -ed adjectives are also compatible with these degree modifiers because they have a lower closed scale (Section 2.1) and thus behave as minimal standard adjectives.
First, in Section 1, we saw that the said prediction is borne out with respect to well. See the data in (4)-(7). In some cases, the goodness of Ned adjectives implies a high degree of N's quantity. Thus, a well-brained vertebrate refers to a vertebrate possessing intelligence to the amount that counts as good. In others, the goodness scale within well evaluates a non-quantitative dimension of N. Thus, well-branched in (32a) is concerned with N's quantity, but (32b) employs a qualitative dimension of measurement.
(32) (a) In the midst of the fruit trees, and towering high above them, was an oak, well-branched and leafy. ('having many branches') (b) When you're buying bare-root stock or balled-and-burlapped trees, be sure to select a well-branched specimen. ('having a pleasing arrangement of branches')

Covert degree modification
Proceeding to much, the predicted much-Ned construction, such as muchbranched or much-brained, seems very marginal. However, this apparent problem disappears once we assume that the semantic function of much in (31) is cumulatively expressed by the suffix -y. A CUMULATIVE EXPRESSION (also called FUSION) is 'the expression of multiple morphological meanings simultaneously by a single un-analyzable element' (Haspelmath & Sims 2010: 324). That is, we do not have overtly modified adjectives such as much-branched or much-brained most probably because cumulative expressions such as branchy and brainy BLOCK (Aronoff 1976(Aronoff , 2021 them. If Xy adjectives lexically contains the function of (31), their open-scaledness naturally follows. Here, it is important to notice that (actually-occurring) much-Ved composites exhibit totally open scales. Thus, while unmodified Ved adjectives are incompatible with very, as in (33a), much-modified counterparts accept it (33b).
(33) (a) *very needed (rain) (b) very much needed (rain) This fact is explained as follows. Example (33a) is ungrammatical because very is sensitive to a relative standard (Section 2.2), which -ed adjectives do not have (except those derived from causative psychological predicates and lexicalized examples such as dogged). Example (33b) is grammatical due to the relative standard introduced by the function in (31), i.e. 'greater than by a large amount'. As a result of applying this function, much-Ved composites obtain a relative standard and become compatible with very (see also Kennedy & McNally 2005: 373n21). The totally open scalarity of -y adjectives can be explained following the same logic, if the suffix cumulatively expresses the function in (31).

Summary
This section introduced a new set of data into the study of affixal rivalry and showed that they can fill in the missing gap observed in (1 (34) (a) a much-admired statesman (b) much-needed rain (c) a much-regretted action (d) a much-praised piece of work (e) a much-looked-for treasure (f) a much-talked-about program Kennedy & McNally (2005: 364-365) observe that most of the much-Ved composites can be paraphrased as Ved for a long time, but the temporal duration is not the only way to gauge admiration, need, regret, etc. Thus, much admired (34a) is also paraphrasable as admired by many people, in which case each admiration could be short. Further, it can mean the intensity of one person's admiration toward the subject of the adjective. Therefore, we observe that in Japanese, much in (34) is translated by several lexical adverbs catering to different dimensions, such as nagaku 'long', hiroku 'widely', and hukaku 'deeply'.
As predicted from our analysis, dimensional indeterminacy also holds for -y adjectives. First, let us consider the measurement dimension with windowy in (16b). Witness the following example: (35) She paints in a huge, sunny, windowy room.
In (35), the proprietive reading of the derived adjective is based on a number-based scale, expressing 'having more windows than the standard degree'.
However, unlike the number of windows of a room, the number of body parts does not vary. For example, the number of legs of a human body is universally the same: two. In such a case, number-based measurement is not meaningful. As predicted, when leggy is used to describe a person or a plant, it is usually interpreted in the sense of long-legged: (36) (a) a leggy Qazaq youth riding one wild-eyed pony and leading another (b) Pansies became leggy and were attacked by slugs.
Like window, leg is a count noun, which explains why it yields an -ed adjective that is modifiable by a quantifier, as in three-legged and many-legged. However, leggy does not exhibit a number-based scale because 'having more legs than the standard degree' is virtually impossible due to our world knowledge about human bodies and pansies. Instead, leggy employs an amount-based scale, and its 'long-legged' sense comes from 'having a larger amount of leg than the standard'. This analysis applies not only to leggy but also to other -y adjectives in (16a). Consider why brainy 'clever, intelligent', handy 'dexterous', and nosy 'inquisitive, prying' express such senses, as illustrated below.
(37) (a) So I invited all of the brainy gentlemen I could think up.
(b) He's very handyhe is a bit of an electrician and plumber, and also knows his way around auto engines. (c) I'm nosy and I like to see what people have been up to.
Significantly, in (37a), brainy is based on mass plural brains 'one's intellectual capacity'. The degree of 'having brains' in this sense can be meaningfully specified as 'greater than the standard by a large amount' by (31), unlike the universally same degree of 'having a brain'. The same applies to (37b, c) because the bases of handy and nosy do not refer to physical, atomic body parts either.
Next, consider an example from (16c): (38) Meat has become a very pricey business for most households.
Again, a number-based interpretation is very difficult because each selling article is attached with only one price. Rather, what can be meaningfully degreespecified by the function in (31) is a degree on the amount dimension inherent in price. In lexical semantics, price is defined as 'the amount of money expected, required, or given in payment for something'. If the adjective in (38) uses this base lexical information for degree measurement, together with (31), its 'highpriced' reading ensues. Ambiguity can be explained in a similar way. Toothy differs slightly from the items discussed above in that the standard number of human or animal teeth is not so obvious. Biologically speaking, there should be a standard number for each species, but such knowledge is not as common or obvious as knowledge about the number of human eyes or legs. Moreover, animal species may be compared to human beings in the number of teeth, while such a comparison would be unrealistic concerning the number of eyes, a head, or a brain. As a result, toothy is ambiguous between amount-based and number-based proprietives. Being predicated of an animal or a person, it expresses 'having NUMEROUS, LARGE OR PROMINENT teeth': (39) toothy wolves in lambswool amount-or number-based In fact, leggy is also ambiguous. When it is predicated of an animal whose leg count is unidentified, it may employ a number-based scale: (40) Wild scorpions are the most leggy, hairy, fangy, scrabbly creatures you could ever hope not to find in your desert tent.

MUCH in the lexicon
How can we explain the observations in the previous section? In Section 2.3, we introduced MUCH (Wellwood 2019) in the lexicon. 11 This analysis faces a challenge about MUCH's argument selection. A predicate is measurable if its domain has a non-trivial structure and is non-measurable otherwise (Wellwood 2019: 6). Thus, in syntax, mass NPs and plural count NPs can be measured by MUCH (41a, b), but singular count NPs cannot (41c) (Wellwood 2019: 99-100).
(b) Al had {more/as many} ideas.
(c) *Sue has more idea than Al does.
Wellwood, Hacquard & Pancheva (2012) observe a similar contrast between atelic and progressive/imperfective/habitual predicates (which are measurable) and perfective telic predicates (which are non-measurable). What does this mean for the degree measurement in the lexicon? Lexical derivation and compounding do not involve grammatical plural or aspectual morphology. As pointed out by Borer (2005: 133), the first item of the compound flea-infested cannot take the plural form (*fleas-infested) but receives a generic plural interpretation. A single flea does not represent an infestation. Lexemes underlying -y adjectives can also be interpreted as semantically plural even though they are not morphologically plural-marked. To examine this issue, we look at Wellwood et al. (2012) and Acquaviva (2016) in this order.
Discussing nominal and verbal comparatives, Wellwood et al. (2012) argue that the presence or absence of number or aspectual morphology correlates with the variability of the measurement dimension. As first observed by Bale & Barner (2009), in nominal comparatives, when MUCH takes a plural-marked NP as its argument, the measurement dimension is in terms of cardinality only. (This generalization excludes lexical plurals; see below.) Thus, (42) is compared in terms of the number of servings or kinds or of some other individuated quantity (Wellwood et al. 2012: 212).
In contrast, when MUCH takes non-plural-marked NPs, the measurement dimension is variable, and it is determined by the properties of the nominal predicate. Usually, such comparatives are evaluated in terms of portions of matter measured by volume or weight, as in (43) (Wellwood et al. 2012: 212).
(43) More beer than wine was drunk.
[11] Strictly speaking, Wellwood's (2019) MUCH is a general-purpose measure function, so we need to assume that the suffix -y introduces MUCH plus the degree modifier function in (31).

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However, when comparatives are based on luggage and furniture, as below, what is compared is typically the number of individuals satisfying each NP's description (Wellwood et al. 2012: 212).
(44) Mary has more luggage than furniture.
Examples (42-44) suggest that 'the absence of plural morphology underdetermines the scale, so that it is idiosyncratic to the NP's "lexical" properties' (Wellwood et al. 2012: 212). What needs to be clarified here are the contents of the NP's 'lexical properties' that are supposed to distinguish (43) from (44). Following Borer's (2005) non-lexicalist exoskeletal approach, Acquaviva (2016) examines furniture and other fake mass nouns and proposes a derivation involving functional head Div(ision). Div divides the set of sums denoted by a mass predicate into a set of mutually disjointed elements. Acquaviva (2016: 223) states: the elements of Div are individuals in the sense that they are cut up in a determined way … but not in the sense that they are atoms in any sense. The elements of a partition are not necessarily similar to each other in size, or based on a uniform criterion.
Thus, furniture differs from beer/wine in the positive function of Div in their underlying structures; the former, but not the latter, refers to an aggregate of nonuniform individuals (chairs, desks, tables, etc.), which results from Div's partitioning function. However, '[t]he partition introduced by Div is a necessary but not sufficient condition for countability' (Acquaviva 2016: 223). Hence, furniture is uncountable and rejects -s. Nouns such as table are countable because their semantics are not only partitioned into individuals but also contain a specific criterion for atomicity: 'the domain of its denotation is partitioned into stable atoms, each of which is named as a table-entity' (Acquaviva 2016: 223). Although Acquaviva (2016) does not discuss the contrast between (42) and (43), we assume the following line of thought: Beverage nouns are ambiguous between atomic and non-atomic readings, with the atomic nouns corresponding to the reading containing a piece of world knowledge about how the beverage is served.
Adopting the above analysis of furniture, we assume that MUCH is sensitive to the lexical semantic property [AEDiv] of its argument when it is not plural marked. We also assume the significance of the property [AEanimate] based on the work of Corbett (2000). Then, as predicted from the lack of grammatical plural morphology, -y adjectives are under the influence of these lexical properties. Concretely, such adjectives exhibit amount-based or number-based scales, depending on the base noun's [Div] and [animate] properties. First, let us consider the case when the base noun is [-animate, -Div], as in the following: (45) base noun [-animate, -Div] (a) rusty, sandy, watery (b) greedy, guilty, healthy, hungry The proprietive reading 'having more {rust …/greed …} than the standard degree' is based on the amount scale, just as we saw for the measurement in (43). The examples we saw in (36)-(38) belong to this type. Next, the base noun is of type [-animate, þDiv] below.
(46) base noun: [-animate, þDiv] (a) gemmy 'abounding in gems' jointy 'having numerous joints' (b) moony 'moon-shaped, stupidly dreaming' churchy 'exceedingly pious' In (46a), MUCH inside the -y adjectives use the same type of scale as employed for (44). As a result, they express a proprietive reading that involves an aggregate of small objects. The number-based readings we observed in (35) and (39)- (40) belong to this case. The items in (46b) seem limited to SIMILATIVE readings because the base denotes something unique (moon) or very large (church). The proprietive/similative polysemy is discussed in the next section.
Base nouns of type [þanimate, þDiv] are interesting in that animals are quantitymeasured in the semantics of the -y adjective. Therefore, as in (47a), animal-based adjectives allow a proprietive reading.
(47) base noun: [þanimate, þDiv] (a) mousy 'infected with mice' horsy 'addicted to horses' (b) matey 'sociable' actressy We assume that the sense 'infected with mice' of mousy is a variant of 'having more mice than the standard degree', and the sense 'addicted to horses' of horsy is a variant of 'having more horses than the standard degree'. Human-based adjectives, however, are usually limited to similative readings. The items in (47b) do not have a proprietive reading comparable to those found in (47a). Before closing this section, let us consider the following colloquial examples where -y attaches to -s marked nouns: (48) (a) sudsy 'full of soap-suds' (b) gutsy 'possessing or requiring guts' cf. gutty (c) nutsy 'mad, crazy' cf. nutty (d) rootsy 'of music, characteristic of folk or blues traditions' cf. rooty 'full of roots' (e) woodsy 'characteristic of the woods' cf. woody (f) tricksy 'full of tricks; playful' cf. tricky (g) outdoorsy 'fond of an outdoor life' (h) antsy 'agitated, restless' (i) booksy 'characterized by an interest in books or literature' cf. booky Those cited as 'cf.' do not contain -s and may or may not be a near-synonym to the one containing -s. 12 Despite the appearance, (48) does not involve the Number-Phrase level because except for (48h-i), all the underlying -s forms are lexical plurals (Acquaviva 2008;Gardelle 2019). In fact, the bases in (48a-g), suds, guts, nuts, roots, woods, tricks, and (the) outdoors are all used as independent lexemes (rather than word-forms) with their own semantics and grammar. Lexeme-creating -s is not a marker of atomicity-based plurality ('many a one'), but can be seen as a marker of property partitioning. That is, the -s marked bases in (48) are morphologically complex [þDiv] lexemes.
For (48h), ants does not seem to have lexical plural use, but significantly, antsy is based on the following IDIOM involving a plural-marked form: (49) have ants in one's pants 'be restless' Being a possessive construction, this idiom makes perfect sense as a base of a proprietive adjective.
In brief, proprietive adjectives use amount-or number-based scales depending on the lexical semantics of the base noun. Crucially, this observation is consistent with what has been noted with nominal comparatives based on non-plural-marked NPs.

Proprietive/similative polysemy
As discussed by Beard (1995: 219-227), proprietive adjectives, whose base noun is the possessee with respect to the head noun, and similative adjectives, which express 'similar to the base noun', are cross-linguistically the most productive and widely distributed semantic types of denominal gradable adjectives. In Section 2.1, we observed this point among French -eux adjectives based on concrete nouns, which consist of the ciel nuageux type (proprietives) and the champignon laiteux type (similatives) (see Table 1).

(a) rust (b) hair
First, (51a) and (52a) represent the extensive and intensive readings of rust, respectively. As indicated in (51b) and (52b), the derived adjective's prenominal modification is done differently based on the compatibility of the semantics of rust and the head noun. Details aside, the proprietive reading in (50a) arises when the R-representation of rust as a whole combines with any of the semantic features of [13] The usage in (i) is basically proprietive but very close to the other use.
(i) My tennis is very rusty these days [14] In English, -rich and -like do not show this common polysemy, with the former being uniquely proprietive (e.g. oil-rich) and the latter being uniquely similative (e.g. cat-like). This is related to the fact that -rich and -like each originate from a lexical adjective denoting the sense in question.

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Fradin (2007) proposes this constraint for French -eux adjectives produced from concrete nouns. Significantly, all English denominal adjectives examined thus far also follow this constraint, whether the suffix is -ed or -y. A proprietive reading of Ny results when MUCH picks a quantitative dimension (such as volume, weight, number, etc.). In contrast, a similative reading of Ny is obtained when MUCH picks a qualitative dimension (such as color, taste, texture, form, manner, etc.) to maintain the natural PART-WHOLE relationship between the base and the head. Specifically, in (50a), the base noun rust (w) is a natural occurrence in the head noun knife (z), and its volume is measured by MUCH. After the degree argument of MUCH (w) = d is supplied by (31), the value is ascribed to z because w is part of z. As a result, the denominal adjective denotes that the head noun has the base noun as an inherent part, and its volume exceeds the standard volume. Next, similative readings may arise from the same process. In (50b), the measure function gauges the state of the color BROWN and returns a degree argument. Such a qualitative scale is employed so that the intrinsic relationship between the base and head nouns suggested in (53) is maintained. The rest is the same as what we said above about (50a).

DOUBLE-LAYERED SEMANTIC DIFFERENTIATION
Xy adjectives we discussed so far are denominal ones. In this section, we address deverbal data.

Observations
Since MUCH is cross-categorially available (Doetjes 2008;Wellwood et al. 2012;Wellwood 2019), our analysis correctly predicts that -y produces not only denominal but also deverbal open-scale adjectives. However, a closer observation reveals that Ny and Vy adjectives are not completely parallel in their BASE SELECTION. As we observed in Sections 1 and 2, there are many Ned/Ny doublets, that is, the suffixes may attach to identical base nouns. However, Ved/Vy doublets, such as (8)-(10), are very limited in number. In fact, more productive types of Vy adjectives are based on the verb types which are complementary to the verb types selected by -ed.
To be specific, it is widely agreed that productive -ed adjectives are based on verbs whose lexical semantics contain a result component (Gehrke 2012); see -ed adjectives based on change of state verbs and incremental theme verbs in (29)-(30). Incremental theme verbs such as to load and to write do not possess a result component themselves, but their internal argument introduces it, so strictly speaking, we should say that -ed adjectives are based on result verbs or result verb phrases. Such RESULT VERBS (Rappaport Hovav & Levin 2010) are not productive inputs to -y, so we do not find Vy adjectives such as *acquainty. Rather, the majority of Vy come from nonresult verbs. Particularly profitable for -y are VERBS OF BODY-INTERNAL MOTION and VERBS OF EMISSION. The first class includes verbs describing movements of particular body parts (Levin & Rappaport Hovav 1995: 226): (54) Verbs of body-internal motion fidget, flap, flutter, gyrate, jiggle, pivot, rock, squirm, stir, sway, totter, twitch, wave, wiggle, wobble, wriggle, etc.
The second class consists of verbs that describe 'non-voluntary emission of stimuli that impinges on the senses' (Perlmutter 1978: 163) and take the stimulus emitter as the subject (Levin & Rappaport Hovav 1995:  Neither (54) nor (55) are result verbs. Levin & Rappaport Hovav (1995) observe certain syntactic behaviors shared by these verb classes, such as generally unergative properties and participation in locative inversion. However, they miss the morphological fact that both are highly prolific of -y adjectives. As shown in (56) and (57)  In addition to the lack of a result component, the verb classes in (54)-(55) share the lack of a volitional agent. Thematically, the subject of verbs of body-internal motion is the Experiencer, and the emitter subject of emission verbs is the Causer (see Potashnik 2012 for details). In our view, this is one reason for their productivity with -y: non-agentive verbs can easily satisfy the constraint in (53), read with 'BseV' instead of 'BseN', when they adjectivalize. Verbs of sound and light emission may occur with an agentive subject, as in The postman buzzed the doorbell/We shone the flashlight (Levin & Rappaport Hovav 1995: 115), but more fundamental is the usage taking a stimulus-emitter subject, as in The doorbell buzzed/The flashlight shone (see Potashnik 2012;Rappaport Hovav & Levin 2012: 170-172;Isono 2013: chs 5, 6).
As evidence for the totally open-scale structure, deverbal -y adjectives can be naturally modified by very: (58) (a) Their marriage was very rocky from the start. (

b) A very buzzy bar in Kyoto
To summarize the observed tendency, -ed produces closed-scale adjectives from result verbs, whereas -y produces totally open-scale adjectives from non-agentive non-result verbs. In principle, the semantic resolution of affixal rivalry can take place at the base and/or derivative level(s). Thus, according to Aronoff & Cho (2001), -ship is semantically differentiated from -dom and -hood in its base selection, as suggested in (1). However, the rivalry between -less and -free (Aronoff 2020) are resolved in the semantico-pragmatics of their derived adjectives (see Section 1). What we saw above is the third case because -ed and -y attaching to verbs are doubly differentiated, both at the base and derivative levels. This is why Ved/Vy doublets are limited in number. A question is, why the rival affixes are distributed this way when deverbal?

Verbs specifying scalar and non-scalar changes
The above observations suggest that the rival suffixes are sensitive to the MANNER/ RESULT COMPLEMENTARITY, according to which '[m]anner and result meaning [16] Cited from Merriam-Webster's Dictionary components are in complementary distribution: a verb lexicalizes only one' (Levin & Rappaport Hovav 2013: 50). According to Rappaport Hovav & Levin (2010: 28), 'all result roots specify scalar changes, while all manner roots specify non-scalar changes'. If so, it is expected that result verbs, but not manner verbs, produce gradable adjectives using their inherent scalarity. Below, we discuss this possibility based on Kennedy (2012).
A representative type of result verb is change of state verbs such as to widen, to warm and to heat. First, let us observe that such verbs produce -ed adjectives, as in well-warmed soup and well-heated room. Kennedy (2012: 107) demonstrates that this type of verb specifies a scalar change using various data, including: (59) (a) The canyon widened for/??in one million years.
(b) The canyon widened 30 kilometers in/??for one million years.
In (59) (59b) does not indicate that the canyon became 30 km wide; rather it indicates that the difference between the degree to which the canyon manifests width at the beginning and end of the event is 30 km. The analysis above crucially depends on the morphological relationship between wide and widen (A > V derivation). Then, if the 'conversion' between measure function and measure of change function is not limited to this case, as argued by Kennedy, it is natural to assume that the morphological relationship between result verbs (or result verb phrases) and -ed adjectives involve the same functional conversion working in the opposite direction: measure of change function (associated with to warm, to heat, and to load hay) converted into measure function (associated with (well-)warmed, (well-)heated, (well-)loaded). This line of thought brings us to a deeper question about the source of the measure function of derived gradable adjectives in general. A default position would be to assume that the adjectivalizing suffix introduces a general purpose or parameterized measure function of the sort discussed by Wellwood (2019). In Section 3, we tacitly employed this assumption, using her concept of MUCH (see Note 11). Maintaining this position, we further posit that the parameterized measure function introduced by -ed should be substantiated in such a way to align itself with the measure of change function found in the host result verb (or verb phrase). In contrast, -y is exempt from this constraint. This idea, while awaiting further articulation, can explain the observations in Section 4.1. That is, in the deverbal domain, the rival suffixes are distributed in the way they are because -ed, but not -y, is subject to a constraint that refers to the scalarity inherent in the host verb.

Deriving -y adjectives from non-result verbs
In this section, we clarify how deverbal -y adjectives are derived from verbs expressing non-scalar changes.

Manner verbs
Manner verbs are adjectivalized by -y rather than -ed, as evidenced by (54) > (56). Verbs of bodily movement are characterized by a semantic component that ascribes a particular manner to the core motion event. Concretely, in the framework taken by Rappaport Hovav & Levin (2010) and Levin & Rappaport Hovav (2013), the lexical conceptual structure (LCS) of manner verbs integrates the manner as a MODIFIER of a core predicate (Rappaport Hovav & Levin 2010: 25); thus, the verbs in (54) share the following LCS (and differ from one another in the manner contents): Based on this LCS, the derivation from rock to rocky (58a) proceeds as follows: Example (61) depicts a derivational process in which transposition (Beard 1995) changes MOVE to BE, while MUCH selects the shaded manner component as the measurand. The resulting adjective rocky and similar formations in (56) express the conspicuous manifestation of the manner in question by the subject or head noun referent.
In English, there are many ambiguous manners of motion verbs that exhibit usages with or without a volitional agent (Levin & Rappaport Hovav 1995), such as: (62) bounce, creep, float, jump, run, shake, swim, swing, twist, etc.
(a) Agentive She jumped into the water to save them.
Can you run as fast as Mike?
Her heart jumped when she heard the news. Water was running all over the bathroom floor.
(b) The (very) jumpy boy is my cousin.
The participial prenominal modifier in (64a) is agentive and does not accept the modification by very (Meltzer-Asscher 2010: 2216, 2233). In contrast, (64b) accepts very and is totally independent of the notion of agency; the -y adjective merely expresses the conspicuous manifestation of the manner lexicalized in the base verb. This is further confirmed by the way runny and swimmy are used: (65) (a) A 'runny' jelly is very difficult to manipulate.
(b) Karajan 1972 was altogether more passionate … but the recording was swimmy.
In both sentences, the -y adjectives are linked with a non-agentive entity and ascribe to it only the manner component within the base verb.
(68) (a) loc (y, P(x)) loc = localization, P = spatial prep. Turning to our case, -y adjectives from emission verbs are also linked to an NP that is thematically the Ground and express that it is filled with the emitted stimulus. For example, consider buzzy derived from to buzz: (69) (a) New York was buzzy with parties.
(b) a very buzzy bar (= (58b)) We propose that the operation in (68a) is applied to a base semantic representation equivalent to (66) and binds the emittee constant within, such as buzz, as the Figure argument (y in (68a)). Then, the localization function links it to the adjective's subject or head noun which acts as the Ground (x in (68a)). Crucially, in this process, MUCH selects the same emittee constant as its measurand and gives rise to the 'filled with buzz' sense. Since the measurement dimension is the amount of buzz, this type is parallel to denominal proprietive -y adjectives.

Summary
For our major concerns in (1), it seems safe to conclude that in the deverbal usage, -ed and -y are doubly differentiated. That is, semantically, these rival affixes differ not only in the output scale type, but also in the input base selection. Primarily, -ed base-selects result verbs, and -y non-agentive manner and emission verbs. This is why doublets in the forms Ved/Vy are much less frequent than doublets in the forms Ned/Ny. Also, the base-level differentiation is far from random; rather, it is done aligned with the independently motivated lexical semantic principle of the manner/ result complementarity.

CONCLUSION
To summarize this paper, we set (1) as our research question within the research paradigm of affixal rivalry and closely examined the competition between -ed and -y. Compared with the privative pair -less and -free studied by Aronoff (2020), the proprietive pair has the advantage of enabling us to examine semantic differentiation cross-categorially. Indeed, we found that whether denominal or deverbal, -ed and -y are purely semantically differentiated in terms of the scale type of the derived adjective. Also, we found that the rival affixes base-select semantically complementary types of verbs. The findings of this paper provide fruitful inputs to more formal semantic analyses. In particular, scale structures of derived adjectives are worthy of indepth research. Syntactically inclined researchers would be interested in how high in a multi-layered structure of the base item each affix can be attached to. In a non-lexicalist view, legged in well-legged would be produced at the Division-Phrase level while legged in many-legged at the Number-Phrase level. Such analyses are in fact popular when dealing with multi-faceted deverbal participial adjectives.
In our own research paradigm, the findings can be tested using various data and methods suggested by Aronoff (2020) for the -less/-free pair. Also, considering the breadth of Lieber's (2016) study of English nominalization and how intricately a multitude of nominalizing suffixes are interrelated with one another and live side by side in their ecological niches, we can proceed to the ecology of various adjectivalizing suffixes in the future study.
We believe that this paper successfully broadened the research perspective by examining the target affix cross-linguistically (Renner & Nagano 2019). While awaiting an in-depth cross-linguistic comparison, it seems safe to say that the English Ny and French Neux adjectives are basically similar. In Section 2.1 (see Table 1), we observed their similarity in the base/derivative types and, in Section 3.3, we further saw that they obey the same semantic constraint shown in (53). The summary of comparison is shown in Table 2.
However, -eux also raises a serious challenge for our analysis. Although it predicts the existence of Veux as the counterpart of Vy, this prediction is not empirically borne out. According to Fradin (2007: 3-4), -eux does not attach to any eventive verb. 17 Why is -eux limited to denominal adjectivalization? We leave this question for future research. 18

Constraint
Base category Derivative type -eux -y the Natural Origin constraint Concrete N proprietive ✓ ✓ similative ✓ ✓ V see §4.3 rare ✓ Table 2 Summary of the French-English comparison in this paper.
[18] One possibility in Aronoff's (2019Aronoff's ( , 2021 theory is that morphological competition is a local phenomenon; as such, different scenarios among different languages should be expected. In particular, the way a competition is resolved deeply depends on the resources available to do so, among other things. In the history of English, Vy developed later than Ny (Marchand 1969). The encroachment of -y into eventive verbal domains was possible because English, being a satelliteframed language (Talmy 1985(Talmy , 2000, possesses a wealth of manner verbs. It is also very rich in emission verbs. Crucially, French is a verb-framed language in this typology.

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