On the privativity of number and the possibility of negative feature specifications

It has been argued, most recently and forcefully by Omer Preminger (2014, 2019), that the feature specification for singular must be contained in the feature specification for plural, as on a privative representation where [pl] is privative and singular is the absence of plural (i.e., there is no [sg], nor is there [-pl]).

One argument (Preminger 2019) comes from agreement neutralization: when agreement is blocked or disrupted, if the form that emerges is identical with some non-disrupted form, it is third singular, never plural. If there were a way to explicitly specify third singular, then there could be a language in which a third singular exponent was so specified, and the form appearing in third plural, for example, could be a default, also surfacing in the absence of any local agreement controller. It appears that no language shows such a pattern.

Another argument (Preminger 2014) comes from “omnivorous agreement” (Andrew Nevins’ term). In Omnivorous agreement, there is an agreement exponent which can be controlled by either of two arguments depending on which one has the relevant feature. The paradigm looks like this, where V is verb, S is subject, and O is object:

V[sg] S[sg] O[sg]

V[pl] S[pl] O[sg]

V[pl] S[pl] O[pl]

V[pl] S[sg] O[pl]

The first three examples are consistent with subject agreement. It is the fourth example that shows that this is an omnivorous agreement pattern: If the nearest target of agreement fails to deliver the features being sought, a more distant target can supply them.

Theories of omnivorous agreement developed by Béjar, Rezac, Nevins, and Preminger involve a number probe searching a domain containing both S and O, registering when it finds a plural feature.

No language has been described as having omnivorous agreement where singular is preferred over plural, the inverse of the pattern above. Preminger argues that this can be explained if singular is always contained in plural; any probe satisfied by singular would also be satisfied by plural, so no probe would ever pass over a plural to preferentially agree with a singular argument. This means languages must not be at liberty to specify [-pl] on a probe.

However, Daniel Harbour (2007) has argued that Kiowa does exactly that. Harbour motivates a theory of number which is stated in terms of the features [±singular] and [±augmented], or in later work [±atomic] and [±minimal]. The labels are not important, so for exposition we can use [±sg] and [±pl]. The number system of Kiowa works as follows:

Singular: [+sg, -pl]

Dual: [-sg,-pl]

Plural: [-sg,+pl]

These numbers control agreement on the verb, so that the verb will show singular, dual, or plural agreement with a noun phrase headed by a noun like ‘shoe’ depending on what number the noun is combined with. Schematically,

V[sg] Num[+sg,-pl] N ‘shoe’

V[du] Num[-sg,-pl] N ‘shoe’

V[pl] Num[-sg,+pl] N ‘shoe’

Harbour argues that the gender system of Kiowa is based on these same features. For example, there is a class of nouns which is specified lexically as having [-sg] as a gender, including the word for ‘pencil’. In the dual and plural, these nouns control number agreement on the verb as usual, because there is no feature clash between the number of the noun phrase and the gender of the noun. But in the singular, there is a conflict between the features [+sg,-pl] on the Num head in the noun phrase and the feature [-sg] on the noun, and the agreement shows an invariant “inverse” form. Schematically,

D[in] Num[+sg,-pl] N[-sg] ‘pencil’

D[du] Num[-sg,-pl] N[-sg] ‘pencil’

D[pl] Num[-sg,+pl] N[-sg] ‘pencil’

The category of the head bearing the probe is D here because as Harbour shows, the inverse pattern is reflected in the nominal morphology. The agreement on the verb could either be showing inverse because of feature clash or else copying some kind of “inverse” feature from the D. Harbour calls ‘pencil’ an IDP noun, because it controls inverse-dual-plural agreement (in singular-dual-plural number respectively), as compared to ‘shoe’ which is an SDP noun (with unmarked gender producing no clashes).

The class of nouns which includes the word for ‘young man’ is lexically specified as [-pl], so it agrees as usual when it is singular or dual, because those numbers are also [-pl], but when ‘young man’ is plural, it triggers the same invariant inverse agreement that is triggered by ‘pencil’ in the singular; in Harbour’s terms, ‘young man’ is SDI.

D[sg] Num[+sg,-pl] N[-pl] ‘young man’

D[du] Num[-sg,-pl] N[-pl] ‘young man’

D[in] Num[-sg,+pl] N[-pl] ‘young man’

A noun like ‘tomato’ is specified as [-sg,-pl], with the result that it only triggers normal agreement in the dual; in both the singular and the plural there are feature clashes, and the inverse agreement arises; the patterns is IDI.

D[in] Num[+sg,-pl] N[-sg,-pl] ‘tomato’

D[du] Num[-sg,-pl] N[-sg,-pl] ‘tomato’

D[in] Num[-sg,+pl] N[-sg,-pl] ‘tomato’

There is another gender class which is specified as [+sg], and accordingly it agrees as usual when it is singular, but triggers inverse agreement in the dual and plural.

Effectively, then, Kiowa has an agreement probe which sees [+sg] on a Num head but continues to probe further into the noun phrase to see whether there is also a [-sg] feature on N; and it also sees [-sg] on Num and continues to probe further to see whether there is also a [+sg] on N.

If singular were a subset of plural in Kiowa, then it seems that any effect triggered by singular would be triggered by plural. If a feature match triggers inverse agreement, then there should be no IDP nouns like ‘pencil’: whatever triggers I on the singular should do so in the other numbers as well. If, on the other hand, it is the failure of a probe to find a feature to match with which triggers the inverse, then there should not be any SDI nouns like ‘young man’: if a probe of some kind fails to find any match in the plural it would have to also fail to find that match in the singular.

Preminger’s arguments seem sound and are based on broad typological observations, the observations that singular is never favored over plural in agreement neutralization or omnivorous agreement (and third is never preferred over first and second person). The intuition that markedness of features is directly reflected in containment relations enjoys wide support in current theory (e.g., Harley and Ritter 2002). On the other hand, Harbour’s argument from a single language seems compelling, and it is embedded in a rigorous and typologically motivated theory of number (Harbour 2011, Harbour 2014).

Taking both arguments at face value, is there a way to reconcile them? Could reference to negative values of features somehow be restricted so that it allows Kiowa but disallows omnivorous agreement which prefers singular, and disallows neutralization to plural? This is what’s currently keeping me up at night.

 Part II of Harbour’s argument for [-sg], added after the above was posted.

Part II of Harbour’s (2007) argument from Kiowa is that the gender features are semantically grounded. As with most (or all) gender systems, Kiowa gender is grammaticized and nouns are listed with gender specifications that may be synchronically arbitrary. But Harbour shows that there is a semantic core to the gender classes, and he argues that the semantic core is captured in his number specifications.

For example, the default class SDP with no gender specification, to which ‘shoe’ belongs, is semantically heterogeneous. The class to which ‘pencil’ belongs, IDP, is the usual class for vegetation and implements, while the class to which ‘young man’ belongs, SDI, consists mainly of animates and entities capable of self-directed motion. In Harbour’s analysis, IDP is specified as [-sg], the negation of [+sg], and [+sg] in the number domain defines atomicity, which as Harbour puts it “is conceptually close to individuality. So, inherently [-singular] nouns are those that are not salient, or recognizable, as individuals. This is obvious for vegetation, and for other members of the class, such as implements” (Harbour 2007: 95).

The class SDI is specified as [-pl]. In Harbour’s feature system in his book, this corresponds to [-augmented], which ensures that properties of proper subparts do not have the properties of the whole, which is true of animates ([-augmented] is the negation of [+augmented], which requires that something have subparts with the same properties as the whole).

The class IDI (e.g., ‘tomato’) is specified as [-sg,-pl]. When the semantic values of those features are combined by function application in Num, the result is dual. But Harbour argues that they do not combine semantically when used as gender values. Instead, they are simply conjoined, meaning that IDI class nouns are both non-individuable (like the [-sg] IDP nouns) and also non-homogeneous (like the [-pl] SDI nouns). Harbour argues that this is true of collections and clusters which deemphasize the parts, including ‘tomato’ but also the words for hair, brains, blackberries, plums, and similar things which are typically encountered as collections of discrete objects.

To my mind, the semantic grounding of the gender features renders even stronger the argument that the same features are involved in gender and number, and hence strengthens the likelihood that something like Harbour’s actual feature specifications are correct for Kiowa.


Harbour, Daniel. 2007. Morphosemantic Number. Springer.

Harbour, Daniel. 2011. Valence and atomic number. Linguistic Inquiry 42.4:561-594.

Harbour, Daniel. 2014. Paucity, abundance, and the theory of number. Language 90.1:185-229.

Harley, Heidi and Elizabeth Ritter. 2002. Person and number in pronouns: A feature-geometric analysis. Language 78.3: 482-526.

Preminger, Omer. 2014. Agreement and its Failures. MIT Press.

Preminger, Omer. 2019. What are phi-features supposed to do, and where? Talk presented at workshop on Thirty Million Theories of Features at the University of Tromsø, May 27–28 2019. Handout here.