Calibrating complexity: How complex is a gender system?

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Calibrating complexity: How complex is a gender system?

Jenny Audring Draft, Sept 23, 2015

ABSTRACT Grammatical gender is a many-‐sided phenomenon, involving complex relations between semantics, morphology, phonology, and syntax. Yet, not all gender systems across the world are equally complex. This paper presents a way to assess the descriptive complexity of gender systems in natural languages, building on the typological data collected in Corbett (1991 and 2013) and applying the insights from Canonical Typology (chiefly Corbett 2006, 2012; Corbett & Fedden 2017). The result is a typologically responsible evaluation of the ways in which grammatical gender can be more or less complex. The analysis provides a descriptive basis for experimental assessments of difficulty in acquisition and processing. Moreover, it demonstrates the set-‐up and use of calibration tools for the complexity of a grammatical subsystem, a methodology that can be applied to other linguistic domains. 1. INTRODUCTION Speakers have intuitions about language complexity, and so do linguists. Asked about complex grammatical gender systems, most linguists would mention French or Swahili rather than Italian or English. However, the gender systems of Swahili and French differ markedly in the way they are complex, and English gender might be complex in yet other ways. One of the languages with a proverbially complex gender system is German. In a famous monograph, Köpcke (1982) proposed a set of rules that account for the gender of 90% of the language’s monosyllabic nouns. This was – and still is – hailed as a remarkable feat, since German gender was thought to be complex to the point of arbitrariness (Maratsos 1979). Yet, Köpcke’s model in itself is considerably complex: it involves a total number of 44 different rules. Köpcke’s study, however, only investigates a single dimension of complexity: it focusses entirely on the rules of gender assignment. Other central aspects of gender, especially agreement, are not considered. This leaves the question of how simple or complex German gender might be in other dimensions, and indeed what these dimensions are. How can the complexity of a gender system be described and evaluated in a typologically responsible way? Following up on a preliminary attempt in Audring (2014) and drawing on the wealth of available typological and theoretical work, this paper develops a methodology to answer this question. Here, the focus is on absolute rather than relative complexity (see Miestamo 2008 and Kusters 2003 for details on the

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difference). That is, the objective of this paper is a descriptive evaluation of the system as such rather than an assessment of how difficult it is to produce, perceive, or acquire. The main reason is that difficulty cannot be studied directly – the only observable parameters are error patterns and processing time. If the acquisition, production, or processing of a structure proves to be slow or error-‐prone, an explanation for this fact will require an informed description of the complexity of this structure. Providing such a description, as well as suggesting a methodology for complexity calibration that can be applied to other areas, is the objective of this paper.1 2. A TWO-‐STEP APPROACH TO COMPLEXITY CALIBRATION In the following, we will assess the complexity of a grammatical subsystem in two steps. The first step is to identify the dimensions of variation for which it makes sense to evaluate a system or compare it to another. The second step establishes for each dimension what it means to be more or less complex. The point where all dimensions are at their lowest complexity is established as a theoretical zero, from which the degree of complexity can be calibrated outwards. The first step requires cross-‐linguistic knowledge of the grammatical system in question. The second step is not straightforward either. For example, an inflectional paradigm showing syncretism may be considered less complex since it involves fewer than the expected forms. To illustrate, Table (1) gives the paradigm of the German singular definite article, which has 12 cells, but contains only 6 different forms. (1) German singular definite article

Case Gender

NOM GEN DAT ACC

M der des dem den

F die der der die

N das des dem das Yet, the simplification in morphology does not carry over to the syntax – German syntax requires the full range of case/gender pairings. This has the effect that a smaller form paradigm has to map onto a larger function paradigm. Hence, simplification in one area may bring complexification in another. Cases such as this require principled decisions on how complexity is evaluated. A two-‐step approach in which the dimensions of complexity are identified and a hypothetical minimum is established, yields a theoretical space in which

1 Note also that a description of a complex system already entails a basic assessment of its difficulty, if only in defining the amount of what needs to be learned in order to master the system. Thanks to Ray Jackendoff (p.c.) for pointing this out.

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languages can be situated.2 This methodology is borrowed from Canonical Typology (Corbett 2006, 2012 and Brown et al. 2013). We will go further and argue that the parameters developed in Canonical Typology for agreement, morphosyntactic features and, indeed, gender can be directly applied to calibrate complexity. However, since canonicity and complexity are explicitly different issues, a brief theoretical discussion is in order.3 3. CANONICITY VS. COMPLEXITY Canonical Typology has been developed with the aim of mapping out the theoretical and typological variety of individual linguistic phenomena. At the center lies the “canonical core”, which is the ideal instance of the phenomenon in question, the point in which all definitions agree (2a). From this point outwards, a number of properties are identified in which real instances can diverge from the canonical, resulting in more debatable cases (2b). (2) Canonicity space a) The canonical core: an ideal system b) A real system To give an example: in canonical agreement we expect an agreement marker to be redundant, i.e. to not add any new information to the utterance (Corbett 2006: 11). This can be illustrated in example (3a) from French: the pronoun introduces the properties F and M, respectively, and the adjective repeats them redundantly. In (3b), by contrast, the noun is ambiguous for gender, with the effect that the first overt appearance of F and M is on the adjective, which thus introduces new information. (3b) illustrates a non-‐canonical situation – some linguists may see occasion to say that it is not a case of agreement. (3) a) elle/il est sotte/sot 3SG.F/3SG.M be.PRS.3SG stupid-‐SG.F/stupid.SG.M ‘she/ he is stupid’ b) leur ministre est sotte/sot 3PL.POSS minister(F/M) be.PRS.3SG stupid-‐SG.F/stupid.SG.M

2 Note that the the two steps as outlined above allow for calibration, but not for quantification. In order to actually measure complexity, the zero point and the dimensions of variation would need to be complemented by a scale that tells us how far a phenomenon diverges from zero. Devising such a scale is a third step, which goes beyond the limits of this paper. An exception is the dimension of gender values, which involves straightforward counting. 3 This paper is not the first attempt to link canonicity and complexity. For a different approach, see Walther 2011 and Sagot & Walther 2013.

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‘their minister is stupid’ We will return to this issue in 6.2 below. Canonicity is explictly not the same as simplicity. Since canonicity is all about theoretical expectations, the canonical core can be complex if complexity is what is expected. For example, a canonical gender system is not marked in just one syntactic domain, such as the phrase, but across several domains, say the phrase and the clause. A language that has gender agreement in only a single domain (such as English, which has only pronominal gender) is non-‐canonical in this respect, despite the fact that it is – as we will argue in 6.3 below – less complex. On the other hand, canonicity and complexity share a number of theoretical concerns. Both can be viewed as a space of possibilities, in which instances from real languages are situated. For both it makes sense to establish a yardstick in the form of a zero point – the canonical core in one case and a point of minimal complexity in the other. Moreover, neither theory makes claims about the commonness of instances. As Corbett puts it, “It follows that canonical instances, which are the best and clearest examples, those most closely matching the ‘canon’, may well not be the most frequent. They may indeed be extremely rare.” (2006: 9) Similarly, a minimally complex gender system may be hard to find. On the other hand, it might turn out that certain complexity parameters tend to occur in tandem. For example, as argued in Audring (2014), low complexity in agreement often correlates with simple assignment rules and a small number of gender values. Both canonicity and complexity involve a space that may reflect diverse kinds of convergences and contradictions. Therefore, it is useful to unpack this space and evaluate phenomena separately for each dimension. 4. DIMENSIONS OF VARIATION Work on the typology of gender systems (Corbett 1991), canonical agreement (Corbett 2006), canonical morphosyntactic features (Corbett 2012), and canonical gender (Corbett & Fedden 2017) provides an excellent roadmap for the dimensions of variation that are relevant for gender systems. In the following, we will explore these dimensions briefly. This section also serves as a outline of the characteristics of grammatical gender systems and the terminology used to describe them. A gender system can be said to involve the following dimensions (Corbett 1991):

− Controllers − Agreement targets − Domains − Values − Assignment rules − Conditions

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In the usual case, the controller role is taken by the head noun of an NP. The noun is the central player in the system, since it carries gender as an inherent lexical feature. However, nouns may or may not be overtly marked for gender. The constitutive markers for gender appear on other words which are controlled by the noun and co-‐vary with it in gender. The controller function can also be served by other elements than nouns, among them various types of pronouns (see example (3a)). The presence of agreement is a definitional property for gender – agreement sets gender apart from other nominal properties such as inflectional class or derivational formatives. This is captured in Hockett’s definition: “Genders are classes of nouns reflected in the behaviour of associated words” (Hockett 1958: 231). The “associated words” are referred to as agreement targets. They co-‐vary in gender with the noun and express this relation formally. Common agreement targets are articles, adjectives, verbs, and pronouns, but across the languages of the world, we also find more unusual targets such as adpositions, conjunctions, adverbials, and even words like yes and no, as seen in varieties of Dutch in Belgium: (4) Wambeek Dutch (van Craenenbroeck 2010: 211) Kom Marie mergen? – Jui-‐s. come.PRS.3SG Mary tomorrow – yes-‐F.SG ‘Is Mary coming tomorrow? – Yes.’ Nouns and the words that agree with them in gender appear in certain syntactic configurations that we call domains. The most local domain for gender agreement is the noun phrase, which comprises the noun and any attributive elements such as articles, adjectives, numerals, or possessives, some or all of which may function as agreement targets. Many languages, however, show gender agreement in larger domains, such as the clause, or anaphoric agreement on free pronouns, which can stretch across sentences and even across turns in conversation. The most obvious dimension in which gender systems vary is their range of values. While Indo-‐European typically has two or three genders (usually called masculine, feminine, neuter, common, or uter), many language families display richer systems (often called noun classes4 and labeled with numbers rather than names). The range of values can be read off from the variation in agreement markers – a method requiring careful analysis as well as theoretical choices if one agreement target happens to show a larger or smaller value range than another. We will return to this issue in 6.2. New nouns have to be assigned a gender value; this requires assignment rules. Such rules are straightforward and clear in a number of languages, but difficult

4 I follow Corbett 1991 in treating genders and noun classes as one phenomenon (but excluding classifiers), with agreement as the definitional condition.

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to state in others. Rules fall into three classes: semantic, phonological, and morphological. Examples are:

− nouns denoting women are feminine, all others are masculine (Diyari (Pama-‐Nyungan), Austin 1981, discussed in Corbett 1991: 11)

− monosyllabic nouns ending in /ʃ/ are masculine (German, Köpcke 1982) − nouns of declensional types II and III are feminine (Russian, Corbett

1991) Phonological and morphological rules are usually subsumed under “formal rules”. A majority of languages has mixed assignment systems involving semantic as well as formal rules (Corbett 2013, but percentages of mixed rule systems can be much higher in certain macro-‐areas, see Di Garbo 2014 for Africa). Moreover, it may be useful to distinguish between general rules that account for a large part of the noun vocabulary, and parochial rules with a much smaller scope. This distinction cross-‐cuts the semantic/formal split. Finally, gender systems differ in the degree to which they involve conditions. Conditions come in a wide variety; the most common are interrelations with other types of features such as person, number, or tense. A well-‐known condition is that languages may have fewer gender distinctions in the non-‐singular than in the singular (but not vice versa; this is Greenberg’s universal #37). Table (5) illustrates another widespread kind of condition. (5) Singular personal pronouns

Language Ngala (Sepik) Arabic (Afro-‐Asiatic) Italian (IE)

Gender/ Person

M F M F M F

1st wn ñǝn ana io 2nd mǝn yn anta anti tu 3rd kǝr yn huwa hiya lui lei

(Ngala personal pronouns from Siewierska 2013)

The three languages contrasted in (5), which all have two genders, differ in their possibilities to mark the feature on personal pronouns. While in Ngala, pronouns distinguish gender formally across all three person values, Arabic marks gender only in the 2nd and 3rd person, while Italian gender marking is restricted to the 3rd person. Since conditions always apply in relation to the other dimensions sketched above – typically controllers and targets – we will not discuss them as an isolated dimension. Taken together, we arrive at a complexity space that spans five dimensions and can be visualized as in (6).

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(6) Complexity space for grammatical gender Agreement targets Controllers Domains Values Rules For each dimension, complexity can be calibrated individually, with the help of a number of parameters. To this end, it is necessary to establish what behaviour in each domain counts as less or more complex. In the following, we review some of the issues and propose three principles to guide the analysis. 5. PRINCIPLES Intuitive judgments on complexity are usually based on the general idea that less is less complex. This is fairly straightforward for properties that can be counted or measured. For example, we can readily posit a principle that captures the intuition that a language with two gender values is less complex than a language with four. Following Miestamo 2008, we may call this the Principle of Fewer Distinctions. I Principle of Fewer Distinctions This principle might be defined as follows: The higher the number of values of a grammatical feature, the more complex the feature. Note again that we are speaking of absolute, i.e. descriptive complexity here. Though we have to speculate on this point, it is likely that in terms of relative complexity, e.g. in language acquisition, a four-‐gender language is not significantly more difficult than a two-‐gender language. Principle I on its own is not sufficient, since not all phenomena lend themselves to a quantitative evaluation. For example, it might be argued that alliterative, i.e. same-‐looking markers result in a simpler agreement system than markers differing in form (this point is made for canonical agreement in Corbett 2006: 15 f.; “alliterative concord” is discussed in Corbett 1991: 117). Thus, the gender marking associated with class 7/85 in Chichewa is simple: the noun and almost all possible agreement targets carry the markers chi-‐/zi-‐ (only one type of demonstrative pronoun has o instead of i; the forms being icho/izo (Bentley & Kulemeka 2001: 14)). 5 Bantu noun classes (here also regarded as genders) are traditionally numbered in pairs of singular and plural classes. Class 7/8 is one such pair, with 7 being the singular and 8 the associated plural class.

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(7) Alliterative agreement in Chichewa chi-‐patso chi-‐kugwa -‐ zi-‐patso zi-‐kugwa 7-‐fruit 7-‐fall.PRS 8-‐fruit 8-‐fall.PRS ‘a fruit (sg.) is falling’ ‘fruit (pl.) are falling’ Here and in other cases, the general credo of “less is less complex” does not apply since the form of the marker is not a quantifiable property. Instead, we assume a principle that is well motivated in the complexity literature (see Leufkens 2014): the Principle of Transparency. II Principle of Transparency This principle states that: Minimal complexity is characterized by a 1:1 mapping of meaning and form. In (7) above, we see two instantiations of this principle. First, the grammatical property CLASS 7 is expressed by means of a formal marker. This holds both for the noun and for the verb, since both have this property.6 Second, whatever item has the same grammatical property should also have the same marker. This kind of transparency is found in alliterative agreement, as in (7) above. Not all genders in Chichewa are fully transparent in this sense. In (8) below, the prefix on the class 1 noun looks different from the prefix on its agreement target and the verb is syncretic for singular and plural. Both facts slightly increase the complexity of the system. (8) Non-‐alliterative agreement in Chichewa mwa-‐muna a-‐kuyimba -‐ a-‐muna a-‐kuyimba 1-‐man 1-‐sing.PRS 2-‐man 2-‐sing. PRS ‘the man is singing’ ‘the men are singing’ In other instances, “less is less complex” may lead to the wrong predictions. For example, a word may generally co-‐vary with a noun in gender but fail to do so under certain circumstances. Consider the Dutch attributive adjectives in (9). They agree in gender (9a), but are invariantly suffixed in definite contexts (9b). (9) a) een nieuw huis – een nieuw-‐e vriend INDF new.N house(N) INDF new-‐C friend(c) ‘a new house’ ‘a new friend’ b) het nieuw-‐e huis – de nieuw-‐e vriend DEF.N new-‐N house(N) DEF.C new-‐C friend(C) ‘the new house’ ‘the new friend’

6 Here, we are abstracting from the fact that gender is an inherent, lexical property of the noun but a contextual property of the verb.

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The neutralization of the gender marking in (9b) could be seen as a simplification, but it creates complexity elsewhere: why does the suffix -‐e signal common gender in a) but not in b)? When does this happen?7 What consequences does it have elsewhere in the utterance? Such cases show that another principle is needed, which – following the terminology of Di Garbo (2014) – we call Principle of Independence. III Principle of Independence This principle states that: In the least complex situation, a grammatical feature is independent of other grammatical features or other linguistic or non-‐linguistic domains. That is, the behaviour of elements in a grammatical subsystem is self-‐contained. It is predictable without conditions, and it does not rely on outside information. Thus, gender marking should be independent of properties such as part of speech, other features such as person, number, definiteness, or case, and indeed impartial to semantic or pragmatic choices by the speaker.8 Where independence is violated, we see the need for a more elaborate description of the system and therefore higher complexity. Together, Principles I-‐III (repeated below) allow for the evaluation of the properties or behaviour observed in the various dimensions of the complexity space outlined in section 4. above. I Principle of Fewer Distinctions II Principle of Transparency III Principle of Independence In the remainder of the article, we will bring together dimensions and principles and work our way through the calibration of the complexity of a gender system. Again, we are building on the work on canonicity, especially on canonical gender (Corbett & Fedden 2017), with adjustments where needed for the question at hand.9 7 The examples suggest that the adjectival suffix is invariantly present when the determiner expresses gender. However, it also appears after a possessive (mijn nieuwe huis ‘my new house’, mijn nieuwe vriend ‘my new friend’) which itself is invariant for gender. 8 The independence of a grammatical feature from other logically compatible features is captured in Criterion 2 for canonical morphosyntactic features in Corbett 2012: 158. 9 In Corbett & Fedden’s discussion of canonical gender, three canonicity spaces are combined: canonical agreement, canonical morphosyntactic features, and canonical gender proper. We will consider the three aspects together in a single complexity space.

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6. COMPLEXITY PER DIMENSION For each of the five domains sketched in section 4. above, complexity can be assessed for a number of parameters. These serve to highlight individual characteristics or traits of behaviour that reflect higher or lower complexity. 6.1 Controller complexity The first controller-‐related parameter to be discussed is its overt presence or absence in the utterance. A cross-‐linguistically common reason for the absence of the controller is pro drop. Consider (10): (10) Spanish está cansad-‐a be.PRS.3SG tired-‐F.SG ‘she is tired’ According to the Principle of Transparency, an overtly present controller constitutes the less complex situation, since both participants in the agreement relation – controller and target – should be formally realized. Moreover, a controller that is absent in some cases but present in others – e.g. to express emphasis – would violate the Principle of Independence, since its distribution requires reference to properties outside the gender system proper.

Controller present < Controller absent Note that this is a case where an unspecified “less is less complex” would give the reverse prediction: an absent controller might count as less complex. The operationalization by means of Principles I-‐III provides the theoretical space for an evaluation geared to the phenomenon at hand. Second, the controller should have the relevant property. This means that in a language with grammatical gender, any noun should belong to a gender. While there are various languages with number systems involving only a subset of the noun vocabulary (Corbett 2000), it is highly uncommon for a language to have a gender system that only covers a subset of the nouns.10

Controller has feature < Controller lacks feature Yet, there are two widespread scenarios in which controllers may lack the relevant feature. First, personal pronouns – see the example of Arabic and Italian in (5) above – often distinguish gender only in a part of the paradigm, for example in the second or third person. This violates the Principle of Independence, since it involves interaction with other grammatical features,

10 A possible exception is Mopan Maya, a language with a highly non-‐canonical gender marker that is a free word and only occurs with a subset of the noun vocabulary (Contini-‐Morava & Danziger 2015).

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here, the feature PERSON. Second, many languages lack gender distinctions in the non-‐singular. Here, the situation is subtly different. The neutralization of gender in the plural stretches both across controllers and targets. Operating across the board, it does not create a featural mismatch and hence no extra complexity elsewhere in the system. By contrast, genderless pronouns functioning as controllers to gender-‐marked targets such as verbs or predicative adjectives (example (13) below) raise the complexity for the target whose gender value will have to be inferred from elsewhere (see section 6.2). Note, however, that singular-‐only gender may count as complexifying in the relative sense, e.g. in language acquisition. A gender system that is expressed both in the singular and the non-‐singular is in all likelihood easier to detect and master.11 The third property related to the controller is whether or not it expresses gender overtly or allows for gender to be ‘read off’ from its form.12 We find the following three scenarios: (11) a) Dedicated gender marker (Turkana, Eastern Nilotic, Dimmendaal 1983: 224) ɛ-‐sikin-‐a a-‐ŋasep M.SG-‐breast-‐SG F.SG-‐placenta ‘breast’ ‘placenta’ b) Form-‐based gender assignment (Italian) tavol-‐a libr-‐o table-‐F.SG book-‐M.SG ‘table’ ‘book’ c) Covert gender (Dutch) tafel boek table(C)SG book(N)SG ‘table’ ‘book’ In (11a), the nouns show overt gender in the form of class prefixes. In (11b), gender is associated with certain word-‐final vowels and therefore can be read off with some degree of reliability from the noun’s form. In (11c), by contrast, the nouns do not provide any formal indication of their gender.

11 On the other hand, gender agreement in the plural necessitates resolution rules for antecedents of different genders, which can complexify the system considerably. 12 In Corbett 1991: 62, both situations are treated together. However, it may be useful to distinguish between dedicated gender markers on the one hand and phonological or morphological properties that correlate with particular genders on the other. In the latter case, the association between form and feature may be less reliable. This is indeed the case in Italian: not every noun of the –o class is masculine (la mano ‘the.F hand’), and not every noun of the –a class is feminine (il papa ‘the.M Pope’, Thornton 2001: 485).

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In canonical typology, the issue is related to the general point of “clear marking” – a feature is more canonical when it has clear formal exponents. For complexity, overt marking falls in the domain of the Principle of Transparency, which decrees that whatever has a feature should mark it. Therefore, overt gender on the noun constitutes the less complex, covert gender the more complex situation.

Overt marking on controller < No overt marking on controller The following parameter to be considered is the behaviour of the controller with regard to its targets. According to both the Principle of Transparency and the Principle of Independence, nouns should be consistent controllers, i.e. trigger the same agreement on any target in any case. This captures the insight that hybrid nouns such as German Mädchen (N) ‘girl’, which takes neuter agreement on some targets and feminine agreement on others, are a complexifying phenomenon in a gender system.

Consistent controller < Hybrid controller As argued in Audring 2013, variation in agreement can be viewed as a property of the target instead of the controller, which is why this point will be taken up again in 6.2 below. A related property is that controllers, i.e. nouns, should have only one gender value each. Thus, the following nouns make the Dutch gender system more complex: (12) Double-‐gender nouns in Dutch de/het deksel ‘the (C/N) lid’ de/het matras ‘the (C/N) mattress’ de/het solo ‘the (C/N) solo’ de/het octaaf ‘the (C/N) octave’ de/het uniform ‘the (C/N) uniform’ The Principle of Transparency applies here, paired with considerations about the difference between inherent and contextual features (Booij 1996). For nouns, gender is an inherent, lexical feature. Agreement targets, by contrast, have gender as a contextual feature and so should be able to assume any value depending on the controller. Therefore, the two domains need to be treated differently in the complexity calibration. For nouns, a single, invariable gender value is the simplest scenario.13 Controller has a single, fixed gender < Controller has variable gender 13 Corbett & Fedden (2017) point out that gender differs in this respect from other morphosyntactic features. For gender, inherent means lexically fixed, so each noun only has a single gender value (in the canonical case). Other inherent features such as number, person, or tense have values that are chosen on semantic grounds, so various values are available for each controller.

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Note that this point is not the same as the previous one: double-‐gender nouns as in (12) can be consistent agreement controllers for each of the two options. Conversely, hybrid nouns such as Mädchen are normally not considered to belong to two genders (Corbett 1991: 225). Note further that the considerations above include the expectation that the gender value of a noun should not be manipulable for semantic or pragmatic purposes. Languages allowing for such manipulation are assumed to have more complex gender systems. Finally, controllers should function the same whether they are nouns, pronouns, or belong to any other word class. This falls under the Principle of Independence – a gender system that is independent of the controller’s part of speech is less complex than one which has different rules for, say, pronouns and nouns. Examples for the latter situation can be found in Corbett (2006: 167) for Jarawara, Skou, Burmeso, and Bayso. Another phenomenon that might be included here are special agreement rules for non-‐nominal controllers. Part of speech of controller does not

matter < Part of speech of controller matters

6.2 Target complexity Moving on to targets, there are a number of expectations that follow straightforwardly from those formulated for controllers. For example, saying that in the least complex case the controller is present, that it bears the relevant feature and that it marks this feature formally means that the target should be redundant with respect to grammatical information – the controller already expresses it.

Gender value on target is redundant < Gender value on target is informative

A sentence such as (13) from French illustrates the more complex situation in which the pronominal controller lacks gender and the target, the adjective, introduces the feature into the syntax. (13) je suis forte/fort 1SG be.PRS.1SG strong-‐SG.F/strong-‐SG.M ‘I am strong’ Equating redundancy with low complexity is not uncontroversial. After all, redundancy is often seen as a violation of transparency, since it is a many-‐to-‐one relation between form and meaning (see e.g. Leufkens 2014). Two arguments might be given in favour of the approach taken here. First, the violation of transparency in Leufkens’ sense is an inbuilt consequence of a language having a gender system in the first place. Since genders are, in fact, agreement classes, and agreement always involves multiple expressions of a single property, a transparent gender system does not exist. Within gender, however, transparency

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can be recovered by assuming, as in 6.1 above, that any word that carries a feature should mark it formally. This expectation is met in some cases and contradicted in others, thus providing a useful point for evaluation. Second, the seemingly simpler feature structure of the controller of the gender-‐agreement in (13) leads to new problems, since the gender values F and M on the adjective will have to come from elsewhere, e.g. from the grammatical gender of an implicit noun (an example is given in 7.2 below) or the sex of the referent. Also, we have to theoretically account for the fact that the syntax allows for the occurrence of a gender-‐marked target with a genderless controller. The next item on the list of canonical properties concerns the nature of the morphological markers. In a canonical world, “gender is realized through agreement by canonical inflectional morphology, which is affixal” (Corbett & Fedden 2017). For complexity, the issue might look different. As argued in Leufkens (2014), it may not matter so much whether a marker is free or bound, as long as it shows a 1:1 match of meaning and form. Indeed, it may be more relevant to distinguish dedicated markers for gender from portmanteau markers that also express other features. According to these considerations, fusional morphology is potentially more complex, since it is more likely to show portmanteau marking. Since we do not see any strong reasons to regard free markers as more complex than affixal markers (although they are clearly less common and less canonical), we will formulate the relevant parameter only with respect to the functionality of the marker. Gender marker has unique function < Portmanteau gender marker The Principle of Transparency decrees that in the least complex situation, a gender marker has a unique form for each gender value.14 The alternative is syncretism, an issue we touched on above. Syncretism is a multifaceted phenomenon, and whether or not it should be considered a case of simplification of complexification depends on the perspective, as we saw in section 2 above. Considering, as we do, the individual agreement target rather than the number of different forms within a paradigm, and applying the principles developed above, a straightforward criterion emerges. Gender marker has unique form < Gender marker is syncretic

A related property of gender agreement targets is that they should be obligatory rather than optional. This expectation falls under the Principle of Independence: an optional marker would require extra machinery to account for its distribution.

Gender marking is obligatory < Gender marking is optional

14 The relevant insight is captured in Principle I, Criterion 2 for canonical morphosyntactic features “Canonical features and their values are uniquely distinguished across the other logically compatible features and their values” (Corbett 2012: 158).

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For the same reason, gender marking should be productive: the relevant marker should appear on any lexical item that belongs to the right part of speech.

Gender marking is productive < Only a subset of lexical items per agreement target mark gender

In the more complex situation, requiring explanations from outside gender proper, individual lexical items may fail to mark gender while others of the same syntactic category do agree. This situation is fairly common. For example, French has gender agreement on the adjective, but in a wide variety of adjectives the distinction is not observable ((14) lists a few examples). (14) French gender-‐invariant adjectives drôle ‘funny’ facile ‘easy’ magnifique ‘magnificent’ propre ‘clean’ triste ‘sad’ Moreover, as argued in section 5. above, gender markers are simpler when they are alliterative, i.e. have the same form per gender value, whatever the target. Note that the most complex alternative would be a suppletive marker, which bears no formal resemblance to its peers. Gender marking is alliterative per

value < Gender markers have different forms per value

The next issue was pointed out by Comrie (2003) and developed further in Corbett (2006). Comrie discusses the phenomenon of “trigger-‐happy” agreement, meaning that the agreement target has a choice in which controller it agrees with. An example involving gender is found in the Nakh-‐Daghestanian language Tsez (15): (15) a) eni-r [už-ā magalu �� b-āc'-ru-łi] mother-DAT boy-ERG bread:ABS:III III-eat-PSTPRT-NMLS.ABS r-iy-xo. IV-know-PRS b) eni-r [už-ā magalu �� b-āc'-ru-łi] mother-DAT boy-ERG bread:ABS:III III-eat-PSTPRT-NMLS.ABS b-iy-xo. III-know-PRS ’The mother knows that the boy ate the bread.’ (Comrie 2003: 323) Here, the matrix verb meaning ‘knows’ can agree either with the whole subordinate clause indicated by square brackets ((15a), requiring the default

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gender IV because the controller is not nominal and thus does not have gender) or with the noun meaning ‘bread’, which belongs to gender III (15b). This is a complex situation according to the Principle of Independence – in the simple case, any agreement slot on a target is specialized for agreement with a particular controller, with no further conditions or choice. While trigger-‐happy agreement is rare in general, there are at least two languages in which it involves gender: Tsez as mentioned above (Polinsky & Comrie 1999, Comrie 2003) and the Papuan language Skou (Donohue 2003). Target specified for one controller < Target has a choice of controllers The last two parameters to be discussed have to do with targets and the gender values they express. As mentioned in 6.1 above, controllers and targets differ in the way value choices are restricted. For controllers, only one value should be available, as gender in nouns is a lexical feature. For targets, all values should be available in general, but only one per controller, as targets are meant to co-‐vary with the noun. In the least complex case, agreement targets should simply match whatever value is found on the controller. There are two kinds of deviations from the expected situation. The first is that the target ‘has its own opinion’ about value choice and ends up marking a different gender than the controller’s. Usually, this goes hand in hand with variation: given the same controller, the target sometimes has matching gender, sometimes not. The second deviation is a systematic mismatch between controller and target genders, so that targets can never match the controller. This happens when the target has gender morphology for less or more values than the controller’s. Let us look at the two scenarios in turn.

Targets have a choice in value < Targets do not have a choice in value

Targets with ‘their own opinion’ are found in semantic agreement, illustrated in (15), a spoken example (Corpus Gesproken Nederlands). Here, the agreements have two different values: the demonstrative determiner is invariantly and expectedly neuter, while for the relative pronoun, the speaker first chooses a neuter form, then hesitates and picks a common gender form. (16) Semantic agreement (Dutch) dat meisje dat uh die daar achter het stuur DEM.SG.N girl(N)SG REL.SG.N eh REL.SG.C there behind DEF.SG.N wheel(N) zat sit.PST.3SG ‘that girl who sat behind the wheel’ Here we see a case of choice, as a consequence of which the target ends up not matching the controller in gender. Behaviour as illustrated in (16) is often called

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“semantic agreement” as it is licensed by nouns whose gender is perceived to be in conflict with their semantics.15 Semantic agreement makes the system more complex because it involves semantics in a place where only syntax should matter (Principle of Independence). Targets can fail to match their controllers for other reasons, though. It happens that in a language, a target has a paradigm with less or more values than its controller. Such mismatches are more widespread than might be expected; Corbett (1991) discusses the issue and its theoretical implications in detail (chapter 6). By way of a brief illustration, let us look at Dutch again (not discussed in Corbett 1991). Most agreement targets in Dutch mark two genders, referred to as common (C) and neuter (N). Two targets, marked bold in (16), diverge from this pattern. The personal pronouns distinguish not two genders but three, reflecting the traditional distinction in masculine, feminine, and neuter that used to pervade the whole system. The possessive pronouns, by contrast, have syncretic forms that result in a split between feminine and non-‐feminine. Note that gender agreement is restricted to the singular, so only the singular paradigm is given. (17) Gender agreement in Dutch

Target/ Gender

DEF DEM ADJ REL PRO POSS

C /M de deze/die -‐e die hij zijn

C/ F zij haar

N het dit/dat ø16 dat het zijn Personal pronouns thus add a gender distinction that is not available for the majority of the other targets. Possessive pronouns, by contrast, collapse the distinction between C and N and replace it by a feminine/non-‐feminine split. While for the possessive, the mismatch can be put aside as sporadic syncretism, the non-‐neuter pronouns are paradigmatically unable to match their controller in gender.

Targets match controller in value < Targets do not match controller in value

Again, such inconsistencies are a violation of the Principle of Independence, as they require additional information about the target type, as well as other motivations for the setting of the value.

15 For the pervasiveness of semantic agreement in Dutch, see Audring (2006 and 2009). 16 In contrast to the common gender adjective that has the suffix -‐e, the neuter adjective is a bare stem. This distinction only occurs in indefinite contexts (in definite context, the adjective has the suffix in both genders).

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With this, we leave the dimension of the agreement targets and move on to the dimension of syntactic domains. 6.3 Domain complexity For domains, there are fewer complexity parameters than for controllers and targets. The first parameter follows directly from the considerations in 6.1 and 6.2: the domain of agreement involves an asymmetric relation between controller and target. This is part of the definition of agreement and is therefore not easily violable – even though there are cases where the target fails to accommodate the controller, there is never the reverse situation, in which a noun adjusts in form to one of its targets. We will therefore not discuss this parameter any further. The second parameter, borrowed again from Canonical Typology, is that domains should be local. Thus, gender agreement within the noun phrase counts as more canonical than predicative agreement or agreement on anaphoric pronouns. The question arises whether gender agreement within the noun phrase should also count as more complex. With the observation in mind that agreement involves “displaced information” (Moravcsik 1988: 90), i.e. information marked in a place where it is not relevant, we might assume that longer-‐distance agreement means longer-‐distance displacement and thus higher complexity. However, as argued in Audring (2013: 43), the argument does not hold for anaphoric pronouns, which should be the most distant targets in anybody’s theory of agreement. Pronouns are coreferent with the noun, so whatever information is encoded in agreement is also relevant to the pronominal target. Therefore, greater syntactic distance does not necessarily involve greater semantic distance, so the alignment does not hold. Other roads towards an answer involve theoretical issues, such as whether phrasal agreement is assumed to involve the same mechanism as agreement in the clause or any other domain. Since theories of syntax differ in this respect, the question will have to remain unresolved here. The last parameter to be considered, briefly mentioned in section 3. above, is another case where canonicity and complexity come out differently. In a canonical world, agreement involves not one domain but several. This follows from the fact that more domains provide better analytical evidence for the existence of an agreement system. However, with regard to absolute complexity, each additional domain makes the system larger and therefore more complex.

Single domain < Several domains Domain complexity is a parameter for which English ranks on the low extreme: it only marks gender in the pronominal domain. Yet, this absolute simplicity does not translate into relative simplicity, i.e. greater ease for the learner. Since Mills 1989, it is known that English gender is acquired comparatively late. One of the reasons is that a lower range of agreement domains decreases the number of syntactic cues available to the child. The (not unreasonable) expectation that

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fewer domains should be a lighter burden for the learner does not hold. Here is an area where absolute and relative complexity can be teased apart insightfully. 6.4 Complexity of values Assessing the complexity of gender values, we face an easier task since two of the parameters are also relevant for other dimensions and have been discussed there. The first is that gender values should be no independent choice of the speaker – neither for the noun, for which it is a lexical property, nor for the target, which is expected to mirror the gender value of the noun. Therefore, variation or choice make the system more complex.

No choice of values < Choice of values The relevant principle is the Principle of Independence: gender should be a self-‐contained system and not require reference to outside factors such as other features or the speaker’s semantic or pragmatic purposes. Second, feature values should match both between controller and target and across targets. This parameter has been discussed at length in section 6.2. We repeat the complexity scale from the target perspective:

Matching values < Mismatching values Finally, we touch on what might be the most obvious parameter, which is the number of genders values in a language. While this measure may not always be easy to assess descriptively, the complexity argument is that fewer values constitute a simpler system.17

Fewer values < More values Here, the Principle of Fewer Distinctions can be applied straighforwardly. 6.5 Complexity of rules While it is clear how agreement targets are assigned a gender value – by the controller – a comprehensive account of gender also requires an explanation for how assignment works for nouns. Depending on the language, assignment rules range from perfectly straightforward to bewilderingly opaque. Starting from the assumption that a straightforward system is less complex than an opaque one, we will discuss three parameters: productivity, number of rules, and rule types. In this section, we diverge somewhat from the work on canonicity, both in the parameters assumed and in their evaluation.

17 The number of gender values is not discussed in detail in the context of Canonical Typology. The only criterion for canonicity is that the values should form a closed rather than an open class (Corbett & Fedden 2017).

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The first parameter to be considered is the productivity of assignment rules. Depending on the definition, for a rule to be productive means that it covers a substantial range of its possible instantiations and/or that it accounts for the behaviour of new cases. Not all rules that have been proposed for gender assignment – famously those for German in Köpcke (1982, Köpcke & Zubin 1984 and elsewhere) and for French in Tucker, Lambert & Rigault (1977) – are of this kind. This is not surprising: gender is likely to be stored in the mental lexicon rather than assigned on the spot each time a noun is used (although loanwords and new formations do require active gender assignment). Therefore, the synchronic distribution of nouns over genders reflects assignment events that took place at some point in the past, just as the lexicon of a language shows evidence for no-‐longer productive rules of word formation. Such patterns are best seen as redundancy rules (in the sense of Jackendoff 1975) – rules accounting for the behaviour of stored exemplars. Redundancy rules typically match an unpredictable subset of possible instances, which does not get extended easily. Due to the Principle of Independence, productive rules are less complex than pure redundancy rules, since redundancy rules require information about the individual lexical entries for which they do or do not hold.

Productive rules < Pure redundancy rules Next off, rule systems can involve a higher or lower number of rules. As mentioned in section 4., the Pama-‐Nyungan language Diyari makes use of only two rules, which together account for entire noun vocabulary (Austin 1981, discussed in Corbett 1991: 11):

− Nouns referring to women are feminine − All others are non-‐feminine

By contrast, the work of Köpcke (1982) on German – mentioned in the Introduction – proposes 44 different rules for monosyllabic nouns only. According to the Principle of Fewer Distinctions, as well as to common sense, Diyari has the simpler rule system. Note that this parameter is inherently wedded to the scope of rules: simpler rule systems contain more general rules, while rules in complex systems are more parochial, each accounting for only a small subset of nouns.18

Lower number of rules < Higher number of rules The last complexity parameter to discuss concerns the type of rules. As mentioned earlier, it is common to distinguish semantic and formal rules, whereby formal rules can refer to phonological or morphological properties of the noun (see Corbett 1991 for details). Corbett & Fedden (2017) argue that

18 A nice example of a parochial rule can be found in many pedagogic grammar sources for L2 learners of German: nouns denoting the seasons are masculine. This rule is exceptionless, but it covers only four instances.

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semantic rules are more canonical since they can make use of the lexical information about the noun without needing to refer to other sources.19 For complexity, we follow a suggestion by Di Garbo (2014) and posit that a language with a single type of rule is simpler than a language with several rule types. In effect, this also favours semantic rules, as languages with form-‐based gender always also show semantic rules, while the reverse does not hold. However, if a language were to be found that uses only formal rules (a candidate might be the Nilo-‐Saharan language Uduk, Killian 2015), it would score as simpler for this parameter than a mixed rule system.

Single type of rule < Several types of rule This concludes our discussion of complexity parameters. In the final part of this paper, we will demonstrate how the tools developed above can be applied to an individual language. 7. THE COMPLEXITY OF GERMAN GENDER This article opened with the question how the complexity of a gender system can be assessed systematically. In the following, we will answer this question for the proverbially complex gender system of German. First, we will give the list of parameters, numbered for easier reference. Shading in the cells indicates the judgement for German as predominantly simple or complex for the respective parameter. Some of the choices, including all that involve the judgement “complex”, will be motivated below. 7.1 Overview of parameters Dimension Simple Complex Controller 1. Controller present Controller absent 2. Controller has feature Controller lacks feature 3. Overt marking on controller No overt marking on controller 4. Consistent controller Hybrid controller 5. Controller has a single, fixed

gender Controller has variable gender

6. Part of speech of controller does not matter

Part of speech of controller matters

Targets 7. Gender value on target is redundant

Gender value on target is informative

8. Gender marker has unique function

Portmanteau gender marker

9. Gender marker has unique Gender marker is syncretic

19 An argument against this point might be that semantic properties – while they are indeed part of the lexical entry of the noun – need to be singled out as relevant for gender for each language individually. Besides, the phonological or morphological properties are also part of the lexical entry and need to be identified as relevant for gender in the same way.

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form 10. Gender marking is

obligatory Gender marking is optional

11. Gender marking is productive

Only a subset of lexical items per agreement target mark gender

12. Gender marking is alliterative per value

Gender markers have different forms per value

13. Target specified for one controller

Target has a choice of controllers

14. Targets have a choice in value

Targets do not have a choice in value

15. Targets match controller in value

Targets do not match controller in value

Domain 16. Single domain Several domains Values 17. No choice of values Choice of values 18. Matching values Mismatching values 19. Fewer values More values Rules 20. Productive rules Redundancy rules 21. Lower number of rules Higher number of rules 22. Single type of rule Several types of rule 7.2 Motivation German does not allow pro drop, so the only instance of a target without an overt controller (parameter 1) is the occasional exophoric pronoun, i.e. a pronoun referring to an implicit antecedent as in (looking at a dropped watch): “Und, geht sie noch?” – the feminine pronoun matches the feminine Uhr ‘watch, clock’. Nouns all have genders; the only pronouns that lack it are first and second person pronouns (parameter 2.). Moving on to parameter 4, German noun are generally consistent controllers, with only a small number of hybrid nouns. While German Mädchen is the poster-‐child example of a hybrid noun, hybridity is not overall common in the language. The only productive source of hybrids are diminutives referring to persons. Likewise, double-‐gender nouns (parameter 5) are very rare (not counting homophones that have different gender, but also different meanings). Examples are mostly loans such as Yoghurt (M/N) or Ketchup (M/N). Manipulation of gender values for semantic or pragmatic purposes is not possible. German gender morphology is of the portmanteau type (parameter 8), and paradigms show a lot of syncretism, within gender and across genders (parameter 9). Table (1) in section 2 gives a taste of its pervasiveness. Skipping ahead to 14, targets are usually consistent among each other, except for those occurring with one of the few hybrid nouns. For parameter 15, it is interesting to note that possessive pronouns are syncretic as in Dutch – see Table (16) above – with the effect that they distinguish feminine – non-‐feminine

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rather than masculine – feminine – neuter. However, this deviation is so marginal that it does not justify a reanalysis of the system. The domains (parameter 16) of German gender are complex, but not exceptionally so; we find agreement on several targets in the noun phrase and in the relative and the anaphoric domain. However, there is no gender agreement in the predicate, neither on verbs nor on predicative adjectives. Many languages would score higher on this parameter. As is well known, German has only three genders (parameter 19), so its complexity of values is medium or low. The only domain where German displays truly remarkable complexity is in the assignment rules. Most rules are redundancy rules (inspiring huge research efforts to explain or predict gender assignment to loanwords, see e.g. Onysko 2007). As pointed out before, Köpcke (1982) identified 44 different rules for monomorphemic nouns only; an exhaustive number for the whole noun vocabulary is (to my knowledge) not available. Furthermore, rules of all types have been proposed:

− semantic: general rules pertaining to the sex of the referent, parochial rules such as ‘alcoholic drinks are masculine’,

− morphological: rules referring to derivational morphology, e.g. individual suffixed being associated with certain genders, and rules referring to inflectional morphology, as in a partial alignment of gender and inflection class

− phonological: rules involving word-‐initial as well as final phonemes and phoneme clusters.

Here, we find the main source of the notoriety of German gender. For the other parameters, the systematic evaluation paints the picture of a fairly run-‐of-‐the-‐mill, even simple gender system. 8. CONCLUSION In this article, we have developed an evaluation matrix for the complexity of grammatical gender systems. Standing on the shoulders of previous work in typology (Corbett 1991) and Canonical Typology (Corbett 2006, Corbett 2012, Corbett & Fedden 2017), we have identified the dimensions of variation that together form the complexity space for this grammatical subsystem. We have explored the space with the help of parameters for each dimension and armed with three Principles to guide the evaluation. The result is a tailored test battery that can be used to calibrate the complexity of an individual gender system or to compare two or more systems from different languages. The model allows for the disentangling of phenomena that bear on different domains of complexity, such as syncretism or hybridity. By being explicit about the perspective, multi-‐faceted phenomena can be split and evaluated depending on domain or parameter. Explicitness is considered a strength of the approach:

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choices are motivated on every level; domains, perspectives, and principles are clearly stated. This renders the model open to comparison or amendment and keeps it useful for researchers who might find themselves disagreeing with individual choices made. The application of the methodology is demonstrated for German. On the way, we have encountered a number of issues that are of theoretical interest, such as what it means for an aspect of the system to be transparent or the importance of featural independence. The analysis is presented in the hope of inspiring more endeavours of this kind, such that larger generalizations may emerge and the principles for calibrating complexity may stand on a broader, better-‐motivated founding. REFERENCES Audring, J. 2006. Pronominal Gender in Spoken Dutch. Journal of Germanic Linguistics 18.2, 85-‐116. Audring, J. 2009. Reinventing Pronoun Gender. Utrecht: LOT Dissertation Series Audring, J. 2013. A Pronominal View of Gender Agreement. Language Sciences 35. 32-‐46. Audring, J. 2014. Gender as a complex feature, Language Sciences. 43, 5-‐17. Austin, P. 1981. A grammar of Diyari, South Australia. Cambridge: Cambridge University Press. Bentley, M. and Kulemeka, A. 2001. Chichewa. München: Lincom Europa. Booij, G., 1996. Inherent versus contextual inflection and the split morphology hypothesis. In: Booij, G. & van Marle, J. (eds.), Yearbook of Morphology 1995. Dordrecht: Kluwer, 1-‐16. Brown D. P., Chumakina M., Corbett G. G. 2013. Canonical Morphology and Syntax. Oxford University Press. Comrie, B. 2003. When Agreement Gets Trigger-‐Happy. Transactions of the Philological Society, 101(2), 313–337. Contini-‐Morava, E. & Danziger, E. 2015. Non-‐Canonical Gender in Mopan Maya. Paper presented at SLE 2015, Workshop on Non-‐Canonical Gender, 2 September 2015, Leiden, The Netherlands. Corbett, G. G. 2013. Systems of Gender Assignment. In: Dryer, Matthew S. & Haspelmath, Martin (eds.) The World Atlas of Language Structures Online. Leipzig: Max Planck Institute for Evolutionary Anthropology. (Available online at http://wals.info/chapter/32, Accessed on 2015-‐01-‐16.)

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Calibrating complexity: How complex is a gender system?

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