Fluctuations in allomorphy domains: Applying Stump 2010 to Armenian ordinal numerals

Abstract

Numerals and ordinals occupy a special place in the typology of suppletion. In generative work, one basic cross-linguistic parameter is whether ordinal allomorphy displays internal vs. external marking. Internal marking is when irregular forms propagate from lower ordinals to higher ones (English ‘first’ $ \to $ ‘twenty-first’), whereas external marking is the lack of propagation. We catalog ordinal formation in Armenian dialects through both formal-generative and functional-typological perspectives. We find that Eastern Armenian and Early Western Armenian are uniformly external-marking systems for the ordinals of ‘1–4’. However, Modern Western Armenian is a mixed system: ‘1’ displays external-marking while ‘2–4’ display internal-marking. Simultaneously, the ordinal of ‘1’ uses a suppletive portmanteau, while the ordinals of ‘2–4’ use agglutinative allomorphs. We formalize these differences in a derivational approach to morphology (Distributed Morphology). We argue that mixed systems arise from allomorphy rules that are sensitive to either constituency or linearity. The Western mixed system seems typologically rare and novel. Given our formal analysis, we then uncover other asymmetries in the propagation of irregular ordinals and the retention of portmanteau morphology across 35 Armenian varieties. The end result is a strong functional correlation between suppletion, external marking, and lower numerals.

1. Introduction

Within morphology, numeral systems often show restricted types of morphosyntactic relationships. There is a wealth of work on the formation of cardinal numbers from each other (Hurford 1975; Ionin & Matushansky 2013; Veselinova 2020; Sudo & Nevins 2022) and the syntax-semantics of ordinals (Ionin & Matushansky 2018; Tatsumi 2021). This paper focuses on a small corner of ordinal typology: the derivation of ordinals from cardinals (Stump 2010). We catalog this phenomenon across a sample of 35 Armenian varieties with both a generative and typological goal. ¹

Within ordinal morphology, a common cross-linguistic tendency is for the lower cardinal numbers to have suppletive ordinal forms, e.g., English ‘one’ and ‘first’ (Veselinova 1997; Stolz & Veselinova 2013; Stolz & Robbers 2016). Although the suppletion of low numbers is common, languages vary in whether these suppletive forms are propagated to higher forms (Hurford 2003; van Drie 2015). ² For example, alongside ‘twenty-one’, English does not use a form *twenty-one-th; instead ‘twenty-first’ is used, showing inheritance from ‘first’. French, however, blocks this inheritance in higher forms, e.g., 1 and 21 are un and vingt-et-un respectively, but their ordinals are premier and vingt-et-unième instead of *vingt-et-premier. Based on this difference in inheritance patterns of suppletion, Stump (2010) categorizes ordinal formation as externally marked in French, while it is internally marked in English.

In this paper, we apply these typological and generative findings to Armenian. Armenian is an independent branch within the Indo-European family with two standard lects: Western and Eastern Armenian. ³ In both standard dialects (Table 1), the suppletive ordinal of 1 is a portmanteau that is not propagated to higher numbers like 21. In contrast, the ordinals of 2–4 are agglutinative and use special root and suffix allomorphs. These allomorphs are propagated to higher numbers like 24 in Modern Western Armenian but not in Eastern Armenian. We thus find dialectal variation in that Eastern Armenian blocks propagation for all ordinals, regardless of whether the ordinal is a portmanteau or agglutinative. We underline these irregular forms throughout this paper.

Table 1 Overview of ordinals in Standard Armenian.

The Western Armenian data demonstrate an unexpected mixed system of external marking for ‘1’ but internal marking for ‘2–4’. In terms of our generative analysis, we develop an analysis based on Stump’s 2010 foundational work on ordinals. We translate his Paradigm Function Morphology (PFM)-based analysis to a piece-based realizational model of morphology like Distributed Morphology (DM) (Halle & Marantz 1993; Arregi & Nevins 2012), but our generalizations can easily extend to other models. We adapt these generalizations on propagation and internal/external marking to DM-based work on allomorphy domains (Embick 2010, 2015; Bobaljik 2012; Moskal 2015). Briefly, external marking requires that the sequence √-ord forms a morphosyntactic constituent, while internal marking weakens this restriction to just requiring linearity.

Typologically, the ordinal data from the two standard dialects suggests multiple asymmetries between ‘1’ and ‘2–4’. The ordinal of ‘1’ is a suppletive portmanteau and never propagates, while the ordinals of ‘2–4’ are numerically higher, agglutinative, and variably propagate. To foreground these asymmetries, we go through a sample of non-standard Armenian dialects that we had access to. The end result is a typological application on ordinal allomorphy across 35 Armenian varieties. The application demonstrates the utility of Stump’s original typology and foregrounds functional correlations for suppletion in lower numbers.

This paper is organized as follows. In Section 2, we first explain Stump’s 2010 groundbreaking generative typology of ordinal allomorphy. We then catalog ordinal formation in Modern Standard Armenian (Section 3). We formalize the Armenian data in Section 4 and develop our generative analysis. We then go through a wider typology of Armenian varieties in Section 5. We discuss and summarize our findings in Section 6. We conclude in Section 7.

2. Stump 2010’s typology of ordinal formation

Stump (2010) is a large cross-linguistic study of ordinal formation. That paper sets up both typological and generative benchmarks for studying suppletion and allomorphy in ordinal formation. He sets up a basic parameter for ordinal formation: whether there is percolation of irregular forms (internal marking) or not (external marking).

Informally, a language has an internal-marking ordinal system if complex numerals inherit the ordinal allomorphs of their simple forms, while a language has external marking if there is no such inheritance. To illustrate, consider the numbers ‘1’ and ‘21’ in English and French in Table 2.

Table 2 Internal vs. external marking in English and French.

In English, the ordinal form of ‘one’ is a suppletive ‘first’, and not an agglutinative *one-th. This suppletive form is inherited by higher numbers such as ‘twenty-first’. Informally, such an allomorphy pattern is called internal marking because the ordinal form of the entire number ‘21’ is based on the ordinal form of the internal unit ‘1’.

In contrast, French has external marking. The suppletive ordinal of un ‘1’ is premier. But this suppletive form is not propagated to higher numbers. We thus get vingt-et-unième and not *vingt-et-premier, even though *un-ième is not a free-standing form. Such a system is called external marking because the ordinal form is determined based on examining the entire number ‘21’, and not just the internal ‘one’ unit.

Structurally, for [[20-1]-Ord], the allomorphy pattern resembles a bracketing paradox in English but not in French (Pesetsky 1985; Stump 1991; 1996; Newell 2019).

Stump (2010) further elaborates this typology by introducing other parameters of variation, such as extended marking and conjunct marking. We set these aside for now and return to them later (Sections 4.4 and 5.2). The next section discusses how the Armenian data fit into this basic parameter system.

3. Numerals of Modern Standard Armenian

Armenian is a pluricentric language made up of two standard dialects (Standard Western and Standard Eastern) and a host of non-standard dialects. We first focus on the two standard varieties. The two standard forms share largely the same morphology but with some systematic phonological differences. We go through the cardinal (Section 3.1) and ordinal systems (Section 3.2) and then patterns of ordinal inheritance (Section 3.3).

3.1. Cardinal numerals of the two standards

Numerals can be categorized as either cardinals (card) or ordinals (ord). There is variation in the morphological structure of the cardinal (Table 3). Numbers 1–6 are monomorphemic from a simple root (√), while 7–10 can variably take the definite suffix -ə (def). The decade 20 is a single root, while the decades 30 and higher are made up of a bound root plus the decade suffix -sun (dec). The higher numbers ‘100, 1000’ are also single roots.

Table 3 Simple cardinal numbers in Standard Armenian.

As for combining numbers to form complex numerals (Table 4), the teens are formed by combining the number ‘10’ + the definite suffix -n + a connective schwa (con) + the ones unit. ⁴ The higher numbers (25, 35, …) are formed by simple concatenation of the larger numeral and then the smaller numeral.

Table 4 Complex cardinal numbers in Standard Armenian.

This completes cardinal numerals. We next discuss ordinals.

3.2. Ordinal numerals in the two standards

For most cardinal numbers, their ordinal form is transparently created by adding the ordinal suffix -eɾoɾtʰ after the cardinal. There is limited allomorphy, which we discuss in Section 3.3.

For simple numbers 5–10, decades, and their complex numeral combinations, the ordinal is formed by adding the suffix - eɾoɾtʰ in both dialects (Table 5). Numbers 7–10 and the teens can variably include the definite suffix -n- before the ordinal suffix.

Table 5 Regular ordinals for most numerals in Standard Armenian.

We see suppletion and allomorphy, however, for the smaller numbers (Table 6). Number ‘1’ has a fused suppletive form: ‘one’ mek/ meɡ vs. ‘first’ ɑrɑt͡ʃʰin/ɑɾɑt͡ʃʰin. ⁵ In contrast, numbers 2–4 use different allomorphs for both the root and ordinal suffix: ‘four’ t͡ʃʰoɾs vs. ‘fourth’ t͡ʃʰoɾ-ɾoɾtʰ.

Table 6 Irregular ordinals for numbers ‘1–4’ in Standard Armenian.

For the number ‘1’ and its ordinal form, Standard Eastern and Western Armenian follow the common typological pattern of using a separate lexeme for the ordinal, such as in English (Veselinova 1997). The form ɑrɑt͡ʃʰin can be considered a portmanteau form.

For numbers 2–4, the ordinal is an irregular reduced form of the regular forms. There is a separate allomorph for the root and the suffix. Such reductions are allomorphic because they are unique to these numerals. ⁶ There is no general phonological rule that deletes obstruents like /s, k^h, k, ɡ/ before a vowel or rhotic. Such alternations are restricted to these three roots. ⁷

3.3 Propagation or inheritance of irregular ordinals

The previous section established the basic patterns of regular ordinals and irregular ordinals. This section shows how the standard dialects vary in the inheritance of these irregular forms in complex numerals. Briefly, Standard Eastern and Early Standard Western are uniformly external marking languages, while Modern Standard Western is a mixed system.

For the numeral ‘one’ mek, its ordinal is a suppletive portmanteau ɑrɑt͡ʃʰ in, like English ‘first’. This suppletive form, however, is not inherited by complex numerals (Table 7). Like French, complex numerals instead attach the regular ordinal suffix to create a sequence of morphemes, which is not attested as a separate word: - mek -e ɾoɾtʰ. Such external marking is found in both dialects. We underline the irregular forms.

Table 7 Blocked suppletion for derivatives of ‘one’ in Standard Armenian.

For the numeral ‘one’, the two dialects show external marking. However, the dialects diverge for numbers ‘2–4’. First, consider Standard Eastern Armenian (Table 8). The ordinal forms of ‘2–4’ involve special allomorphs for both the root and suffix. Such irregular allomorphs are not propagated to complex numbers. We underline the irregular forms. ⁸

Table 8 Blocked suppletion for derivatives of ‘2–4’ in Standard Eastern Armenian.

For Eastern Armenian, the irregular portmanteau of ‘1’ and the irregulars allomorphs of ‘2–4’ are not propagated to higher numbers. Thus, Eastern Armenian is uniformly external marking, like French. ⁹

For Standard Western Armenian, we see variation ( Table 9). In early variants of Standard Western Armenian, we again find that the numbers ‘2–4’ do not propagate their irregular allomorphs: ‘23rd’ kʰəsɑn -je ɾek ʰ- eɾoɾtʰ. Such forms are attested in older grammars and in some modern teaching grammars, which we later list. In contrast, contemporary or Modern Standard Western does propagate these irregular forms: ‘23rd’ kʰəsɑn- je ɾ- ɾoɾtʰ . Such forms are attested marginally in some older grammars but often in more modern grammars.

Table 9 Variable propagation of irregular forms for derivatives of ‘2–4’ in Standard Western Armenian.

Within Stump’s typology, Early Standard Western is classified as always an external marking language, like Standard Eastern. In contrast, Modern Standard Western does not easily fit into either of these categories. The ordinals of ‘1’ and its higher numbers are uniformly external marking (like French), while the ordinals of ‘2–4’ and their higher numbers are internal marking (like English). We label this system as a mixed system.

Because such variation data is subtle, the list in (1) shows the few references that we found that explicitly provided data on the complex ordinals for Standard Eastern and Western. ¹⁰ A few sources explicitly contrast the uniformly external marking system of Eastern against the mixed system of Modern Western (Սարգսյան 1985: 209; Hagopian 2005: 308).

For Western Armenian, some sources prescribe uniform external marking for the derivatives of ‘1–4’, but they also report that internal marking for the derivatives of ‘2–4’ is attested (Bardakjian & Thomson 1977: 85; Bardakjian & Vaux 2001: 108) although discouraged (Չոլաքեան 2018: 45; Եղիայեան 2022: 159). In contrast, some sources report that mixed marking is the norm for Western and that some speakers are using uniform external marking due to contact with Eastern Armenian (Եղիայեան 2017: 173). Some sources report that both uniform and mixed marking are attested, without giving a prescriptive or descriptive preference (Ավետիսյան 2007: 96).

The modern internal-marking forms are quite pervasive across Western Armenian communities. I am a speaker of Standard Western from the Lebanese community. I confirmed my judgments against other people from Lebanon, Turkey, and the US (all under 40 years old). In my own anecdotal experiences, I had never heard of external-marking forms like kʰəsɑn-jeɾek ʰ- eɾoɾtʰ outside of a) Standard Eastern, b) Early Standard Western grammars, and c) some modern pedagogical grammars.

Given this empirical landscape, the next section formalizes the various ordinal forms.

4. Formalizing ordinal formation

This section formalizes the concepts of external, internal, and mixed marking systems. We first explain Stump’s 2010 original analysis, couched in PFM (Section 4.1). We adapt his analysis to an alternative framework, DM (Section 4.2). We then apply it to Armenian (Section 4.3) and briefly discuss alternatives (Section 4.4).

4.1. Stump’s formalization of internal vs. external marking

Stump (2010) is a benchmark for exploring the morphological structure of ordinal allomorphy. Before we formalize the Armenian data, we show how the basic parameter of internal vs. external marking is modeled in Stump’s framework: PFM (Stump 2001).

Recall that English and French are our canonical examples for internal vs. external marking. In a model like PFM, morphological operations are informally conceived as item-and-process operations (Hockett 1942). By default, a process of ordinal formation adds a suffix to the input (2a) (cf. Stump 2010: 214). For suppletive forms like ‘one’, a special ordinal operation is defined for this numeral (2b). The two rules are in competition with each other, and the latter wins for ‘one’ by being more narrowly defined.

For higher numbers like ‘21’, the languages vary. French is external marking: French merely adds the ordinal suffix -ième (2a-ii). The suppletion rule (2b-ii) is defined only for ‘1’ un and not ‘21’ vingt-et-un. But English is internal-marking. A rule of decomposition (2c) defines the ordinal form of a large number ‘21’ in terms of a concatenation of ‘20’ and the ordinal of ‘1’. Such a rule exists for English but not French; and this rule applies for all ordinals in English.

Stump’s PFM account is elegant and captures the data. For this paper, however, we translate Stump’s system into an entirely separate formalization of morphology: DM (Halle & Marantz 1993). The reasons are the following.

The first reason is scientific replicability. It is a strength for Stump’s generalizations and analyses that his system can be translated to a separate framework. By converting his analysis to DM, we reinforce the cross-linguistic and cross-theoretic utility of his typology. They are not tied down to any one specific formalism but can be generalized across frameworks.

The second reason is operational ease. PFM is an inferential-realizational framework (essentially item-and-process) whereby morphology is defined in terms of operations/processes and not morphemes/morphs. The formalism allows restricted uses of word-internal hierarchical structure (mostly for compounds and syntax-like complex numerals). DM in contrast is lexical-realizational (essentially item-and-arrangement), where morphology works over morphemes/morphs, and there is hierarchical structure for everything. We use DM to highlight the role of hierarchical constituency in ordinal allomorphy and to more visibly distinguish suppletive portmanteaus (a single morph) from agglutinative allomorphy (two morphs).

The third reason is theoretical refinements. Stump’s original PFM account made certain assumptions on the syntactic structure of complex ordinals like ‘21st’, which would differ in external vs. internal marking systems (footnote 12) and in languages with extended marking (Section 5.2). In contrast, DM assumes that the input to the morphology is directly motivated by the semantics or abstract syntax. This means that at an abstract level, we would expect that the syntactic structure of ‘21’ should be essentially the same in different languages, or at least for different dialects of the same language. The morphology can then apply operations that would change this structure and thus create mismatches between the (universal) semantics and the (language-specific) morphology. By using a DM-based syntactic structure, we discover points of ambiguity and possible controversy in Stump’s typology. These points do not negate Stump’s work, but they set up paths for future refinements of the typology and discovering possible connections between the typology of ordinal morphology and the typology of ordinal syntax/semantics.

The fourth reason is theory-internal benefits. The Armenian data provide theory-internal evidence on how different allomorphy domains can be defined in DM. In fact, Stump’s dichotomy between internal vs. external marking ends up analogous to linearity vs. constituency (spans) in the DM toolkit.

Fifth, the diachronic change from Early to Modern Western Armenian is formalized as rule simplification for DM but as a rule addition for PFM (Section 4.2). This paper cannot answer the typological question of whether the change from external-to-internal marking is cross-linguistically common. But such a change is subjectively more obvious to analyze and interpret in DM than in PFM.

Finally, computationally speaking, PFM and DM are inter-translatable. Within formal language theory, both models computationally define regular languages and thus have the same weak generative capacity or expressivity (Karttunen 2003; Roark & Sproat 2007; Ermolaeva & Edmiston 2018). Thus, any linguistic process that can be defined in one model is a priori definable in another. The mathematical equivalency between the two models should encourage the dialogue between the two formal camps (Kramer 2016; Siddiqi & Harley 2016).

4.2. Linearity vs. constituency in allomorphy

Having shown how PFM formalizes internal vs. external marking, this section sets up a formal system for DM. Briefly, internal marking references locality domains, while external marking references constituency domains.

For clarity, we describe some basic assumptions in DM that are relevant for ordinal allomorphy. More information can be found in more dedicated surveys (Harley & Noyer 1999; Embick & Noyer 2007; Bobaljik 2017). We focus on a handful of tools from DM.

DM works over lexical items (pieces), often called morphemes or morphs. The input to the morphological derivation is a sequence or structure of feature bundles. These bundles are then realized by specific morphs. For English and French, there is no ordinal process but an abstract ordinal morpheme ord that is realized in a multitude of ways, one of which is a default form (3a). Such realization rules are called Vocabulary Insertion (VI) rules. For number morphs, we assume that the roots are indexed items (Harley 2014), such that a root for ‘one’ is underlyingly $ \sqrt{1} $ (3b). ¹¹

DM assumes that the input to the morphological derivation is a structured sequence of morphemes. This structure by default matches syntactic-semantic scope, but it can be modified during the course of the morphological derivation. We illustrate the structure of cardinal and ordinal for ‘1’ and ‘21’ in Figure 1. ¹²

Figure 1 Structure of cardinals and ordinals for ‘1’ and ‘21’.

Given such elaborated structures, VI can target an individual item (terminal node) such as the ord morpheme (3a), but it can also be sensitive to a larger cluster of units. This sensitivity allows refined allomorphy domains that distinguish internal vs. external marking. For portmanteaus like ‘first’ and ‘premier’, they simultaneously expone the root $ \sqrt{1} $ and the ord suffix. For English (4a), the portmanteau expones the linear sequence $ \sqrt{1} $ -ord regardless of internal structure. In contrast, the French portmanteau (4b) requires that $ \sqrt{1} $ -ord form a morphosemantic constituent, and VI targets the non-terminal node ‘21’. ¹³

We illustrate a derivation for the two systems in Figure 2. The dashed lines indicate portmanteau forms. We underline the irregular forms.

Figure 2 Deriving ordinals for ‘1’ and ‘21’ in English (internal) and French (external).

For English, the allomorphy rules derive internal marking because the portmanteau ‘first’ is sensitive only to the linear sequence of ‘1’ and ord (4a). This allows the propagation of the suppletive form. Internal marking is thus reduced to linearity-conditioned allomorphy in DM.

In contrast, the French premier is only allowed when the ‘1’ and ord form a semantic constituent (4b). This means that the allomorphy cannot be propagated to higher numbers. The ordinal of ‘21’ instead resorts to using an otherwise unattested sequence -un-ième made up of the default forms for the root and ordinal suffix (3). External marking is thus reduced to constituency-conditioned allomorphy.

This division between external vs. internal marking can be easily modeled in DM in terms of different allomorphy domains, as shown above. Specifically, it is common for the participating morphemes in a suppletive or allomorphic process to be both linearly local to each other and to form a structural constituent (Bobaljik 2012); some argue that the portmanteau form can then target insertion at a non-terminal node (Caha 2009; Radkevich 2010; Embick 2017). This creates external marking as in French. However, there are patterns of allomorphy where the component morphemes are linearly adjacent but do not form a constituent. In this case, some phenomena treat the component morphemes as structurally adjacent, i.e., a span (Svenonius 2012; Merchant 2015; Middleton 2021). Other phenomena treat the morphemes as structurally non-adjacent with intervening but linearly non-adjacent material, i.e., stretches (Ostrove 2018), post-linearization fusion (Embick 2015: 215; Felice 2021; Banerjee 2021), or post-linearization spanning (Haugen & Siddiqi 2016). Internal marking in English ordinals can be considered either a span or stretch depending on one’s analysis of the internal structure of ordinals, i.e., whether ‘1’ and ord form a contiguous sequence of nodes in an extended projection.

Thus, the ordinal of ‘one’ is suppletive in both English and French. This suppletive form is inherited by higher numbers in English but not French. To block the propagation (external marking), the relevant rules define allomorphy as delimited by constituency (targeting a non-terminal node), while to allow propagation (internal marking), the rules are delimited by just locality (a span or stretch). Within DM, there have been various camps of practitioners who argued for using one of the above two modes for portmanteau formation (linearity and constituency), and often exclusively only one mode. The basic typology of ordinals is, however, evidence that both modes of allomorphy are attested and required.

Before we move on to formalizing the Armenian data, notice the subtle difference between the two DM rules in (4), repeated below. The internal marking rule (English: 5a) targets a string $ \sqrt{1} $ -ord which is representationally simpler than the string [ $ \sqrt{1} $ -ord] of the external marking rule (French: 5b). Thus for the DM analysis, internal marking is representationally simpler than external marking. In contrast, the PFM analysis (2) required adding a rule for internal marking (5c). Thus, PFM treats external marking as derivationally simpler than internal marking.

The above distinction of simplicity is quite formal: an analysis is simpler if it uses fewer symbols or rules. Given this formal distinction, one question is whether such a formal distinction has any empirical significance. For the Armenian case, it seems that the language has a tendency to gain internal marking for numerals ‘2–4’; this suggests that internal marking is simpler (= more default) than external marking.

Having set up how the basic typology of ordinal marking can be modeled in DM, the next section applies the formalization to Armenian.

4.3. Formalizing the mixed system of Armenian

Recall from Section 3.3 that Eastern Armenian and Early Western Armenian are uniformly external-marking systems (like French). Modern Western is instead a mixed system. This section formalizes the two systems, and shows how the systems differ in subtle rule reformulations. For brevity, we do not formalize Eastern Armenian but just the two Western registers. ¹⁴

Consider the forms of ‘one’ in Western Armenian. Both Early and Modern Western Armenian use the same rules for this number (6). The ordinal suffix is by default - eɾoɾtʰ and the root 1 is by default meɡ. Because the system is external marking like French, then the ordinal ‘1st’ is a portmanteau ɑɾɑt͡ʃʰin that is defined in terms of constituency.

Figure 3 illustrates how these rules derive external marking for ‘1’ and ‘21’ in essentially the same way as French (Figure 2). Portmanteaus are underlined.

Figure 3 Deriving external marking for ‘1’ and ‘21’ in Western Armenian.

In contrast, for the numerals ‘2–4’, we see agglutinative allomorphy instead of portmanteaus. The ordinal suffix uses a special allomorph -ɾoɾtʰ instead of the default -eɾoɾtʰ (7a). The numeral roots differ in the cardinal and ordinal forms for ‘2–4’ (7b).

For Early Western Armenian, these special allomorphs for ‘2–4’ are restricted to numbers ‘2–4’ and do not percolate to higher numbers. This system of external marking is represented in the above rules via referencing constituency brackets in the rules for both the ordinal suffix (7a) and numeral roots (7b).

Figure 4 illustrates the cardinal and ordinal forms for ‘4’ and ‘24’ for Early Western. We underline irregular forms. The use of constituency brackets in our rules (7) blocks the percolation of irregular forms.

Figure 4 Deriving external marking for ‘4’ and ‘24’ in Early Western Armenian.

The above is for Early Western Armenian. Modern Western Armenian, however, does propagate the irregular forms of ‘2–4’. Within our rule system, this means that Modern Western abandons the use of constituency brackets for the irregular forms of ‘2–4’ and the ordinal suffix (8).

The system in (8) references linearity instead of constituency. This allows the propagation of irregular forms, creating internal marking instead of external marking, as Figure 5 illustrates.

Figure 5 Deriving internal marking for ‘4’ and ‘24’ in Modern Western Armenian.

For easier illustration, Table 10 shows how the relevant rules for ‘1–4’ changed from Early to Modern Western. The rules for ‘1’ stayed the same (external marking) because the modern form references constituency. The rules for ‘2–4’ abandoned constituency, creating internal marking.

Table 10 Diachronic change in rule formulation for Western Armenian.

In this way, the above formalization straightforwardly captures the mixed system of ordinal marking in Modern Western Armenian. Modern Western Armenian is a mixed system in terms of ordinal formation because it references structure and linearity in different parts of the grammar (cf. Lee & Amato 2018). The data are evidence that multiple types of allomorphy domains (linearity and constituency) can coexist within the same grammatical system. The data and formalization likewise suggest that internal marking is ‘representationally simpler’ because Western Armenian went through a diachronic change of removing constituency conditions, thereby moving from external marking to internal marking.

4.4. Ambiguity of mixed vs. conjunct systems in Western Armenian

The previous sections presented our DM analysis of internal marking (English), of uniform external marking (French, Eastern Armenian, Early Western), and of mixed marking (Modern Western). This section discusses an alternative analysis in terms of conjunct morphology.

French is categorized as an external marking system because the ordinal for $ \sqrt{1} $ is different for the simple number ‘1’ vs. complex numbers like ‘21’. However, Stump (2010: 228) notes that suffixal external systems like French can be alternatively analyzed as using conjunct morphology. ¹⁵ Conjunct morphology is when a morpheme uses one allomorph when used in isolation (the absolute form: 9a) vs. another allomorph when used as part of a complex phrase (the conjunct form: 9b). Example (9) shows a hypothetical PFM analysis, adapted from Stump (2010: 222).

The above PFM analysis incorporates the concept of conjunct morphology into the process Ordconjunct(X). A hypothetical DM version would decompose this process into an allomorphy domain that references a word-initial boundary.

In DM, a conjunct analysis essentially just replaces references to constituency boundaries (7, 8) with references to word-initialness (11). For Early Western, the numbers ‘1’ (11a) and ‘2–4’ (11b) have separate absolute and conjunct forms. Both sets of numbers reference the word-initial boundary. But in the modern form, the ordinal of ‘1’ has separate allomorphs (11a) that reference the # boundary, while the ordinals of ‘2–4’ (11c) have identical absolute-conjunct forms that do not reference the # boundary.

Thus, if we assume Armenian has conjunct morphology, then both early and Modern Western Armenian can be categorized as external marking systems. The difference between the early and modern registers is just the leveling of the absolute-conjunct forms /t͡ʃʰoɾ-ɾoɾtʰ, t͡ʃʰoɾs-eɾoɾtʰ/ to identical absolute-conjunct forms /t͡ʃʰoɾ-ɾoɾtʰ, t͡ʃʰoɾ-ɾoɾtʰ/.

This alternative analysis works but we do not consider it further for the following reasons.

First, it is a formal ambiguity that any suffixal external marking system (or a mixed marking system) can be analyzed as a conjunct system. This point is acknowledged by Stump (2010: 227). There is thus no empirical evidence that prefers one analysis over another. Any possible arguments for one of the two systems will ultimately be conceptual.

Second, once we decompose conjunct morphology into an item-and-arrangement system like DM, the differences between conjunct morphology (word-boundaries) vs. external-marking (constituencies) look notational.

Third, if we adopt a conjunct system for Armenian, then it seems difficult to separately classify the early and modern registers of Western Armenian. If we assume that there is no conjunct system in Armenian, then Early Western is labeled as uniformly external marking, while the modern system is mixed. But if we assume a conjunct system, then terms such as ‘uniform’ and ‘mixed’ are not obviously interpretable.

Fourth, outside of these four numerals ‘1–4’ and their derivatives, we have not found evidence of conjunct morphology elsewhere in the language. There is ample work on Armenian compounds (Donabédian 2004; Dolatian 2021b, 2022b), but we cannot find any evidence of conjunct marking in compounds. This is in contrast to languages where conjunct morphology is argued to exist because of multiple phenomena (Stump 2010, citing Stump 1995:264–273, 2001:119–126).

Having acknowledged this formal ambiguity, the rest of this paper focuses on just using our external vs. mixed labels for illustrative ease.

5. Asymmetries and dialectal variation

The previous sections formalized the system of uniform external marking in Standard Eastern and Early Western Armenian vs. mixed marking in Modern Standard Western Armenian. This section explores diachronic and further dialectal variation. We uncover asymmetries in the difference between the portmanteau allomorphy for ‘1’ vs. the agglutinative allomorphy for ‘2–4’ when it comes to external vs. internal marking (12):

The above asymmetries cannot be easily captured in a formal generative analysis, but they make sense in terms of a functional account that emphasizes the importance of lower ordinals like ‘first’ over higher ordinals (Veselinova 1997; Barbiers 2007; Stolz & Robbers 2016).

5.1. Asymmetries in Modern Standard Armenian

The previous PFM and DM analyses both capture the relevant data from Early and Modern Western Armenian. However, our formal analysis does not capture a striking correlation in the data. The ordinal of ‘1’ uses portmanteau allomorphy and it always uses external marking (= never propagates). In contrast, the ordinals of ‘2–4’ use agglutinative allomorphy, variably show internal vs. external marking, but they always behave as a single set for Standard Armenian.

In other words, the numerals ‘2–4’ either all show external marking as in Early Western, or they all show internal marking as in Modern Western. Table 11 summarizes the range of variation. It is not the case that ‘2’ acts differently from ‘3–4’. To illustrate, an unattested variety of Western Armenian is to make ‘2’ have have internal marking in ‘22’ /kʰəsɑn-jeɾɡ-ɾoɾtʰ/, while ‘4’ is external marking in ‘24’ /kʰəsɑn-t͡ʃʰoɾs-eɾoɾtʰ/. Similarly, we do not know of any register of Armenian where ‘1’ propagates, while ‘2–4’ do or do not.

Table 11 Asymmetries in portmanteau vs. agglutinative allomorphy.

Note that we later find that some non-standard dialects regularize a larger number like ‘4’ while still maintaining the irregularity of ‘2–3’.

The above sample is obviously small with only three language varieties, but the data are suggestive. The next two subsections go through more Armenian varieties in order to establish these generalizations. We first discuss the diachrony of Armenian.

5.2. Diachronic origins of the ordinal system

The earliest known attested variety of Armenian is Classical Armenian ( $ \sim $ fifth century). ¹⁶ The cardinal and ordinal words are virtually the same across the ancient and modern languages but have subtle combinatorial differences (Աճառյան 1952a: 283–284; Thomson 1989: 94–97). These differences again indicate an asymmetry between ‘1’ vs. ‘2–4’.

First, consider the numbers ‘1–5’ and ‘20’ (Table 12). The ordinal suffix -(e)ɾoɾd is the ancestor of the modern form -(e)ɾoɾtʰ. The suffix -eɾoɾd is the default form. Like the modern language, the ordinal of ‘1’ is a portmanteau, while ‘2–4’ use agglutinative allomorphy. We underline the irregular forms. ¹⁷

Table 12 Cardinals and ordinals for ‘1–5, 20’ from Classical Armenian (Thomson 1989: 94–97).

For the teens (Table 13), Classical Armenian places the morpheme for ‘10’ on the right, and it takes the regular ordinal suffix -eɾoɾd. Thus, the teens cannot inform us on whether the irregular allomorphs of ‘1–4’ propagate. Note that cardinals were taken from Thomson (1989: 94), while the ordinals are from the Classical Armenian Bible.

Table 13 Cardinals and ordinals for ‘11–15’ from Classical Armenian.

Matters get complicated for higher numbers (Thomson 1989: 95–97). For a complex numeral like ‘25’, Classical Armenian uses a more syntactic method. The larger number ‘20’ and the smaller number ‘5’ are separated by the conjunction եւ [ew] (Table 14).

Table 14 Cardinals ‘21–25’ from the Classical Armenian Bible.

For these complex numbers, the ordinal is formed by turning each cardinal numeral into an ordinal (13a). The conjunction [ew] can sometimes be dropped in some contexts, although it is unclear when (13b). ¹⁸

Based on the above data, Classical Armenian can be classified as using an extended ordinal system (Stump 2010: 214). Multiple constituents in the complex numeral receive ordinal marking.

We see this same extended pattern for numerals that use allomorphy. For derivatives of ‘2–4’ like ‘22–24’, the irregular form is used (Table 15).

Table 15 Cardinals and ordinals for ‘21–25’ from Classical Armenian.

Because complex ordinals like ‘24th’ inherit the irregular ordinal of ‘4’, Stump (2010: 223) would classify Classical Armenian as an extended internal system based on his PFM formalization. However, from the perspective of DM, such ordinals are ambiguously either internal or external. In a phrase like ‘20-ord 4-ord’, this phrase would have the constituency structure of [ [20-ord] [4-ord]]. The right member is a constituent and would use the irregular ordinal form regardless whether we think the system is internal or external (cf. the rules in Table 10).

As a brief caveat though, the Bible corpus did have a few cases where the left numeral does not get ordinal marking (14). Thus, it is possible that some complex ordinals have structures like [ [20 and 4]-ord] and would necessarily require an internal-marking formalization.

Matters are more complicated for derivatives of ‘1’ (15). In a complex ordinal like ‘21st’, the ‘1’ unit uses a portmanteau and the regular ordinal suffix. This inheritance system for ‘1’ resembles multiple exponence. Ordinality is marked both in the portmanteau and in the default ordinal suffix. ¹⁹

It is unclear to me what is the most elegant way to model the above multiple exponence of ‘21st’ in either PFM or DM. We set that aside. But what matters for us is that even in Classical Armenian, where there is ambiguous distinction between internal vs. external marking, we still find an asymmetry between the inheritance of portmanteau allomorphy of ‘1’ vs. agglutinative allomorphy of ‘2–4’.

5.3. Decay of the ordinal system across Armenian dialects

Besides the two standard lects, there are dozens of non-standard Armenian varieties with varying degrees of mutual (un-)intelligiblity (Աճառեան 1911). These dialects can be loosely categorized as being part of the Western branch (W) vs. the Eastern branch (E). The former branch developed in the Ottoman Empire and the latter in the Persian/Russian Empires. This section goes over the few Armenian dialects for which I could find grammars at hand. ²⁰ What we find is that no dialect ever develops internal marking for ‘1’, but it can lose irregular marking for ‘2–4’.

Standard Eastern is uniformly external marking and neither portmanteaus nor agglutinative allomorphy propagate. The Karin dialect (W) is reported to be the same (Մկրտչյան 1952: 56–57). The cardinal ‘1’ is [meɡ], and its ordinal is a portmanteau [ɦɑrd͡ʒi]. The grammarian reports that the irregular suffix [-ɾoɾtʰ] is used for ordinals of ‘2–4’, while other ordinals take default [-eɾoɾtʰ].

Modern Standard Western is a mixed system such that portmanteaus do not propagate while agglutinative allomorphy does. Tehrani Iranian Armenian (E) is reportedly the same (Table 16: Dolatian et al. in review). The portmanteau of ‘1’ does not propagate to higher numbers, while the irregular agglutinative forms of ‘2–4’ do propagate.

Table 16 Mixed marking from Tehrani Iranian Armenian.

The dialects so far still treat the numeral set ‘2–4’ uniformly. The numerals all take irregular agglutinative allomorphy. And they either all propagate (Modern Standard Western), or none of them propagate (Standard Eastern). Some dialects show, however, that this set can be reduced in size. The dialect of Kirzen (E) maintains largely the same morphemes as Standard Eastern Armenian (Table 17: Բաղրամյան 1958: 80). The ordinal ‘1’ is a portmanteau, while the numerals ‘2–3’ use agglutinative allomorphy with an irregular -ɾoɾtʰ suffix. ²¹ But the numeral ‘4’ uses the regular suffix -eɾoɾtʰ without any root allomorphy. Thus, it is possible for an irregular ordinal like ‘4’ to be regularized without affecting the lower numbers ‘1–3’. Unfortunately, the source does not discuss higher ordinals.

Table 17 Loss of irregular ordinal for ‘4’ in the Kirzen dialect.

Other Armenian dialects show more variation. Many dialects have simplified or levelled away ordinal allomorphy through various means. Some attested methods are a) losing the irregular ordinal suffix, b) replacing ordinal suffixes with other suffixes, and c) replacing Armenian ordinals with cardinals or Turkish/Azerbaijani ordinals (Martirosyan 2019: 195). But in some of these levelled dialects, we find an asymmetry between the ordinals of ‘1’ vs. other numerals.

In some dialects like Malatya (W), the numeral ‘1’ has a portmanteau ordinal that does not propagate to higher numbers (Table 18: Դանիելյան 1967: 95–98). But this dialect lost the irregular ordinal suffix -ɾoɾtʰ and irregular root allomorphs for ‘2–4’. There is only one ordinal suffix -eɾɾoɾtʰ, and this suffix is used for numerals ‘2’ and above. ²²

Table 18 Loss of irregular ordinal suffix in Malatya Armenian.

The retention of the non-propagating portmanteau ordinal for ‘1’ and the loss of other irregular ordinals is also found in some dialects that have replaced the Armenian -(e)ɾoɾtʰ suffix with other morphemes.

In the Sasun dialect (W), the cardinal ‘1’ has a portmanteau ordinal (Table 19: Պետոյան 1954: 38–39). But all other ordinals are formed by borrowing the Turkish suffix -inci. The grammarian does not report any propagation of the ordinal of ‘1’ to higher numbers. Other dialects that behave this way include Agulis (E: Աճառեան 1935: Section 293), Burdur (E: Մկրտչյան 1971: 105), Kesab (W: Չոլաքեան 2009: 87), Meghri (E: Աղայան 1954: 178), and Old Istanbul (W: Աճառյան 1941: 106). Some of these may have borrowed the suffix from Azerbaijani instead of Turkish. ²³

Table 19 Retention of portmanteaus but replacement of the ordinal suffix in Sasun Armenian.

Some dialects replaced the ordinal suffixes -( e)ɾoɾtʰ with the suffix -um that is a reflex of a locative suffix from Classical Armenian. Adjarian (Աճառյան 1952a: 287) reports three such dialects: New Julfa (E), Suceava (W), and New Nakhichevan (W: Table 20). The ordinal ‘1’ is a portmanteau that does not propagate. The other numerals (2 and beyond) do not show any allomorphy (Աճառեան 1925: 203). ²⁴

Table 20 Retention of portmanteaus but replacement of the ordinal suffix in New Nakhichevan Armenian.

The pattern so far is that the portmanteau ordinal of ‘1’ is perseverant and resistant to wide-scale morphological changes. For example, some dialects lost almost the entire ordinal system except for ‘1’. In the Bayazet dialect (E: Կատվալյան 2016: 331–335), the cardinal ‘1’ [mek] has a portmanteau ordinal [ɦɑrt͡ʃʰi]. But the other numerals do not have any ordinal form; instead, cardinals are used, often with some type of case suffix. Other such dialects include the general dialect area of Ararat (E: Մարկոսյան 1989: 126). ²⁵ Middle Armenian ( $ \sim $ twelfth century) had an ordinal for ‘1’ but there is little attestation of other ordinal numbers (Karst 1901: 222).

However, some dialects are on the path to losing the special status of the ‘1’ ordinal. In the general dialect area of Karabakh (E: Դավթյան 1966: 125), all ordinals are formed by adding the Turkic suffix -inci after the cardinal. But for the cardinal ‘1’ [min], its ordinal is either the cardinal plus this suffix [min-ind͡ʒi], or a reflex of the portmanteau plus the suffix [ɑɾɑt͡ʃʰ-ind͡ʒi]. ²⁶

Some dialects have finalized the loss of the native ordinal allomorphy. For example, the Goris dialect (E: Մարգարյան 1975: 154–157) replaced all the native ordinals with just the cardinal plus a Turkic suffix: ‘1’ [min] vs. ‘1st’ [min-ind͡ʒi]. Other such dialects include Aresh (E: Բաղրամյան 1979: 82).

Some dialects removed all native ordinal morphology but did introduce some allomorphy for ‘1’. For example, the Maragha dialect (E: Աճառյան 1926: 182–183) replaced the native ordinal suffixes with a Turkic suffix (Table 21). They borrowed a special root allomorph for ‘1st’ from Turkic/Persian <avval>, but this root does not propagate to higher numbers. This dialect thus still maintained an external-marking system despite changing all the ordinal morphemes. Cross-linguistically, borrowing is known to affect ordinal systems in this way (Stolz & Robbers 2016: Section 3.1.4).

Table 21 External marking ordinals in Maragha via borrowings.

Some dialects have replaced all native ordinals with Turkish or Azerbaijani ordinals (as borrowings). These include Arapgir (W: Դաւիթ-Բէկ 1919: 215), Artvin (E: Ալավերդյան 1968: 234), and Kayseri (W: Անթոսյան 1961: 80).

And finally, some dialects have simply lost all ordinal morphology. For example, one variant of the Hamshen dialect (W: Աճառյան 1947: 109) uses cardinals instead of ordinals. Other dialects without ordinal morphology include Çatak or Šatax (W: Մուրադյան 1962: 115), Van (W: Աճառյան 1952b: 148), and Vozim (W: Արևիկյան 1967: 78). Some dialects like Urmia (E: Ասատրյան 1962: 86) and Lori (E: Ասատրյան 1968: 106) lost their ordinal morphology, but its speakers have started to adopt Standard Eastern ordinals because of education.

In sum, ordinal morphology is quite susceptible to diachronic change across Armenian dialects. However, even across such changes, we find that the ordinal of ‘1’ never develops internal marking, not propogation (= no propagation) and that ‘1’ resists regularization before ‘2–4’. These asymmetries fall out from a functional account that would emphasize the semantic significance, high frequency, and portmanteau morphology of the ordinal ‘first’ (Veselinova 1997). We emphasize this point next.

6. Form and function: The special status of ‘first’

The bulk of this paper has looked at ordinal allomorphy in two modern standard Armenian varieties: Standard Eastern and Standard Western. Given a formalization based on the modern standard forms, we then examined a larger scale of variation in ordinal allomorphy across other varieties of Armenian: Classical Armenian and a host of non-standard dialects. Table 22 summarizes some of the key properties of some of these varieties.

Table 22 Patterns of ordinal allomorphy across Armenian.

As the earliest known Armenian variety, Classical Armenian already had suppletive allomorphy for ‘1’ and agglutinative allomorphy for ‘2–4’. In this way, Classical Armenian already resembles modern Standard Armenian. But unlike all of its descendants, Classical Armenian had an extended marking for higher numerals, such that the ordinal form of ‘21’ would have ordinal marking twice as in ‘20th and 1st’. In Stump’s PFM analysis, extended marking would be classified as internal marking; but in our DM-based analysis, the data are ambiguous between external vs. internal marking. Classical Armenian is, however, atypical. The modern dialects seem to have all lost extended marking.

Across our sample, we see that the numeral ‘1’ is quite resistant to change. Many of the modern varieties retained a suppletive portmanteau morphology for its ordinal. They likewise developed external marking for it. ²⁷ Some regularized the entire ordinal system and removed allomorphy, except for the numeral ‘1’ (Malatya). Some lost all ordinal morphology except for ‘1’ (Bayazet). Some even replaced their ordinal morphology with borrowings that still privileged the role of ‘1’ (Maragha).

In contrast, as said, for the numerals ‘2–4’, Classical Armenian had agglutinative allomorphy. But the behavior of this set is unstable across the descendants. Some dialects kept the allomorphy and developed either external or internal marking (Standard Eastern vs. Standard Western). It seems that external marking developed first, and that internal marking arose as an innovation (Early vs. Modern Standard Western). However, most dialects simply lost these allomorphic forms, whether by regularizing these numerals (Malatya) or by losing most ordinals (Bayazet).

Despite the above fluctuations, we see the following strong correlations. The numeral ‘1’ has suppletive allomorphy, prefers external marking, and it is resistant (but not immune) to regularization and morphological change. In contrast, numerals ‘2–4’ have agglutinative allomorphy, have no consistent pattern with external vs. internal marking, and are susceptible to regularization and loss. We can see these correlations simultaneously in varieties like Early vs. Modern Standard Western Armenian. The numeral ‘1’ stayed external marking, while ‘2–4’ went from external marking to internal marking. For some dialects like New Nakhichevan, ‘1’ retained its suppletive external-marking allomorphy, while ‘2–4’ lost their allomorphy. As a rare case study, Kirzen kept suppletion for ‘1’ and allomorphy for ‘2–3’ but regularized ‘4’.

These correlations seem strong within our sample of 35 Armenian varieties. However, our formal generative analysis cannot directly capture them. On the one hand, our DM analysis provides us with explicit tools to formalize internal vs. external marking allomorphy in terms of linearity-sensitivity vs. constituency-sensitivity. But regardless of whether we use PFM or DM, our morphological rules do not create any obvious connections between suppletive allomorphy and external marking nor do they connect the patterns of allomorphy with individual numerical values. That is, a formal analysis cannot tell us why the Armenian numeral ‘1’ should prefer suppletive external marking, while the Armenian ‘2’ has no such preferences. Our formal analysis helps us to classify the range of variation, but it does not naturally explain it.

Furthermore, from a diachronic perspective, it is not obvious how a generative analysis can predict which of the above diachronic changes would have been possible, preferred, or neither. In terms of formal simplicity and learnability, we briefly entertained the idea that that PFM seems to treat external marking as simpler, while DM treats internal marking as simpler. It is unclear if this distinction between the two types of generative analyses can be connected to the fact that the numeral ‘1’ prefers external marking, while the numeral ‘2’ can change from external to internal marking. Future work can better refine a computational notion of simplicity with respect to language change.

Instead, it seems that the Armenian data underlie a set of asymmetries that cannot be transparently derived from any formal generative analysis. A synchronic generative analysis like DM or PFM does not obviously restrict or delimit the sets of possible suppletive patterns. Such frameworks can at most describe and contrast the patterns that exist. Instead, such asymmetries make more sense from a typological-functional orientation. The numeral ‘one’ has an important communicative function in human culture and language. Its importance then correlates with its frequency, its resistance to change, and its role in language contact (Veselinova 1997; Stolz & Robbers 2016).

7. Conclusion

This paper has discussed ordinal formation in Armenian. Cross-linguistically, a basic dimension for ordinal allomorphy is whether suppletive forms propagate to higher numbers (like in English) or not (like in French). For Standard Armenian, the low numerals ‘1–4’ have portmanteau or agglutinative allomorphs. The portmanteau of ‘1st’ never propagates (always external marking), while the agglutinative ordinals of ‘2–4’ variably propagate (variably external marking). Based on this Armenian case study, this paper had two analytical goals: generative and typological.

For the generative goal, we modeled this behavior in DM by making our realization rules reference either structural constituency (Bobaljik 2012) or linear adjacency (Ostrove 2018). Structural constituency blocks the percolation of irregular allomorphy, while linear adjacency licenses the percolation. Within a single Armenian dialect, a realization rule is free to pick either type of condition. This creates the appearance of a mixed system like Modern Western Armenian. Such mixed systems are evidence that the same grammar can utilize both linearity-sensitive allomorphy and constituency-sensitive allomorphy.

For the typological goal, we catalogued the wide set of possible ordinal systems that are attested across Armenian registers or dialects (n = 35). We found further asymmetries that foregrounded the fact that the ordinal of ‘1’ never propagates and that it is the most resistant to morphological changes in the language. Instead, this finding is functionally grounded (Veseliova 1997).

In sum, this paper acts as a single in-depth case study on the developments of ordinal allomorphy in a single language (and its dialectal varieties). We discovered a mixed system of ordinal marking. We interpreted the data from multiple generative perspectives (PFM and DM) in order to find ambiguities in the typology and analysis, while foregrounding similarities and other points of theoretical interest. With our generative analysis laying out the extremes of changes, we then argued for a functional asymmetry between low vs. high numerals and between suppletive vs. agglutinative allomorphy. The end result is that we better understand a narrow domain of morphological inquiry (ordinal allomorphy) by contrasting how multiple nuanced theories work on it. We encourage future research on similar developments of ordinal morphology. Given a wider set of such case studies, it is then a worthwhile question if the Armenian patterns of development are diachronically and synchronically rare or whether they reflect a general cross-linguistic tendency.