5 Alternations: Stems and Allomorphy Mary Paster 1 Introduction This chapter discusses stem allomorphy and its theoretical analysis. Four different general theoretical approaches to the analysis of stem allomorphy are presented, and their positive and negative attributes are evaluated relative to what is currently known about properties of stem allomorphy cross-linguistically. It is argued that no single model is ideal to account for all types of stem allomorphy; therefore, it is proposed that multiple frameworks may be needed. The distribution of labor among those models is discussed as an issue for future research, pending refinement of our understanding of the typology of stem allomorphy based on further crosslinguistic research and in-depth empirical studies of morphologically complex languages. “Allomorphy” is defined here as any case of a single set of semantic/ morphosyntactic features having two or more different context-dependent phonological realizations. This includes cases where a straightforward phonological rule/constraint may be invoked as well as more complex examples involving suppletive allomorphy, where multiple underlying forms are involved whose distribution may be morphologically, lexically, and/or phonologically governed. A “stem” is defined as a form that can be inflected (meaning that a stem may consist only of a root, or it may be a root plus one or more derivational and/or inflectional affixes). Although most allomorphy probably occurs in affixes rather than stems, the examples in this chapter will be of allomorphy specifically in stems wherever possible, given the focus of the chapter. (For discussion of affix allomorphy, as it relates to paradigms, see Chapter 9 of this volume.) The chapter will be structured as follows. In Section 2, I present an overview of the basic types of allomorphy, giving examples of each. In Section 3, I describe four different theoretical models, explaining how each would analyze a sample case of stem allomorphy. In Section 4, Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 94 MARY PASTER I discuss some outstanding research questions relating to stem allomorphy. Section 5 concludes the chapter. 2 Types of Allomorphy Allomorphy was defined above as “any case of a single set of semantic/ morphosyntactic features having two or more different context-dependent phonological realizations,” but it should be noted that there exist other definitions of the term. Before describing the types of allomorphy, I will provide some background regarding the concept and other understandings of it. See also Paster (2014, to appear) for further discussion. The definition of allomorphy being used here subsumes phenomena that many researchers would view as having two fundamentally different loci/ sources—namely, some would be considered phonological in nature and others morphological. Section 5 will provide further discussion of the architecture of the grammar and how different theoretical approaches to allomorphy relate to different ideas of the distinction (if any) between phonology and morphology. The present definition of allomorphy is focused on the surface form of the stem. Instances where the phonological form of the stem varies contextually are all considered to be examples of allomorphy under this definition, regardless of which component of the grammar is responsible for the variation. A distinction can then be made between what I refer to as “suppletive allomorphy” (defined below, and used interchangeably here with the term “suppletion”), which involves multiple underlying forms and is therefore a result of morphological functions of the grammar, versus non-suppletive allomorphy, which involves a single underlying form where variation is due to the action of regular rules/ constraints in the phonological component of the grammar. Some researchers, however, would refer to non-suppletive allomorphy as “morphophonology,” reserving the term “allomorphy” specifically for suppletive allomorphy. Further, at least one definition of “allomorphy” (Stockwell and Minkova 2001: 73) is not only limited to what I call suppletive allomorphy, but it also requires allomorphs to have a “historically valid” relationship—in other words, that they are etymologically related. In Stockwell and Minkova’s typology, cases of what I call suppletive allomorphy but where the underlying forms are not phonetically similar would not be described as allomorphy; the phenomenon would be labeled “suppletion” (but not “suppletive allomorphy”) in the case of stems, or “rival affixes” in the case of affixes. Under the definitions of “allomorphy” and “suppletive allomorphy” (or “suppletion”) that I am using in this chapter, there is no distinction between the phenomena referred to by Stockwell and Minkova as “rival affixes” versus “suppletive allomorphs.” Having defined some important terms and provided some clarification regarding how my use of the relevant terminology relates to that of other researchers, I turn now to a discussion of the types of allomorphy. Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 Alternations: Stems and Allomorphy 95 To begin, it is useful to distinguish two major types of allomorphy, as alluded to above. The first is non-suppletive phonologically derived allomorphy. This is a situation where a regular phonological rule of a language applies in a particular phonological context, yielding alternations. This type of allomorphy commonly applies to stems, even if it applies preferentially to affixes and not stems in some languages. An example of regular phonologically conditioned stem allomorphy is found in Polish, which exhibits word-final obstruent devoicing. When a stem underlyingly ends in a voiced obstruent, if there is no suffix after the stem, the devoicing rule produces a stem allomorph with a final voiceless obstruent, as can be seen by comparing the genitive singular versus nominative singular forms of the nouns in (1) (note that examples are given as phonetic transcriptions rather than in the Polish orthography, which does not reflect devoicing). (1) Gen sg klub-u ob jad-u targ-u gaz-u stav-u gruz-u Nom sg klup ob jat tark gas staf grus Gloss ‘club’ ‘dinner’ ‘market’ ‘gas’ ‘pond’ ‘rubble’ A straightforward analysis would have a single underlying form of the stem, reflected in the genitive singular form, and a regular phonological rule applying in the nominative singular, where the lack of a suffix puts the stem-final segment into the word-final environment that triggers devoicing. Thus, the allomorphy is derived purely in the phonology. (Note that this must be analyzed as word-final devoicing rather than pre-vocalic voicing, since stem-final underlyingly voiceless obstruents do not alternate; cf. pobɨt~pobɨt-u ‘stay.’) The second major type of allomorphy is suppletive allomorphy. This is a type of allomorphy where there are two or more underlying forms that express the same set of semantic/morphosyntactic features. The grammar must somehow select among the different underlying forms, whose surface realizations are in complementary distribution. The basis for selection may be morphosyntactic, lexical, or phonological—or a combination of these. We deal with each of these types of suppletive allomorphy below. In morphosyntactically conditioned suppletive allomorphy, the selection of an allomorph is conditioned by the morphological or syntactic category of the word. In the case of stem allomorphy, a specific form of a stem might be used in a particular morphological context such as past tense versus other tenses, or when the word belongs to a particular syntactic category such as when it is used to form a noun vs. a verb. An example is found in Hopi, as shown in (2), where certain nouns have a stem form used in the plural that differs in unpredictable ways from the stem form used in the singular and dual (Hill and Black 1998: 865; Haugen and Siddiqi 2013). Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 96 MARY PASTER (2) Singular wùuti tiyo pöösa Dual wùuti-t tiyo-t pöösa-t Plural momoya-m tooti-m pövöya-m Gloss ‘woman’ ‘boy, young man’ ‘house mouse’ This case of allomorphy is treated as suppletive since there is no uniform phonological change to the stem in the plural relative to the singular/dual form. It is morphologically conditioned since it is the plural category that triggers the use of the special stem form. Crucially, a given case of stem allomorphy is only analyzed as morphosyntactically conditioned suppletive allomorphy if it is the morphosyntactic category per se that conditions the use of the allomorph, rather than a phonological property of that morphosyntactic category. For instance, the use of the allomorph [twɛlf] with a voiceless stem-final consonant in the English word twelfth is conditioned by the ordinal suffix, but this should probably not be considered morphosyntactically conditioned suppletive allomorphy because (1) it is arguably the voicelessness of the suffix (and not the fact that it is an ordinal form) that conditions the use of a stem allomorph with a voiceless final consonant; and (2) the allomorphy is not suppletive since it can be analyzed via a phonological devoicing rule. Lexically conditioned suppletive allomorphy defines a situation where suppletion is idiosyncratic to particular lexical items. Lexically conditioned suppletion is probably more relevant in the domain of affix allomorphy than stem allomorphy, and in fact lexically conditioned suppletion in the domain of stem allomorphy will necessarily involve some additional type of conditioning (since some other property in addition to the lexical item needs to vary in order for allomorphy to manifest itself). Lexically conditioned suppletive allomorphy often occurs in tandem with morphosyntactic conditioning—for example, different classes of verbs in a language may have different conjugation patterns (which would usually be categorized as allomorphy in the inflectional endings, rather than in the stem). A parallel example involving stem allomorphy would be one where, for example, a certain class of verbs has a special stem form that is used in certain tenses. An example is the so-called “strong” verbs in Germanic languages (verbs like eat, sing, and break), whose past tense forms have a special stem allomorph that is historically derived from phonological ablaut but is arguably suppletive (at least in modern English). The remainder of this chapter will not consider the lexically conditioned type of suppletion in as much detail as the other types, given its limited relevance to stem allomorphy specifically. A final type of suppletive allomorphy is phonologically conditioned suppletive allomorphy (PCSA). This is a phenomenon where the selection of suppletive allomorphs is determined by a phonological criterion. This situation is crucially different from the type of regular phonological allomorphy described earlier where a single underlying form corresponds to multiple surface forms due to the operation of a phonological rule, since Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 Alternations: Stems and Allomorphy 97 PCSA by definition involves multiple underlying forms. Interestingly, although many cases of PCSA seem to mirror the effect of phonological rules in terms of the surface results of a particular distribution of allomorphs, this is not always the case; sometimes the distribution of allomorphs appears to be phonologically arbitrary (though still phonologically determined). In the realm of stem allomorphy, cases of PCSA as defined here seem to be rare. In fact, as discussed below in Section 3.1, in lexical subcategorization-based approaches to allomorphy, strictly speaking, PCSA in stems is predicted not to exist. However, some cases are known. An example that could be seen as phonologically conditioned stem allomorphy is found in Italian (Hall 1948), where some stems have allomorphs ending in /isk/ that occur only in morphological contexts where the word stress falls on the stem-final syllable—namely, in the present and subjunctive 1sg, 2sg, 3sg, and 3pl and in the 2sg imperative (Hall 1948: 25, 27). One such stem is fin- “finish”; some examples are shown in (3) (Hall 1948: 214) with the forms in [isk] (and its surface phonological variant [iʃʃ ]) shown in bold. (3) Present finísk-o finíʃʃ-i finíʃʃ-e ‘I finish’ ‘you (sg) finish’ ‘s/he finishes’ fin-iámo fin-íte finísk-ono ‘we finish’ ‘you (pl) finish’ ‘they finish’1 Subjunctive finísk-a finísk-a finísk-a ‘that I finish’ ‘that you (sg) finish’ ‘that s/he finish’ fin-iámo fin-iáte finísk-ano ‘that we finish’ ‘that you (pl) finish’ ‘that they finish’ ‘(you (sg)) finish!’ fin-iámo fin-íte ‘let’s finish’ ‘(you (pl)) finish!’ Imperative finíʃʃ-i Other stems of this type include ağ- ‘act,’ argu- ‘argue,’ dilu- ‘add water,’ mεnt- ‘lie,’ diminu- ‘diminish,’ and ammon- ‘admonish’ (Hall 1948: 43–5, 52, 61). There appears not to be any semantic or phonological generalization regarding which stems pattern with this class of verbs in Italian, so the allomorphy must be lexically conditioned (arbitrarily, by the specific verb stem) in addition to being phonologically conditioned.2 1 Thanks to Anna Thornton for correcting the transcription of this form, which was incorrectly reported in Paster 2006. 2 I have described the Italian case in terms of the phonological generalization, but the standard analysis appears to be in terms of arbitrary stem patterns. A number of verbs other than the isc verbs have the same pattern in the present tense (having a stem form that appears with 1sg, 2sg, 3sg, and 3pl subjects and a different form occurring with 1pl and 2pl); Maiden 2004 terms this the “N pattern.” Interestingly, there are multiple other types of N-pattern stems that do not involve isc, including some where a vowel differs between the two versions of the stem but not in a way that is described by a regular synchronic phonological rule, and the verb andare, whose two stem variants are etymologically unrelated. The fact that these three very different types of N-pattern stems can all be described in the same phonological terms may be used in support of an account in terms of phonological optimization, but a more standard view seems to be that the N pattern is an abstract morphological pattern that diachronically has attracted a number of stems into its class (see, e.g., Thornton 2007; Da Tos 2013). Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 98 MARY PASTER Phonological Suppletive (multiple underlying forms) (one underlying form) Phonological Morphosyntactic (PCSA) Lexical Figure 5.1. Types of allomorphy To summarize the typology of allomorphy that I have presented above, we have discussed two main types of allomorphy (regular phonological allomorphy and suppletive allomorphy), and, within what I have called suppletive allomorphy, three subtypes based on the type of conditioning involved. We can schematize this conception of allomorphy as in Figure 5.1. It should be pointed out that many cases of suppletive allomorphy are conditioned simultaneously by more than one of the factors represented in Figure 5.1. It has already been observed that for stems specifically, lexical conditioning is accompanied by another type of conditioning, such as morphological conditioning, as in the example of the Germanic strong verbs. Another example of multiple types of conditioning is the Hopi case, where it was noted that only certain nouns exhibit the pattern in (2). Other nouns have uniform stem forms for singular, dual, and plural. Thus, in addition to being morphologically conditioned (by the plural category), this case of stem allomorphy is also lexically conditioned by the noun being used. The morphologically conditioned stem suppletion only applies if the noun does not belong to the regular class, whose membership, if arbitrary, would have to be called lexical. Any adequate theory of suppletive allomorphy will have to be able to accommodate the common situation where more than one type of conditioning factor is involved. Having seen a few examples of stem allomorphy and discussed how the different types are categorized, we turn now to the discussion of how stem allomorphy can be analyzed theoretically. 3 Analyzing Stem Allomorphy In this section, I present four different theoretical approaches to the analysis of stem allomorphy. In each case I give an overview of how stem allomorphy is handled using each theory, and then I discuss the advantages and drawbacks of each theory with respect to how well the known cases of stem allomorphy are handled. Some discussion, particularly in Section 3.1 and Section 3.2, draws considerably from Paster (2015), to which I refer the reader for more detail about the treatment of the PCSA type of suppletive allomorphy in particular. The four approaches to be discussed in this section are lexical subcategorization (§3.1), constraint-based approaches (§3.2), allomorphy rules (§3.3), and indexed stems (§3.4). We begin with lexical subcategorization. Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 Alternations: Stems and Allomorphy 99 3.1 Lexical Subcategorization In a subcategorization model (Lieber 1980; Kiparsky 1982; Selkirk 1982; Inkelas 1990; Orgun 1996; Yu 2003, 2007; Paster 2006), affixation satisfies missing elements specified in the lexical entries of morphemes. In this type of model, suppletive allomorphy is a phenomenon that results when two or more different morphemes with identical morphosyntactic and semantic specifications3 have different phonological forms and different subcategorizational requirements. These requirements are schematized via subcategorization frames, which indicate the selectional requirements imposed by morphemes. To illustrate how this model works, we return to the Hopi example presented in Section 2, repeated in (4). (4) Singular wùuti tiyo pöösa Dual wùuti-t tiyo-t pöösa-t Plural momoya-m tooti-m pövöya-m Gloss ‘woman’ ‘boy, young man’ ‘house mouse’ Representations of subcategorization frames for the two stem forms of ‘woman’ are given in (5a), and a subcategorization frame for the plural suffix is given in (5b). (5) a. b. ‘woman’ (plural stem) [[momoya-]stem, plural ] word, [[ ]stem -m ] word, plural plural ‘woman’ (elsewhere stem) [wùuti-]stem A higher-level node representing the plural word momoya-m ‘women’ is shown in (6), with the plural stem and plural suffix as its daughters. (6) [[momoya-]stem, plural -m] word, plural [[momoya-]stem, plural ] word, plural [[ ]stem -m] word, plural This is a complete word, since the missing elements in the subcategorization frames of both daughters have filled each other in, yielding a representation with no gaps. Some theoretical questions arise in the representation of the two stem variants in this example. First, why is it not specified that the plural suffix 3 By some definitions of the term “morpheme,” multiple underlying phonological forms that have identical morphosyntactic and semantic features would all be considered to be stored as one “morpheme.” That definition is not useful in the present context, since suppletive allomorphy relies on there being multiple stored underlying forms (soundmeaning pairs), and we need a term to identify each of those stored forms. Some researchers might use the term “morph” for this purpose, but since the term “morph” does not capture the fact that we are referring to underlying forms rather than surface alternants, I use the term “morpheme” instead. In this chapter I will not address the question of whether there is a linguistically significant higher-level unit that subsumes all of the stored forms that have the same morphosyntactic and semantic properties but possibly different phonological forms and/or subcategorizational requirements (i.e., groups of what I am calling “morphemes” that have identical morphosyntactic/semantic features). Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 100 MARY PASTER subcategorizes for a plural stem, and given this, how does the plural suffix select for the plural stem in words like “woman”? The reason that the plurality of the stem is not specified in the subcategorization frame of the plural suffix is that, as mentioned earlier, some stems do not have a special allomorph in the plural. Some examples of these regular nouns are given in (7) (Hill and Black 1998: 870; Haugen and Siddiqi 2013). (7) Singular sino kawayo Tasavu Dual sino-t kawayo-t Tasavu-t Plural sino-m kawayo-m Tasavu-m Gloss ‘person’ ‘horse’ ‘Navajo’ Specifying that the plural suffix subcategorizes for a plural stem would have the undesirable consequence of requiring that nouns like those in (7) have two homophonous, listed stems—one specified as plural and one not. This is why the subcategorizational requirement of the plural suffix is stated only as a “stem” rather than a plural stem. The plural suffix’s selection of the plural stem, in nouns where a special plural stem exists, follows from Pānini’s principle (i.e., the selection of the elsewhere stem is _ blocked by the availability of a more highly specified stem that is still compatible with the affix). Now that we have seen how this model deals with morphosyntactially conditioned suppletive allomorphy, I will briefly discuss how it handles other types of allomorphy. Regarding lexically conditioned allomorphy, as we have already discussed, some additional type of conditioning will always be present when the allomorphy involves stems. Consider the lexically conditioned aspect of the Hopi example discussed above. What differentiates the suppletive stems from the regular stems in this case, in a lexical subcategorization approach, is simply the fact that the suppletive stems have two separate stored forms, while the regular stems have only one. Examples like the Germanic strong verbs would be treated similarly, except that the past tense form of a strong verb stem would not subcategorize for a suffix; it would merely be limited to occurring in the context of a past tense word. A representation of the past tense of a strong verb might be as shown in (8). (8) [[sang]stem, past]word, past [[sang]stem, past ] word, past [[ ]stem Ø] word, past A possible criticism of this approach to Germanic strong stems is that it fails to capture the phonological systematicity of the stem alternations (i.e., that the past tense stem is identical to the elsewhere stem except for the last vowel, which exhibits ablaut). This relates to the more general criticism of the subcategorization approach (what Embick 2010 refers to as the “putative loss of generalization argument”) that it treats apparent Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 Alternations: Stems and Allomorphy 101 regularities in allomorph distribution as arbitrary or coincidental. The position that will be adopted here, regarding the Germanic example, is that the apparent ablaut is the reflex of a phonological rule that is inactive in the phonology of modern English. Thus, from the point of view of the synchronic grammar, the apparent systematicity of the vowel changes in strong stems is indeed coincidental; the stem variants are lexically listed, and as far as the grammar is concerned, the vowel alternations could just as easily be completely unsystematic and random-seeming if the history of the language had somehow unfolded that way. Support for this view comes from the lack of a regular ablaut rule in the phonology of modern English and the impossibility of writing a plausible rule (or constraint ranking) to account in phonological terms for the alternations. I have discussed the treatment of PCSA in the subcategorization approach at length elsewhere (see Paster 2005, 2006, 2009, 2014, 2015, to appear, and references therein). Briefly, the approach to PCSA is identical to the approach to morphosyntactically conditioned suppletion, except that the element that is subcategorized for in PCSA is phonological, rather than morphosyntactic. This possibility was made explicit by, for example, Orgun 1996 and Yu 2003. This allows the subcategorization frame to account not only for PCSA, but also for affix placement (prefix, infix, suffix). See Paster (2009) for an overview. Regarding the Italian example discussed in Section 2, because the lexical subcategorization approach requires words to be built from the inside out, the model as I have defined it here does not allow phonological properties of affixes to condition PCSA in stems. This does have the advantage of explaining the apparent extreme rarity of examples of this type (see, e.g., Paster 2006), but it also requires a reanalysis of those examples so that we can understand them as being consistent with the “inside-out” generalization. One important fact about the Italian case is that, segmentally, the shorter stem allomorph is a subset of the longer allomorph. This allows us to analyze -isc as a separate affix. Some previous analyses of Italian stem allomorphy (e.g., DiFabio 1990; Schwarze 1999) do treat -isc as an affix or “stem extension.” Analyzing -isc as an affix is helpful in reconciling the example with the lexical subcategorization model, but it is still problematic since this would still appear to be an example of PCSA with an “inner” suffix being conditioned by an “outer” suffix, which is also not allowed by the model. A further move that we need to make in order to maintain the “inside-out” generalization is to analyze -isc- an infix rather than a suffix. This allows us to assume that the word is built as follows: first, the subject agreement suffix is added to the root, and then the -isc- infix (which I assume to have inherent stress) will be inserted between the root and the suffix whenever the suffix is not inherently stressed. The infixing analysis may provoke some skepticism, but, in fact, this has been proposed independently; for example, DiFabio (1990) and others analyze -isc- (or -sc-) as an infix. While the infixing analysis may seem like a trick to uphold the “inside-out” Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 102 MARY PASTER generalization, one must concede that the lack of cases of phonologically conditioned stem allomorphy is striking given the number of cases involving affix allomorphy. Furthermore, it is not the case that any possible putative case of stem allomorphy could be explained away. The infixation account is possible for Italian because isc is present in all of the extended stems. Regarding the treatment of cases of non-suppletive allomorphy such as the Polish example described in Section 2, the lexical subcategorization model does not necessarily dictate a particular approach. It is compatible with both constraint-based and rule-based theories of phonology. One thing to be mentioned in this regard is that in the version of lexical subcategorization that I have articulated here and elsewhere, it is assumed that phonology and morphology are separate components of the grammar, and that all regular phonology occurs after morphology, modulo interleaving as in Lexical Phonology (Kiparsky 1982). Given this, subcategorization frames, being part of the lexicon/morphology, are not especially relevant to regular phonological alternations in stems. The morphology, via subcategorization, merely supplies the underlying forms to which the regular phonology later applies. An advantage to this approach is that it correctly predicts opaque interactions between suppletive and non-suppletive allomorphy in a single language. An example of this, as I have discussed in Paster (2009), comes from Turkish (Lewis 1967) (from the domain of affixes; I am not aware of cases of stem allomorphy that behave this way). As seen in (9), the third-person possessive suffix has suppletive allomorphs /-i/ and /-si/. The /-i/ form occurs when the stem ends in a consonant, while the /-si/ form occurs when the stem ends in a vowel (examples are from Aranovich et al. 2005 and from Gizem Karaali, personal communication; note that vowel alternations are due to regular Turkish vowel harmony). (9) bedel-i ikiz-i alet-i ‘its price’ ‘its twin’ ‘its tool’ deri-si elma-sɪ arɪ-sɪ ‘its skin’ ‘its apple’ ‘its bee’ At first, this looks like a straightforward case of PCSA. We could analyze the /-i/ form as subcategorizing for a consonant at the end of the stem, and/ or the /-si/ allomorph subcategorizing for a vowel at the end of the stem. However, Aranovich et al. (2005) point out that the selection of the suffix allomorph is opaque in some words due to the operation of a regular Velar Deletion rule (Sezer 1981) that deletes intervocalic /k/. Some examples are given in (10). (10) açlɪ-ɪ bebe-i gerdanlɪ-ɪ ekme-i ‘its ‘its ‘its ‘its hunger’ (cf. açlɪk ‘hunger’) baby’ (cf. bebek ‘baby’) necklace’ (cf. gerdanlɪk ‘necklace’) bread’ (cf. ekmek ‘bread’) Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 Alternations: Stems and Allomorphy 103 In these examples, it appears that the /-i/ form has been incorrectly selected after a vowel, but the citation forms show that each of these stems is underlyingly consonant-final. The lexical subcategorization approach allows for a simple explanation of the pattern: the morphology selects the /-i/ allomorph of the possessive suffix in these forms due to the presence of stem-final /k/ in the underlying form. The affixed forms are then passed on to the phonology. Due to the presence of the /-i/ suffix, the /k/ is now in intervocalic position and is therefore deleted. Such cases of opacity are more difficult to deal with in constraint-based approaches, to which we now turn. 3.2 Constraint-based Approaches A constraint-based approach to allomorphy uses conflicting constraints to account for allomorph distribution. In the case of suppletive allomorphy, a classic constraint-based approach to PCSA in Optimality Theory (OT) is the ‘P >> M’ ranking schema (McCarthy and Prince 1993a, 1993b), later updated by Wolf (2008, 2013) (see also Chapter 20 of this volume for more on OT approaches). The basic idea is that a phonological markedness constraint (P), such as a constraint on syllable structure, outranks a morphological constraint (M), such as one requiring that a certain morphological category should always be marked by one particular variant of an affix. Where relevant, the phonological constraint can force the morphology to deviate from the preferred surface realization of the morpheme in question, instead choosing an allomorph that allows the word to satisfy the phonological constraint while still expressing the function/meaning of the morpheme in question. Crucially (in the P >> M approach and most other constraint-based approaches), the separate listed allomorphs of the morpheme are all present in the input, so that even the selection of a special or dispreferred allomorph satisfies faithfulness constraints. The Italian example discussed earlier would be modeled as a conflict between, on the one hand, a set of P constraints relating to stress (perhaps one requiring exactly one stress per word, in conjunction with one requiring faithfulness to inherent stress on suffixes), and on the other hand an M constraint such as Uniform Exponence (Kenstowicz 1996) (11). (11) Uniform Exponence: Minimize the differences in the realization of a lexical item (morpheme, stem, affix, word) Both allomorphs of the stem would be present in the input (for “we finish,” for example, the input would be /{finísk-, fin-}, -iámo /). The ranking P >> M would select a form with the short stem allomorph (fin-), i.e., fin-iámo. There is less published work on constraint-based theories of morphology per se, since the P >> M approach emerged from the OT phonology literature. Therefore there is no definitive statement as to how the OT approach would handle morphosyntactically or lexically conditioned suppletive Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 104 MARY PASTER allomorphy. Regarding morphosyntactic conditioning, presumably it would be conflicts among M constraints (rather than between P and M constraints) that would yield suppletive allomorphy in an approach along the lines of the P >> M approach to PCSA. In the case of the Hopi example discussed above, for example, the M constraint being violated in forms with the special allomorph might be Uniform Exponence, discussed above. The higherranked constraint forcing violations of Uniform Exponence in plural words would need to have the function of Pānini’s principle, combining with _ the specification of the plural stem form with a plural feature to force the selection of the special plural stem allomorph in plural words where such a stem allomorph exists. For ease of exposition, let us call this constraint Special Plural (12), although it may reduce to something more general4 (see also Chapter 17 of this volume for discussion of Pānini’s principle). _ (12) Special Plural: Use the plural stem allomorph in plural forms. As in the P >> M approach to PCSA, for other types of suppletive allomorphy, all listed allomorphs would appear in the input to the tableau for any word containing the stem in question, such that input-output faithfulness constraints do not distinguish between candidates containing one allomorph versus the other. This assumption, combined with the ranking Special Plural >> Uniform Exponence, would cause the plural stem to be selected in plural forms (13a) and the elsewhere stem to be selected in non-plural forms (13b). (13) a. momoya-m ‘womenPL’ /{momoyaPL, wùuti}, -mPL/ Special Plural a. momoya-m b. wùuti-m b. wùuti-t ‘womenDU’ /{momoyaPL, wùuti}, -tDU/ a. momoya-t Uniform Exponence * *! Special Plural Uniform Exponence *! b. wùuti-m Other analyses are possible in a constraint-based approach depending on one’s theory. For example, if constraints on inputs are allowed, Pānini’s _ principle could be considered a constraint on inputs rather than a violable 4 One proposal to capture Pānini’s principle in constraint form is SUBSET BLOCKING (Xu 2007: 80): “An exponent _ (Exponent1) cannot co-occur with another exponent (Exponent2) if the latter (Exponent2) realizes a subset of feature values that are realized by the former (Exponent1).” This was proposed to deal with inflectional morphology; attempting to use this constraint for stem allomorphy seems to backfire. In the present case, SUBSET BLOCKING would only be satisfied either by choosing the less specified stem or by not expressing the plural suffix, since the plural feature of the suffix is a subset of the features of the plural stem. If a higher-ranked constraint forced the plural suffix to surface anyway, this would then force the selection of the less specified stem in order to satisfy SUBSET BLOCKING. Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 Alternations: Stems and Allomorphy 105 constraint, such that only the most highly specified stem allomorph that is compatible with the features of the word as a whole appears in the input. In this type of model, non-suppletive phonological allomorphy would be handled using ranked phonological constraints, as in OT phonology and its relatives. A full explanation of constraint-based analyses of phonological alternations is of course far beyond the scope of this chapter. One point to be made here is that a putative advantage of the constraint-based approach to allomorphy is that the same P constraints are responsible both for PCSA and non-suppletive phonological allomorphy. This is claimed to be an advantage because in some languages there are instances of suppletive allomorphy that appear to be driven by the same phonological considerations as regular phonological alternations and/or phonotactic generalizations in the language. For example, Wolf (2008: 103–5) discusses an example from Kɔnni (Cahill 2007) where the noun class system appears to conspire with the regular phonotactics of the language to avoid flaps in adjacent syllables. No flap-final roots occur in the noun class that has a flapinitial suffix, and in addition, the sequence [ɾVɾ] does not occur within morphemes. Wolf argues that OT offers a better analysis of this example than the lexical subcategorization approach does, because the OT analysis unifies the two phenomena via a single markedness constraint, while the subcategorization approach would have to treat the two phenomena separately. Because the OT approach handles both PCSA and regular phonological allomorphy (as well as static phonotactics) with the same P constraints in the same component of the grammar, it predicts that examples of PCSA will be phonologically “optimizing” (since they are driven by phonological markedness constraints in this model). This means that the distribution of allomorphs should be better from the point of view of some phonological markedness constraint(s) than it would be if the distribution of allomorphs were reversed. As I have pointed out elsewhere (Paster 2005, 2006, 2009), and as also noted by Bye (2007), this does not seem to be an accurate prediction; there are many languages having instances of PCSA that are not phonologically optimizing in any identifiable way and that apparently cannot be analyzed using markedness constraints which have been proposed elsewhere in the literature. A well-known example comes from Haitian creole, where the definite determiner suffix has the form /-a/ after vowel-final stems and /-la/ after consonant-final stems. As discussed by, for example, Bye (2007), this distribution of suffix allomorphs is the opposite of what syllable structure constraints (Onset, NoCoda) would predict. 3.3 Allomorphy Rules and Readjustment Rules The Distributed Morphology (DM) approach to grammar (Halle and Marantz 1993; see also Chapter 15 of this volume for an overview), like lexical subcategorization, distinguishes between suppletive and morphophonological Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 106 MARY PASTER allomorphy, but the distinction is made differently. In DM, suppletive allomorphy is modeled via competition between different vocabulary items (VI; essentially morphemes, including phonological content) for insertion into syntactic nodes during what is called “spell-out.” The competing VIs are specified as to the environment (morphosyntactic or phonological) into which they will be inserted, just as in lexical subcategorization. Morphophonological allomorphy, where the allomorphs in competition are phonologically similar, is handled via a single VI being inserted, followed by the application of readjustment. Readjustment rules are different from phonological rules in being less constrained formally; for example, where rules in most versions of rule-based phonology can target only a single segment, readjustment rules in DM can change entire sequences. Related to the readjustment rule is the allomorphy rule (see, e.g., Aronoff 1976), which changes the segments of a morpheme into another string of segments in some morphologically defined environment. A possible critique of both readjustment rules and allomorphy rules is that they are overly powerful; while “rewrite” rules in phonology have been criticized for their excessively powerful ability to change any segment into any arbitrarily different segment in any stable environment (see, e.g., Coleman 1998), readjustment rules and allomorphy rules have exponentially greater power since they can target entire sequences of segments. Another drawback of the allomorphy rule approach that has been discussed in the literature (see, e.g., Rubach and Booij 2001) is that it is often not possible to write a rule that applies in a natural class of environments. Any theory has to acknowledge that stem allomorphy often occurs in unnatural groupings of morphological environments, but incorporating this fact into an analysis greatly diminishes the simplicity and elegance of an allomorphy rule, while it is more straightforward to capture in other approaches like stem indexation, to be discussed in Section 3.4. In DM, the Hopi example discussed earlier would presumably be treated as suppletive allomorphy since the allomorphs are not phonologically similar. Early statements in the development of DM suggested that roots do not compete with each other for lexical insertion, but stems do apparently compete. For example, in the analysis of Latin stem allomorphy given by Embick (2010: 85–6), multiple forms of the verb stem “be” including fu- and es- are in competition, resolved by fu- being limited to occurring in the perfective form. Using Embick’s notation, the VIs for the two Hopi stem allomorphs would be as given in (14), where ‘__ ͡ Num[pl]’ indicates that the momoya allomorph is limited to the context where it is concatenated with the plural suffix. This VI will take precedence since it is the more specific of the two. (14) [nwoman] $ momoya / __ ͡ Num[pl] [nwoman] $ wùuti In contrast to the Hopi nouns, the Germanic strong verbs would be handled in DM via readjustment rules since the competing allomorphs Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 Alternations: Stems and Allomorphy 107 are more closely phonologically related. See, for example, Embick and Marantz (2008: 2): “A morphophonological readjustment rule changes the phonology of give to gave in the context of the past tense morpheme.” The treatment of PCSA in DM is considered in detail by Embick (2010). A key feature of DM that is relevant to PCSA is late lexical insertion. In other theories, affixation and other morphological operations apply to morphemes whose phonological form is visible to the grammar from the beginning of the derivation. In DM, most such operations apply in the syntax to abstract nodes prior to spell-out, meaning that the phonological content is not yet visible. Under the strongest interpretation of late lexical insertion, no phonological content would be available to the grammar at the point of spell-out, meaning that PCSA should not be possible. However, it has been proposed that spell-out applies cyclically by phase,5 meaning that phonological material is visible to the grammar if it was spelled out on an earlier cycle (see Embick (2010) for a detailed articulation of this mechanism). Thus, PCSA is possible when the phonological environment needed for the insertion of a particular VI is under a node in the same phase or a phase that triggered an earlier cycle of spell-out, but not in a phase that will undergo spell-out later in the derivation. This limits the possible types of PCSA in interesting ways, in that it allows for limited instances of ‘outside-in’ suppletive allomorphy conditioning, where a phonological property of an affix conditions the selection of an allomorph of an affix “inside” it (closer to the root) or of the stem itself. The possibility of “outside-in”-conditioned PCSA has been a point of contention between proponents of the subcategorization versus constraint-based approaches, since Paster’s (2006) large cross-linguistic survey of examples of PCSA revealed no clear cases, while Wolf (to appear) has since identified some languages that he claims instantiate outside-in conditioning, and Embick (2010: 61) presents a possible case of outside-in conditioning from Hupa (Golla 1970) he claims supports the DM approach specifically. (The generalization in Hupa is that the 1sg subject prefix allomorph e- is used when preceded by perfective prefix and the verb is non-stative; the prefix W- occurs elsewhere. If this example holds up, it constitutes outside-in conditioning since the perfective prefix occurs farther from the root than the prefix whose allomorphy is sensitive to it.) The Italian example discussed earlier would also be compatible with the DM approach, if it could be demonstrated that the stem and the inflectional suffixes (whose stress patterns are claimed to drive the stem allomorphy) are spelled out in a single cycle. As with the lexical subcategorization approach, the DM approach and allomorphy rules do not necessarily specify an approach to regular nonphonological allomorphy. 5 On phases, see Chomsky (2008) and references therein. Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 108 MARY PASTER 3.4 Indexed Stems A final approach to be considered here is the use of stem indexation (see, e.g., Aronoff 1994). The concept of stem indexation has been incorporated into multiple different frameworks, including Network Morphology (Hippisley 1998; see also Chapter 18 of this volume) and Paradigm Function Morphology (Stump 2001; see also Chapter 17 of this volume). As a result of the observation that in many languages stem allomorphs are distributed in unnatural ways, in this model stem allomorphs are indexed such that all the different stem contexts can be coindexed to match the correct stem allomorph, obviating the need for the stem itself to bear a list of the contexts in which it appears. Following Hippisley’s (1998) notation, a representation of the Hopi lexeme meaning “woman” in an indexed stem approach might be as in (15). (15) WÙUTI syntax: noun semantics: ‘woman’ phonology (stem inventory): 0 /wùuti/; 1 /momoya/ The rules for realizing singular and dual forms would then reference the stem index 0, while the rule for realizing a plural form would reference the stem index 1. In this case, the distribution of stem allomorphs could alternatively be characterized as [+plural] versus [-plural], so the advantage of the stem indexation approach is not as clear as in other examples. The benefits of stem indexation are more dramatically observable in languages where stem allomorphy occurs in large inflectional paradigms (see, e.g., Stump 2001, Chapter 6 on Sanskrit; Hippisley 1998 on Russian). Essentially, the approach is similar to lexical subcategorization approach in that morphemes select for other morphemes, but it is different in that affixation is handled by realization rules here, so the stem is not necessarily present in the representation prior to affixation, as opposed to the way that words are built from the inside out under the version of lexical subcategorization that I have described. On the one hand, this is an advantage of the indexed stems approach if there are examples of stem allomorphy that cannot be handled by lexical subcategorization; on the other hand, it is a liability if it turns out that affix-conditioned stem allomorphy in general is extremely rare (i.e., if Paster’s (2006) findings in the domain of PCSA turn out to be generalizable to morphologically conditioned suppletion as well) and all the putative examples turn out to be reanalyzable. PCSA in stems conditioned by phonological properties of affixes can be handled in this approach via a “morphological metageneralization” rule Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 Alternations: Stems and Allomorphy 109 (Stump 2001: 180–3). Such a rule would look at all of the realization rules and could create a set of rules whose output contains affixes with a certain phonological property (for example, in the Italian case, inherent stress). That set of affixes would then be subject to a rule referring to a specific stem index (in the Italian example, the rule for the inherently stressed suffixes would refer to the index of the fin- allomorph). Note that, as in the lexical subcategorization approach, the indexed stems/morphological metageneralization approach treats PCSA as phonologically arbitrary rather than being driven by phonological markedness. Thus, it has the same apparent advantage of the lexical subcategorization model in terms of predicting and being able to account for cases where PCSA seems to be arbitrary rather than optimizing; on the other hand, it is vulnerable to the same criticism that proponents of constraint-based models have leveled against lexical subcategorization, namely that in the cases of allomorphy that do appear to be optimizing, the model does not explain the relationship between the choice of allomorph and the conditioning environment. As with the subcategorization approach and the allomorphy rules/ readjustment rules approach, the indexed stem approach does not necessarily presuppose a particular theory of phonology. Therefore, it does not appear to prescribe a treatment of non-suppletive allomorphy. Having demonstrated and evaluated four possible approaches to the analysis of stem allomorphy, in Section 4 we will discuss remaining problems and issues for future research. 4 Outstanding Issues In Section 3 we have seen four different theories/frameworks for analyzing stem allomorphy: lexical subcategorization, constraint-based approaches, readjustment rules, and indexed stems. For each theory, we have discussed how the various types of stem allomorphy would be approached. We have also discussed some advantages and drawbacks of each model. The question now remains as to which model is superior and ought to be adopted—or, if some combination of these approaches is indicated, how can they be reconciled with each other in terms of an appropriate division of labor? As has been discussed, the various models make “cuts” in different places between different types of allomorphy. In the typology that I presented in Section 2, there are two basic types of allomorphy: phonological (nonsuppletive) vs. suppletive, defined as involving one underlying form of the morpheme (in the non-suppletive case) versus two or more (in suppletion). The version of the lexical subcategorization approach that I have presented here aligns with this typological division, since non-suppletive allomorphy is handled by the phonology, while a distinct morphological component of the grammar is responsible for suppletive allomorph selection. Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 110 MARY PASTER Both the readjustment rules approach and the indexed stems approach also appear to leave non-suppletive allomorphy to the domain of phonology, but the readjustment rules approach makes an additional distinction relative to the subcategorization and indexation approaches. With readjustment rules, some cases of suppletion are dealt with as separate underlying forms that compete for insertion, while some other cases of what the other two models would deem “suppletion” (and would handle via two separate underlying forms, whether as separate listed morphemes under subcategorization or as separately indexed stems in a single lexeme under stem indexation) are treated via a single underlying form. The criterion distinguishing the two cases is phonological similarity: if the two allomorphs are similar, it is assumed that there is only one basic form of the VI that is inserted and may then be subject to readjustment rules, which are more powerful than phonological rules/constraints and can therefore handle greater variability between surface forms of a single underlying form than the other two models would tolerate. A major challenge and source of vulnerability for the readjustment rules approach relative to the other two is to define what constitutes sufficient phonological similarity to reduce the allomorphs to a single underlying VI. Presumably the answer is that they must be similar enough to be relatable via one or more valid readjustment rules, but this then raises the equally challenging question of what is a possible readjustment rule. At present, there does not appear to be any consensus—for example, among practitioners of Distributed Morphology—regarding a theory of readjustment rules. One could level a similar critique against the other two models on the grounds that the decision to analyze allomorphy as suppletive or not depends on a theory of rules/constraints, but it can be argued that there has been more progress in this area and that this is not as hard a problem as a theory of readjustment rules. I will take this point up again later. The constraint-based approach differs from the other three in that it does not distinguish significantly between PCSA and what the other models would treat as non-suppletive phonologically driven allomorphy. Both are handled within a single component of the grammar (which contains both phonological and morphological constraints). The only difference between the two phenomena from the point of view of a constraint-based theory is that in PCSA, all of the different stem allomorphs are present (in curly brackets) in the input to a tableau, as opposed to non-suppletive allomorphy where there is only one listed form in the input. This does align with the idea of separately listed morphemes (in the subcategorization approach), indexed stems (in the stem indexation approach), or VIs (in the readjustment rules approach), but its effect is very different since the stem allomorphs have equal status in the input for any form that will contain one of the allomorphs on the surface. For a given case, it is essentially trivial whether one or multiple underlying forms are posited, since as far as faithfulness constraints are concerned, whichever allomorph is chosen on Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 Alternations: Stems and Allomorphy 111 the surface will already have been present in the input as if it were selected in advance. The ability of the constraint-based model to generalize to morphologically and lexically conditioned suppletive allomorphy will be determined by the successful development of a constraint-based theory of morphology. See Caballero and Inkelas 2013 for one recent effort in this area. In deciding which model offers a superior approach to allomorphy (setting aside non-suppletive allomorphy, since of the four models only the constraint-based approach actually dictates an approach to that type of allomorphy), considerations of empirical adequacy are relevant. In the domain of PCSA, as referenced above, there has been a detailed crosslinguistic survey of the phenomenon (e.g., Paster 2006) and considerable argumentation over details of the cross-linguistic generalizations (see references above), particularly as they relate to the debate between lexical subcategorization and constraint-based approaches, but more recently the readjustment rules approach in Distributed Morphology as well. Much of the debate has concerned (1) whether allomorphy is optimizing and (2) whether it can be conditioned from the outside in. Regarding optimization, I and others (Bye 2007; Embick 2010) have argued elsewhere that being able to capture apparent phonological optimization in PCSA is not an advantage of the constraint-based approach in light of the fact that not all cases are optimizing. The purported advantage is entirely self-generated: the theory is claimed to have an advantage in being able to account naturally and without stipulation for cases that it treats as optimizing via a theory of optimization, but the fact remains that this model treats the non-optimizing cases (when they are discussed at all in the OT literature) via stipulative, language-specific, and sometimes decidedly unnatural constraints. The superior “explanatory power” of the model is thus reduced to an ability to explain some subset of the attested examples, in comparison to other models which are said not to explain any of them. Thus, this does not in my view constitute a valid argument in favor of the constraint-based approach. I argue in Paster (to appear) that the synchronic grammar is not the proper locus for the “explanation” of any of the patterns, whether they appear on the surface to be optimizing or not. Regarding the direction of conditioning, I asserted (Paster 2006), extrapolating from results of a cross-linguistic survey of PCSA, that true “outside-in” conditioning does not exist, meaning that PCSA in stems should not be conditioned by a property of an affix. Some examples that appeared on the surface to constitute outside-in conditioning were shown to be reanalyzable. However, as noted earlier, some examples have since been put forward that may pose tougher challenges to the claim (see Wolf 2008, 2013; Embick 2010). A closer look at the details of these examples will determine whether they do constitute counterexamples. If so, what explains the crosslinguistic rarity of outside-in conditioned PCSA? And is there a strict limit to the theoretically possible cases (as Embick 2010 proposes) or not? The case Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 112 MARY PASTER from Sanskrit discussed by Stump (2001: Chapter 6), where verb stem allomorphs are distributed based on whether the inflectional suffix is consonant- or vowel-initial, should be added to the list of examples to be evaluated. Outside the domain of PCSA, more cross-linguistic research would be helpful to the analysis of other types of suppletive allomorphy in stems and more broadly. A broad cross-linguistic search for known cases of morphologically conditioned stem allomorphy, for instance, would be useful. Considerable progress on the typology of suppletion has been made by the Surrey Morphology group (see, e.g., Brown et al. 2004; Chumakina 2004; Corbett 2007). A fuller understanding of the range and parameters of suppletive allomorphy in the world’s languages will shape the development of theoretical approaches to the phenomenon. Setting aside the empirical questions raised above that do not yet have answers, there are some ways in which the decision among competing approaches to allomorphy will rely on theoretical argumentation. For example, it was mentioned earlier that the readjustment rules approach is lacking a coherent theory of the form and limits of readjustment rules. Such a theory is needed both for the development of the general theory (e.g., of Distributed Morphology) and also for the analysis of a given language, since the question of whether a single underlying form or multiple underlying forms is involved in a given case of phonologically conditioned allomorphy depends on what readjustment rules can or cannot do. The related question of what the “regular phonology” of a language can do (whether in a rule- or constraint-based framework) is relevant to similar decisions about underlying forms in the lexical subcategorization and indexed stems approaches. For the lexical subcategorization approach, I have elsewhere discussed a number of criteria for determining whether a given case of phonologically conditioned allomorphy is suppletive or not. Fuller discussion of these is given in Paster (2006: 27–31) (see also Paster 2014), but to restate it briefly here, the criteria are adapted from Kiparsky (1996: 17): (16) Suppletive A item-specific B may involve more than one segment C obey morphological locality conditions D ordered prior to all morphophonemic rules Non-suppletive general (not item-specific) involve a single segment observe phonological locality conditions follow all morpholexical processes Kiparsky does acknowledge that these criteria “cannot claim to provide an automatic resolution of every problematic borderline case” (1996: 16). I have argued that criterion (A), involving the generality of the pattern, is one of the more useful criteria. If a phonological rule needed to analyze a Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 Alternations: Stems and Allomorphy 113 pattern of allomorphy in one morpheme can also account for other patterns of allomorphy in the language, this suggests that the allomorphy is not suppletive. On the other hand, if the rule needed to account for a pattern of allomorphy would only apply to that particular morpheme, then the allomorphy is more likely suppletive. A related factor is the plausibility of the proposed rule. If the rule is itemspecific but is also formally simple, then this is an argument in favor of nonsuppletive allomorphy. On the other hand, if the proposed rule would be formally complex (perhaps involving multiple operations or affecting multiple segments simultaneously—thus relating to Kiparsky’s criterion (B)), the pattern should be analyzed as suppletive. Applying this criterion does require a commitment to some formal model for which it is clear what constitutes an allowable operation, trigger, target, and so forth, so that the plausibility of a rule can be assessed. I have assumed a rule-based phonology that includes autosegmental representations and extrinsic rule ordering, though what I have said here may be compatible with a wide variety of approaches to phonology. Any model of allomorphy will have to be paired with its own statement of criteria for distinguishing between types of allomorphy. A comparison among models could then be based in part on theoretical argumentation regarding how powerful a phonological system is required by each model and the plausibility of such a model. 5 Conclusion In this chapter, I have presented an overview of the logically possible types of stem allomorphy, giving examples of each type. I have discussed four different theoretical approaches to stem allomorphy and shown how each would deal with the different types of allomorphy. In the preceding section, I have compared some features of the different approaches and discussed how further empirical research and/or theory development might help to distinguish among them. In some respects, the choice of theoretical approaches to allomorphy may be a subject on which there will never be consensus. Some of the four approaches discussed in this chapter are radically different from each other, and of course these four do not represent the full range of possible approaches that exist in the literature or could be proposed. It is daunting to imagine finding common ground among them, and perhaps it is tempting to remain agnostic or to continue working within one’s own theory while allowing that other models may also have their advantages and may be scientifically useful theories in the way that they inspire new research and thinking. On the other hand, the decision as to which approach to take is important not only in itself but in some cases in much larger questions about the nature of human language. For example, the Downloaded from https://www.cambridge.org/core. UZH Hauptbibliothek / Zentralbibliothek Zürich (Bill To for 21002 Zurich Uni), on 27 Sep 2021 at 12:38:59, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/9781139814720.005 114 MARY PASTER constraint-based approach treats phonology and morphology as part of a single component of the mental grammar, while the lexical subcategorization approach treats them as crucially distinct from each other, and the realization rules approach within Distributed Morphology conceives of the division among components of the grammar in yet another radically different way. Thus, while it may be difficult to demonstrate the superiority of one approach over another, the effort to do so is crucial to advancing our understanding of human language. References Aranovich, Raúl; Sharon Inkelas, Orhan Orgun, and Ronald Sprouse. 2005. Opacity in phonologically conditioned suppletion. Paper presented at the 13th Manchester Phonology Meeting. 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