3.1 Configurations and constraints

Zimmermann's book lays the explanation for the MLM phenomenon firmly at the door of representation: extraordinary effects (MLM) are caused by ordinary processes (addition) operating on extraordinary things (defective morphemes). What makes this approach so insightful is that the configurational possibilities of phonological objects are predicted by autosegmental first principles.

In addition to the well-known one-to-one, one-to-many and many-to-one configurations, there are also three other contrastive arrangements of phonological objects, which be referred to as involving fixed, floating and empty nodes respectively. Following Zimmermann's conventions, the representations in (4b) and (c) can be grouped together as ‘defective’.

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For PDM, however, proposing defective morphemes requires some rethinking of the classical assumptions behind the prosodic hierarchy, something anticipated in Kiparsky's (1991) catalexis-based solution. The PDM framework shows particularly clearly that the prosodic hierarchy is not a series of projections sensu stricto, as they are in syntax, where (5a) is impossible. Prosodic constituents are independent phonological objects that are related to each other via association lines (not by projection), as in (5b), and regulated by weak layering.

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Once the prosodic hierarchy is seen as a collection of independent phonological objects, each on their own tier, mismatches between the tiers are actually predicted. So, although the defective representations shown in (4b) and (c) may look strange, or overly rich, to exclude them would actually require extra stipulations or conditions. In Zimmermann's terms, the defective structures are predicted by richness of the base, and should not be arbitrarily excluded, since they predict phonological surface effects (p. 40).

By definition, defective morphemes are inputs whose nodes fail to dominate or be dominated by nodes that they would ordinarily dominate or be dominated by. Consequently, in PDM constraints regulate the association of each prosodic node on tier n with nodes on both tiers n+1 and n−1. One constraint-type (DD) ensures that a node is dominated by a node on tier n+1 and another (Do) ensures that a node dominates a node on tier n−1 (p. 42). These are collectively known as parsing constraints; examples are μ-DD-σ and μ-Do-S (S=segment). Full integration occurs in outputs where the relevant Do and DD are unviolated, while any violation signals the presence of a defective node in the output. The basic configurations for full and defective integration are shown in (6). (Phonological objects that are shaded are phonetically invisible.)

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Zimmermann's central claim is that prosodically defective morphemes can result in MLM. Therefore, the contrast between underlyingly incomplete and complete prosodic structures does not become neutralised in the output (p. 43). The state of affairs where underlying states are preserved throughout the derivation is well modelled by the principle of containment: ‘every element of the phonological input representation is contained in the output’ (cf. Prince & Smolensky 1993). In containment theory there is no deletion of phonological objects from the input, though these can be left unpronounced in the output, as indicated by shading in (6).

Zimmermann's theory of containment goes even further, demanding that the whole of the input must be reconstructable from the output at any time: not just the phonological objects, but also the relations between those objects: the association lines. Following Trommer (2011) and Trommer & Zimmermann (Reference Trommer and Zimmermann2014), association lines can be marked as being invisible to the phonetics, resulting in the stray erasure of any phonological objects they dominate, as shown in (7) (p. 45).Footnote ²

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This distinction is carried over into constraints that specifically penalise epenthetic association lines. The principles of visibility follow naturally, ensuring that (a) every association line linking a phonetically invisible object to a lower object is phonetically invisible, and (b) every object is phonetically invisible iff it is not associated to a higher prosodic node by a phonetically visible association line (p. 45).

3.2 Morphological colour

Zimmermann's containment theory is based on the theory of morphological colour, which claims that every morpheme has an underlying colour (van Oostendorp Reference Oostendorp2006, Revithiadou Reference Revithiadou, Blaho, Bye and Krämer2007, Trommer Reference Trommer, van Oostendorp, Ewen, Hume and Rice2011). In what follows, morphological colour is shown as a subscript symbol. Each morpheme has a unique colour, therefore each subscript is also unique. Morphological colour cannot be changed throughout the derivation, so the morphological structure of words is always reconstructable at any point in the derivation. Epenthetic objects do not have a morphological colour. Consequently, colour is also the mechanism by which epenthesis is regulated, with constraints such as Col!S: ‘assign a violation mark for every segment not licensed by morphological colour’ (p. 51).

3.3 Demonstration of PDM

Before turning to a critical discussion of the book's two main contributions, I will demonstrate how the PDM framework operates for Yine, which has a process of morphologically conditioned vowel deletion. Zimmermann explains this using a mechanism she terms ‘mora usurpation’. Some affixes trigger the deletion of a morpheme's preceding vowel (pp. 86–96). These affixes are said to be ‘subtractive’, and are underlined.

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The process does not appear to be phonologically or syntactically conditioned; subtractive affixes form an arbitrary set, which is not identified by any morphosyntactic property. Furthermore, subtractive affixes can be homophonous with non-subtractive affixes: /hata-nu/ → [hatnu] ‘light, shining’ vs. /heta-nu/ → [hetanu] ‘going to see’ (p. 87).

To account for the data in PDM, Zimmermann proposes the following analysis, which relies chiefly on three constraints: V<DD_p ^m<μ, a parsing constraint that regulates association between syllables and moras, *σ-Col!μ, which penalises syllable nodes that dominate colourless (epenthetic segments), and *VμV, which penalises moras associated to multiple vowels (p. 89).

The representational component of PDM is the assumption that subtractive morphemes are prosodically defective, in the sense that they do not have underlying moras. For the input /neta-lu/ in (8a), the output in (9), [ne.tǝ.lu], is selected as optimal because the subtractive affix does not have its own mora.Footnote ³

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Consequently, it could either acquire a mora epenthetically or share an underlying base mora. The fact that both of these strategies are suboptimal is explained by the high-ranked constraints against a vowel sharing two moras: * VμV and *σ-Col!μ. As a result, the defective vowel of the subtractive affix must associate to a coloured mora of the base (which is not allowed to remain phonetically linked to its underlying segment, due to * VμV). Accordingly, subtractive affixes usurp the moras from segments of the base, resulting in their phonetic non-interpretation.

4.1 MLM has the same distribution as infixation

The central aim of Zimmermann's book is to show that MLM phenomena result from the ‘ordinary’ affixation of prosodically defective morphemes. Treating all instances of MLM as affixation leads to some impressive typological conclusions, as can be seen in Table I.Footnote ⁴

Table I Right vs. left edge of the base: (a) additive MLM; (b) subtractive MLM.

Suffixation is a far more common affixal strategy than prefixation, and as a result MLM is strongly biased to the right edge. In stark contrast, the competing approaches (summarised in Chapter 7) must conclude that MLM's preference for the right edge is a result of chance (p. 250).

The specifics of what positions in a base can be targeted by MLM phenomena is equally striking. In some original and highly effective diagrams, Zimmermann schematically lays out the positions of the base that are affected by MLM in 100 languages. These come from 33 language ‘stocks’, covering seven continent-sized ‘macro-areas’ (p. 241). Compellingly, no segment further inside its base than its first or last vowel is ever affected by subtractive MLM (p. 253). For additive phenomena, if the MLM affix joins from the left, no additive effect is seen further right than the first coda of the base, whereas, if the MLM affix comes from the right, no position further left than the penultimate vowel of the base is targeted that is. In the ‘vast majority of cases’, additive MLM affects the first or last vowel of the base (p. 250).

Zimmermann rejects ‘phonological dislocation’ (Prince & Smolensky Reference Prince and Smolensky1993, Halle Reference Halle and Kenstowicz2001), where phonological optimisation can in principle involve morphological changes in any part of the base (p. 68). She predicts that all MLM is affixal, so the question becomes one of how to analyse the cases where MLM effects occur within the base. As we have seen, MLM cannot intrude very far into the base, but it is not restricted to segments and positions at its very edge. As Zimmermann notes, it is particularly interesting that the contexts for MLM are strictly parallel to the landing sites for infixation (‘morphological pivot affixation’; Yu Reference Yu2007) in (10). This is in fact predicted if MLM is thought to proceed like infixation and affixation. This is confirmation of a major prediction of the PDM model.

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Zimmermann attempts to provide her own Coloured Containment reanalysis of Yu's pivot points, but, unfortunately, the mechanism she introduces, the colour index (p. 74), lacks independent motivation. The colour index is an abstract object that has no equivalent either in the morphosyntax or the phonetic interpretation. Confusingly, PDM claims that the colour index contains ‘purely morphological information’, but it exists only at a specific tier of the phonology, and ‘functions as a placeholder’ for a phonological object. In (11) we see the colour index represented as a solitary black dot. It is located on the same tier as the mora, so the colour index functions essentially as a ‘placeholder’ on that mora tier.

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Though the colour index has no phonetic interpretation of its own, it is claimed to have indirect effects. In order to eliminate colour indexes (presumably by analogy with the removal of uninterpretable features in syntax; Chomsky Reference Chomsky1995), the operation in (12) is introduced.

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The introduction of colour indexes in Zimmermann's Coloured Containment theory allows Gen to construct outputs with morphological colours in the base, as in (13).

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The formal application of index fusion is elegant and intelligent, which is characteristic of the whole of the book, but the mechanism employed suffers from arbitrariness. Both the colour index and the operation of index fusion are argued to be ‘purely empirically motivated’ (p. 75), but in fact they seem to provide an arbitrary explanation for the observed empirical fact that the distribution of MLM is like that of infixation. Various questions arise with respect to colour indexes and index fusion: why can morphemes contain only one colour index?; why not two or three?; why can they not be preceded and followed by a colour index on the same tier? The stipulation that there can only ever be one colour index gets the facts right, but does not follow from any formal principle or interface/learnability condition. From the formal perspective, colour indexes are like placeholders for phonological objects, which begs the question: why not have multiple ‘placeholders’, just like multiple phonological objects in the representation of a morpheme? From the interface and learnability perspectives, the MLM phenomena would be equally learnable if morphemes were to contain multiple colour indexes.

The problem with this aspect of the colour index is quite serious, because it undermines PDM's explanatory force in generating the typology. Although PDM allows non-concatenative morphology to be analysed as root affixation, it does not appear to replace Yu's (2007) pivots with anything more explanatory.

4.2 Subtraction through addition

The second major analytical contribution of Zimmermann's PDM framework is the audacious claim that even subtractive morphology is purely additive. This step is crucial to restricting morphology to a purely Item-and-Arrangement system. This is a wonderfully counterintuitive notion (foreshadowed in Trommer & Zimmermann Reference Trommer and Zimmermann2010, and adopted by D'Alessandro & van Oostendorp Reference D'Alessandro, van Oostendorp, Torres-Tamarit, Linke and van Oostendorp2016). Although the logic of the mechanism is intriguing, I think it is fair to say that its implementation in this book is somewhat underdeveloped. Before I present my criticisms, I give a simple example in (14).

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Verbs in Canela Krahô come in either ‘long’ or ‘short’ forms, roughly corresponding to ‘non-finite’ and ‘finite’ syntactic contexts (Popjes & Popjes Reference Popjes, Popjes, Derbyshire and Pullum1986). Certain ‘long’ forms are marked by the presence of a final consonant, which seems to delete in the ‘short’ contexts, as in (14a). Vowel-final forms show no alternations, as in (b).

The PDM analysis is a simple but representative example of how subtractive morphology works in this framework. The short forms are a consequence of the affixation of a prosodically defective mora to a base (p. 111). A number of constraints and candidates are involved in Zimmermann's analysis, but the real interest revolves around the choice between the candidates where the affixed mora has an additive effect, k⚬a⚬t⚬ɔ⚬ː•l = [katɔːl] or k⚬a⚬t⚬ɔ⚬l⚬ː• = [katɔlː], and the optimal subtractive output, k⚬a⚬t⚬ɔ⚬<l>•= [katɔ] ‘he arrives’.

In Zimmermann's framework, the reason for the prosodically defective mora causing segment deletion are the high-ranked constraints μ>Do>V and *σμ. The former forces the affixal mora to link to a segment, while the latter simultaneously penalises the attachment of an affixal mora to a syllable node. The optimal candidate will therefore be one where the affixal mora links to a base segment and at the same time does not link to a syllable. This lack of attachment to a syllable in the optimal candidate results not only in the mora's phonetic invisibility, but also in the phonetic non-interpretation of any segments it dominates. This leads to the appearance of deletion, as shown in (15).

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As far as I see, the mechanism or formal explanation behind the constraint family *x y is underdeveloped, because [+Affix] is not a feature, and not part of the representation.

Zimmermann effectively suggests that there are base colours and affix colours. The phonology can directly access the distinction between base and affix, a distinction that is frequently found in phenomena discussed in the literature (p. 50). However, the motivation or reason for them having base vs. affix colours is not given. It is reasonable that each morpheme should have its own colour, because each is a unique object. So phenomena that show sensitivity to this uniqueness (conditions on integration) can be explained by each morpheme having its unique colour, an independent fact which supports this representational status. But the difference between bases and affixes cannot work in this way. What defines the classes of base and affix? If the answer is ‘the colour’, then the explanation is circular. Using colours like this amounts to no more than giving a description of the fact that phonological phenomena can recognise the difference between bases and affixes. The argument would work, however, if bases and affixes had different sets of colours because of some independent distinction; for instance, if they came from different lexicons, or if their representations were independently distinguished in some way, allowing them to form a natural class.