1 Introduction
In Inflectional morphology in harmonic serialism (IMHS), Gereon Müller provides proof of concept for a new theory of the morphology–phonology interface. IMHS proposes a lexicalist (presyntactic), realisational theory of morphology, built around the tenets of Harmonic Serialism (McCarthy Reference McCarthy2008): the derivation begins with the root and proceeds through the affixes, whereby the optimal exponent is selected at each step. The monograph goes through a range of data in different languages, developing and refining the theory in order to account for increasingly complex empirical scenarios.
The book holds together well. IMHS is a young theory, still finding its bearings in a world full of counterbleeding, multiple exponence and root suppletion. It would be harsh to expect it to provide thorough accounts of many different phenomena. The monograph takes the challenge head on, though, applying the serialist framework to case after case. What we get as a result is the first systematic overview of the theory, delivering more than it originally promised. This achievement makes it possible to dig into the architecture of IMHS, comparing it with other approaches in a way that a theory this novel would not usually facilitate. I devote the first half of this review to outlining IMHS itself (§2), before considering it on its own terms (§3) and highlighting points of contrast with other approaches (§4).
2 Structure of the book
Chapter 1 (‘Background’) presents a general overview of harmonic serialism (HS) and its application to phonology, syntax and morphology. It first lays out the basics of HS by showing how standard parallel OT (Prince & Smolensky Reference Prince and Smolensky1993) can be translated into HS, going through case studies in phonology (onset avoidance in Classical Arabic) and syntax (do-support in English). We then see cases in these two domains where the serialist architecture is argued to be superior to parallel OT: stress and syncope in Macushi Carib, and expletives in Spec,CP in German.
The main structure-building operation in IMHS is the Merge Condition (MC), a constraint which can be thought of as encoding selection or Merge. An affix with a number feature, for example, satisfies MC(Num) when suffixed to the stem. The serialist derivation consists of taking a root and adding one affix at a time, optimising as we go. Words then enter the syntax fully inflected. The introductory chapter lays out the basics of this theory very clearly overall, making the case for HS over OT in a number of cases.
Chapter 2 (‘From optimality theory to harmonic serialism’) tackles two classic phenomena in inflection, namely ‘disjunctive blocking’ (the Subset Principle) and affix ordering. The Subset Principle amounts to picking the most specific exponent for a given morphosyntactic input. Taking determiner inflection in German as a worked example, IMHS revisits an existing analysis in parallel OT, showing how to transfer it to HS: MC forces an affix to be chosen, and Max constraints ensure that it is the one with the right feature combination.
Affix ordering is next. The first dataset comes from the Wardaman verbal template [person–number–verb]. Modifying an existing OT analysis, IMHS relies on the ranking MC(Num) ⪢ MC(Pers) ⪢ L⇐Pers ⪢ Coherence ⪢ Number⇒R. What happens here is a case of what IMHS calls ‘movement in morphology’: number is merged first, and placed on the right: [verb–number]. Person is merged in the next step, and placed on the left, [person–verb–number]. But Coherence wants the two to be adjacent, so number ‘moves’ linearly leftwards in the last step while still keeping to the right, giving the desired order.
IMHS also adopts the Strict Cycle Condition (SCC; Chomsky Reference Chomsky, Anderson and Kiparsky1973) as part of Gen, ensuring in the general case that the system picks an affix that is closer to the stem before another affix that attaches outside. However, the derivation just sketched violates the SCC, in that number ‘tucks in’ under person, manipulating an existing domain. In order to ensure that movement is minimal, IMHS adopts local conjunction of constraints: the ranking L⇐Pers2 ⪢ Coherence ⪢ L⇐Pers allows the grammar to violate Coherence if two violations of L⇐Pers would otherwise arise. Under this revised analysis, number moves all the way to the left in the third step, [number–person–verb], with no violation of the SCC, and then person is moved leftwards. A similar example from verbs in Island Kiwai rounds off affix ordering.
The last part of the chapter surveys a number of cases in which morphological movement can be identified in derivational and inflectional morphology. The case studies consist of the ordering of causative and applicative in Lomongo, and despirantisation in Barwar Aramaic. Overall, the chapter does a clear job of accounting for a number of phenomena while motivating the theoretical constructs it assumes.
Chapter 3 (‘Extended exponence’) is dedicated to multiple exponence and to the theoretical innovation of Minimise Satisfaction (MinSat). Take the German dative Kindern ‘child.pl.dat’, for instance, segmentable as Kind-er[pl]-n[pl,dat]. In parallel OT, the output that shows multiple exponence is harmonically bounded by the output candidate that does not: why express the input as Kindern when you can capture all relevant features already with *Kind-n[pl,dat]? The same problem would arise with standard HS, which is why IMHS introduces MinSat: this constraint ensures that each step in the derivation leads to as few new constraint satisfactions as possible, while still allowing the rest of Eval to choose the optimal candidate as usual. In the first step, -er is merged before -n, because -n would satisfy too many constraints, violating MinSat. The second step adds -n, leading to convergence, because -n is also in the input, as part of a morphological array which must be exhausted.
One intriguing claim made in this chapter is that the workings of MinSat can be found in other modules of the grammar as well. In phonology, it is presented as a solution to issues of opacity in Bedouin Arabic. In syntax, it is motivated by Merge over Move, the principle that merging an appropriate element from the numeration (for example, in the specifier of a syntactic head) is preferred to moving an existing element to that position (in this case to the specifier). The exposition is once again thorough, relying on datasets in a number of unrelated languages and introducing a significant amount of technical machinery. The data are clearly consistent with MinSat in IMHS, although they do not yet form an argument for it, as opposed to other accounts (with the exception of one comparison with Stratal OT; see §4).
With MinSat established, it is now less clear how the Subset Principle can be maintained: returning to single exponence, MinSat would derive the most general candidate, not the most specific one. Chapter 4 (‘Disjunctive blocking revisited’) addresses this challenge by suggesting that the general (wrong) exponent is indeed chosen at an early step of the derivation, but that additional steps optimise the choice and lead to the specific (right) exponent. To reach this result, IMHS requires removal constraints, on a par with merge constraints. The book first makes a preliminary case for remove in syntax, and then returns to morphology, where the idea is that general exponents are removed by the more specific exponents that are merged after them. I cannot think of other morphological theories built around this notion, which renders this chapter a particularly compelling read.
To get this idea off the ground, IMHS revisits the morphological array, postulating that all members of it (all potential exponents of a given morpheme) have a remove feature except for the most general one, since it cannot remove anything else. For German demonstratives, for example, the most general exponent is -e; all other exponents remove the one that came before them, if they are added by MC. The derivation ends up proceeding as in (1) for the dative masculine singular demonstrative ‘this’, where different exponents in the array of inflectional affixes are merged and removed one after the other. Similar analyses are given for the English present tense, with handy diagrams summarising the detailed derivations.
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(1)

In the final set of case studies, Chapter 5 (‘Suppletion’) turns to non-local stem suppletion (root allomorphy) and the collection of phenomena now known simply as *ABA. The discussion of *ABA refers to the patterns uncovered by Bobaljik (Reference Bobaljik2012) and discussed intensively since. In the canonical example from comparatives, many languages have positive–comparative–superlative adjectival forms such as strong–stronger–strongest (AAA) and bad–worse–worst (ABB), but none have good–better–*goodest (*ABA). Bobaljik's explanation was that superlative contexts have the feature specification [sprl,cmpr], which contains the comparative [cmpr], which in turn contains the positive [∅], in a hierarchical structure. IMHS recasts these features as binary, for reasons having to do with the evaluation of candidates. In addition, the features must be added according to a certain functional sequence, which ensures that, for example, cmpr is attached before sprl.
For stem suppletion, the question is whether it can be accounted for without the extra assumptions that various accounts have had to make. Its existence indicates that stems (or roots) undergo optimisation, meaning that they belong to morphological arrays of the same lexeme or root. IMHS assumes that stems cannot be enriched with features, so in order to trigger the initial selection of a root exponent from the array, that exponent needs to have some other feature; this is assumed to be the category feature. This feature must then originate elsewhere, so categorising heads are postulated (n for nouns, v for verbs; cf. Arad Reference Arad2003). The categorising head can therefore merge only with the stem and with no other element such as an affix; this result is ensured once we stipulate that inflection can only be added to a stem that is fully specified with all its features. Finally, the categoriser itself is never overt. The theory is exemplified using Russian nouns, where suppletion is locally triggered, and Tamil pronouns, where it appears to be non-local. Once again, IMHS first takes the most general root allomorph, then attaches the more specific one, and then removes the general one. Movement ensures that the affixes end up in the right positions.
Chapter 6 (‘Consequences’) outlines how the current approach can be extended to cover a number of other phenomena, without fully committing to these tentative analyses. The section on impoverishment is an outlier, in being less easy to read, not due to the content but rather the structure of this section, as it introduces a number of OT approaches one after the other, without explaining their importance in advance. We do learn that there are two kinds of approaches, the second of which can be captured straightforwardly in IMHS terms (although this is not fleshed out). Deponency is also given a promissory note, which is just as well, given that it is relatively easy to encode in OT. Paradigm gaps, in contrast, are given a novel analysis, so this is one place where IMHS's architecture gets a chance to shine. The intuition here is that two constraints conspire to create an infinite loop: each step of the optimisation satisfies one at the expense of the other, so that the derivation never converges. This is an attractive idea, which singles out IMHS among existing approaches to paradigm gaps.
In sum for this overview, the monograph is remarkably clear, using many explicit derivations. IMHS hardly takes any shortcuts in presenting the analyses, using various typesetting conventions to highlight different parts of a derivation. I do have a few minor gripes, though. On repeated occasions, IMHS notes that a certain assumption or principle will be revised later in the book. This is fine, but I would have appreciated a very brief note indicating what the revision will be. On very few occasions, forms are given without glosses. That said, the author's typesetting is impeccable and typos are vanishingly few. The DRM version of the book that I received does not have clickable links (for example to references or example numbers), and the publisher did not provide me with a hard copy, so going back and forth between datasets and different analyses was a bit tedious at times. But these minor annoyances aside, the intricate datasets and analyses are very easy to follow, allowing the reader to think beyond the proof of concept presented in the monograph.
I next present a few preliminary thoughts.
3 The theory on its own terms
The clear exposition in IMHS allows us to probe the proposed architecture a bit further. Acknowledging that the monograph is meant as proof of concept, I mention a few points that would be of interest, some of which are discussed in preliminary fashion in the book itself.
One of the main innovations of IMHS is MinSat, which ensures a very gradual satisfaction of constraints. IMHS suggests that this constraint is active in the phonology, morphology and syntax, but why would we expect the same constraint across components? The same question can be asked about the Strict Cycle Condition, the syntactic constraint adopted by IMHS for morphology. One consideration put forward in Chapter 3 is that MinSat is an undominated transderivational constraint in syntax and morphology, but not in phonology (it must be dominated in some cases in order to derive bleeding), indicating that it is part of Gen, rather than Eval. IMHS suggests that this state of affairs makes sense, since syntax and morphology build up structure compositionally, in contrast to phonology, which modifies and licenses existing structures (p. 124). This discussion is extremely interesting, although it does suggest that syntax and morphology are architecturally similar – a point that some theories adopt explicitly and which could be developed in future versions of the current one.
Another innovation is the use of ‘removal’. Here it is unclear to me whether the grammar encodes the same information twice: once by underspecifying the most general element in a morphological array and once by marking all the other items with a remove feature. Ideally, the ability to be removed should follow from the featural make-up. It makes sense that all elements have a remove feature except for the most general one, because it will have nothing to remove; but the array does not know that in advance. If the array knows which element is most general, that seems equivalent to knowing which candidates can be the most specific, which in turn is tantamount to marking them [general] and [specific], essentially encoding the Subset Principle. Perhaps relatedly, Chapter 5 requires the grammar to make reference to [+F] in a Dep[+F] constraint, but not assume Dep[―F] for binary features. The [+F] version is motivated by the analysis (p. 278), but it is unclear whether [+F] is more marked than [―F] in the theory in general.
Regarding binary features, recall that IMHS requires them for its analysis of *ABA. The account of ABCD/AACD in German supports this claim. Yet, as pointed out on page 276, suppletion in the present tense is limited to the 2nd and 3rd person singulars. Since this isn't a clean case throughout present tense, I would be wary of treating it as one; perhaps it's just ABC with some additional residue in some present tense contexts. Now, such an approach may or may not be appealing, but it is similar to a claim on the very next page. The system predicts the possibility of ABAB, which does not exist, and which IMHS cannot exclude either: ‘the prohibition against this pattern in the grammar of German, if it can be shown to be of a systematic nature, has a different source, which is not related to *ABA considerations’ (p. 277). The same could be said for the present tense ‘D’ in ABCD.
Since the theory is based in OT, its mechanics are envisioned as constraints. Nevertheless, some principles exist outside of the tableau proper, such as the structure of arrays, the SCC, the assumption that inflection only attaches to a fully specified stem and the use of extrinsically ordered functional sequences (Chapter 5). The discussion of this point in Chapter 6 notes that the SCC, as well as the constraints forcing the derivation to exhaust a morphological array before moving to the next, might better belong in Gen than in Eval (p. 315). It would be interesting to see a bird's eye view of the grammar, with its conception of Gen and Eval across the different modules.
4 The theory in comparison to others
One consequence of presenting proof of concept for a new theory is that explicit comparisons with other theories are few and far between. The monograph is almost a victim of its own success, in that the clear exposition does invite such comparisons. To conclude this review, I mention the comparisons which I think future work – in whatever framework – would need to focus on.
4.1 Affix ordering
The correct ordering of affixes in IMHS is ensured by ranking the MC constraints correctly, and adding MinSat or any constraints that are needed to enforce movement. In Chapter 2, this state of affairs is claimed to be preferable to theories such as Distributed Morphology, in which an initial order of functional heads is manipulated by movement and ad hoc rules. While I understand this argument, I don't think it goes through quite yet: the order of affixes is not arbitrary – as one might think if it were up to the free reranking of constraints – but depends on a number of factors, including the scope that affixes take with respect to each other (Rice Reference Rice2000). Work on what is known as the Mirror Principle has further argued that this scope respects the order of syntactic primitives for the most part (Baker Reference Baker1985, Muysken Reference Muysken, Everaert, Evers, Huybregts and Trommelen1988, Myler Reference Myler, Newell, Noonan, Piggott and Travis2017), something that IMHS as currently conceived cannot capture. This point is conceded once in the discussion of *ABA (p. 261): ‘Given that tense information is lower on f-seq [functional sequence] than φ (more generally, finiteness) information (also cf. the order CP-AgrP-TP-vP in the syntax), what is added at first is just [+past] or [―past]’.
One possible way to counter this objection is to claim that the Mirror Principle only describes tendencies, not absolutes, because ad hoc adjustments are needed at times. Yet this sort of reasoning is rejected by IMHS in its discussion of suppletion; inferential approaches to morphology have little to say about allomorphy, losing the ability to derive existing generalisations, even if these do have exceptions (p. 226). I agree that in both cases there are strong generalisations that require architectural explanations.
Another example brought forth in Chapter 2 is the ‘CARP’ pattern in Lomongo: the tendency of many Bantu languages to order suffixes as causative–applicative–reflexive–passive. What is impressive here is that IMHS derives the eventual surface order as well as counterbleeding effects. Nevertheless, the same objections arise, since at least in other Bantu languages the surface order of affixes correlates with semantic scope (e.g. Manova et al. Reference Manova, Hammarström, Kastner and Nie2020). Simplifying considerably, [causative–passive] would be a passive of a causative, whereas [passive–causative] would be a causative of a passive. How this result can be achieved in IMHS is unclear, if MC(Caus) ⪢ MC(Pass). Even though IMHS acknowledges that other architectural assumptions could be fruitful (p. 87), it does not take the extra step of implementing one. In addition, the counterbleeding effects are also less surprising under contemporary views in which infixes are affixes that have ‘moved’ (Kalin Reference Kalin2020).
It is also noteworthy that MCs outrank all Ident, Max and Faith constraints. Whether or not these patterns can be traced back to architectural properties is left open (pp. 316–317). That's a shame, because some theories do have answers that can be used as a foil; if morphology is structurally derived from syntax (or even semantics), this is a natural consequence. That said, the very next paragraph on page 317 reminds us that the goal of the monograph is merely to provide proof of concept.
4.2 Conceptual arguments
Any formal theory needs to balance empirical coverage with expressive power, and IMHS is no different. At times the monograph grapples with this question in insightful ways, and at times less so. Conjoined constraints are a case in point (Chapter 2), because they are required for morphological movement but might also predict unlikely typologies. Since the introduction wants to make the case against theories that rely on ad hoc operations, statements to the effect that all IMHS constraints are independently needed (p. 76) should be substantiated more fully in the future.
Another example is the discussion of discontinuous exponence. IMHS notes that the phenomenon is problematic for all theories, but that morphological movement is a ‘reasonably simple’ implementation (p. 77). That may well be the case, but we are not given a thorough enough comparison with discontinuous vocabulary items in a realisation framework, or rules of exponence and referral in an inferential one, to allow the claim to be convincing.
Similarly, the discussion of non-local root allomorphy in Chapter 5 implies that IMHS provides a more parsimonious account than those in recent analyses where the theory needed to be enriched. As we have seen, though, IMHS itself does require additional constraints to account for non-local suppletion (the categoriser, movement, arrays and also subarrays). One retort could be that having additional constraints is still part of the theory, as opposed to enriching the theory and losing restrictiveness, as in the alternatives. Such a point would need to be made more concrete; it does not strike me as an argument against Moskal & Smith (Reference Moskal and Smith2016), for example, who propose to extend the domain in which allomorphy can be triggered.
4.3 Alternative analyses
I close by noting a few alternative analyses that either suggest themselves or receive short shrift in the book. Most of these issues arise from the fact that the main comparison is made with parallel OT, except in a few cases. It is not surprising that OT fares worse than IMHS, given that OT is not a theory of morphology as such (Embick Reference Embick2010). So while IMHS is superior to parallel OT for the analysis of Spec,CP in German (Chapter 1), for example, the resulting account seems equivalent to a ‘mainstream’ generative analysis in which the expletive es either is or isn't in the numeration to begin with.
Considering next how IMHS compares with other variants of OT, the theory relies on MinSat for counterbleeding (Chapter 3). There are two brief mentions of OT-CC (McCarthy Reference McCarthy2007) in this context (pp. 110, 112), but, unfortunately, no direct comparison of the two theories. Stratal OT is also discussed, in the context of plurals in Archi (also in Chapter 3), where a convincing argument is made for IMHS. Then again, IMHS does allow for subarrays (Chapter 4), which go through TAM exponents before optimising agreement exponents, in a set-up reminiscent of strata (p. 205).
Other case studies invite comparison with very recent work; the infix-as-suffix account of Kalin (Reference Kalin2020) was mentioned above. The IMHS analysis of discontinuous exponence (Chapter 2) assumes that one part of the exponent is purely morphophonological, with no morphosyntactic features, as in the German past participle. But Pross & Roßdeutscher (Reference Pross and Roßdeutscher2019), for instance, argue that the two parts of the German circumfix make different semantic contributions.
In conclusion, a single book would be hard pressed to lay out a new theory, ruminate on its finer details and compare it with all other relevant theories. Yet IMHS has somehow come very close to all of the above. It provides a welcome contribution to the landscape of both morphological theories and OT formalisms, drawing our attention to similarities and differences between frameworks, and highlighting data from a variety of understudied languages. IMHS is provocative in the best possible way: not by virtue of heavy-handed rhetoric, but through clear argumentation.
