According to a Swedish proverb, a beloved child has many names. The central topic of this volume is a phenomenon which is referred to in the literature by a variety of terms: ‘ineffability’, ‘absolute ungrammaticality’, ‘paradigm gaps’ (or ‘gaps’ for short), ‘paradigm lacunae’, ‘defectiveness’, ‘defective paradigms’ and so forth. In essence, ineffability is the situation when the grammar fails (in the words of Hetzron Reference Hetzron1975) to provide an acceptable output. Consequently the relevant slot in the paradigm of the word in question is left unfilled, and speakers must resort to alternative means (circumlocutions or other lexical items) in order to convey the intended meaning or speech act.Footnote ¹ Rather than being arbitrary curiosities (cf. the [–Lexical Insertion] diacritic of Halle Reference Halle1973), effects of this kind are often strongly correlated with phonological factors. These may be phonotactic requirements; for instance, Tagalog /-um-/ (actor focus) cannot be infixed after a labial sonorant (/saja/+/-um-/→[s-um-aja] ‘become happy’, but not /mahal/+/-um-/→*[m-um-ahal] ‘become expensive’), due to an OCP restriction of some kind (Orgun & Sprouse Reference Orgun and Sprouse1999, McCarthy Reference McCarthy2003, Klein Reference Klein2005). Alternatively, the relevant factor may have to do with morphophonological alternation patterns within the paradigm: for example, the main class of defective verbs in Spanish are all -ir verbs with /e/ or /o/ as the stem vowel and display gaps in precisely those forms where diphthongisation to [ie ue] might be expected (see Albright Reference Albright2003 and the volume under review).

On the face of it, absolute ungrammaticality poses a particularly vexing problem for Optimality Theory (OT; Prince & Smolensky Reference Prince and Smolensky1993) and related models. For a given input, an OT grammar will always succeed in identifying the best – or least egregious – among all candidate outputs, whereas ineffability provides a situation where it appears that even the ‘best’ is not ‘good enough’. At the same time, however, the constraint-based character of OT makes it ideally suited for capturing the notion that ineffability results from the avoidance of output structures that are disfavoured or illegal in the language (Hetzron Reference Hetzron1975, Iverson Reference Iverson1981). This intriguing paradox has given rise to a burgeoning literature on gaps and ineffability in recent years, and the collection of studies reviewed here reflects this development. The volume consists of eight papers; following an introductory overview by the editors, these are organised into three parts (‘Architecture’, ‘Paradigms’ and ‘Ineffability in syntax’).

Part I contains three papers. In the first of these (‘Less than zero: correspondence and the null output’), Matthew Wolf & John J. McCarthy follow Prince & Smolensky (Reference Prince and Smolensky1993) in considering ineffability as resulting from a null output (or ‘null parse’) emerging as the optimal candidate. However, they recast this analysis within a novel, string-based formulation of Correspondence Theory. This allows for a more rigorous definition of the null output ⊙ and its formal properties, including how ⊙ is formally distinct from a massive-deletion ‘null’ representation Φ. Prince & Smolensky's notion that the constraint MParse regulates morphological parsing (see also the discussion of van Oostendorp's chapter below) is rejected. Instead, MParse is redefined as a demand that the correspondence relation be a ‘total bijective function’ from <i> to <o> (where <i> and <o> are concatenative decompositions of the input string i and output string o respectively).Footnote ² Since the null output violates only MParse, it is the optimal candidate whenever all non-null (and MParse-compliant) competitors violate constraints that outrank MParse. Some broader implications of the shift to string correspondence are considered; for example, transderivational anti-faithfulness (Alderete Reference Alderete2001) is shown to be incompatible with it.

Marc van Oostendorp (‘Dutch diminutives and the question mark’) offers another take on the MParse analysis, couched within his own revised version of Containment Theory (van Oostendorp Reference Oostendorp, Blaho, Bye and Krämer2007). He applies this analysis to a complex set of facts from Dutch diminutive formation (van de Weijer Reference Weijer, Broekhuis and Fikkert2002). In van Oostendorp's reformulation, MParse(M) constraints, which are relativised to individual morphemes, demand that a morpheme of type M be parsed into a morphological word. When MParse(M)-compliant candidates are ruled out by higher-ranked constraints, the optimal output is not a ‘null output’ in the usual sense, but a representation in which the morpheme M is present covertly, as it were, but is parsed neither into the morphological structure of the word nor (therefore) into its phonological structure. In terms of surface realisation, then, the output is a form which would be phonologically and morphologically indistinguishable from a word that lacks morpheme M altogether. For example, given a ranking {Faith, *C_iəC_i}≫MParse(Dim), the input /lentə+tjə/ ‘spring-dim’ yields an output form [lentə] that ‘is not a diminutive in any relevant sense’ (p. 87), not even in terms of its morphology or semantics. Another significant aspect of the Dutch facts is their variability: many of the diminutives are not categorically ungrammatical but merely ‘questionable’. An account is outlined in which the variation results from underspecified ranking relations (Anttila Reference Anttila, Chambers, Trudgill and Schilling-Estes2002) and sporadic lexicalisation.

Orhan Orgun & Ronald Sprouse (‘Hard constraints in Optimality Theory’) argue for their Control model (Orgun & Sprouse Reference Orgun and Sprouse1999), in which the optimal output from H-Eval is subject to a separate component (Control, reminiscent of the filter of Halle Reference Halle1973) that contains one or more inviolable constraints. If the optimal output violates any constraint in this ‘filter’, ineffability results. Orgun & Sprouse answer some of Raffelsiefen's (Reference Raffelsiefen2004) criticisms of the Control model (especially with regard to prosodic minimality effects in Turkish; Orgun & Sprouse Reference Orgun and Sprouse1999), and they offer an analysis of the maximum size condition on English re-verb nominalisations by stress shift (ˈreˌmake, ˈreˌcount, but *ˈrediˌstribute, *ˈreˌstudy; Raffelsiefen Reference Raffelsiefen and Aronoff1992). This analysis relies on a construction-specific ranking of the violable constraints in H-Eval, combined with a similarly construction-specific (and fairly ad hoc) inviolable constraint in Control. In addition to installing initial primary stress, the ranking in H-Eval forces the original primary stress of the verb to be preserved (as a secondary stress), but shifted rightwards whenever possible due to high-ranking *Clash. Thus ˌreˈstudy→(*)ˈrestuˌdy, ˌreˈaggreˌgate→(*)ˈreaggreˌgate, but ˌreˈcount→ˈreˌcount, since in a disyllabic form the stress clash cannot be avoided. In Control, these nominalised forms are subject to a constraint SSN-Stress, which requires that the output have ‘initial primary stress and peninitial secondary stress’ (p. 106). Due to the stress shifts induced in H-Eval, the only cases for which this remains true are disyllabic forms like ˈreˌcount or ˈreˌmake; consequently, all others are rendered ineffable.

Part II likewise contains three papers, all of which address individual case studies in somewhat greater depth. Adam Albright (‘Lexical and morphological conditioning of paradigm gaps’) focuses on those cases of gaps that are to some extent lexically arbitrary, affecting some words but not others (as with the problematic past participles of dive, strive, stride; cf. drive, ride, hide). Revisiting his experimental findings on Spanish (Albright Reference Albright2003), Albright argues for an analysis of such gaps as resulting from speakers' relative uncertainty about the choice of output, where this (gradient) uncertainty is in turn a consequence of lexical statistics, such as the relative (un)reliability of the relevant form-to-form mappings. Albright briefly sketches an OT implementation, and discusses how the stochastic account can be applied to the well-known case of Russian 1st singular non-past forms (Halle Reference Halle1973), to which I will return below.

Outi Bat-El (‘A gap in the feminine paradigm in Hebrew: a consequence of identity avoidance in the suffix domain’) takes on cases where OCP-violating sequences such as […t…t…] or […j…j…] are actively avoided within the suffix string in Modern Hebrew. Depending on a variety of factors, this restriction either triggers repair or results in a paradigm gap. Bat-El provides a ‘null output’ analysis, in which OCP≫MParse. She draws a distinction between ‘absolute’ gaps (such as these) and ones which are merely ‘unstable’ in that speakers are able to produce the form in question, but hesitate to do so, judging the form as ‘strange’ (cf. Albright Reference Albright2003 on gradient gaps; see above). Bat-El suggests that ‘upon request’, speakers are able to (temporarily) reverse the ranking of MParse and the relevant dominating constraint, but that they will only do so if the resulting output receives support from similar forms occurring elsewhere in the paradigm (essentially a lexical conservatism effect; cf. Hansson Reference Hansson1999, Pertsova Reference Pertsova2005). When no such cross-paradigm support is available, the gap is absolute rather than unstable.

Péter Rebrus & Miklós Törkenczy (‘Covert and overt defectiveness in paradigms’) lay out a typology of those paradigm gaps that are correlated with phonological factors in one sense or another. Rebrus & Törkenczy pay particular attention to the relationship between the gaps in question and patterns of allomorph distribution within the paradigm. They then turn their attention to the well-known case of Hungarian -ik verbs (Hetzron Reference Hetzron1975). This case is particularly complex, in that it is phonotactically motivated (avoidance of CCC clusters with an offending sonority profile) but simultaneously ‘arbitrary’ (in Albright's sense) in that some reference to morphological and/or lexical information seems also to be required. Rebrus & Törkenczy argue for an analysis in which the unavailability of the expected phonotactic repair, epenthesis (in their words, ‘reclassification’ of the verb stem into the ‘epenthetic’ class), is due to the fact that this would produce an unattested pattern of allomorph distribution across the paradigm.

Finally, Part III contains two papers that address the issue of ineffability in syntax. Géraldine Legendre (‘The neutralization approach to ineffability in syntax’) argues against a null-parse approach (Ackema & Neeleman Reference Ackema, Neeleman, Dekkers, Leeuw and de Weijer2000), favouring instead a neutralisation analysis which is reminiscent of van Oostendorp's MParse(M) account described above. By relaxing the requirement that all competing output candidates be LF-equivalent, Legendre analyses phenomena like the ungrammaticality of multiple wh-questions in many languages as a matter of forced unfaithfulness to the target (i.e. input) interpretation. A multiple wh-question in Italian or Irish (‘Who ate what?’) would thus receive an interpretation that is indistinguishable from that of a single wh-question (‘Who ate?’), due to the forced underparsing of one of the input [Q] features.

Ralf Vogel (‘Wh-islands: a view from Correspondence Theory’) adopts roughly the same assumptions as Legendre. However, the wh-island phenomena he deals with are strictly speaking not examples of absolute ungrammaticality – situations where no grammatical output seems to exist (for a given input) – since a ‘repair’ appears always to be available (e.g. insertion of a resumptive pronoun). Rather, these cases illustrate ungrammaticality in the ordinary, and unproblematic, sense of ‘ill-formedness’. As such, they are more akin to the language-specific ungrammaticality of complex syllable onsets, say, or the (allegedly) universal ungrammaticality of word-final voicing neutralisation to [+voice].

The volume would have benefited from a more rigorous process of reviewing, editing and proofreading. The quality and style is uneven: while some of the papers are quite polished, showing meticulous attention to detail and argumentation, others have a rather informal feel and provide sketchy outlines rather than elaborate analyses. Reading through the collection, one encounters an unfortunate number of typographic errors and misspellings, of which I will mention only a few. In a crucial tableau for Dutch on page 87, a copy-and-paste error has created the mutant output candidate [lentətjəlentjə] for intended [lentətjə] (from /lentə+tjə/ ‘spring-dim’). On page 67, we learn that the null-parse analysis is a ‘typo of solution’ to the problem of ineffability, while on pages 101–102, the constraint Foot.orm is consistently misabbreviated Ft.rom, both in tableaux and in the text. In a footnote on page 100, a citation of Halle (Reference Halle1973) is missing the year, with only white space instead; the converse happens in a footnote on page 237, where we find this cryptic citation: ‘See also (1997)’. Spelling errors are not uncommon, especially among the contributions by non-native English speakers (‘analitic’, ‘emptyness’, ‘familynames’, and the like). Such regrettable sloppiness detracts from the overall quality of an otherwise excellent collection of papers. The series in which this volume appeared is quite recent, and the publisher is likewise relatively new; these editorial shortcomings may be due in part to such factors. It is to be hoped that Equinox can find ways to ensure somewhat better quality in future volumes.

Editorial issues aside, this volume is a welcome contribution to the growing literature on ineffability effects, and many of the individual chapters will provide important points of reference for future studies in this area. With the exception of Rebrus & Törkenczy (who do not formalise their analysis in OT terms), the studies in the volume fall into three categories with respect to their basic assumptions about what a ‘gap’ is, formally speaking. Ineffability results (a) when the optimal output candidate is an unpronounceable ‘null output’ (Wolf & McCarthy, Albright, Bat-El); (b) when it is an overt form that is unusable due to neutralisation (morphosyntactic and semantic, not just phonological) with a different form (van Oostendorp, Legendre, Vogel); or (c) when it is blocked in a separate ‘filter’ component (Orgun & Sprouse).Footnote ³ Cross-cutting this division is the range of factors that the authors consider as possible triggers of gaps. These can be ordinary phonological markedness restrictions (Son.eq, Foot.orm, OCP), constraints on morphosyntactic well-formedness (van Oostendorp's Lex.im ‘There is no diminutive of function words’; Bat-El's *Mismatch, by which the subcategorisation of a suffix must match the features of the rightmost morpheme in the base) or more parochial and construction-specific constraints (Orgun & Sprouse's SSN-Stress, mentioned above). Alternatively, the underlying cause of the gap may be attributed to paradigmatic factors or lexical statistics, such that the speaker refrains from producing a form which does not receive (adequate) support from elsewhere in the paradigm or the lexicon as a whole (Albright, Bat-El, Rebrus & Törkenczy).

For some of the cases that figure in this volume, a clearer picture of the full range of empirical facts would be helpful, in particular those that are characterised by a great deal of variability (between lexical items and/or between speakers). This is true, for example, of the Dutch diminutives discussed by van Oostendorp as well as for Bat-El's ‘unstable gap’ vs. ‘absolute gap’ distinction. Given the title of the book, it is hardly surprising that the studies it contains are largely focused on questions of formal modelling within OT, rather than on probing the properties of individual cases with quantitative or experimental methods. Albright's paper is a notable exception to this, and is representative of a growing body of work that draws upon statistical and psycholinguistic experiments to investigate the empirical ‘underbelly’ of paradigm gaps. The results can sometimes be surprising. For example, recent findings suggest that gaps in Russian verb paradigms are in fact quite productive (new verbs like frendit' ‘to friend’, apgrejdit' ‘to upgrade’, etc., are typically defective), and appear to reflect competition between alternative output choices (Sims Reference Sims2006, Kulinich Reference Kulinich2010). This is very much in line with Albright's predictions, but flies in the face of the standard claim that the relevant stem alternations are completely predictable and exceptionless in Modern Russian, and that the gaps in existing verbs are lexicalised (Halle Reference Halle1973, Baerman Reference Baerman2008). For the Hungarian case discussed by Rebrus & Törkenczy, it appears that competition is likewise involved (Szakay & Hansson Reference Szakay and Hansson2010), which calls into question the distinction between ‘phonotactically motivated’ and ‘arbitrary’ gaps (cf. Albright's scepticism in that regard; pp. 158–160). In sum, it seems clear that if our goal is to gain a better understanding of gaps and ineffability, a multifaceted approach, combining a variety of methodologies and data sources with formal-theoretical modelling, has the best chances of success.