In Underlying Representations, Martin Krämer discusses current and past thought on underlying representations (URs) in phonology, with particular emphasis on the role that economy and underspecification play in the theory. The stated audience of the book is students in advanced undergraduate or early graduate courses; this review will focus on the role this book could play in such a setting. The book would probably be difficult to assign in the classroom, as the discussion is not detailed enough to help ensure student mastery. However, the centrality of the topics covered ensure that it should form an important part of an instructor's course preparation.

The book is organized largely along historical lines, with Chapters 2–4 covering topics from the structuralist period to the 1980s, and Chapters 5–8 considering developments from the 1990s onwards. Chapter 1 serves as an introduction to the book, outlining major topics and suggesting ways to engage with the text. Chapter 2 summarizes structuralist work on phonemic contrast and early work on distinctive feature theory. Chapter 3 discusses morpheme structure constraints, the abstraction controversy of the 1960s and 1970s, and the role that underspecification played during those decades. Chapter 4 is concerned with underspecification proposals from the 1980s. Chapter 5 discusses exemplar theory. Chapter 6 provides an overview of psycholinguistic work that attempts to probe mental representations, and concludes that mental representations are composed of underspecified features. Chapter 7 revisits distinctive feature theory, focusing on proposals made in the 1990s and later. Chapter 8 discusses whether the Optimality Theoretic (OT) concepts of Richness of the Base and Lexicon Optimisation prevent OT grammars from determining underspecified URs. Chapter 9 concludes the book.

As can be seen from the topics in each chapter, the book starts from the position that a UR is a string of segments, and focuses tightly on the featural representation of those segments, with the only major pause coming during the review of exemplar theory. This tight theoretical focus means that many topics associated with URs are covered lightly, if at all. For instance, the reader will need to look elsewhere for in-depth discussions of theories that force URs to be identical to surface forms (Albright Reference Albright2002, Burzio Reference Burzio and Boucher2002), algorithms for recovering URs (Jarosz Reference Jarosz2006, Tesar Reference Tesar2013, and Cotterell, Peng & Eisner Reference Cotterell, Peng and Eisner2015), acquisition studies (Curtin Reference Curtin2011, Reference Curtin2014), and data from diachronic change (Kiparsky Reference Kiparsky1968 inter alia, Albright Reference Albright2002, Bermúdez-Otero & Hogg Reference Bermúdez-Otero, Hogg and Eric Holt2003).

The tight theoretical focus has the benefit that the narrative arcs are very coherent across the book. The first arc is historical, as each chapter gives highlights of a couple decades of phonological thinking, spanning from the structuralist period to modern OT. This is undoubtedly a boon to readers, since the rapid pace of theoretical change often leaves students at best unaware of earlier proposals and at worst re-inventing the wheel. The second track is much more theoretically and pedagogically germane, as it attempts to determine whether URs are maximally economical lexical storage units. While this topic is quite central to the book, and well worth debating in courses, the reader might not feel fully informed upon finishing the book.

Possibly the main hindrance is that the book does not fully explore either the quantities to be minimized or the complicating factors for economical storage. In brief, the book identifies parsimonious feature theories with economical lexical storage. The idea is that URs must contain the smallest number of binary features possible. The familiar rationale behind this is that features encode phonological contrast, and that by sparsely representing contrast in a parsimonious feature theory, memory will not be wasted on information that cannot reliably distinguish words.Footnote ¹ At first glance, this is unobjectionable. The only problem is that minimality and the countervailing pressures against it in feature theory are not explored in a substantial way.

The failure to investigate minimality is most easily seen in the discussion of a feature theory with twelve binary features (Jakobson, Fant & Halle Reference Jakobson, Fant and Halle1952, Jakobson & Halle Reference Jakobson and Halle1956). The book suggests that the ostensibly small number of features makes the theory highly economical for encoding phonological contrast. However, a twelve-feature theory is far from compact, as twelve freely combinable binary features afford the possibility of 2¹² = 4096 contrastive segments, a veritable efflorescence of phonological contrast. Clearly, there is more to feature theory and the theory of URs than just the parsimonious storage of lexical items.

The obvious reason why feature theories typically assume even more than twelve features is that feature theories serve masters besides parsimony. That is, a feature theory is also expected to predict possible inventories, group segments into natural classes, allow for easy descriptions of phonological processes, and offer sufficient information to phonetics to encode or decode signals. In light of these competing demands, economical lexical storage is more of a sideshow than the main act in feature theory. Ideally the book would have explicitly situated the question of economy in this context so that students would clearly understand the nature of the question.

This is not to say that the book ignores the countervailing influences on feature theory, though they are addressed quite tersely. For instance, the drawbacks of Jakobson's twelve-feature theory are given in a single paragraph (pp. 31–32). Furthermore, when discussing the feature theory of SPE (Chomsky & Halle Reference Chomsky and Halle1968), the book states in a single sentence (p. 32) that the theory was intended to avoid Jakobson's under-representation of possible segment inventories, mis-identification of contrast relationships, and failure to correctly capture natural classes. No further information is given regarding how SPE improved these aspects of the theory. More broadly, the reader can find discussion of phonetic information in features in Chapter 7; the remaining desiderata do not receive more than passing attention anywhere.

The end result is that instructors will need to take a very active role to make sure that students solidly understand and evaluate the argument. Ideally students would walk through the full contrast between a truly maximally economical feature system and the more popular heterogeneous proposals. Further, enough information would be given so that students could not only debate the merits of the theories but could also get a start in pursuing independent research. As it stands, the book does a good job of posing the question, but does not go far enough to properly situate the discussion.

The reader should know that the book goes beyond economy and feature theory. As can be seen in the chapter-by-chapter summary above, the book ventures into exemplar theory, the results of psycholinguistic experiments and other current topics. Some of the most noteworthy proposals in the book come from such explorations. For instance, the second half of Chapter 7 features an attempt to unify the feature inventories for signed and spoken languages. To circumvent the speech-centricism of most feature theories, the proposal grounds features not in phonetics, but in syntax and semantics.

For spoken language, the effect is that familiar notions of place and manner are mapped to features used to differentiate the location, direction and telicity of events in natural language syntax. For instance, labials, coronals and velars are designated with [location[out]], [location[in[front]]] and [location[in[back]]], respectively. Stops and continuants are distinguished with [telic] and [atelic] features.Footnote ² The upshot of this is that signed languages receive a representation that describes the motions of signs, and the representations are unified with those for spoken language.

Unfortunately, beyond the fact that signs and speech are both employed by humans and so might be represented similarly, there is little reason given for why the theory should be adopted. For instance, it would be desirable to see whether the parallelism between spoken and signed language makes tangible predictions about the natural classes that appear in each modality. That is, would we expect bilabial stops and the signs bearing [location[out], event[telic]] to pattern phonologically in similar ways?Footnote ³ If it were so, such a result would be highly interesting. In the presumably more likely case where they do not pattern similarly, the book could still help students’ theoretical development. For instance, students could debate whether the cause is purely ‘phonetic’, whether signed and spoken languages should have similar phonology, or what evidence (perhaps neurological) might allow parallels to be manifested.

While the above discussion outlines lacunae that make it difficult to assign this book directly to students, the subject matter is central to theoretical phonology. This book is an important contribution to the linguistic literature, and especially to the libraries of dedicated instructors. It is unlikely that many instructors control the full range of perspectives covered even in the admittedly narrow scope of the book. What's more, reading and debating the book will certainly deepen understanding of both the core questions of the theory and how to guide students to understand them. I strongly recommend that teachers of all levels of phonology engage fully with this work.