This new book by Peter Gärdenfors continues and elaborates on the framework introduced in the previous book, Conceptual Spaces (Gärdenfors Reference Gärdenfors2000). It now offers a systematic exploration of the role that it could play in a theory of linguistic meaning (mostly, but not exclusively, word meaning). While Conceptual Spaces tried to deliver a proof-of-concept for a number of specific ideas, like the use of similarity spaces, I would describe the successor volume rather as serving to broaden and refocus the conception itself. This means it is at least as programmatic in nature as the first. The two volumes clearly have to be seen, and maybe have to be read together since the present book often cross-refers the previous one for details on core issues. There are many new ideas, though, and in the course of 15 chapters, the author covers a broad array of topics, from fundamental questions of how meaning arises in communication to specific problems of linguistic semantics.

Chapter 1, ‘What is semantics?’, serves to situate linguistic meaning at the crossroads of perception, action and communication, arguing that there are continuous transitions between perception, concept formation, and linguistic meaning, between communicative behaviour and linguistic representations, and, hence, pragmatics and semantics. Conceptual Spaces are therefore meant to play a role both as an interface between sensorimotor activity and a discrete symbol system, and as a representation of certain aspects of the knowledge shared between the partners in a communication situation. It aspires not only to be a ‘cognitivist’ approach to semantics, but also a ‘sociocognitive’ one (as it is called later, on p. 93).

Chapter 2 summarises what ‘Conceptual spaces’ are, mostly by way of highlighting some main issues which are treated in more detail in Gärdenfors (Reference Gärdenfors2000). It briefly sketches the basic idea of a geometry of feature spaces (using the classic example of the ‘colour spindle’), introduces the distinction between (‘1-dimensional’) properties and (‘multidimensional’) concepts, and the notion of a domain, which is very central to this whole work. A conceptual domain is to be understood as ‘a set of integral [property] dimensions that are separable from all other dimensions’ (p. 22). Being separable means that having a feature in one domain is independent of the occurrence of features from other domains. For instance, the colour of an object occurs independently of its shape properties. An example of features from different dimensions of the same domain would be the hue and the brightness which are both part and parcel of the concept of a colour. Moreover, the chapter hints at some possible extensions of the geometrical tools, such as ways of encoding relational concepts in ‘product spaces’. Further topics, which occupy large parts of the chapter, are the view of categorisation as a convex partition of a conceptual space, which is also crucial for explaining concept learning, and a comparison of these leading ideas with similar sounding ideas from the linguistic literature. In particular, there is a fairly critical discussion of the notion of ‘domain’ in the sense in which it is used by Langacker, in which a number of imprecisions are pointed out, and which differs from the ‘domains’ of the present work.

Chapter 3 offers a sketch with brief qualitative descriptions of some ‘conceptual domains’ in the above sense, though without offering a rigorous procedure of how domains are established. Here, it is more or less assumed that qualitative labels are sufficiently suggestive of domain distinctions, such as ‘emotion’, ‘visuospatial structure’, ‘force and action’, ‘object categories’, ‘value’, ‘goal and intention’, ‘age and time’ (pp. 58–65). It is then shown that sorting semantic knowledge into domains allows some useful generalisations about the steps observable in the acquisition of word meaning by children.

Chapters 4 and 5 deal with the emergence of intersubjective linguistic meaning from communication. Chapter 4 describes a process of bootstrapping that leads from pointing gestures to the use of words. Pointing is argued to involve connections between the focusing of attention to an object and other cognitive domains. Most importantly, the function of a pointing act can be decided only in a context (such as acting on things in imperative pointing, communicating the reason for an emotional reaction, etc., p. 83). This means that an act of pointing concerns not just the objects being pointed at, but already targets parts of a conceptual representation, too, and so it already appears as a connection of the mental sphere with the outside and intersubjective world. Hence, a common ground must be present for pointing to work, which is then said to take the form of a ‘product of domains’, i.e. a conceptual space. In sum, pointing is a direct precursor of naming, and naming is seen as a kind of verbal pointing. Chapter 5 deals with the synchronisation of conceptual spaces in communication and the question of how two different individuals with their individual conceptual representations can converge on a description, which here would mean fixing a region in their conceptual spaces in tandem. Such a conceptual fixpoint is argued to be akin to the equilibria of game theory. It can then be shown that the existence of such fixpoints depends on the very same type of partition around a prototype that has earlier been argued to underlie the formation of prototype categories as such. I found the discussion in Chapter 4 interesting and illuminating, even though it does not seem to interact closely with the later parts of the book, but rather demonstrates the range of applications of the basic conception. Chapter 5 is maybe not as self-contained as the others and more difficult for me to judge. It is very short both on the game-theoretical foundations of semantics and on the details of the conceptual representations that are to be employed.

Chapter 6 starts the second part of the book, which is devoted to semantic applications. From here onwards, the text proceeds by aligning the discussion of the conceptualisation of objects and events with a discussion of typical semantic phenomena associated with the different word classes. Chapter 6 reviews some relevant properties of objects. For physical objects, their shapes and part–whole structures are especially important, and difficult to model, but the author is able to point to a body of literature on meronomic analysis that can be expected to help solving the representational problem for the conceptual spaces approach. The chapter also presents a very quick overview of various other issues relating to object concepts such as levels of abstraction, the distinction between mass and count, the nature of proper names, etc., on the average spending less than one page on each. The upshot for the remainder of the book is the richness of the domain structure that can be found, which also requires that phenomena like the relative prominence and the correlations among domains should be captured. This leads to the picture of ‘multidimensionality’ as the most remarkable point about object concepts.

Chapter 7 sketches the issue of ‘properties’ (in the sense of Chapter 2) as the basis of the semantics of adjectives. What I would emphasise here, although it remains somewhat in the background of this chapter, is that the classical finding of scales underlying the semantics of certain adjectives, the gradable as opposed to non-gradable ones, seems to form the prime example of the ‘geometric’ conception pursued here. This is to say, scales as they are already used in the semantic literature are an example of the decomposition of a property into property values (with the comparison classes of degree semantics as their extensional counterparts), and their representation in terms of a spatial arrangement, i.e. the linear order. I think Gärdenfors’ whole endeavour could be seen as an attempt at generalising this perspective to other types of denotations. What is in the foreground of this chapter is a variety of domains that different adjective classes refer to, along with the hypothesis that adjectives always have their meaning in one single domain. The author admits of not having presented ‘any sharp criteria for what can count as a domain’ (p. 137), and the issue, it seems, is deliberately kept open for further exploration. For example, a putative counterexample to the single-domain-thesis, the adjective healthy, is addressed by way of the speculation that ‘the product space of all the dimensions relevant for “healthy” forms an illness–health domain’ (p. 138).

Chapters 8, on ‘Actions’, and 9, on ‘Events’, provide the groundwork for a treatment of verb meaning. The central idea of the chapter on actions is that the perception of movements is used by the brain to calculate the forces that would have effected such movement (pp. 148–152). The representation of action categories will then be couched in terms of different force constellations. Additionally, it seems possible that more abstract forms of causality can also be conceptualised in terms of forces. The general representation format for actions that suggests itself, then, are vectors, which ultimately will allow one to set up similarity spaces. The chapter reports results from the psychological literature on the classification of movements (gaits), using multidimensional scaling, and notes that gradients appearing in such representations might find qualitative interpretations in terms of force distinctions. Building on this, Chapter 9 proposes a ‘two-vector-model’ of events, distinguishing a force domain and a change domain. Agents and patients as the most prototypical participant roles of events are assigned to the force and the change domain, respectively. More precisely, a conceptual representation called ‘patient space’ appears, whose points are interpreted as states of the patient, and in which vectors are defined that encode a change in properties of the patient via their origin and endpoint (p. 170). Further event components and thematic roles may appear in enriched versions of this basic system (an important addition being intentional representations), but it is stipulated that ‘an event must contain at least . . . a result vector representing a change in properties of the object and a force vector that causes the change’ (p. 162).

This model feeds the treatment of verb meaning in Chapter 10, which I will comment in some more detail since I consider a number of points to be potentially controversial. The chapter revolves around the idea that a verb – in its lexical semantics, or at least in each particular use – has to be unambiguously classified in that it denotes either force properties or result properties. This thesis thus takes up the much-debated complementarity hypothesis of Levin & Rappaport (Reference Levin, Hovav, Arsenijević, Gehrke and Marín2013 and elsewhere), and takes the CAUSE–BECOME decomposition used by those authors to reflect basically the same distinction as that between the force and result domains (p. 164). The author formulates his version of the complementarity hypothesis as the so-called single domain thesis for verbs: ‘The meaning of a verb root is a convex region of vectors that depends only on a single domain’ (p. 184). The way I understand it is that an event representation may eventually be complex, but a verb's meaning would leave information about all domains unspecified except for one. What we would be dealing with then is the difference between event conceptualisation and linguistic categories. Very plausibly, the difference should be that semantic categories are abstractions from conceptual knowledge. Furthermore, on page 189, the author explicitly says that lexical variants of a verb may exist that switch the specification from one domain to another, thus mirroring Levin & Rappaport's claim that apparent counterexamples like climb (if it were to denote a manner of movement plus a change of position in upward direction) can be explained away because they actually show two polysemic variants, one being a manner use and the other a change of position use. Consequently, a fully-fledged event representation would have to provide both aspects, and it is a matter of the linguistic surface that only one of them can be active. If this is correct, it is confusing to encounter the claim that ‘the single-domain thesis for verbs is analogous to the thesis that adjectives denote single domains’ (p. 184). It makes good sense to have adjective meanings as single-domain concepts and both noun and verb meanings as multidimensional concepts, because the obvious account of modification (briefly sketched in Chapter 13) would be that modifiers refer to single domains in order to restrict the values from their respective domain in the more complex structure of the modified head. Hence, noun and verb meaning under modification would betray multidimensionality if they support modification by adjectives/adverbs from different domains, and indeed this seems to be the case. But then, the one-dimensionality of adjectives is conceptual in nature while the one-dimensionality of verb meanings is only in the semantic form (and, moreover, modification would have to look beyond the impoverished semantic form for verbal one-dimensionality to be maintained). Furthermore, I have difficulties with applying the force/manner distinction to examples. Gärdenfors classifies the causative use of sink as a manner verb (p. 189), simply because he sets up an equation ‘force/causation = manner’ (p. 188). On Levin & Rappaport's account, however, causation is present here only in terms of an event structure skeleton, and causative sink is still a result verb because only the result part carries a qualitative specifiation for conceptual content. The mirror-image of this problem would be raised by unaccusative manner of motion verbs like roll (it is counterintuitive to say that this cannot be a manner verb, as done on page 191). Given that this whole discussion touches a controversial topic, it is also of interest why such a complementarity should hold, to begin with. Here, I also see a weak point in the argumentation. The author proposes that doubly specified verbs would simply be too difficult to learn: ‘A verb involving mapping between domains may be hard to learn . . . No verb exists that simultaneously expresses change in location and change of taste . . . In particular, the coupling of force and change vectors is complicated since it concerns the way actions relate to their effects . . . the movement of a physical object . . . is well understood; but the relationship between the two [i.e. two objects – WG] is unstable, being subject to unknown counterforces’ (p. 185). I am worried that we might have a flat contradiction with the idea of Chapter 8, according to which movement and force have an especially close relationship in that the conceptualisation of force constellations has to start out from the perception of movement. The problem of unknown counterforces in examples with pull notwithstanding, there are also many verb meanings that require an homomorphism between force exertion and movement (e.g. cut, which denotes the separation of an object happening along the trajectory of a moving instrument). To my mind, force and movement, of all pairs of domains, should be expected to be the most closely interdependent ones. After all, this should be the reason behind the stipulation in Chapter 9 that every event needs exactly those two types of vectors in its description. This makes them almost look like a single domain. And I fail to see why verb meanings with force + result should pose a learning problem, especially if complementarity is a property of lexical forms, but not concepts.

To complete the treatment of single word classes, there is next a very substantial chapter on prepositions. This time, we also find a fairly detailed account of the spatial modellig, which is done in terms of polar coordinates (which makes it compatible with the literature on vector models of prepositional meaning). Based on polar coordinates, a betweenness relation can be formulated, which in turn allows one to formulate a convexity condition on the conceptual representation, as it was also postulated for other word classes. Next, the domain question reappears in form of the thesis that prepositions, too, have their meaning in a single conceptual domain, and that this can be the visuospatial or the force-dynamic domain. This is to say, the meanings of prepositions like in or on are taken to reside (entirely) in the force-dynamic domain (while in the literature often a combination of conditions from both domains has been invoked). In the same vein, the author also develops the thesis that over has a single unified meaning, and that it also is of a force-dynamic nature. These single-domain analyses of in and over are probably the only parts of the chapter that are bound to be controversial, but for space reasons I will refrain from discussing this here.

What follows are three chapters that can be characterised as summary and outlook. Chapter 12, after offering some brief remarks on minor word classes that do not have a chapter of their own, summarises the basic results on word classes in terms of a generalised single-domain thesis: ‘Words in all content word classes, except for nouns, refer to a single domain’ (p. 239). In this way, the domain issue, and the single domain thesis are identified as a central topic of the book. Chapter 13 adds a perspective on compositionality in the conceptual spaces approach. It confines itself to issues in which composition involves a modulation of the representation in terms of the regions in property spaces. Both modification of nouns and verbs, and verb–object complementation are shown to have such effects on the property spaces. Of course, these are the problems that the conceptual spaces approach is especially well-equipped to deal with (however, there is no alternative theory of scope, for example, or of compositionality in general). Chapter 14 gives a brief outlook on possible connections between the conceptual spaces approach and robotics, and Chapter 15 is a concise summary of the main claims advanced in the book.

In sum, the book first and foremost contains a programme for uniting a number of semantic problems, and I should even say, an impressive array of topics, under a single perspective. I think that focusing on the domain structure of meaning indeed opens up an interesting perspective for theorising in lexical semantics. Also, having one-domain constraints seems generally reasonable in that this eventually says that a word meaning is built on a single, coherent classification criterion, and I agree that this could be preferable in view of learnability considerations. Still, after reading the book, I have not stopped wondering what is really going on in verb meanings, and why the constraint should not have to hold for noun meanings. It remains to be seen how far the single-domain thesis can be taken, and the book should inspire some amount of research in this direction. It has to be pointed out that an answer still depends on an answer to the question of precisely how domains are going to be delimited, which has been left open to some extent here.

In doing what it does, the book is, admittedly, more true to its subtitle than to its main title, since it contains comparatively little detail on geometrical representations. Domain distinctions as such need not be called a geometry. My impression is that the idea of ‘conceptual spaces’ is being used by Gärdenfors as a general workspace for developing tools and theories – a meta-framework so to speak, which allows work on single issues with a unified background (that even reaches out to robotics, which is impressive). Also, the book makes it very clear from the beginning what kind of perspective it is going to take: In the preface, the author metaphorically describes his viewpoint as that of a giraffe, as opposed to that of the (metaphorical) dung beetle that is ‘often found in linguistics departments’ (p. xi). Having thereby become a denizen of that latter taxon, the present reviewer feels that many of his critical comments may have been all too foreseeable. I found the metaphorical characterisation a bit risky, perhaps, but mostly still very funny, and I don't disagree.