In linguistic anthropology, linguistic pragmatics, and sociocultural linguistics, numerous attempts have been made to explain non-linguistic aspects of communication more informally, while the book under review treats these phenomena within the field of formal linguistics. Unlike other works, in which formal mathematical modelling of language and variation is used, this work, rather than targeting grammatical or psychological aspects of change, is focused on the social ones. In its pursuit to formalize linguistic inquiry into such non-linguistic issues as pragmatic goals and intentions underlying verbal choices, the processes of meaning making, gender inequality, and identity construction, the book presents a new approach to studying the relation between language, the social world, and ideology. Linking linguistic and non-linguistic behaviour of language users to the analysis of social meaning and sociolinguistic variation, the author deploys mathematical frameworks of Decision Theory and Game Theory.

The study develops two main theoretical approaches to social meaning investigation—internalist ideological semantics and externalist materialist semantics. The former is used to explain the social meaning of a sociolinguistic variant as an indexical field, while the latter is focused on strategic vision of speech behaviour and its consequences for meaning-making. As Burnett puts it, ‘this materialist approach allows us to give a unified formal externalist semantics for a wide range of socially meaningful expressions’ (77).

The volume is divided into two parts, preceded by an introduction and finalized by a conclusion. The first part dwells on the problems of sociolinguistic variation and identity construction, while the second part explains the triadic relations between language, gender, and social change. The introductory chapter gives an overview of social meaning as the main concept of this work, presenting Decision Theory and Game Theory as the main mathematical tools of the study. The author builds many of her considerations on earlier work devoted to studying the structure of indexical fields and orders of indexicality (e.g. Silverstein 2003, Eckert 2008), offering her own framework named Social Meaning Games (SMGs) in chapter 2. The next chapter shows how the SMG methodology can be used for testing the hypothesis about social meanings associated with sociolinguistic variants. The author incorporates the notion of ‘agency’ into the SGM framework and formalises her findings through numbers and calculations. The second part of the book extends the developed framework and explores how formal semantics can formalize speaker and listener ideologies, focusing mainly on gender and the use of slurs. Before summarising the key outputs of the study in chapter 6, Burnett formalizes ideologies about social gender and their relation to the social meaning of grammatical gender in the French language.

Having made formal adaptations of informal theories, this book provides a formalization of linguistic research on social meaning, identity, and sociolinguistic variation. This opens up new aspects of these theories and promises new perspectives for their further development. A framework grounded in Game Theory, enriched with formal semantics, and guided by sociolinguistic theory, has the potential to enhance our understanding of how individuals employ their linguistic abilities to shape their identities.