The chapter ‘Concepts in Greek Mathematics’ by Reviel Netz problematises a set of assumptions commonly encountered in the literature on Greek mathematics, which typically derive from a supposedly objective, a-historical conception of mathematical theory and practice. In sharp opposition to that tradition, Netz raises the possibility that the purpose of engaging with mathematical concepts may have been different in antiquity than what it has been taken to be. He asks central questions afresh, for instance: why do mathematical texts begin with definitions, and what is the purpose of mathematical definitions and of axioms. In connection to these issues, he highlights new aspects of the relationship between Greek mathematics and Greek philosophy, between engaging with mathematical concepts and philosophical thinking. He also advances the thesis that the relations between mathematics and philosophy changed through the various eras of antiquity, as did mathematical concepts and the role of mathematical definitions. We should seriously entertain the idea that even mathematical concepts need to be viewed within a given historical and cultural context.

This chapter outlines established disciplines that have addressed the study of clichés, from lexicography to formulaic language and problematises the issue of defining clichés based on form. The chapter positions linguistic clichés within discourse studies and conceptualises them as socio-semiotic resources and discourse strategies that fulfil a range of specific functions across different discourse types and sites. The chapter also provides a working definition of cliches and outlines what constitutes cliches for the purposes of the book.

Drawing on second language acquisition theory, this chapter establishes why language input is so fundamental to language learning. It explores ‘teacher talk’ as one major way for learners to get maximum exposure to input and discusses the challenge for teachers and learners of teachers using the target language in the classroom. Examples from classrooms and teachers’ comments/perspectives are included. The chapter explores, with examples, how teachers may offer ‘environmental support’ to help learners deal with challenging language input. The chapter discusses the type of input that learners need for learning and the type of input that is likely to engage adolescent language learners. It suggests ways that teachers can address the difficulty of maximising access to the target language, looking at opening up opportunities beyond the language classroom. The use of the learners’ first or other languages, in the language classroom, is discussed.

This chapter reviews the quantitative corpus linguistic literature on formulaic language development in writing. It first provides a theoretical and methodological context by discussing the construct of formulaic language and the various ways in which it has been operationalised in studies of writing development. It then critically reviews the literature to establish what substantive conclusions can be drawn and what might constitute productive foci for future research. The review highlights a lack of interest in first-language studies. However, second-language studies have seen a rapid expansion of interest over the last decades, which has yielded a number of consistent patterns. In particular, writing quality is positively associated with the percentage of n-grams attested in a reference corpus, the mean strength of association between collocates (again as attested in a reference corpus), and the prevalence of sequences which analysts subjectively identify as formulaic. It is also negatively associated with use of formulas copied from source materials. Key areas in which further methodological development is needed include: understanding how analysts identify sequences as formulaic; increasing the size and rigour of studies looking at discourse functions of lexical bundles; understanding the impact of reference corpus on findings; developing corpora representative of learner input.

Chapter 1 provides background about key vocabulary concepts that will be important throughout the book. This includes issues concerning meaning, collocation, morphological knowledge, and frequency. It discusses different categories of vocabulary, and then explores how much vocabulary is necessary to operate in English.

Chapter 4 discusses corpus linguistics and how electronic corpora have informed vocabulary studies. The main insights have been in the areas of frequency and phraseology. The chapter includes an extended discussion of formulaic language, which has been shown to be a major component of vocabulary knowledge.

Chapter 5 looks at individual cases of cultural motivation of change in formulaic language. First, the functional paradigm of motivation and the methodology used to identify change are discussed. Nine detailed case studies of cultural motivation of linguistic change in action follow. These examples make a strong case for a very close link between linguistic change and changes in the culture of the speech community. Two issues raised by some of the case studies are also addressed. The first concerns the difference between merely topical fluctuations reflected in language and actual linguistic change – conclusions here show that while there is no clear dividing line, the shape of frequency developments and the type of linguistic item involved can make an intersubjective determination possible. The second concerns the issue of whether the development of MWEs explained by the behaviour of key lexical items they contain. It is shown that this is not generally the case. The case studies show that striking insights into prevailing attitudes and circumstances among the speech community are possible through the study of linguistic data.

The final chapter draws together results of the analyses of the different chapters and synthesises findings: the analyses have shown that social and cultural change plays a very important role in language change. Investigations of individual cases supply clear evidence for a close connection between cultural change and MWE-change. Significantly, analyses have demonstrated that cultural motivation of linguistic change extends to types of MWE-change traditionally analysed as semantic, syntactic and morphological change, which suggests that language as a system, rather than merely language use, is more closely tied to the specifics of the culture of a speech community than has hitherto been acknowledged. The chapter closes with an outlook.

In Chapter 2, it is argued that a diachronic perspective on the connection between culture and formulaic language is a useful one. The first half of the chapter looks at how linguistic change, and change in formulaic language in particular, has been understood (and misunderstood) in previous research. The thorny issue of what motivates linguistic change, which is key to the analyses presented in later chapters, is also addressed. In the second half of the chapter, the reader is introduced to ways in which culture and society have been understood and the comprehensive understanding of these concepts, as employed in the present work, is developed and presented. Previous research on the relation between language and culture is then drawn upon and worked into the conceptualisation of this relation proposed in the book.

Chapter 3 presents a new procedure for extracting formulaic language from corpus materials and further methodological aspects. In the first section, the speech community whose language is investigated is introduced and it is shown that the community of users of the Swiss variety of standard written German is a speech community sharing not only this common language variety but sharing in a culture that, at one level, is distinguished both from other linguistic communities within the country and from German-speaking communities elsewhere. The specifics of the linguistic data that form the basis of subsequent investigations are also presented. The second section concerns the identification of instances of formulaic language in corpus data. A robust operationalisation of the MWE-concept is presented, and the final section of the chapter documents a new procedure for extracting operationalisation-compliant sequences from corpus materials. It is shown that this procedure delivers accurate as well as comprehensive results and is therefore well suited for the purposes of the study.

The fourth chapter offers an overview and discussion of empirical examples of formulaic language in the data. This is important to draw out the characteristics of the linguistic structures that constitute the material analysed in remaining chapters. For example, it is demonstrated that conversational formulae that have in the past been studied in relation to cultural frames in fact only account for a marginal percentage of MWEs in the data. It is also established that over half of all MWEs in the data contain at least one variable position and as such the material investigated is markedly different from lexis.

Chapter 1 starts off by introducing the reader to the concept of formulaic language and its significance. In the second section, an up-to-date view of this phenomenon is presented, and a fresh way of making sense of its complexities. The term multi-word expression (MWE) is then introduced in Section 3 to describe the phenomena of formulaic language that will be the subject of analysis. The reader is also introduced to some of the various types of evidence for the importance of formulaic language and its significance to both linguistic knowledge and language use (Section 4). The chapter ends by highlighting the reasons why looking at language and culture from the prism of formulaic language is particularly insightful.

The introduction takes a look at an item of formulaic language (die Forderung nach X [the demand for X]), the development of which is closely linked to cultural change. It uses this example to introduce the aims of the study and gives an overview of the book.

The insights gained in Chapter 5 are then contextualised in Chapter 6. This is done in two ways: by investigating instances of non-cultural types of motivation, to contrast with cultural motivation, and by quantifying the extent of cultural motivation among instances of change in the data. For this purpose, the chapter opens by presenting a comprehensive typology of motivations of change (based on research discussed in Chapter 2) and then presents the method used to assess motivation in a random sample of instances of significant change in the corpus. Conclusions from six closely researched instances of non-cultural motivation suggest that there are various other strong motivators of change, but also that some of the commonly applied categories of non-culturally motivated change offer less than satisfactory accounts of motivation. In some of these cases, more interesting but difficult to ascertain social factors play a role. At the end of the chapter, an assessment is made of the relative proportions of the different motivators of linguistic change in the sample. This shows that cultural change plays a greater role than language-internal factors.