Only two complete works on the philosophy of mathematics survive from Antiquity, Iamblichus’ De communi mathematica scientia and Proclus’ commentary on Euclid’s Elements Book I. Chapter 21 lists works by Proclus concerning mathematics and the sources he used in these works. Concentrating on Proclus’ commentary on Euclid, I describe his conception of the ontological status of the objects with which mathematics is concerned: these objects are originally concepts innate in human soul, forming part of its very nature, concepts which the mathematician then seeks to articulate, project, construct through various methods so as to constitute an elaborated science. I present also the distinctions made between the mathematical sciences and their methods, the importance of mathematics for other sciences (both superior and inferior to it), and Proclus’ relations with other mathematicians of his time.

Chapter 2 describes the Resilience Alliance, resilience theory, and the data and methods on which this investigation is based. It starts by detailing the discovery of resilience as narrated to me by C. S. “Buzz” Holling, RA’s charismatic leader and one of the twentieth century’s most influential ecologists. I then discuss Holling’s early collaborations where he developed, tested, and honed his own theory of group interaction and refined a set of socio-emotional practices for fostering creative group work – methods that he continued to use in RA. The chapter traces RA’s evolution from its beginning as the Resilience Network to becoming one of the main theory groups in sustainability science. Key aspects of resilience theory are outlined, and RA’s intellectual contributions and the immense influence of their ideas are highlighted to demonstrate their impact on sustainability science and how their theory and creative vision diverged from previous scientific understanding. The chapter closes by outlining the methods used in this study, the five longitudinal datasets underpinning this book, and discussing my relationship with RA.

In this chapter I explore theories, models, and methods. The narrative turn in the social sciences and in the analysis of world politics has been fostered by and drawn attention to McCloskey’s work and the importance of story-telling (section 1). Theories and models tell stories that are created by acts of individual imagination and that exist as collective imaginaries (section 2). Experiments and experimentation are different ways of testing and test-driving scientific theories and models in a world that is both risky and uncertain (section 3). And the simplicity or complexity of the stories told by theories and models always grapples with the risk-uncertainty conundrum (section 4).

This chapter outlines the basic principles of qualitative research in the context of mental health. We begin by discussing the philosophy of reality and knowledge production, demonstrating how these discussions filter through to every aspect of qualitative research. We then explain the fundamental elements of qualitative research, including how to formulate a research question, different methodological approaches, the application of qualitative methods in clinical trials, data collection, sampling, and analysis. This chapter also focuses on how qualitative research can make a change, providing unique insights on how to influence policy and engage government. We devote a substantial part of the chapter to research ethics and reflexivity, summarising not only basic bioethical principles, but thinking about ethics from an anti-colonial perspective. We end the chapter by exploring what constitutes high quality qualitative research, laying out some guiding principles and practices for promoting quality. Our aim with this chapter is not to provide an exhaustive account of qualitative research, rather to offer guidance and inspiration to fledgling researchers who would like to find out more.

This chapter takes a perspective on Shakespeare’s language that is more in tune with linguistics than literary criticism. Hence, it covers areas of language typically and traditionally discussed within linguistics, including phonology, grammar, lexis and semantics, but also includes pragmatics and, briefly, Conversation Analysis. It begins with a consideration of the label ‘Shakespeare’s language’ and what exactly that might encompass; the role of Shakespeare’s language in the study of the history of English; and popular myths that have arisen around Shakespeare’s language. It concludes with a reflection on methods of study, especially digital methods. It strives not only to acknowledge key research, but also to give the flavour of some of the findings of that research.

Chapter 1 sets out the methodology of the work-task approach in more detail before providing an overview of the findings. It introduces the sources used, the challenges they present, and the methods adopted to mitigate those challenges, as well as presenting the overall results of our research.

The final section of the book is structured to provide pathways forward for other researchers, practitioners, and scientists to use conceptualized peace. In this chapter, I detail the methodological approaches that can guide a study of meaning making, identity, and young people’s development. The chapter begins with a deeper dive into meaning making and ecological validity, as well as how to approach studying them. Then, I argue that the SAGE and MOVE models provide both theoretical and practical insights to study the complex nuance of everyday lived experiences and their role in cognition and psychosocial processes. To do this, I show how these two models connect to conceptualized peace and discuss how they directly informed the research studies from the previous two chapters. The methodological similarities and differences in these two studies also motivates a discussion about the flexibility and broad applicability of conceptualized peace.

The opening chapter sets the stage for the book. It starts with a recount of the author’s first day at The Villages and her motivation to explore the aging experience in this "city for seniors." The second part details the study that forms the book’s foundation, including the research questions, methods, and participant descriptions. The third part outlines the book’s structure, providing a brief overview of each chapter.

This chapter outlines the ethnographic and qualitative methodology employed in this study. The methodological choices focus on understanding language ideologies in a multilingual setting. The study does not engage in a linguistic focus on speech patterns and instead emphasizes the cultural and social meanings that speakers attach to language. It challenges monolingual, Western-centric assumptions by exploring complex links between language and social structures. Data collection included interviews, field notes, observations, classroom recordings, and surveys on language use. The study uses grounded theory to analyse data, and it prioritizes speakers’ perspectives as experts of their own language culture. The chapter argues that decolonising research practices have to treat local language ideologies as legitimate frameworks rather than folk beliefs. A linguistic analysis examines public English, inspecting its variability and influence from both local and external norms. By integrating linguistic, cultural, and social data, the methodological approach provides a holistic view of how language ideologies emerge and intersect with broader social discourses.

Legal research is a repeat offender – in the best sense of the term – when it comes to making use of empirical and experimental methods borrowed from other disciplines. We anticipate that the field’s response to developments in eye-tracking research will be no different. Our aim is to aid legal researchers in the uptake of eye-tracking as a method to address questions related to cognitive processes involved in matters of law abidance, legal intervention, and the generation of new legal rules. We discuss methodological challenges of empirically studying thinking and reasoning as the mechanisms underlying behavior and introduce eye-tracking as our method of choice for obtaining high-resolution traces of visual attention. We delineate advantages and challenges of this methodological approach, and outline which concepts legal researchers can hope to measure with a toy example. We conclude by outlining some of the various research avenues in legal research for which we predict a benefit from adopting eye-tracking to their methodological toolbox.

The imposition and execution of the death penalty are not per se violations of general international law and thus may amount to lawful sanctions in certain circumstances. This is so, even though the global trend towards the ending of capital punishment continues. As of August 2024, 53 States retained the death penalty for ordinary criminal offences. This chapter discusses the legality of capital punishment and its different forms. Certain categories of person may never be executed.

Epidemiology is the study of patterns and determinants of disease and other health states in populations. It primarily uses quantitative methods (those methods dealing with counting, measuring and comparing things) that definitely use statistics and include statistical methods, but in this book we will not be talking about performing any statistical acrobatics more complicated than completing a sudoku puzzle.

This chapter begins by highlighting three ways in which K-12 urban educators and college faculty working in MSIs experience similar challenges managing cultural differences between themselves and their students from low-income and other minoritized communities. It then segues into the empirical portion of the book, by introducing the study context, as well as methods and materials used to collect the data analyzed in-depth across the following four chapters.