Chapter 12 extends students’ understanding of Statistics and introduces foundational concepts in Probability for Years 3 to 6. You will explore how to support students in collecting, organising, and interpreting data, identifying patterns, and predicting outcomes using simple probability language. The chapter also highlights strategies for integrating digital tools, adapting tasks to meet diverse learning needs, and making cross-curricular connections to enhance relevance and engagement.

Chapter 9 focuses on how students develop foundational understandings of Measurement and Space in the early years (Foundation to Year 2). It explores how young learners engage with concepts such as length, area, time, and mass through hands-on experiences and everyday contexts. You will consider how to structure learning experiences that build conceptual understanding, support spatial reasoning, and introduce key mathematical vocabulary and thinking processes.

Chapter 11 introduces students’ early engagement with Statistics in the Foundation to Year 2 level. It focuses on key concepts such as posing questions, collecting data, and interpreting simple visual representations. You will explore essential language, sample activities, and assessment strategies, along with common misunderstandings to look for when supporting young learners in developing foundational data skills.

Chapter 10 builds on earlier learning and explores how students extend their understanding of Measurement and Space in the middle and upper primary years (Years 3 to 6). It focuses on the development of key concepts such as units of measure, angles, transformations, and geometric properties. You will investigate strategies for using precise mathematical language, addressing common misconceptions, and applying spatial and measurement thinking to solve purposeful, real-world problems.

Chapter 8 builds on early understandings and examines how students deepen their conceptual grasp of Number and Algebra in the middle and upper primary years (Years 3 to 6). It clarifies key language and concepts and highlights common misconceptions to support diagnostic teaching. You will explore engaging classroom activities and assessment opportunities to consolidate mathematical reasoning and promote accurate, flexible thinking.

In this concluding chapter, I summarize my arguments for the study of the global politics of religion, international political theory, and the study of colonial, postcolonial, and de-colonial politics. In the field of religion and politics, I illustrated the productive power of the exclusion narrative and reconstructed the concept of ‘religion’ at work in the rehabilitating narrative of recognition. In the field of IR theory, I emphasize the need to study the costs of recognition and argue for a greater attentiveness to its conditions of possibility, that is to say, the processes through which the subjects and objects of global politics become intelligible, or recognizable, as such. In the field of colonial history, I show how the entwined histories of Pakistan and Israel both structured the possibilities of and were structured by the capacious concepts of ‘religion’, the ‘Muslim’, and the ‘Jew’.

This introductory chapter contextualizes the inquiry and delimits the theoretical, historical, and practical concerns that motivate the study. After discussing key concepts informing the analysis, including the terms ‘religion’ and ‘recognition’, it summarizes the book’s main arguments and contributions and locates them in current International Relations (IR) scholarship as well as in the disciplines of religious studies and colonial history. It introduces the empirical case studies and illustrates how the quest for statehood, the contested question of minorities, political representation, and international border-making shaped and were shaped by the concepts, agents, and identities associated with ‘religion’ that broke through the threshold of political recognition to establish themselves as taken-for-granted political entities on the global stage. The chapter argues that religion is a space, concept, and realm of social and political life rather than separate from it. Consequently, struggles over authority, power, and political order shape the contours and meanings that ‘religion’ can take on. By the same token, analysing changes in such meanings and understandings help us understand the political structures and orders that characterize that particular place and time.

Chapter 10 PRACTICAL CONCEPTS AND PRODUCTIVE REASONING reviews arguments for positing practical concepts and discusses a novel empirical argument for the psychological reality of practical concepts that relies on evidence for a distinctively productive kind of reasoning.

Chapter 1 sets the stage by describing several linguistic and psychological aspects of word meaning, with emphasis on those that have received the most attention in cognitive neuroscience. Specific topics include the treatment of word meanings as public concepts for social coordination; the decomposition of word meanings into semantic features; the characterization of word meanings in terms of frames, prototypes, mental models, and background situations; the nature of word associations and co-occurrence patterns; the influence of context on interpretation; and the importance of crosslinguistic similarities and differences.

The Introduction develops the idea that Hegel’s philosophy is distinctive by its endorsing an artifactual paradigm for philosophy, in contrast to a natural one. The artifactual paradigm says that our knowledge of humanly constructed artifacts, rather than natural things represent the standard-setting case for objects of philosophical knowledge. The world of spirit or Geist is thus the central topic of philosophy. But the philosophical basis for the centrality of Geist is Hegel’s theory of concepts. Hegel presents a theory of concepts which allows for concepts not only to represent their objects but also to constitute them, akin to the artifactual production of an object. This interpretation contrasts with metaphysical readings of Hegel that make “the Concept” a part of the structure of reality, as well as with more deflationary interpretations that understand Hegelian concepts on the model of Kantian categories.

Chapter 5 argues that Hegel’s interest in the Concept Logic is to determine when a concept and its object are in a “true” or fully unified relation. This requires developing both the least adequate logical relation of concept to object, which he calls judgment, and the most adequate such form, which is the syllogistic form of teleology. For Hegel, what best corresponds to its concept is what is conceptually constituted. And Hegel’s model for conceptual constitution is a teleological process governed by some universal. It is argued that the Teleology chapter of the Logic does not reject the artifactual model for teleology but in fact embraces it, for the teleology of artifacts requires that an intention come “first” in the construction of its object. Artifactual teleology shows in a concrete way how the moments of conceptual form can be unified in the objective domain.

Chapter 3 concerns Hegel’s use of the term “the Concept” (der Begriff) in the Doctrine of the Concept. The chapter argues that the use of this term is closer to its ordinary philosophical meaning than is claimed by standard metaphysical readings of the Logic. In particular, the singular use of “the Concept” is a synecdoche for the structure of conceptual thought as exemplified in philosophy in general. Hegel argues that conceptual thought has a formal structure of universality, particularity, and singularity. However, in contrast to many interpretations, these are not treated as properties that all concepts must have to be concepts. Rather, these formal features are exhibited variously in different concepts, judgments, and syllogisms. Hegel’s discussion of the formal dimension of thought sets up his attempt to show that some structures of thought more perfectly exemplify the form of the Concept than others.

Chapter 6 concerns the contentious issue of the role of the concept of life in the Logic and its consistency with the artifact-centered conception of teleology defended in chapter 5. There is a common tendency in the literature to think that the Life chapter implicitly imports references to the biological domain in the Logic itself. It is here argued instead that Hegel’s Life chapter must be read in “topic-neutral” terms: in a way that requires application neither to the natural or cultural domains. Once it is read in this neutral way, we can see that “logical life” is simply the notion of a self-determining purpose. However, the concept of life as developed by Hegel is not at all opposed to the artifactual domain; this is especially because the social and cultural domain (social ontology) give us prime examples of “living artifacts,” the kind of artifacts that can be based in a process guided by thought.

Wittgenstein was associated with conceptual analysis and it is widely presumed that that there is a Wittgensteinian account of concepts, yet sustained treatments of the topic in his work are difficult to find. My contribution shows that this irony is more apparent than real. Wittgenstein discussed concepts at some length in material from the early 1930s and manuscripts and lectures from his final period. On that basis I discuss Wittgenstein’s answers to five crucial questions about concepts – concerning their definition, possession, individuation, function and how best to investigate their nature. Wittgenstein and thinkers who influenced or were influenced by him (Frege, Dummett, Peacock) have contributed substantially to our understanding of concepts in two ways: first, methodological reflections on how to approach philosophically contested concepts, the concept of a concept included; secondly, elucidation of the nature and role of concepts through their connections with linguistic meaning, explanation, understanding, abilities and rules.

Both of the two main Hellenistic philosophical schools, the Epicureans and the Stoics, can be said to have an explicit theory of concepts that is broadly speaking empiricist. For both of them assume that all concepts originate in experience and that none are innate. But while their respective accounts appear similar, they arise from contrasting worldviews: atomist materialism for the Epicureans, and corporealism and a belief in providence and the all-pervading logos of God for the Stoics. Our chapter aims to piece together these two accounts of concepts and interpret them afresh. We will explore their commonalities and differences, show how they are impacted by the respective philosophical frameworks to which each of them belongs, and highlight their philosophical value.

In early Chinese philosophy, the work done by concepts is not explained by appeal to abstract entities or mental representations but rather through the appropriate use of names. In this chapter, I attempt to follow the contours and coherence of early Chinese views centring on two key terms: míng 名 (names) and lèi 類 (categories/kinds). After introducing the key terms and general context, I develop a systematic account of names from the ‘Correcting Names’ chapter of the third-century BCE Confucian text the Xunzi. I then examine the more sceptical views found in the Zhuangzi. The last part of the chapter turns to debates about the proper categorization of things, particularly as they appear in later parts of the Mozi. Early Chinese discussions of the proper use of names tend to privilege social factors over epistemic ones, drawing attention to the ways in which concepts create social order and guide behaviour.