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This overview discusses the development of the catacombs of Rome, focusing on their architectural evolution and their role in Christian burial practices. Tracing the transformation of subterranean cemeteries from the late second to the fourth century, it argues that the catacombs were distinct from contemporary pagan hypogea. Unlike their pagan counterparts, Christian catacombs featured vast networks of interconnected tunnels, a structured layout designed for expansion, and an intensive use of subterranean space. A defining characteristic of these burial sites was the deliberate placement of tombs near those of martyrs, which in turn became focal points for pilgrimage and veneration. The Callixtus catacomb exemplifies this trend, as it was developed with carefully planned access points and designated areas for noble burials. The chapter also challenges earlier assumptions that pagans continued to use catacombs extensively after the legalisation of Christianity. Instead, it argues that these spaces became increasingly exclusive to Christian communities, serving as both burial grounds and sacred spaces that reinforced communal identity and the cult of the martyrs.
Conservatives claim that taxes in America are too high. Cross-national data and historical data from the United States raise serious doubts about this claim. As a percentage of GDP, the tax burden in America is low compared with many other advanced capitalist countries. Tax rates for individuals and corporations in America are also comparatively low. Yet conservatives have long complained that taxes in America are too high regardless of historical fluctuations in the tax burden and tax rates, and regardless of economic and geopolitical circumstances. Nowadays, about half of Americans believe that their own taxes are too high. Yet the overwhelming majority feel that taxes on corporations and the rich are too low and that they should be paying more, not less in taxes. Republicans and especially wealthy Republicans are the most likely to be concerned that taxes on corporations and the affluent are too high.
The increasing acceptance of marquee “liberal” doctrines such as liberty of conscience, limited government, and universal adult suffrage occurred mainly during a period in which social contract theory was dormant and other philosophies – Hegelianism, Marxism, and utilitarianism –largely prevailed in the West. If Rawls’s social contract apparatus can deliver something beyond mere “yea-saying” to the liberal consensus, one could confidently say that contract doctrine has helped. Substantive political equality might be that something, but its delivery is still contested.
This textbook is meant for first-year undergraduates majoring in mathematics or disciplines where formal mathematics is important. It will help students to make a smooth transition from high school to undergraduate differential calculus. Beginning with limits and continuity, the book proceeds to discuss derivatives, tangents and normals, maxima and minima, and mean value theorems. It also discusses indeterminate forms, functions of several variables, and partial differentiation. The book ends with a coverage of curvature, asymptotes, singular points, and curve tracing. Concepts are first presented and explained in an informal, intuitive, and conceptual style. They are then covered in the form of a conventional definition, theorem, or proof. Each concept concludes with at least one solved example. Additional solved examples are also provided under the section "More Solved Examples". Practice numerical exercises are included in the chapters so that students can apply the concepts learnt and sharpen their problem-solving skills.
Chapter 9 examines the principle of the duty of care in the context of climate litigation. The authors explore how this principle has been invoked in a growing range of jurisdictions, in different ways, to hold governments and corporations accountable for their respective contributions to climate change. By analysing judicial decisions in prominent cases such as Urgenda and Milieudefensie in the Netherlands, Neubauer in Germany, and Notre Affaire à Tous in France, the authors explore the potential of the duty of care principle to compel more ambitious climate action in pending and future cases. The emerging best practice they identify suggests a growing willingness of courts to recognise a duty of care for governments and corporations towards citizens in relation to climate change.
This chapter explores the spread of Christianity in Late Antiquity, focusing on archaeological evidence and methodological challenges in tracing its expansion. It examines how Christianity transitioned from a marginalised faith to an institutionalised religion, emphasising regional differences in its adoption across the Mediterranean and beyond. The chapter discusses a variety of materials, including early Christian inscriptions, artefacts, funerary practices and architectural remains such as churches, baptisteries and monasteries. Sites like the house church at Dura Europos and early Christian catacombs provide crucial insights into the religion’s early development. The study also highlights the role of missionary activity and the influence of state policies, particularly after Constantine’s legalisation of Christianity in the fourth century. A major argument is that Christianity spread unevenly, with urban centres adopting it earlier than rural areas. The transition was not uniform, as some regions experienced periods of resistance or syncretism with existing religious traditions. The chapter underscores the difficulty of identifying Christian material culture due to the overlap with pagan symbols. The chapter rounds off by calling for a more critical approach to interpreting archaeological evidence and suggests that future research should focus on regional case studies to refine our understanding of Christianity’s complex expansion.
Hobbes argues that in a “condition of meer nature,” lacking a common power, reason requires that we appoint one, lest our lives be “solitary, poore, nasty, brutish, and short.” No covenant of peace can be effective without a Sovereign arbiter to enforce it. Therefore, reason requires each of us to surrender the natural right to judge for ourselves, and to appoint a Sovereign. An effective Sovereign must have authority to determine religious practice and to raise an army – precisely the powers the “Roundhead” rebels had denied Charles I.
In this chapter, the contrast between two models of expatriate masculinity developed earlier is brought to a head, with a fresh twist on the history of masculine identity. In retirement William Cooper indulged his passion for global wanderlust at the expense of his family, whereas Edgar Wilson happily abandoned his expatriate frustrations for a conventional model of settled suburban domesticity with his wife in England, spurning the mobile attractions of the cosmopolitanism they had long nurtured, but with Winifred continuing to exercise her public activism and independence. Ironically, the domestic model, rather than William’s continuing mobility, was most closely associated with the lower middle class, recalling Edgar’s origins and early white-collar labours. The disparity is underlined by a tragic account of William’s last years, interned by the Nazis in wartime Paris after an ill-advised excursion across France. Wartime domesticity for Edgar and Winifred was a struggle, only relieved by a comfortable inheritance from William. Winifred’s Will reflected her long commitment to chosen causes like the Mothers’ Union, a statement of her lifetime priorities.
Chapter 5 on Admissibility delves into the factors determining whether a climate case can be heard in court. It presents a clear understanding of the criteria for admissibility and their potential implications on the trajectory of climate litigation. The chapter also delves into the interplay between domestic and international legal rules and norms and their influence on the criteria for admissibility. The author’s analysis reveals that a restrictive interpretation of admissibility criteria can present formidable access to justice barriers, particularly for those most impacted by climate change. In light of these challenges, the author’s distillation of emerging best practice highlights instances where courts and quasi-judicial bodies have interpreted admissibility criteria to ensure access to justice. Specifically, the chapter highlights cases where these bodies have considered human rights and justice imperatives in their admissibility decisions. These decisions highlight the potential for an inclusive and equitable approach to climate litigation, one that aligns with the global nature of the climate crisis and the urgent need for climate justice.
Chapter 16 on Causation explores the challenges of proving causation in an interconnected system like the climate, where multiple actors contribute to the overall impacts. The authors highlight the significance of probabilistic approaches, recognising that establishing direct causation can be challenging due to the nature of climate change and the cumulative nature of greenhouse gas emissions. In their exploration of emerging best practices, the authors underscore the growing recognition among courts of the need for nuanced interpretations of causation requirements in climate litigation. They highlight innovative judicial strategies that utilise scientific evidence and expert testimony to assess the contribution of specific actors to climate impacts, even in the absence of direct causation. They emphasise the importance of interdisciplinary collaboration between legal and scientific experts to navigate the complexities of causation in climate cases. By incorporating and further developing these emerging best practices, courts can facilitate an accurate and fair distribution of responsibilities through the cases they adjudicate.
This chapter examines travel and communication in Late Antiquity, analysing the complexities of movement across the Roman and Byzantine worlds from the third to the eighth century. Rather than viewing this period as one of declining mobility, the chapter argues that travel remained vital, though its dynamics shifted due to political, economic and religious transformations. A major focus is on the infrastructure that supported travel, including roads, bridges, way stations and ports. The cursus publicus, the state-run courier system, is highlighted as a crucial mechanism for imperial communication and administrative efficiency. Trade networks, both maritime and overland, played a fundamental role in sustaining long-distance movement, with Mediterranean seaports, river transport and caravan routes facilitating commercial exchanges. Religious travel, particularly pilgrimage and episcopal councils, became increasingly significant after the rise of Christianity, with the movement of monks, clergy and pilgrims contributing to the spread of religious ideas and artistic traditions. The chapter also addresses migration, discussing the movements of soldiers, officials and entire populations in response to military campaigns, economic opportunities and political upheavals. In this way, this contribution demonstrates that mobility remained central to the late antique world, shaping social, economic and cultural interactions across the empire.