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Let Fn be the free group on $n \geq 2$ generators. We show that for all $1 \leq m \leq 2n-3$ (respectively, for all $1 \leq m \leq 2n-4$), there exists a subgroup of ${\operatorname{Aut}(F_n)}$ (respectively, ${\operatorname{Out}(F_n)}$), which has finiteness of type Fm but not of type $FP_{m+1}(\mathbb{Q})$; hence, it is not m-coherent. In both cases, the new result is the upper bound $m= 2n-3$ (respectively, $m = 2n-4$), as it cannot be obtained by embedding direct products of free noncyclic groups, and certifies higher incoherence up to the virtual cohomological dimension and is therefore sharp. As a tool of the proof, we discuss the existence and nature of multiple inequivalent extensions of a suitable finite-index subgroup K4 of ${\operatorname{Aut}(F_2)}$ (isomorphic to the quotient of the pure braid group on four strands by its centre): the fibre of four of these extensions arise from the strand-forgetting maps on the braid groups, while a fifth is related with the Cardano–Ferrari epimorphism.
Focusing solely on the musical output of composer Igor Stravinsky, this chapter explores the evolution of what would become a characteristic compositional process – so-called ‘block form’ – in later works including Concertino, Symphony in Three Movements and Introitus T. S. Eliot in Memoriam. Close analysis of scores for these works, as well as a 1943 revision of the ‘Sacrificial Dance’ from The Rite, shows how Stravinsky crafted an idiomatic compositional technique that could produce both textural variation and structure coherence, while, in some cases, supporting a musical narrative.
We prove the coherence of multiplier submodule sheaves associated with Griffiths semi-positive singular hermitian metrics over holomorphic vector bundles on complex manifolds which have no nontrivial subvarieties, such as generic complex tori.
From cradle to grave human beings actively strive to abstract meaning from experience. The meaning making capacity builds step-by-step, beginning in the earliest years. At each phase of life, new capacities emerge and previous limitations in meaning making can be overcome. By adolescence all of the basic tools for making meaning have been acquired. All that remains to be achieved is the wisdom that comes from accrued lived experience in the subsequent years. Increasingly, a narrative identity may be formed.
Preschoolers purposefully seek to understand the environment. Their social world expands, as they work hard to interact with peers. Accompanying this active stance are surges in memory and other aspects of understanding the self in the world. Coherence in the organization of the emerging person becomes much more apparent, in both behavior and the child’s internal world, as seen in the child’s representation. Inquisitiveness and beginning understanding of causality are major strengths of the toddler. Because this understanding is limited, toddlers may at times attribute too much credence to their own perspective and too great a role to the self in causation. Thus, they can feel bad when negative experiences such as divorce happen, believing that they are the cause.
This final chapter turns to the other basic question that MacCormick asked himself, again exploring it for over four decades: is reason practical, and if so how? MacCormick engaged in this question in the form of a life-long dialogue with his Enlightenment predecessors, and especially Stair, Hume, Smith, and Kant. This chapter tracks this dialogue, while also keeping in mind the contemporary interlocutors of MacCormick’s theory of practical reason, which included not only the dominant voices in Anglo–American jurisprudence, such as Hart and Dworkin, but also philosophers in the European Continent, such as Perelman and Alexy. The first part of the chapter focuses on what may be called MacCormick’s meta-ethics, showing how MacCormick adopted perspectivalism about value. The second shows how, particularly in his theory of legal reasoning, MacCormick discusses the importance of constructing an inter-subjective space (via universalisation) and how he explores the complexity of deliberation as well as the defeasibility of decision within that space. Throughout, the chapter reads MacCormick’s account of the limited practicality of reason as a matter of character.
This title focuses on the interpretative methodologies and principles employed by international human rights organs in applying and developing human rights norms. It explores the role of various interpreters, including international, regional, and national courts, in shaping the meaning and scope of human rights. The section examines the methods of interpretation used by human rights bodies, such as textual, contextual, purposive, and evolutionary approaches, and the challenges in ensuring consistency and coherence across different jurisdictions. It also discusses the purposes of interpretation, including the protection of human rights, the development of international human rights law, and the promotion of judicial dialogue and coherence. By analyzing the interpretative practices of human rights organs, this title aims to provide a deeper understanding of the dynamics of human rights interpretation and the factors influencing the application of human rights norms in diverse legal and cultural contexts.
This part focuses on the interpretative methodologies and principles employed by international human rights organs in applying and developing human rights norms. It explores the role of various interpreters, including international, regional, and national courts, in shaping the meaning and scope of human rights. The sections examine the methods of interpretation used by human rights bodies, such as textual, contextual, purposive, and evolutionary approaches, and the challenges in ensuring consistency and coherence across different jurisdictions. It also discusses the purposes of interpretation, including the protection of human rights, the development of international human rights law, and the promotion of judicial dialogue and coherence. This part delves into the international legal regime governing human rights and freedoms, covering states’ general obligations, the conditions for engaging state responsibility, and the regime for the enjoyment and exercise of rights and freedoms. By analyzing the interpretative practices and legal obligations, this part aims to provide a deeper understanding of the dynamics of human rights interpretation and the factors influencing the application of human rights norms in diverse legal and cultural contexts.
This title examines the concept of normative pluralism in international human rights law, focusing on the coexistence and interaction of multiple legal systems and norms within the global human rights framework. It explores the treaty-based structure of human rights norms, including various international and regional human rights treaties, and discusses the role of customary international law, general principles of law, and jus cogens in shaping human rights obligations. The section also addresses the impact of nonconventional sources of human rights law, such as judicial decisions and soft law instruments, on the development and enforcement of human rights standards. By analyzing the complexities of normative pluralism, this title highlights the dynamic and evolving nature of international human rights law and the challenges in achieving coherence and consistency across different legal systems and cultures. It also emphasizes the importance of dialogue and cooperation among international, regional, and national actors in promoting and protecting human rights globally.
In the first of two chapters on probability in scientific inquiry, the basic ideas of probability theory are introduced through examples involving games of chance. The chapter then focuses on the Bayesian approach to probability, which adopts the stance that probabilities should be understood as expressions about the degrees of belief. The Bayesian approach as a general framework for probability is explained through examples involving betting that extend beyond games of chance, which also allows the introduction of the idea of probabilistic coherence as a condition of rational partial belief. We are then finally ready for Bayes’s theorem, a theorem of the probability calculus that plays a central role in the Bayesian account of learning from evidence. That account is illustrated with a historically motivated example from the history of paleontology. The chapter considers objections to the Bayesian approach and the resources Bayesians may draw on for answering those objections.
This is the first book to revisit the theory of rewriting in the context of strict higher categories, through the unified approach provided by polygraphs, and put it in the context of homotopical algebra. The first half explores the theory of polygraphs in low dimensions and its applications to the computation of the coherence of algebraic structures. Illustrated with algorithmic computations on algebraic structures, the only prerequisite in this section is basic category theory. The theory is introduced step-by-step, with detailed proofs. The second half introduces and studies the general notion of n-polygraph, before addressing the homotopy theory of these polygraphs. It constructs the folk model structure on the category on strict higher categories and exhibits polygraphs as cofibrant objects. This allows the formulation of higher-dimensional generalizations of the coherence results developed in the first half. Graduate students and researchers in mathematics and computer science will find this work invaluable.
The present study aimed to investigate whether contextual factors influence how a reference is processed in discourse. We used intact and violated presuppositions (PSP), triggered by a definite or indefinite noun phrase, to monitor the reference process. In one sentence set, a contextual referent was explicitly mentioned close or far from the PSP-triggering noun phrase (memory context). In another sentence set, a referent was not explicitly mentioned in the context, but an inference to a referent was either plausible or implausible due to contextual semantic relations (inference context). Participants were asked to rate the coherence of the discourse after listening to it. Our results revealed a strong influence of the temporal distance of the contextual presentation of a referent. When the referent was far in the context (memory context), PSP violations were judged to be less severe than for close referents, suggesting that they are less clearly represented in memory. Furthermore, PSP violations seemed to play a subordinate role when the semantic context provided a basis for the plausible presence of a referent (inference context). Our results suggest that discourse comprehension involves referential processes whose importance may fade with distance in memory or may be obscured by semantic contextual content.
Chapter 10 explores epistemological and methodological implications of ECT. The overarching issue is whether one adopts a reductive logic or an emergent logic, and whether one is mainly concerned with linear causation versus emergence. The former helps map out developmental diversity from a population perspective, and the latter inductively derives the emergence of new structures, properties, and patterns through real-time person–task interaction. The further issue is making decisions on using person-centered versus variable-centered approaches. At a more epistemological level, ECT does not endorse the deductive logic of falsification, which has a deterministic connotation. Given the indeterminacy involved in talent development, ECT argues that theoretical predictions regarding short-term and long-term outcomes can be based on soft constraint satisfaction as a new epistemology guiding predictions, which dictates that talent trajectories, pathways, and achievement patterns are indeterminate but principled. The chapter thereby proposes five terms (emergence, adaptation, divergence, excellence, and coherence) as organizing research that taps into probabilistic epigenesis, proximal processes, and developmental self-organization toward higher-order coherence. Each term constrains the structure of inquiry and methodology, including what timescale of action is appropriate, and whether quantitative or qualitative, deductive or inductive methods should be used.
Polus admires orators for their tyrannical power. However, Socrates argues that orators and tyrants lack power worth having: the ability to satisfy one’s wishes or wants (boulêseis). He distinguishes wanting from thinking best, and grants that orators and tyrants do what they think best while denying that they do what they want. His account is often thought to involve two conflicting requirements: wants must be attributable to the wanter from their own perspective (to count as their desires), but wants must also be directed at objects that are genuinely good (in order for failure to satisfy them to matter). We offer an account of wanting as reflective, coherent desire, which allows Socrates to satisfy both desiderata. We then explain why he thinks that orators and tyrants want to act justly, though they do greater injustices than anyone else and so frustrate their own wants more than anyone else.
This chapter surveys modern progress in physics on the topic of “decoherence,” the physical process by which irreversible behavior can occur in wave systems. A substantial part of the chapter discusses a proposal by the author of this book for a spontaneous collapse theory that is connected to decoherence.
This chapter surveys several different mathematical methods for time-dependent change of quantum states using quantum field theory. The Bloch sphere method is introduced, which can be used to show the physics discussed in Chapter 3, that electronic transitions, or “jumps,” are not instantaneous.
In this paper, we show how to represent a non-Archimedean preference over a set of random quantities by a nonstandard utility function. Non-Archimedean preferences arise when some random quantities have no fair price. Two common situations give rise to non-Archimedean preferences: random quantities whose values must be greater than every real number, and strict preferences between random quantities that are deemed closer in value than every positive real number. We also show how to extend a non-Archimedean preference to a larger set of random quantities. The random quantities that we consider include real-valued random variables, horse lotteries, and acts in the theory of Savage. In addition, we weaken the state-independent utility assumptions made by the existing theories and give conditions under which the utility that represents preference is the expected value of a state-dependent utility with respect to a probability over states.
The primacy of EU law as framed by the Court of Justice pre-empts substantive arguments of principle that originate in other legal orders. This was accepted and acceptable to the extent that the values EU law contained were at least normatively equivalent to values originated from the other legal orders. In this contribution it is argued that this is no longer the case and that the misuse of the Rule of Law rhetoric justifying the primacy of EU law renders the EU less accountable and undermines the dialogical pluralist essence of EU constitutionalism.
Part one gives a description of the characteristics of the wind field over the ocean, including wind shear, turbulence and coherence. It shows how these parameters are modeled and used as an input to wind turbine analyses. The long-term statistics of the mean wind speed are discussed as well as the most common principles for wind speed measurements. In part two, the kinematics and dynamics of ocean waves are given in a form which in subsequent chapters is used in computing wave loads on structures, both in time and frequency domain. Long- and short-term wave statistics are discussed.
Positively experienced relationships with family, partners and friends are the most important source of meaning in life for older persons. At the same time, Western countries are confronted with a growing number of socially isolated older adults who lack those relationships. This study aims to explore whether and how older adults who live in social isolation experience meaning in life. Data were collected via in-depth, semi-structured interviews with 24 socially isolated older adults, ranging in age from 62 to 94, all living in Rotterdam, The Netherlands. The criterion-based sampling of participants took place in close consultation with social workers of a mentoring project for socially isolated older adults. Follow-up interviews with 22 participants improved the credibility of findings and contributed to the breadth and depth of the researched casuistry. Data were analysed using an analytical framework based on seven needs of meaning identified by Baumeister (purpose, values, efficacy, self-worth) and Derkx (coherence, excitement, connectedness). The study demonstrates that isolated older adults may find anchors for meaning in life, although not all needs for meaning are satisfied, and there can also be tension between different needs. The needs-based model provides concrete distinctions for enabling care-givers to recognise elements of meaning.