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We state Peano’s axioms for the positive integers and show how all the properties we have stated for the positive integers can be derived from those axioms. We show how to assign a number to any finite set. We discuss various objections to the way we have discussed numbers.
The century of Russian genius presented in the pages above opened with the soldier who saved Peter the Great from death and closed with Daniil Kharms’s travelers spreading kindness and tolerance. In between, a panorama of extraordinary cultural richness unfolded, with layer upon layer of innovation in the arts. Throughout, the creativity of high culture drew on rich folk traditions, and the burgeoning popular culture took inspiration from above. Three themes – freedom and order; the boundaries of self and society; and the societal obligations of art and artists – played out in an enormous body of literature, music, and the visual arts. The firebird, caged or free, captured or in flight, is central, as is the fox, who (usually) succeeds in securing her objectives through wile and guile. The works of this age of genius were created over decades under conditions of recurrent social disruption and trauma. Despite formidable obstacles, brave and talented writers, artists, musicians and others remained committed to expression of naïve goodness to counter evil. That this message prevailed, even if restricted to a subset of works and a segment of audiences, is a dimension of moral genius comparable to the lauded artistic brilliance of the age.
That governance within the firm is deliberate, conscious and hierarchical, based on authority is considered almost axiomatic. Chester Barnard is cited as an early theorist of this view. In this short article we review Barnard's original theory of authority, his later work and his private correspondence with F. A. Hayek, Michael Polanyi, Bertrand de Jouvenal and others. We show that Barnard focused in his later thinking less on authority and more on ‘responsibility’ and on the spontaneous nature of coordination within the firm, argued for ‘invisible hand’ explanations of coordination within the firm and compared coordination within the firm to market coordination. We use this information to produce novel insights into the work of Chester Barnard and also to demonstrate that his insights into the inner workings of firms is still not completely understood or reflected in the literature on the firm.
In this chapter, we take stock of how scholars of international relations and of elections have previously studied the issues we are interested in. Even if the most dramatic manifestations of outside influence, coups and invasions, are (largely) a thing of the past, without a doubt sustained investments by multiple powers in more (or less) competitive political processes impact polyarchy in a substantial and sustained way. Outsiders can help candidates directly, raising the question of how the who and how of elections figure in the calculus of interventions. Why such investments are made, and their effects, are important subjects to study. We agree with existing works that interest in democracy promotion depends on how many other democracies there are, and on competing geo-strategic objectives. Our contribution is a specific focus on elections, an emphasis on different types of interventions, for the rules, and for candidates, and strategic logic of intervention where opposing sides can battle for influence. We bring together anarchy, the international system, and polyarchy, the domestic fight for power, in a single framework.
An important distinction in signal processing is often made between “signal” and “noise.” This is proposed here to be approached via a contrast between “order” and “disorder,” in the sense of a “coherent” or “incoherent” structure in a time-frequency description. Basic classes of signals and noise models are discussed, focusing on what will be mostly used in the rest of the book.
This essay argues for reading Chinua Achebe’s Things Fall Apart as an intervention in the political philosophical discourse on the structural relation that links violence and order. This argument is built on the evil forest as the means through which violence is instrumentalized and brought under a system of value and order in Things Fall Apart. In the figure of the Evil Forest as the center of a legal and narrative economy built on the management of violence, Achebe introduces an African paradigm of law and order that rivals Hobbes’s state of nature, challenges Hegel’s notion of African unreason, and, thus, serves as the grounds on which the order inherent to the African world can be made visible.
This article focuses on the mobile peoples who engaged in piracy on the borders beyond the territories negotiated by the imperial Chinese and colonial Spanish and Dutch powers, and by doing so, reframe our perception of early modern imperial and maritime history. In pre-modern times, the control of territory within the administrative borders was incomplete, and small pockets of territories with porous borders were beyond governmental rule. The people and the groups that lived along the coast of the northeastern South China Sea were, at different times, recognized differently and many of their activities were at times sanctioned and at other times outlawed. This article reveals a facet of how the non-stateless peoples lived on the borders beyond, claimed their own order in their own way, and worked and became naturalized or classified inside the strengthening borders in pre-modern societies according to the agenda and discourses of the dominant powers. I argue that the coastal societies had their own “order” that created groups “beyond control” or “being registered gradually.”
Multiple studies have found Conscientiousness to be protective against dementia. The purpose of this study is to identify which specific aspects, or facets, of Conscientiousness are most protective against cognitive impairment and whether these associations are moderated by demographic factors and/or genetic risk.
Health and Retirement Study participants were selected for analysis if they completed the facets of Conscientiousness measure, scored in the range of normal cognitive functioning at the baseline personality assessment, and had at least one follow-up assessment of cognition over the up to 6-year follow-up (N = 11 181). Cox regression was used to test for risk of incident dementia and risk of incident cognitive impairment not dementia (CIND).
Over the follow-up, 278 participants developed dementia and 2186 participants developed CIND. The facet of responsibility had the strongest and most consistent association with dementia risk: every standard deviation increase in this facet was associated with a nearly 35% decreased risk of dementia; self-control and industriousness were also protective. Associations were generally similar when controlling for clinical, behavioral, and genetic risk factors. These three facets were also independent predictors of decreased risk of CIND.
The present research indicates that individuals who see themselves as responsible, able to control their behavior, and hard workers are less likely to develop CIND or dementia and that these associations persist after accounting for some common clinical, behavioral, and genetic risk factors.
Wu [‘An order characterization of commutativity for
-algebras’, Proc. Amer. Math. Soc.129 (2001), 983–987] proved that if the exponential function on the set of all positive elements of a
-algebra is monotone in the usual partial order, then the algebra in question is necessarily commutative. In this note, we present a local version of that result and obtain a characterisation of central elements in
-algebras in terms of the order.
Nudging or ‘choice architecture’ refers to strategic changes in the environment that are anticipated to alter people’s behaviour in a predictable way, without forbidding any options or significantly changing their economic incentives. Nudging strategies may be used to promote healthy eating behaviour. However, to date, the scientific evidence has not been systematically reviewed to enable practitioners and policymakers to implement, or argue for the implementation of, specific measures to support nudging strategies. This systematic review investigated the effect of positional changes of food placement on food choice. In total, seven scientific databases were searched using relevant keywords to identify interventions that manipulated food position (proximity or order) to generate a change in food selection, sales or consumption, among normal-weight or overweight individuals across any age group. From 2576 identified articles, fifteen articles comprising eighteen studies met our inclusion criteria. This review has identified that manipulation of food product order or proximity can influence food choice. Such approaches offer promise in terms of impacting on consumer behaviour. However, there is a need for high-quality studies that quantify the magnitude of positional effects on food choice in conjunction with measuring the impact on food intake, particularly in the longer term. Future studies should use outcome measures such as change in grams of food consumed or energy intake to quantify the impact on dietary intake and potential impacts on nutrition-related health. Research is also needed to evaluate potential compensatory behaviours secondary to such interventions.
The differential quadrature method has been widely used in scientific and engineering computation. However, for the basic characteristics of time domain differential quadrature method, such as numerical stability and calculation accuracy or order, it is still lack of systematic analysis conclusions. In this paper, according to the principle of differential quadrature method, it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the important V-transformation feature. Through the equivalence of the differential quadrature method and the implicit Runge-Kutta method, it has been proved that the differential quadrature method is A-stable and s-stage s-order method. On this basis, in order to further improve the accuracy of the time domain differential quadrature method, a class of improved differential quadrature method of s-stage 2s-order has been proposed by using undetermined coefficients method and Padé approximations. The numerical results show that the proposed differential quadrature method is more precise than the traditional differential quadrature method.
The international system may be anarchic, but anarchy is neither fixed nor inevitable. We analyze collective choices between anarchy, a system of inefficient self-enforcement, and external enforcement, where punishment is delegated to a third party at some upfront cost. In equilibrium, external enforcement (establishing governments) prevails when interaction density is high, the costs of integration are low, and violations are difficult to predict, but anarchy (drawing borders) prevails when at least one of these conditions fail. We explore the implications of this theory for the causal role of anarchy in international relations theory, the integration and disintegration of political units, and the limits and possibilities of cooperation through international institutions.
The current UK government's policies include headlong spending cuts and a far-reaching restructuring of public provision. State welfare arguably contributes to political legitimacy and social stability, as well as to better social conditions and economic prosperity. The fact that current policies bear disproportionately on lower income groups may damage legitimacy.
This article analyses a dataset covering twenty-six countries for more than two decades to show that spending cuts, privatisation and increases in poverty undermine legitimacy. It uses a direct measure of legitimacy in terms of the frequency of riots and political demonstrations and strikes, rather than the usual indirect measures in terms of attitudes and trust in government. Findings in relation to the increased work-centredness of the benefit and labour market reforms are more equivocal: a stricter benefit regime may not undermine legitimacy.
We generalize Löwner's method for proving that matrix monotone functions are operator monotone. The relation
on bounded operators is our model for a definition of
-relations being residually finite dimensional.
Our main result is a meta-theorem about theorems involving relations on bounded operators. If we can show there are residually finite dimensional relations involved and verify a technical condition, then such a theorem will follow from its restriction to matrices.
Applications are shown regarding norms of exponentials, the norms of commutators, and “positive” noncommutative
Why are some acts, events, or people elevated to a status of a threat, when no hostile action or direct physical damage appears imminent? Why are some relationships of threat infused with intense emotionality and ethical language? In this paper, I argue that puzzles such as these can be understood if we develop a concept of normative threat. The role of ethical values and beliefs has not been sufficiently integrated with the threat literature. Many writers assume that ethical language tied to constructions of threat serves merely to disguise and palliate the underlying hard reality of struggles for power. This is too simplistic. I offer an approach that takes seriously the normativity of the threat experience for people as members of political bodies. I argue that perceptions of threat emerge and carry a heightened emotional and moral energy when basic features of a political body's normative order appear to be at stake and people believe action affirming their strength as a collective body is required. Normative order comprises a set of principles citizens believe to be necessary for the functioning, justifiability, and indeed ‘reality’ of their political body. A normative threat is perceived as a promise of harm to the political body through defiance of basic principles of order and right that constitute one's group. The paper describes three main types of normative threat: transgression/grievance, subversion/insecurity, abomination/indignant aversion.
‘What is politics?’ is an omnipresent question in Hannah Arendt's work and one which is broadly explored in countless publications. ‘What is law?’, in contrast, is a question which has not been of much interest to Arendt scholarship to date. There is a good reason for this: Arendt's engagement with law seems not to be systematic but, rather, episodic and sporadic. However, on the basis of three different discourses – historical, political-theoretical, and legal-philosophical – I shall point out that Arendt's dealing with legal questions takes place on a continuous basis and should be regarded as crucial for a proper understanding of her thoughts. I shall argue that with her shift from the Greek conception of law as nomos to the Roman lex, Arendt seeks to de-substantiate the concept of law and to highlight the relationship-establishing dimension of law. Both attempts are important for overcoming the dichotomy of law and politics within constitutionalism and for paving the way to a different understanding of legal rationality which seeks not to isolate law from the political sphere but rather to interact with it.
In the perennial discussions about Anglican identity some voices predominate more than others. L’Eglise Anglicane du Congo is a small province with a modest voice in the Anglican Communion. This article looks at Congolese Anglican identity as articulated by its members and examines the way in which the formation of that identity emerges from local concerns as well as wider networks. It uses interviews with members to focus on the majority appreciation of ‘order’, as expressed in governance and ritual, and recent shifts in the discourses surrounding ‘order’ to engage with changes in the country. The article borrows the terms ‘translocal’ and ‘transnational’ from the social sciences to explore the overlapping relational identities that emerge and the multi-directional dynamics of Congolese Anglicans. It suggests that this approach may have wider implications for understanding Anglicanism.
We introduce natural generalizations of two
well-known dynamical systems, the Sand Piles Model and the Brylawski's
model. We describe their order structure, their reachable
configuration's characterization, their fixed points and their
maximal and minimal length's chains. Finally, we present an
induced model generating the set of unimodal sequences which amongst other corollaries, implies
that this set is equipped with a lattice structure.