The Special Composition Question asks under what conditions a plurality of objects form another, composite object. We propose a condition grounded in our scientific knowledge of physical reality, the essence of which is that objects form a composite object when and only when they are in a bound state – whence our Bound State Proposal. We provide a variety of reasons in favour of a mereological theory that accommodates our Proposal. We consider but reject another proposal, which is (...) quantum-physical in nature: the Entanglement Proposal. We close by responding to Teller’s ‘Suit Objection’. (shrink)

This paper provides the first thorough assessment of a physics-based answer, the Bound State Answer, to the Special Composition Question. According to the BSA some objects compose something if they are in a common bound state. The reasons to endorse such an answer, in particular, motivations coming from empirical adequacy and conservativeness, precision, simplicity, and parsimony, are critically addressed. I then go on to compare the BSA to other moderate answers to the SCQ and consider whether objections raised (...) against such answers can be raised against the BSA as well. I finally relate the discussion with mereological pluralism. (shrink)

The energy spectrum of the bound states of the nucleon-monopole system is determined, the monopole harmonics Yq,l,m are related to Wigner's functions D m,m′ (L) of the rotation matrix, and the scattering wave functions of the proton in the dyon source field are calculated.

The basic methods that have been used for describing bound-state quantum electrodynamics are described and critically discussed. These include the external field approximation, the quasi-potential approaches, the effective potential approach, the Bethe–Salpeter method, and the three-dimensional equations of Lepage and other workers. Other methods less frequently used but of some intrinsic interest such as applications of the Duffin–Kemmer equation are also described. A comparison of the strengths and shortcomings of these various approaches is included.

We consider the Bohmian trajectories in a 2-d quantum harmonic oscillator with non commensurable frequencies whose wavefunction is of the form Ψ=aΨm1,n1+bΨm2,n2+cΨm3,n3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi =a\Psi _{m_1,n_1}+b\Psi _{m_2,n_2}+c\Psi _{m_3,n_3}$$\end{document}. We first find the trajectories of the nodal points for different combinations of the quantum numbers m, n. Then we study, in detail, a case with relatively large quantum numbers and two equal m′s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m's$$\end{document}. We find fixed (...) nodes independent of time and moving nodes which from time to time collide with the fixed nodes and at particular times they go to infinity. Finally, we study the trajectories of quantum particles close to the nodal points and observe, for the first time, how chaos is generated in a complex system with multiple nodes scattered on the configuration space. (shrink)

We develop here the general treatment arising from the Bethe-Salpeter equation for a two-particle bound system in which at least one of the particles is spinless. It is shown that a natural two-component formalism can be formulated for describing the propagators of scalar particles. This leads to a formulation of the Bethe-Salpeter equation in a form very reminiscent of the fermion-fermion case. It is also shown, that using this two-component formulation for spinless particles, the perturbation theory can be systematically (...) developed in a manner similar to that of fermions. Quantum electrodynamics for scalar particles is then developed in the two component formalism, and the problem of bound states, in which one of the constituent particles is spinless, is examined by means of the means of the Bethe-Salpeter equation. For this case, the Bethe-Salpeter equation is cast into a form which is convenient to perform a Foldy-Woutyhuysen transformation which we carry out, keeping the lowest-order relativistic corrections to the nonrelativistic equation. The results are compared with the corresponding fermion-fermion case. It is shown, as might have been expected, that the only spin-independent terms that occur for the fermion-fermion system which do not occur for bound scalar particle cases, is the zitterbewegung contribution. The relevance of the above considerations for systems that are essentially bound by electromagnetic interactions, such as kaonic hydrogen, is discussed. (shrink)

We derive the so-called Barbieri-Remiddi solution of the Bethe-Salpeter equation in QED in its general form and discuss its application to the bound-state energy spectrum.

A proof is given for the theorem that at least one bound state exists in a one-dimensional attractive potential however weak it may be. The proof is constructive in that it provides a method to explicitly solve the eigenvalue problem for the eigenvalues as well as the eigenfunctions. The method is well suited to precise numerical calculations.

Recently, in the framework of a relativistic quantum theory with invariant evolution parameter, solutions have been found for the two-body bound state, whose mass spectrum agrees with the nonrelativistic Schrödinger energy spectrum. In this paper, we study the radiative transitions of these states in the dipole approximation and find that the selection rules are identical with those of the usual nonrelativistic theory, expressed in a manifestly covariant form. In addition to the transverse and longitudinal polarizations of the nonrelativistic (...) theory, we find a “scalar” transition, induced by the relative time coordinate, which is of the same type as the longitudinal transition, expressing the Lorentz covariance of the theory. (shrink)

Loneliness is one of the most neglected aspects of emotion history, despite claims that the 21st century is the loneliest ever. This article argues against the widespread belief that modern-day loneliness is inevitable, negative, and universal. Looking at its language and etymology, it suggests that loneliness needs to be understood firstly as an “emotion cluster” composed of a variety of affective states, and secondly as a relatively recent invention, dating from around 1800. Loneliness can be positive, and as much (...) a part of the body as the mind. Using a longue durée approach, I argue that we cannot understand loneliness as a “modern epidemic” without considering its history, its meanings, its practice, and its links with the body. (shrink)

A repulsive core force is derived which, assuming π mesons are the field particles, gives binding energies in good agreement with binding energies per nucleon of heavy nuclei. The physical model consists of a field of relatively short range, in which emission of a π meson by a nucleon and subsequent absorption by a neighboring nucleon is equivalent to a potential well. The binding energy at the equilibrium spacing of the nucleons is the self-energy of the π mesons, which is (...) calculated by analogy with classical electric fields. (shrink)

Contemporary versions of Bell’s argument against local hidden variable (LHV) theories are based on the Clauser Horne Shimony and Holt (CHSH) inequality, and various attempts to generalize it. The amount of violation of these inequalities cannot exceed the bound set by the Grothendieck constants. However, if we go back to the original derivation by Bell, and use the perfect anticorrelation embodied in the singlet spin state, we can go beyond these bounds. In this paper we derive two-particle Bell inequalities (...) for traceless two-outcome observables, whose violation in the singlet spin state go beyond the Grothendieck constant both for the two and three dimensional cases. Moreover, creating a higher dimensional analog of perfect correlations, and applying a recent result of Alon and his associates (Invent. Math. 163 499 (2006)) we prove that there are two-particle Bell inequalities for traceless two-outcome observables whose violation increases to in…nity as the dimension and number of measurements grow. Technically these result are possible because perfect correlations (or anti-correlations) allow us to transport the indices of the inequality from the edges of a bipartite graph to those of the complete graph. Finally, it is shown how to apply these results to mixed Werner states, provided that the noise does not exceed 20%. (shrink)

Harry G. Frankfurt has put the problem of volitional conflict at the center of philosophical attention. If you care fundamentally about your career and your family, but these cares conflict, this conflict undermines the coherency of your decision standard and thereby your ability to choose and act autonomously. The standard response to this problem is to argue that you can overcome volitional conflict by unifying your foundational motivational states. As Frankfurt puts it, the ‘totality of things that an agent (...) cares about’ plus his ‘ordering of how important to him they are effectively specifies his answer to the question of how to live’ (The Reasons of Love(Princeton: Princeton University Press, 2004), p. 23). In this paper, I critically assess the three main reasons given for such a coherency requirement: 1) we can do only one action at a time; 2) our motivational states come with normative pressure towards coherency; and 3) conflicting motivational states provide us with an incoherent decision-making framework. I conclude that these reasons do not ground a coherency requirement for practical deliberation and argue that we can autonomously express ourselves as volitionally conflicted by acting on our conflicting motivational states over the course of multiple actions. (shrink)

We consider several puzzles of bounded rationality. These include the Allais- and Ellsberg paradox, the disjunction effect, and related puzzles. We argue that the present account of quantum cognition—taking quantum probabilities rather than classical probabilities—can give a more systematic description of these puzzles than the alternate treatments in the traditional frameworks of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always provide a deeper understanding and a true explanation of these puzzles. One reason is that quantum approaches introduce additional (...) parameters which possibly can be fitted to empirical data but which do not necessarily explain them. Hence, the phenomenological research has to be augmented by responding to deeper foundational issues. In this article, we make the general distinction between foundational and phenomenological research programs, explaining the foundational issue of quantum cognition from the perspective of operational realism. This framework is motivated by assuming partial Boolean algebras. They are combined into a uniform system via a mechanism preventing the simultaneous realization of perspectives. Gleason’s theorem then automatically leads to a distinction between probabilities that are defined by pure states and probabilities arising from the statistical mixture of pure states. This formal distinction relates to the conceptual distinction between risk and ignorance. Another outcome identifies quantum aspects in dynamic macro-systems using the framework of symbolic dynamics. Finally, we discuss several ideas that are useful for justifying complementarity in cognitive systems. (shrink)

In this paper I have two main aims. My first aim is to introduce the notion of bounded emotionality. This notion is the analogue of that of bounded rationality in behavioural economics. Bounded rationality says, roughly, that human beings are cognitively limited with respect to their processing and memory capacities. Bounded emotionality says that we are limited in our emotional capabilities, notably in the intensity, duration, and possible combinations of our emotional states. Bounded rationality is a foundational notion in (...) behavioural economics and has played an important role in various fields of philosophy as well. In particular, in epistemology bounded rationality has been thought to have implications with respect to our doxastic norms. My second aim in this paper is to suggest that bounded emotionality also has an important role to play in philosophy. As a case in point, I discuss the implications that bounded emotionality has for our doxastic norms. In particular, I argue that one is not obligated to believe something or to stop holding a belief if one could not believe/fail to believe it without having an emotional response that exceeds one's bounded emotional capacities. (shrink)

We introduce a three-tiered framework for modelling and reasoning about agents who (i) can use possibly complete reasoning systems without any restrictions but who nevertheless are (ii) bounded in the sense that they never reach infinitely many results and, finally, who (iii) perform their reasoning in time. This last aspect does not concern so much the time it takes for agents to actually carry out their reasoning, as the time which can bring about external changes in the agents’ states (...) such as arriving of new information or discarding previously available information due to bounds of the agent’s resources. These three aspects are treated with the maximal possible degree of independence from each other. The treatment of layer (iii) can be combined with arbitrary logic at level (ii) which, in turn, can be combined with arbitrary agent logic at level (i). At the level (iii), we discuss briefly the duality (or rather, complementarity) of system descriptions based on actions and transitions, on the one hand, and states and their changes, on the other. We settle for the latter and present a simple language, for describing state changes, which is parameterized by an arbitrary language for describing properties of the states. The language can be viewed as a simple fragment of step logic, admitting however various extensions by appropriate choices of the underlying logic. Alternatively, it can be seen as a very specific fragment of temporal logic (with a variant of ‘until’ or ‘chop’ operator), and is interpreted over dense linear time. The reasoning system presented here is sound, as well as strongly complete and decidable (provided that so is the parameter logic for reasoning about single states). We give the main idea of the completeness proof and suggest a wide range of possible applications, which is a simple consequence of the parametric character of both the language and the reasoning system. We address then in more detail the case of non-omniscient rational agents, (ii). Their models are syntactic structures (sets of available formulae) similar in spirit, though not in the technical formulation, to the models used in other syntax oriented approaches and in active logic. We give a new sound, complete and decidable system for reasoning about such agents. Finally, we illustrate its extensions with the internal reasoning of agents, (i), by equipping them with some example logics. (shrink)

This paper presents the model of ‘bounded revision’ that is based on two-dimensional revision functions taking as arguments pairs consisting of an input sentence and a reference sentence. The key idea is that the input sentence is accepted as far as (and just a little further than) the reference sentence is ‘cotenable’ with it. Bounded revision satisfies the AGM axioms as well as the Same Beliefs Condition (SBC) saying that the set of beliefs accepted after the revision does not depend (...) on the reference sentence (although the posterior belief state does depend on it). Bounded revision satisfies the Darwiche–Pearl (DP) axioms for iterated belief change. If the reference sentence is fixed to be a tautology or a contradiction, two well-known one-dimensional revision operations result. Bounded revision thus naturally fills the space between conservative revision (also known as natural revision) and moderate revision (also known as lexicographic revision). I compare this approach to the two-dimensional model of ‘revision by comparison’ investigated by Fermé and Rott (Artif Intell 157:5–47, 2004 ) that satisfies neither the SBC nor the DP axioms. I conclude that two-dimensional revision operations add substantially to the expressive power of qualitative approaches that do not make use of numbers as measures of degrees of belief. (shrink)

The bounded confidence model has become a popular tool for studying communities of epistemically interacting agents. The model makes the idealizing assumption that all agents always have access to all other agents’ belief states. We draw on resources from network epistemology to do away with this assumption. In the model to be proposed, we impose an explicit communication network on a community, due to which each agent has access to the beliefs of only a selection of other agents. A (...) much-discussed result from network epistemology shows that densely connected communication networks are not always preferable to sparser networks. The aim of this paper is to investigate whether there are any noteworthy network effects in a version of the bounded confidence model augmented with communication networks, and in particular whether the aforementioned result from network epistemology can be replicated in that version. (shrink)

One of the most complex and uncertain areas of international legal doctrine concerns how to deal with the aspiration of a people to achieve self-determination through the establishment of a new state and the related claim to a specific territory over which statehood is to be exercised. Recently, when the General Assembly of the United Nations referred to the International Court of Justice the question of the legality of the declaration of independence by Kosovar Albanians, the Court was given an (...) opportunity to clarify and develop the law on external self-determination. Instead, the Court answered extremely narrowly, confining its analysis to the legality of the act of declaration without determining any consideration of international legal norms applicable to the act of secession that was being proposed. This article intends to fill the gap left by the ICJ’s decision: first by critiquing the inadequacy and tensions visible in the existing doctrine and second by examining how recent developments in international law may allow for a more normatively coherent approach to the problem. (shrink)

The concept of "recognition" lies at the intersection between contemporary identity politics and the philosophy of Hegel. While Hegel's philosophy is often invoked to provide normative grounding for political projects devoted to overcoming misrecognition, Hegel's analysis of recognition actually supports an immanent critique of such politics. It provides us with diagnostic tools that show how the pursuit of recognition, especially in the context of modern, state-centered politics, works both for and against the values of agency and plurality it is supposed (...) to serve. I develop this argument through readings of Hegel's Phenomenology and Philosophy of Right; Sophocles' Antigone; the history Jewish emancipation in nineteenth-century Prussia; and contemporary theorists of multiculturalism, including Charles Taylor and Will Kymlicka. ;In chapter one, establishing connections between Taylor's work on Herder and language and his work on multiculturalism, I show that demands for recognition have a self-obscuring character: recognition constructs identities by seeming only to cognize them. To understand the temptations and risks of political strategies that constitutively involve misunderstanding our own activity in this way, chapters two and three turn to important recognition scenes in Sophocles' Antigone and Hegel's Phenomenology. Read through the lens of tragedy, Hegel illuminates how the pursuit of recognition, blind to its own participation in the workings of power through which identities are constructed, enacts new forms of subjection in the name of an attractive yet impossible vision of masterful agency. Chapters four and five show that, pace the later Hegel, the mediating institution of the modern state cannot salvage the ideal of recognition, because the state itself participates in struggles for recognition, demanding confirmation of its sovereignty. I trace the consequences of the state's involvement in the politics of recognition through the case of Jewish emancipation, and by analyzing contemporary debates over the supposedly divisive effects of multiculturalism as struggles for recognition in which the sovereign imperatives of multicultural states help generate essentialist articulations of identity, foreclosing democratic agency. The conclusion suggests modes of political practice and institution that might enable us to loosen our tenacious attachment to recognition, thereby negotiating its double binds more gracefully. (shrink)

An evidentialist can be extreme about epistemic requirements in a couple of different ways. At the reductionist end of the spectrum are those who think our epistemic obligations are fully satisfied by the mere having of evidential fit—where having implies nothing about doing. Your beliefs ought to align with your evidence, in other words, but there’s nothing you’re obligated to do in order to get yourself into the epistemically optimal position. At the expansionist end of the spectrum are those who (...) think we ought to do more—epistemically-speaking—than just bring about a state of evidential fit. We ought to get more evidence, for instance, if it’s somehow relevant to our beliefs. Rather leery of extremists, we prefer a moderate account of epistemic obligation. It’s a conjunction of three theses: (1) We never have an epistemic duty to believe any particular proposition; (2) We’re epistemically obligated to reflect on our evidence in order to produce a state of evidential fit; (3) We’re never epistemically obligated to acquire any additional evidence. Our aim is to make these plausible. (shrink)

The standard model of knowledge, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}, consists of state space, Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega $$\end{document}, and possibility correspondence, P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P$$\end{document}. Usually, it is assumed that P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P$$\end{document} satisfies all knowledge axioms. Violating at least one of these axioms is defined as epistemic bounded rationality. If this happens, a researcher may (...) try to look for another model, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}, which generates the initial model, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}, while satisfying all knowledge axioms. Rationalizing EBR means that the researcher finds such a model. I determine when rationalization of EBR is possible. I also investigate when a model, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}, which satisfies all knowledge axioms, generates a model, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document}, which satisfies these axioms as well. (shrink)

There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by Rubinstein (), charges an agent for doing costly computation; the second, initiated by Neyman (), does not charge for computation, but limits the computation that agents can do, typically by modeling agents as finite automata. We review recent work on applying both approaches in the context of decision theory. For the first approach, we take the objects of choice in a (...) decision problem to be Turing machines, and charge players for the “complexity” of the Turing machine chosen (e.g., its running time). This approach can be used to explain well-known phenomena like first-impression-matters biases (i.e., people tend to put more weight on evidence they hear early on) and belief polarization (two people with different prior beliefs, hearing the same evidence, can end up with diametrically opposed conclusions) as the outcomes of quite rational decisions. For the second approach, we model people as finite automata, and provide a simple algorithm that, on a problem that captures a number of settings of interest, provably performs optimally as the number of states in the automaton increases. (shrink)

The present work is motivated by recent experiments aimed to measure the propagation velocity of bound electromagnetic field that reveal no retardation in the absence of EM radiation. We show how these findings can be incorporated into the mathematical structure of special relativity theory that allows us to reconsider some selected problems of classical and quantum electrodynamics. In particular, we come to the conclusion that the total four-momentum for a classical system “particles plus fields” ought to be a present (...) state function of moving charges if EM radiation is negligible. In quantum domain, we analyze novel definition of the momentum operator recently suggested in the study of quantum phase effects. It implies that bound EM field energy and momentum are to be present state functions, too. Being in agreement with reported experiments, these conclusions suggest the necessity to carry out more precise experimental verifications for additional and independent determination of propagation properties of bound EM fields. A scheme of a possible experiment on this subject is also proposed. (shrink)

Empirical research on Rational Choice Theory has brought up two focus of the economics laws problem. On one hand, we find the authors who state that the neoclassical economics laws are explanatory and predictive on specific cases: in transparent contexts in which the standard rationality operates successfully. On the other hand, we find the authors who state that the descriptive theories of the rational choice opens up a research path in which fundamental principles of the neoclassical building could be questioned. (...) Both view points have generated an important standard Rational Choice Theory revision what has produced the so called descriptive view point. It implies understanding that most of the choices take place under risky or uncertainty conditions and, that, these choices are far more complex than the normative Rational Choice Theory supposes. This article's main goal is to expand the descriptive point of view in rational choice, theorizing how some factors, coming from the social and cultural environment, operate within the rational choice. Into space of this research essay we find the debatable question of whether these sort of proposals expands the explanation of the deviation of the rational choice normative theory, and that, of the disturbing causes of the microeconomics laws, or they call into question fundamental principles of these laws and therefore they are opening the possibility to focus some economics issues in a new different manner. (shrink)

Multiple explanatory frameworks may be required to provide an adequate account of human cognition. This paper embeds the classical account within a neural network framework, exploring the encoding of syntacticallystructured objects over the synchronicdiachronic characteristics of networks. Synchronic structure is defined in terms of temporal binding and the superposition of states. To accommodate asymmetric relations, synchronic structure is subject to the type uniqueness constraint. The nature of synchronic structure is shown to underlie Xbar theory that characterizes the phrasal structure (...) of human languages. The derivation differentiates core Xbar properties from languagespecific properties. (shrink)

For three centuries, concepts of the state have been animated by one of the most powerful metaphors in politics: the body politic, a claustrophobic and bounded image of sovereignty. Climate change, neoliberalism, mass migration, and other aspects of the late Anthropocene have increasingly revealed the limitations of this metaphor. Just as the human body is not whole and separate from other bodies--comprising microbes, bacteria, water, and radioactive isotopes--Stefanie R. Fishel argues that the body politic of the state exists in dense (...) entanglement with other communities and forms of life. Drawing on insights from continental philosophy, science and technology studies, and international relations theory, this path-breaking book critiques the concept of the body politic on the grounds of its very materiality. Fishel both redefines and extends the metaphor of the body politic and its role in understanding an increasingly posthuman, globalized world politics. By conceiving of bodies and states as lively vessels, living harmoniously with multiplicity and the biosphere, she argues that a radical shift in metaphors can challenge a politics based on fear to open new forms of global political practice and community. Reframing the concept of the body politic to accommodate greater levels of complexity, Fishel suggests, will result in new configurations for the political and social organization necessary to build a world in which the planet's inhabitants do not merely live but actively thrive. (shrink)

This paper studies the role that known bounds on message transmission times in a computer network play on the evolution of the epistemic state over time. A connection to cones of causal influence analogous to, and more general than, light cones is presented. Focusing on lower bounds on message transmission times, an analysis is presented of how knowledge about when others are guaranteed to be ignorant about an event of interest can arise. This has implications in competitive settings, in which (...) knowing about another’s ignorance can provide an advantage. (shrink)

Bodily sensations are mental states typically suitable to be reported in judgments in which a first-person indexical is used to qualify the felt body. In other words, subjects typically have a sense of bodily ownership for the body that they feel in bodily sensations. This paper puts forward, firstly, three desiderata that theories on the sense of bodily ownership should meet. Secondly, it assesses two views that account for the sense of bodily ownership in terms of the spatial content (...) of bodily sensations, appealing to a notion of a sense of boundedness, and argues that they do not meet the goals defined. (shrink)

This paper exploits the modified simple equation and dynamical system schemes to integrate the Klein–Gordon model amid quadratic nonlinearity arising in nonlinear optics, quantum theories, and solid state physics. By implementing the modified simple equation technique, we develop some disguise adaptation of analytical solutions in terms of hyperbolic, exponential, and trigonometric functions with some special parameters. We apply the dynamical system to bifurcate the model and draw distinct phase portraits on unlike parametric constraints. Following each orbit of all phase portraits, (...) we originate bounded and unbounded solitary, periodic, and periodic rogue-type wave solutions of the KG model. These two schemes extract widespread classes of solitary, periodic, and periodic rogue-type wave solutions for the KG model jointly due to restrictions on parameters. We also analyze the effect of parameters on the obtained wave solutions and discuss why and when it changes its nature. We illustrate some dynamical features of the acquired solutions via the 3D, 2D, and contour graphics. (shrink)

Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of. Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which (...) class='Hi'>states that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model. (shrink)

Distortions in memory impose important bounds on rationality but have been largely disregarded in economics. While it is possible to learn, it is more difficult, and sometimes impossible, to unlearn. This retention effect lowers individual utility directly or via reduced productivity, and adds costs to principal-agent relationships. The engraving effect states that the more one tries to forget a piece of information the more vivid it stays in memory, leading to a paradoxical outcome. The effects are based on, and (...) are supported by, psychological experiments, and it is shown that they are relevant in many economic situations and beyond. (shrink)

Where AR is the set of arithmetic Turing degrees, 0 (ω ) is the least member of { $\mathbf{\alpha}^{(2)}|\mathbf{a}$ is an upper bound on AR}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on HYP, whose hyperjump is the degree of Kleene's O. This paper generalizes this example, using an iteration of the jump operation into the transfinite which is (...) based on results of Jensen and is detailed in [3] and [4]. In $\S1$ we review the basic definitions from [3] which are needed to state the general results. (shrink)

Decision theory seems to offer a very attractive normative framework for individual and social choice under uncertainty. The decisionmaker should think of her choice situation, at any given moment, in terms of a set of possible outcomes, that is, specifications of the possible consequences of choice, described in light of the decisionmaker's goals; a set of possible actions; and a "state set" consisting of possible prior "states of the world." It is this framework for choice which provides the foundation (...) for expected utility theory, as demonstrated in the work of Leonard Savage. Problems arise, however, when the decisionmaker is boundedly rational: when the mental process of thinking about outcomes, actions, and states is itself expensive and time consuming. In the case of the unboundedly rational decisionmaker, decision theory enjoins her to employ maximally specific outcomes; to consider all possible actions; and to use a set of mutually exclusive and collective exhaustive states, each of which is sufficiently finely specified so that each action, together with each state, yields one and only one maximally specific outcome. In the case of the boundedly rational decisionmaker, this procedure is either infeasible or, if feasible, irrational. This paper presents the problem of bounded rationality. It surveys possible solutions, none of which are found to be attractive. And it concludes by discussing the difficulties that the problem of bounded rationality poses for the welfarist program for legal scholarship presented by Louis Kaplow and Steven Shavell in their book, Fairness versus Welfare. (shrink)

The AGM paradigm for belief revision provides a very elegant and powerful framework for reasoning about idealized agents. The paradigm assumes that the modeled agent is a perfect reasoner with infinite memory. In this paper we propose a framework to reason about non-ideal agents that generalizes the AGM paradigm. We first introduce a structure to represent an agent's belief states that distinguishes different status of beliefs according to whether or not they are explicitly represented, whether they are currently active (...) and whether they are fully accepted or provisional. Then we define a set of basic operations that change the status of beliefs and show how these operations can be used to model agents with different capacities. We also show how different operations of belief change described in the literature can be seen as special cases of our theory. (shrink)

Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought of as a restricted subset of all potentially available probabilities. A recent publication (Fuchs and Schack, arXiv:0906.2187v1, 2009) advocates such a representation using symmetric informationally complete (SIC) measurements. Building upon this work we study how this subset—quantum-state space—might be characterized. Our leading characteristic is that the (...) inner products of the probabilities are bounded, a simple condition with nontrivial consequences. To get quantum-state space something more detailed about the extreme points is needed. No definitive characterization is reached, but we see several new interesting features over those in Fuchs and Schack (arXiv:0906.2187v1, 2009), and all in conformity with quantum theory. (shrink)

It has long been known that memory need not be a literal reproduction of the past but may be a constructive process. To say that memory is a constructive process is to say that the encoded content may differ from the retrieved content. At the same time, memory is bound by the authenticity constraint which states that the memory content must be true to the subject's original perception of reality. This paper addresses the question of how the constructive (...) nature of visual memory can be reconciled with the authenticity constraint. In what respect and to what extent may the content of a visual memory differ from the original perceptual state while still adequately reflecting the subject's original perception? (shrink)

Empirical research on Rational Choice Theory has brought up two focus of the economics laws problem. On one hand, we find the authors who state that the neoclassical economics laws are explanatory and predictive on specific cases: in transparent contexts in which the standard rationality operates successfully. On the other hand, we find the authors who state that the descriptive theories of the rational choice opens up a research path in which fundamental principles of the neoclassical building could be questioned. (...) Both view points have generated an important standard Rational Choice Theory revision what has produced the so called descriptive view point . It implies understanding that most of the choices take place under risky or uncertainty conditions and, that, these choices are far more complex than the normative Rational Choice Theory supposes. This article's main goal is to expand the descriptive point of view in rational choice, theorizing how some factors, coming from the social and cultural environment, operate within the rational choice. Into space of this research essay we find the debatable question of whether these sort of proposals expands the explanation of the deviation of the rational choice normative theory, and that, of the disturbing causes of the microeconomics laws, or they call into question fundamental principles of these laws and therefore they are opening the possibility to focus some economics issues in a new different manner. (shrink)

Aiming at a better understanding of the extent to which Africa-focused research has helped develop context-bound, context-specific, and context-free knowledge, the authors present the findings from a literature review of journal articles with an African context. A systematic search resulted in 271 articles with African data and 139 Africa-focused articles published in 63 top business journals and related disciplines from 2010 onwards. The sample included all journals belonging to the University of Texas Dallas and Financial Times research rankings, as (...) well as the main international business, and business and society outlets. An in-depth analysis of the 139 Africa-focused articles shows an important imbalance in terms of publication patterns, topics covered, theoretical groundings, types of contributions, approaches to the African contexts, and empirics. Building on this exhaustive literature review, the authors provide specific suggestions regarding potential data sources and empirical strategies in African contexts, propose avenues for future research, and introduce four recent studies included in the special issue. (shrink)

This paper is concerned with the event-based state and fault estimation problem for a class of linear discrete systems with randomly occurring faults and missing measurements. Different from the static event-based transmission mechanism with a constant threshold, a dynamic event-based mechanism is exploited here to regulate the threshold parameter, thus further reducing the amount of data transmission. Some mutually independent Bernoulli random variables are used to characterize the phenomena of ROFs and missing measurements. In order to simultaneously estimate the system (...) state and the fault signals, the main attention of this paper is paid to the design of recursive filter; for example, for all DETM, ROFs, and missing measurements, an upper bound for the estimation error covariance is ensured and the relevant filter gain matrix is designed by minimizing the obtained upper bound. Moreover, the rigorous mathematical analysis is carried out for the exponential boundedness of the estimation error. It is clear that the developed algorithms are dependent on the threshold parameters and the upper bound together with the probabilities of missing measurements and ROFs. Finally, a numerical example is provided to indicate the effectiveness of the presented estimation schemes. (shrink)

Bennett and Schumacher’s postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch’s model. We show that even a single qubit passing through a postselected CTC (P-CTC) is sufficient to do any postselected quantum measurement with certainty, and we discuss an important difference between “Deutschian” CTCs (D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the present outcome of an experiment. Then, based on a suggestion of Bennett (...) and Smith, we explicitly show how a party assisted by P-CTCs can distinguish a set of linearly independent quantum states, and we prove that it is not possible for such a party to distinguish a set of linearly dependent states. The power of P-CTCs is thus weaker than that of D-CTCs because the Holevo bound still applies to circuits using them, regardless of their ability to conspire in violating the uncertainty principle. We then discuss how different notions of a quantum mixture that are indistinguishable in linear quantum mechanics lead to dramatically differing conclusions in a nonlinear quantum mechanics involving P-CTCs. Finally, we give explicit circuit constructions that can efficiently factor integers, efficiently solve any decision problem in the intersection of NP and coNP, and probabilistically solve any decision problem in NP. These circuits accomplish these tasks with just one qubit traveling back in time, and they exploit the ability of postselected closed timelike curves to create grandfather paradoxes for invalid answers. (shrink)

Weight systems on chord diagrams play a central role in knot theory and Chern-Simons theory; and more recently in stringy quantum gravity. We highlight that the noncommutative algebra of horizontal chord diagrams is canonically a star-algebra, and ask which weight systems are positive with respect to this structure; hence we ask: Which weight systems are quantum states, if horizontal chord diagrams are quantum observables? We observe that the fundamental gl(n)-weight systems on horizontal chord diagrams with N strands may be (...) identified with the Cayley distance kernel at inverse temperature beta=ln(n) on the symmetric group on N elements. In contrast to related kernels like the Mallows kernel, the positivity of the Cayley distance kernel had remained open. We characterize its phases of indefinite, semi-definite and definite positivity, in dependence of the inverse temperature beta; and we prove that the Cayley distance kernel is positive (semi-)definite at beta=ln(n) for all n=1,2,3,... In particular, this proves that all fundamental gl(n)-weight systems are quantum states, and hence so are all their convex combinations. We close with briefly recalling how, under our "Hypothesis H", this result impacts on the identification of bound states of multiple M5-branes. (shrink)

Often, when we are angry, we are angry at someone who has hurt us, and our anger is a protest against our perceived mistreatment. In these cases, its function is to hold the abuser accountable for their offense. The anger involves a demand for some sort of change or response: that the hurt be acknowledged, that the relationship be repaired, that the offending party reform in some way. In this paper, I develop and defend an account of a different form (...) of anger, called "outrage anger". Outrage anger does not aim to hold an abuser accountable, nor to demand repair or reform. Drawing on the work of Maria Lugones, I argue that outrage anger is directed at the state of affairs in which a violation is unintelligible to the dominant moral community. The central function of outrage anger is a psychological boundary setting: it closes off the victim’s ability to feel empathy for their abuser. Outrage has an important role to play in the context of political injustice, but that it also comes with significant costs. (shrink)