Deconstruction both by its friends and enemies has come to be associated with a set of cliches that completely misunderstands its ethical aspiration. It is particularly within the field of law that we can see the ethical force of deconstruction, and also illuminate its concrete and practical importance. In The Philosophy of the Limit Drucilla Cornell examines the relationship of deconstruction to questions of ethics, justice and legal interpretation. She argues that renaming deconstruction "the philosophy of the limit" (...) will allow us to be more precise about what deconstruction actually is philosophically and hence to articulate more clearly its significance for law. Cornell explores the ethical and juridical significance of the so-called postmodern rebellion against metaphysics. A shared ethical rebellion links philosophers as different as Theodor Adorno, Jacques Derrida, Jacques Lacan, and Emmanuel Levinas. Together they present a new ethical configuration, new in its difference from both the critical social theory of J$u$urgen Habermas and the analytic jurisprudence of Nagel and Rawls. A key aspect of this newness is the centrality given to the relationship between questions of ethics and sexual difference. Cornell argues that the appeal of Lacan's analysis to feminists is that it helps to explain the profound hold the gender hierarchy has over Western culture, including its theories of political transformation. Under a Lacanian analysis the law of gender identity will be replicated in the laws of an existing legal system. This means that we cannot hope to sustain legal reforms unless the gender hierarchy is challenged. Cornell examines Derrida's position on the significance of the gender hierarchy in philosophy and explores its ethical and political importance. Derrida's intervention against legal positivism has important implications for the legal reforms necessary to protect marginalized groups. His emphasis on the limit, she argues, is crucial to thosewhose well-being and very lives may depend on legal transformation, women and homosexuals, for example. In an important contribution to legal philosophy, Cornell explores the affinities of Derrida's writings with recent liberal analytic jurisprudence. She also explores the differences. Comparing Rawls's and Derrida's accounts of justice, she argues that Derrida gives greater attention to the necessary utopian moment in his insistence on maintaining the divide between law, established norms, and justice. Cornell's focus on the importance of the limit and the centrality of the gender hierarchy allows her to offer a view of jurisprudence different from both critical social theory and analytic jurisprudence. As we watch the long-fought-for civil rights of women systematically overturned, we have reason to think about how the connections she makes shed light on an underlying truth of our social, political, and legal reality. (shrink)

In this paper, we investigated the effectiveness of price limit on stock market with the correlation study and complex network technology. We proposed a time-migrated DCCA cross-correlation coefficient which is beneficial to detect the asynchronous correlations of nonstationary time series. The stock market network is constructed with the threshold method based on time-migrated DCCA. The effectiveness of the price limit during the stock market crash period is studied based on the time-migrated DCCA stock market network. The results indicate (...) that the time-migrated DCCA ensures more relevant results than the equal-time DCCA method. An interesting finding is that the price limit has different effects on the stock market network at different stages of dynamic evolution. Market stabilization will be lowered and the systemic risk will be increased if the price limit is enhanced. Such studies are relevant for a better understanding of the stock market and have a significant contribution to the stock market in reality. (shrink)

We use the path integral form of quantum electrodynamics to show that a causal classical limit to QED can be derived by functionally integrating over the photon coordinates, starting from an initial photon vacuum and ending in a final coherent radiation state driven by the anticipated classical charged particle trajectories. The resulting charged particle transition amplitude depends only on particle coordinates. When the \ limit is taken, only those particle paths that are not constrained by the final radiation (...) state are varied. These results demonstrate that the collapse from an infinity of charged particle paths, a path integral description, to causally interacting classical trajectories, a stationary-action description, is critically dependent on including final coherent state radiation and maintaining the distinction between particle paths that are free to vary and those trajectories that can be monitored by the final state radiation. (shrink)

In exploring the nature of excess relative to a phenomenology of the limit, _Testing the Limit _ claims that phenomenology itself is an exploration of excess. What does it mean that "the self" is "given"? Should we see it as originary; or rather, in what way is the self engendered from textual practices that transgress—or hover around and therefore within—the threshold of phenomenologial discourse? This is the first book to include Michel Henry in a triangulation with Derrida and (...) Levinas and the first to critique Levinas on the basis of his interpolation of philosophy and religion. Sebbah claims that the textual origins of phenomenology determine, in their temporal rhythms, the nature of the subjectivation on which they focus. He situates these considerations within the broader picture of the state of contemporary French phenomenology, in order to show that these three thinkers share a certain "family resemblance," the identification of which reveals something about the traces of other phenomenological families. It is by testing the limit within the context of traditional phenomenological concerns about the appearance of subjectivity and ipseity that Derrida, Henry, and Levinas radically reconsider phenomenology and that French phenomenology assumes its present form. (shrink)

I argue that it is possible to give an interpretation of the classical ℏ→0 limit of quantum mechanics that results in a partial explanation of the success of classical mechanics. The interpretation...

In this paper, the author turns to Hans-Georg Gadamer’s philosophical hermeneutics to examine the experience of grieving. Specifically, the author argues that grieving may be grasped as a limit situation of memory. This approach suggests that grieving cannot be adequately captured by a stage model theory but, instead, poses an infinite task that is fraught with difficulty and ethical demands. The author develops this approach in reference not only to Hans-Georg Gadamer but recent research by Nancy Moules and Kate (...) Beamer. (shrink)

This entry explores Charles Peirce's account of truth in terms of the end or ‘limit’ of inquiry. This account is distinct from – and arguably more objectivist than – views of truth found in other pragmatists such as James and Rorty. The roots of the account in mathematical concepts is explored, and it is defended from objections that it is (i) incoherent, (ii) in its faith in convergence, too realist and (iii) in its ‘internal realism’, not realist enough.

This article revisits a principle of distributive justice accepted by most, if not all, scholars of climate justice. The principle at stake, the limit, protects those who are very badly off from bearing the costs of climate change mitigation. The persistent noncompliance of developed states with their obligations toward burden sharing, however, means that this principle is increasingly in tension with successful climate change mitigation, given it seems to require that those in poverty have continued access to emissions in (...) cases where alternative forms of energy are not provided. In the first half of the paper I outline this tension and show how the dominant expression of the limit in the literature, advanced by Henry Shue, must be abandoned. I argue that any attempt to articulate the limit in current circumstance, where the carbon budget is very scarce, must consider the climate harm associated with continued subsistence emissions. The second half of the article defends a principle, the exemption, which is best able to maintain the strong commitment to shielding those below the minimal threshold from the costs of mitigation, even in light of the potential harm that will result if they require emissions to fuel their energy needs. (shrink)

We claim that the Universe’s fundamental structure is not discoverable through rationalism. The various frameworks studied are logic, mathematics, their application through theories in physics, and finally, the pivotally separate application of logic to historical evidence in formal religious belief. The basis of the prohibition is that rational structure has a limit for consistency that falls short of completeness in absolute terms. The limit of observability reaches only a framework in which correlated elements are formed paradoxically within a (...) parent structure. Apart from our advanced ability in human reasoning, we have the same fundamental sentience possessed by other living creatures. Beyond that limit of awareness, the Universe in its native form is immaculately nonordered. We examine the dimensional relationship between quantum and classical frameworks to justify the theory. Mathematics requires operational consistency across its elements. In contrast, the Universe incorporates a feature of inconsistency in its native form. The companion paper to this document examines in detail how complexity develops from a null condition across dimensional levels. The argument’s foundation applies a general framework of stationary action and self-organization principles to the theory and experimental data on Hardy’s paradox. The complementary format to the dichotomy of paradoxical elements is its sliding scale of uncertainty between their extremes. The argument extends that the root source of societal biases, conflicts, and bigotries is the fundamental and systemic mechanism of paradox. (shrink)

Inspired by recent work on proof theory for modal logic, this paper develops a cut-free labelled sequent calculus obtained by imitating Herzberger’s limit rule for revision sequences as a clause in a possible world semantics. With the help of two completeness theorems, one between the labelled sequent calculus and the corresponding possible world semantics, and one between the axiomatic theory of truth PosFS and a neighbourhood semantics, together with the proof of the equivalence between the two semantics, we show (...) that the theory of truth obtained with the labelled sequent calculus based on Herzberger’s limit rule is equivalent to PosFS. (shrink)

At what point can we concede that the realities of world politics require that moral principles be compromised, and how do we know when a real ethical limit has been reached? This volume gathers leading constructivist scholars to explore the issue of moral limit and possibility in global political dilemmas. The contributors examine pressing ethical challenges such as sanctions, humanitarian intervention, torture, the self-determination of indigenous peoples, immigration, and the debate about international criminal tribunals and amnesties in cases (...) of atrocity. Their analyses entail theoretical and empirical claims about the conditions of possibility and limits of moral change in world politics, therefore providing insightful leverage on the ethical question of 'what ought we to do?' This is a valuable contribution to the growing field of normative theory in International Relations and will appeal to scholars and advanced students of international ethics and political theory. (shrink)

This paper deals with the metaphysics of the notion of quantity in the philosophy of Leibniz, and its aim is to defend the following bi-conditional: for any object x, x has a certain quantity if and only if x has a (metaphysical) limit or a bound. The direction from left to right is justified in §3, while in §4 I develop an argument to justify the direction from right to left. Since the bi-conditional links the metaphysical notion of (...) class='Hi'>limit to the mathematical notion of quantity (and in this way it links Leibniz’s metaphysics with his conception of Mathesis Universalis), it allows the use of metaphysics to clarify the features of the mathematical notion of quantity. This task is accomplished in §5 and §6. Finally, §7 discusses a possible objection. (shrink)

The overall aim of this article is to discuss the organization of limit setting in healthcare in terms of legitimacy. We argue there is a strong ethical demand that such processes should be arranged to provide adversely affected people well-justified reasons to confer legitimacy to the processes despite favouring a different decision-making outcome. Two increasingly popular approaches, Accountability for Reasonableness (A4R) and Multi-Criteria Decision Analysis (MCDA), can both be applied to support legitimate decision-making processes. However, the role played by (...) ‘fair-minded people’ in the A4R framework can be shown to undermine an adequate conceptualization of legitimacy according to the ethical demand. We discuss and specify conditions enabling A4R to meet this ethical demand when being implemented in a real-world setting without having to renounce the aim of striving for ‘reasonableness’ and impartiality. The methodological approach MCDA describes how to arrange for transparent resource allocation. This approach does not encompass any normative guidance on how to shape limit settings in terms of ‘reasonableness’; it basically promotes ‘rational’ decisions. We discuss how this practical methodology can be integrated with the theoretical A4R framework to meet the ethical demand while at the same time promoting politically required impartiality of healthcare limit setting. (shrink)

Central limit theorem for the functional of jump Markov process. Nguyễn Văn Hữu, Vương Quân Hoàng và Trần Minh Ngọc. Báo cáo: Hội nghị toàn quốc lần thứ III “Xác suất - Thống kê: Nghiên cứu, ứng dụng và giảng dạy” (tr. 34). Ba Vì, Hà Tây, ngày 12-14 tháng 05 năm 2005. Viện Toán học / Trường Đại học Khoa học tự nhiên / Đại học Quốc gia Hà Nội.

We present an experimental test of the validity of the Pauli Exclusion Principle for electrons based on the concept put forward a few years ago by Ramberg and Snow. In this experiment we perform a very accurate search of X-rays from the Pauli-forbidden atomic transitions of electrons in the already filled 1S shells of copper atoms. Although the experiment has a simple structure, it poses deep conceptual and interpretational problems. Here we describe the experimental method and recent experimental results, which (...) we interpret as an upper limit for the probability to violate the Pauli Exclusion Principle. We present also future plans to upgrade the experimental apparatus using Silicon Drift Detectors. (shrink)

This article seeks to recover a neglected chapter in the historical and theoretical background of social theory in general and critical theory in particular with a view to refining the understanding of the presuppositions of a cognitively enhanced critical social science appropriate to our troubled times. For this purpose, it offers a brief reconstruction of the mathematical-philosophical tradition from ancient to modern times by extrapolating that part of it that is marked by the ideas of infinity, infinite processes and (...) class='Hi'>limit concepts. It gives suggestive indications not only of how these ideas relate to extant social-theoretical thought, but especially also of the two related cognitive directions – the weak-naturalistic and the socio-cultural – in which such thought is currently challenged to go. (shrink)

For an observation time equal to the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at mH=1.35×10-69\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{H}=1.35 \times 10^{-69}$$\end{document} kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to mH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{H}$$\end{document} is, and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, (...) is equated to the luminosity distance dH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H}$$\end{document} which corresponds to a red shift zH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}$$\end{document}. When using the Concordance-Model parameters, we get dH=8.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H} = 8.4$$\end{document} Gpc and zH=1.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}=1.3$$\end{document}. Remarkably, dH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H}$$\end{document} falls quite short to the radius of the observable universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond zH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}$$\end{document}. Finally, in terms of quantum quantities, the expansion constant H0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_0$$\end{document} reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant. (shrink)

‘The mathematisation of time has limits,’ writes Derrida in ‘Ousia and Gramme.’ Taking this quote in all possible senses, this paper considers Derrida’s definition of limit as gramme, trace, and ap...

Let K denote prefix-free Kolmogorov complexity, and let $K^A$ denote it relative to an oracle A. We show that for any n, $K^{\emptyset ^{(n)}}$ is definable purely in terms of the unrelativized notion K. It was already known that 2-randomness is definable in terms of K (and plain complexity C) as those reals which infinitely often have maximal complexity. We can use our characterization to show that n-randomness is definable purely in terms of K. To do this we extend a (...) certain “limsup” formula from the literature, and apply Symmetry of Information. This extension entails a novel use of semilow sets, and a more precise analysis of the complexity of $\Delta _2^0$ sets of minimal descriptions. (shrink)

This essay deals with Habermas’ concept of truth in his late theoretical philosophy. Assuming his suggestive yet highly inspiring inauguration of a cognitive turn in Critical Theory, it probes his use of the notion of limit concept against the background of the tradition of thought from which it originally derives with the intention of identifying the notion’s potential for taking this promising departure further. It brings to the fore a number of issues in his late writings that reveal the (...) presence of what may be considered the problem of limit concepts in his thought. For present purposes, these issues are located in two areas: Habermas’ revision of his long-held concept of truth and the related criticism of Peirce; and his account of the role of limit concepts like truth and warranted assertibility or rational acceptability in processes of discursive justification. The analysis finds that there is a structural deficit in his presentation that could be filled by cognitively conceived cultural structures that not only correspond to the major types of limit concepts, but also answer to his undeveloped vision of the ‘cultural embodiment of reason’. (shrink)

Resurgent interest in both mechanistic and counterfactual theories of explanation has led to a fair amount of discussion regarding the relative merits of these two approaches. James Woodward is currently the pre-eminent counterfactual theorist, and he criticizes the mechanists on the following grounds: Unless mechanists about explanation invoke counterfactuals, they cannot make sense of claims about causal interactions between mechanism parts or of causal explanations put forward absent knowledge of productive mechanisms. He claims that these shortfalls can be offset if (...) mechanists will just borrow key tenets of his counterfactual theory of causal claims. What mechanists must bear in mind, however, is that by pursuing this course they risk both the assimilation of the mechanistic theories of explanation into Woodward’s own favored counterfactual theory, and they risk the marginalization of mechanistic explanations to a proper subset of all explanations. An outcome more favorable to mechanists might be had by pursuing an actualist-mechanist theory of the contents of causal claims. While it may not seem obvious at first blush that such an approach is workable, even in principle, recent empirical research into causal perception, causal belief, and mechanical reasoning provides some grounds for optimism. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Limit Formations:Violence, Philosophy, RhetoricOmedi Ochieng For Megha Sharma SehdevNow days are dragon-ridden, the nightmareRides upon sleep: a drunken soldieryCan leave the mother, murdered at her door,To crawl in her own blood, and go scot-free;The night can sweat with terror as beforeWe pieced our thoughts into philosophy,And planned to bring the world under a rule,Who are but weasels fighting in a hole.—W. B. Yeats, "Nineteen Hundred and Nineteen"Violence is (...) a limit formation. It is neither reducible to a brute fact nor is it ineffably ethereal. To write about violence, then, is to confront—if only as disavowed remainder—critical limits, no less of the writer than of the writing itself. Fewer subjects have proven as confounding for philosophy and rhetoric, this journal's primary charge. In both its general particulars and its specific manifolds, violence nonpluses philosophical commonplaces, upends rhetorical tropologies.Philosophy imagines itself mediator to reality's arche, the bedrock of being. Ancient Greek philosophy sought to distinguish necessity from contingency, essence from accident, dialectic from rhetoric, logic from fallacy. Those who took up this intellectual tradition came to conceptualize violence as first and foremost a question of "nature"—more specifically, those marked out by nature to rule (propertied male citizens) and those marked [End Page 330] out by nature for subjection (the enslaved, women, nonhuman animals). In the early modern context of European philosophy, still, despite its pretensions, deeply indebted to this Mediterranean legacy, the canonical lexicon of sensemaking centered on legitimacy and its conceptual appurtenances of sovereignty, will, and rights.Strikingly, it is in the opposed registers of analytic and continental philosophy that violence's cataphilosophic figuration appears most salient. Consider, for example, one such famous symposium convened in the analytic journal Philosophy and Public Affairs, as narrated by political philosopher Michael Walzer:In an earlier issue of Philosophy & Public Affairs there appeared a symposium on the rules of war which was actually (or at least more importantly) a symposium on another topic. The actual topic was whether or not a man can ever face, or ever has to face, a moral dilemma, a situation where he must choose between two courses of action both of which it would be wrong for him to undertake. Thomas Nagel worriedly suggested that this could happen and that it did happen whenever someone was forced to choose between upholding an important moral principle and avoiding some looming disaster. R. B. Brandt argued that it could not possibly happen, for there were guidelines we might follow and calculations we might go through which would necessarily yield the conclusion that one or the other course of action was the right one to undertake in the circumstances (or that it did not matter which we undertook). R. M. Hare explained how it was that someone might wrongly suppose that he was faced with a moral dilemma: sometimes, he suggested, the precepts and principles of an ordinary man, the products of his moral education, come into conflict with injunctions developed at a higher level of moral discourse. But this conflict is, or ought to be, resolved at the higher level; there is no real dilemma.(1973, 160–61)Analytic political philosophy's resolute disavowals could not be here better splayed. Morality is construed as all-encompassing. The political is not so much effaced as it is rendered derivative to a foundational drama of will, obligation, choice. Analytic philosophy's oft-preened claim to clear, transparent, terse style proves constitutive of its desire to contain, if it cannot altogether moralize away violence. [End Page 331]Where analytic philosophy conceives of violence as an object, its limits defined by morality's handmaiden, the "well-ordered society" (Rawls 2001, 8), continental philosophy conjures a sublime violence that shatters and transfigures normative violence. Walter Benjamin posits a binary opposition between mythical and divine violence: "If mythical violence is lawmaking, divine violence is law-destroying; if the former sets boundaries, the latter boundlessly destroys them; if mythical violence brings at once guilt and retribution, divine power only expiates, if the former threatens, the latter strikes, if the former is bloody, the latter is lethal without spilling... (shrink)

BackgroundThe Dutch Euthanasia Act applies to patients 12 years and older, which makes euthanasia for minors younger than 12 legally impossible. The issue under discussion specifically regards the capacity of minors to request euthanasia.ObjectiveGain insight in paediatric experts’ views about which criteria are important to assess capacity, from what age minors can meet those criteria, what an assessment procedure should look like and what role parents should have.MethodsA Delphi study with 16 experts (paediatricians, paediatric nurses and paediatric psychologists) who work (...) in Children Comfort Teams in Dutch academic hospitals. The questionnaire contained statements concerning criteria for capacity and procedural criteria. Consensus was defined as ≥80% agreement.ResultsThe experts agreed that five criteria for capacity, found in a previous literature study, are all important. They agreed that some children between ages 9 and 11 could meet all the criteria. Consensus was reached for the statements that the entire medical team should be involved in the decision making and that a second independent expert must assess the case. Experts agreed that the parents’ opinion is relevant and should always be taken into account, but it need not be decisive.ConclusionThis study shows that the age limit of 12 years in the Dutch Euthanasia Act is too strong according to paediatric experts. Letting go of the age limit or lowering the age limit combined with adequate capacity assessment for minors younger than 12 are options that should be discussed further. (shrink)

The application of the maximum entropy principle to determine probabilities on finite domains is well-understood. Its application to infinite domains still lacks a well-studied comprehensive approach. There are two different strategies for applying the maximum entropy principle on first-order predicate languages: applying it to finite sublanguages and taking a limit; comparing finite entropies of probability functions defined on the language as a whole. The entropy-limit conjecture roughly says that these two strategies result in the same probabilities. While the (...) conjecture is known to hold for monadic languages as well as for premiss sentences containing only existential or only universal quantifiers, its status for premiss sentences of greater quantifier complexity is, in general, unknown. I here show that the first approach fails to provide a sensible answer for some \-premiss sentences. I discuss implications of this failure for the first strategy and consequences for the entropy-limit conjecture. (shrink)

This paper examines the accounts of limit decision advanced by Hervaeus Natalis and Durand of St. Pourçain in their respective discussions of the sanctification of the Blessed Virgin. Hervaeus and Durand argue, against Aristotle, that the temporal limits of certain changes, including Mary’s sanctification, should be assigned in discrete rather than continuous time. The paper first considers Hervaeus’ discussion of limit decision and argues that, for Hervaeus, a solution of temporal limits in terms of discrete time can coexist (...) with an Aristotelian continuous time solution because Hervaeus takes continuous and discrete time to be two non-intersecting, but correlated time-series. The paper next examines Durand’s account of limit decision and argues that Durand rejects Hervaeus’ correlation assumption as well as Aristotle’s continuous time solution. (shrink)

In his pioneering work in the field of inductive inference, Gold (Inf Control 10:447–474, 1967) proved that a set containing all finite languages and at least one infinite language over the same fixed alphabet is not identifiable in the limit (learnable in the exact sense) from complete texts. Gold’s work paved the way for computational learning theories of language and has implications for two linguistically relevant classes in the Chomsky hierarchy (cf. Chomsky in Inf Control 2:137–167, 1959, Chomsky in (...) Knowledge of language: its nature, origin, and use, Praeger, 1986; Shieber in Linguist Philos 8:333–343, 1985; Heinz in Linguist Inq 41:623–661, 2010). Within that same framework, Angluin (Inf Control 45:117–135, 1980) provided a complete characterization for the learnability of language families. Mathematically, the concept of identification in the limit from that classical setting can be seen as the use of a particular type of metric for learning in the limit (Wharton in Inf Control 26:236–255, 1974). In this research note, I use Niyogi’s extended version of a theorem by Blum and Blum (Inf Control 28:125–155, 1975) on the existence of locking data sets to prove a necessary condition for learnability in the limit of any family of languages with the Gold property in any given metric. This recovers the most general version of Gold’s Theorem as a particular case. Moreover, when the language family is further assumed to contain all finite languages, the same condition also becomes sufficient for learnability in the limit. Finally, we discuss questions that are left open and outline a research program regarding language learnability in the limit from other input types and cognitive feasibility. (shrink)

In this paper I establish a normative limit of spectator interaction. I argue that attempts by non-participants (e.g. spectators) to affect the outcome of a contest, whether intended or merely foreseeable, are unsporting and ought to be discouraged because they undermine fairness, which is a fundamental premise of ideal competition. Because this is at odds with the participatory ethos of contemporary sports fanaticism (e.g. ?12th man? campaigns, visual distractions by spectators, etcetera) I anticipate several potential objections. I refute concerns (...) that my thesis is empirically dubious; that it is impractical; that it is subordinate to financial considerations; that it is nullified by participant acquiescence; and that it is subordinate to spectator interests. (shrink)

Educational philosophy has not discussed Foucault’s publications on the Iranian Revolution and the related controversy. Foucauldian concepts are applied to education, though his only writings which ‘sidetracked’ him from exploring power within the state, namely, his journalistic accounts of his visits to Iran, remain unexplored in our field. Against moralist accusations of Foucault’s views on Iran as ‘singularly uncritical’, and beyond standard postcolonial charges of Foucault with exoticism and orientalism, I examine how the writings in question reveal ambivalences and limits (...) of Foucauldian philosophy and complicate the glorification of limit-experience in educational theory. (shrink)

This paper considers states on the Weyl algebra of the canonical commutation relations over the phase space R^{2n}. We show that a state is regular iff its classical limit is a countably additive Borel probability measure on R^{2n}. It follows that one can "reduce" the state space of the Weyl algebra by altering the collection of quantum mechanical observables so that all states are ones whose classical limit is physical.

We study the arithmetical schema asserting that every eventually decreasing elementary recursive function has a limit. Some other related principles are also formulated. We establish their relationship with restricted parameter-free induction schemata. We also prove that the same principle, formulated as an inference rule, provides an axiomatization of the Σ2-consequences of IΣ1.Using these results we show that ILM is the logic of Π1-conservativity of any reasonable extension of parameter-free Π1-induction schema. This result, however, cannot be much improved: by adapting (...) a theorem of D. Zambella and G. Mints we show that the logic of Π1-conservativity of primitive recursive arithmetic properly extends ILM.In the third part of the paper we give an ordinal classification of -consequences of the standard fragments of Peano arithmetic in terms of reflection principles. This is interesting in view of the general program of ordinal analysis of theories, which in the most standard cases classifies Π-classes of sentences. (shrink)

There are basically four options to which state the limiting instant in a change from one state to its opposite belongs – only the first, only the second, both or none. This situation is usually referred to as the limit decision problem since all of these options seem troublesome: The first two alleged solutions are asymmetric and thus need something to ground this asymmetry in ; while the last two options leave the realm of classical logic. I argue that (...) including the debate about dispositions enables new options for solutions to the temporal limit decision problem. Metaphysical considerations function as a symmetry-breaker and thus remove the need for a non-classical solution. Dispositions bring about the changes in the world, so they constitute the metaphysical background for the instant of change. In particular, I argue that according to the triadic process account of dispositions, the limiting instant belongs to the second interval and only the second interval. (shrink)

L S Penrose’s Limit Theorem – which is implicit in Penrose [7, p. 72] and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely and the relative quota is pegged, then – under certain conditions – the ratio between the voting powers of any two voters converges to the ratio between their weights. Lindner and Machover [4] prove some special cases of Penrose’s Limit Theorem. They (...) give a simple counter-example showing that the theorem does not hold in general even under the conditions assumed by Penrose; but they conjecture, in effect, that under rather general conditions it holds ‘almost always’ – that is with probability 1 – for large classes of weighted voting games, for various values of the quota, and with respect to several measures of voting power. We use simulation to test this conjecture. It is corroborated with respect to the Penrose–Banzhaf index for a quota of 50% but not for other values; with respect to the Shapley–Shubik index the conjecture is corroborated for all values of the quota. (shrink)

In exploring the nature of excess relative to a phenomenology of the limit, Testing the Limit claims that phenomenology itself is an exploration of excess. What does it mean that "the self" is "given"? Should we see it as originary; or rather, in what way is the self engendered from textual practices that transgress—or hover around and therefore within—the threshold of phenomenologial discourse? This is the first book to include Michel Henry in a triangulation with Derrida and Levinas (...) and the first to critique Levinas on the basis of his interpolation of philosophy and religion. Sebbah claims that the textual origins of phenomenology determine, in their temporal rhythms, the nature of the subjectivation on which they focus. He situates these considerations within the broader picture of the state of contemporary French phenomenology (chiefly the legacy of Merleau-Ponty), in order to show that these three thinkers share a certain "family resemblance," the identification of which reveals something about the traces of other phenomenological families. It is by testing the limit within the context of traditional phenomenological concerns about the appearance of subjectivity and ipseity that Derrida, Henry, and Levinas radically reconsider phenomenology and that French phenomenology assumes its present form. (shrink)

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing (...) real objects in an observer-independent way. (shrink)

This paper presents an ontological perspective that enables evaluating the effectiveness of business models from an integrative worldview. Different groups’ fragmented and reductionist views on this topic create a dichotomy that makes it difficult to compare and analyze them in practice. Such groups use different values for some components, which may result in neglecting others and their interrelationship. This study discusses a functional characteristic of business models that academia still needs to address. It explores new frontiers in the field, such (...) as business models for networks, sustainability, and their practical evaluation. To achieve an integrative ontology and avoid focusing on specific constructs or systems at the expense of others, we draw upon the theory of worldviews from Wilhelm Dilthey, reformational philosophy, and Herman Dooyeweerd’s theory of modal aspects. Society should move beyond dualistic thinking and embrace practical and applicable solutions. To help companies develop effective models, we introduce a new business model framework based on an integrative worldview that enables comparisons and evaluations of companies in practice. Creating competitive advantages and value appropriations synergizes with essential aspects of reformational philosophy. Analyzing and interrelating such elements are fundamental to understanding the real applied value of business models. (shrink)

On Foucault’s own telling, his distinctive approach to critique is to be characterized as a ‘limit attitude’. Definitive of this limit attitude is a problematizing, transgressive style of thinking oriented toward challenging existing ways of being and doing, with a view to liberating new possibilities for advancing ‘the undefined work of freedom’. From the outset, however, the efficacy of this problematizing approach to critique has been beset by doubts about the adequacy of its normative resources. In the present (...) article, it is argued that progress can be made toward a productive resolution of this contested issue if adequate account is taken of both the Nietzschean and the Kantian dimensions of Foucault’s thought. Specifically, it is argued that the balance between these potentially conflictual elements must be appropriately (re)negotiated, if the normative efficacy of Foucauldian critique is to be ensured, while its distinctive problematizing thrust is preserved. In defending this view, the Foucauldian concept of autonomy is seen to have a pivotal role to play both in advancing the task of problematization and, in its relation to intersubjectivity, in securing its normative efficacy. In thus vindicating the integrity of Foucault’s distinctive approach to critique, new light is shed on the structure, dynamics and logic of a contemporary mode of inquiry committed to the problematizing exercise of critical reason. (shrink)

Bohmian mechanics is a realistic interpretation of quantum theory. It shares the same ontology of classical mechanics: particles following continuous trajectories in space through time. For this ontological continuity, it seems to be a good candidate for recovering the classical limit of quantum theory. Indeed, in a Bohmian framework, the issue of the classical limit reduces to showing how classical trajectories can emerge from Bohmian ones, under specific classicality assumptions. In this paper, we shall focus on a technical (...) problem that arises from the dynamics of a Bohmian system in bounded regions; and we suggest that a possible solution is supplied by the action of environmental decoherence. However, we shall show that, in order to implement decoherence in a Bohmian framework, a stronger condition is required rather than the usual one. (shrink)

Discussions of loyalty typically focus on its alleged tendency to encourage pernicious attachments to collectivities. The present article intervenes in these discussions by asking how considerations of loyalty in limit-situations (Karl Jaspers) might illuminate neglected ethico-political intricacies. Rather than suggesting that loyalty, independently of circumstances, is always a virtue or a vice this article explores how loyalty’s complex synergies in limit-situations sometimes advance rather than oppose cosmopolitan justice. This perspective, I claim, helps us see that, instead of always (...) making us partial, as many contemporary discourses on loyalty assume, loyalty sometimes makes us partisan in an ethico-politically enabling sense. (shrink)

This major new work by Anthony J. Steinbock, a leading authority in Phenomenology and Husserl Studies, explores an interrelated set of problems in Husserl's phenomenology and provides an excellent example of phenomenology in practice, demonstrating how its methods and resources shed light on philosophical problems.