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)

There may be a limit on our capacity to suppress anthropocentric tendencies toward non-human others. Normally, we do not reach this limit in our dealings with animals, the environment, etc. Thus, continued striving to overcome anthropocentrism when confronted with these non-human others may be justified. Anticipation of super artificial intelligence may force us to face this limit, denying us the ability to free ourselves completely of anthropocentrism. This could be for our own good.

I analyze the role of infinite idealizations used in the renormalization group (RG hereafter) method in explaining universality across microscopically different physical systems in critical phenomena. I argue that despite the reference to infinite limit systems such as systems with infinite correlation lengths during the RG process, the key to explaining universality in critical phenomena need not involve infinite limit systems. I develop my argument by introducing what I regard as the explanatorily relevant property in RG explanations: linearization* (...) property; I then motivate and prove a proposition about the linearization* property in support of my view. As a result, infinite limit systems in RG explanations are dispensable. (shrink)

BackgroundThis article explores the reasons in favour of revising and extending the current 14-day statutory limit to maintaining human embryos in culture. This limit is enshrined in law in over a dozen countries, including the United Kingdom. In two recently published studies, scientists have shown that embryos can be sustained in vitro for about 13 days after fertilisation. Positive reactions to these results have gone hand in hand with calls for revising the 14-day rule, which only allows embryo (...) research until the 14th day after fertilisation.Main textThe article explores the most prominent arguments in favour of and against the extension of the 14-day limit for conducting research on human embryos. It situates these arguments within the history of the 14-day limit. I start by discussing the history of the 14-day limit in the United Kingdom and the reasons behind the decision to opt for a compromise between competing moral views. I then analyse the arguments that those who are generally in favour of embryo research put forward in support of extending the 14-day rule, namely the argument of the beneficence of research and the argument of technical feasibility. I then show how these two arguments played a role in the recent approval of two novel techniques for the replacement of faulty mitochondrial DNA in the United Kingdom. Despite the popularity and widespread use of these arguments, I argue that they are ultimately problematic and should not be straightforwardly accepted. I end by making a case for respecting value pluralism in the context of embryo research, and I present two reasons in favour of respecting value pluralism: the argument of public trust and the argument of democracy.ConclusionI argue that 14-day limit for embryo research is not a valuable tool despite being a solution of compromise, but rather because of it. The importance of respecting value pluralism needs to be considered in any evaluation concerning a potential change to the 14-day rule. (shrink)

This article asks how can we articulate the limit of artificial intelligence, which virtually has no limit? Or maybe the definition of AI already implies its limit, how Marvin Minsky once declared that there is no generally accepted theory of intelligence, and that AI is only one particular way of modelling it. This article revisits the debate between Minsky and Hubert Dreyfus and repositions them in terms of an opposition between mechanism and organism, in order to expose (...) the limit of Dreyfus’s Heideggerian critique. It suggests reflecting on the relation between noodiversity and technodiversity to methodologically broaden the concept of intelligence, and on how different concepts of intelligence could be thought by introducing the Chinese philosopher Mou Zongsan’s interpretation of Kant’s intellectual intuition. (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...

The structure and style of philosophy has evolved in response to philosophy's confrontation with its own limits. Are these limits real or are they just phantoms haunting the philosophical project? How do philosophy and philosophers attempt to overcome these limits, or at least come to terms with them? In "Philosophy at the Limit" David Wood pursues this theme in modern philosophers from Hegel to Derrida including Nietzsche, Wittgenstein, Heidegger and Gadamer. He focuses on questions of philosophical style, problems with (...) dialogue and in direct communication, the structural closure of philosophical texts, and performative strategy in philosophy. "Philosophy at the Limit" is an accessible discussion of some of the complex issues that empower continental philosophy. It may appeal to students of philosophy and contemporary thought at every level, and to the general reader interested in the heart of the current debates in European thought. (shrink)

The maximum entropy principle is widely used to determine non-committal probabilities on a finite domain, subject to a set of constraints, but its application to continuous domains is notoriously problematic. This paper concerns an intermediate case, where the domain is a first-order predicate language. Two strategies have been put forward for applying the maximum entropy principle on such a domain: applying it to finite sublanguages and taking the pointwise limit of the resulting probabilities as the size n of the (...) sublanguage increases; selecting a probability function on the language as a whole whose entropy on finite sublanguages of size n is not dominated by that of any other probability function for sufficiently large n. The entropy-limit conjecture says that, where these two approaches yield determinate probabilities, the two methods yield the same probabilities. If this conjecture is found to be true, it would provide a boost to the project of seeking a single canonical inductive logic—a project which faltered when Carnap's attempts in this direction succeeded only in determining a continuum of inductive methods. The truth of the conjecture would also boost the project of providing a canonical characterisation of normal or default models of first-order theories. Hitherto, the entropy-limit conjecture has been verified for languages which contain only unary predicate symbols and also for the case in which the constraints can be captured by a categorical statement of quantifier complexity. This paper shows that the entropy-limit conjecture also holds for categorical statements of complexity, for various non-categorical constraints, and in certain other general situations. (shrink)

In this paper, we examine the limit of applicability of Gödel’s first incompleteness theorem. We first define the notion “$\textsf {G1}$ holds for the theory $T$”. This paper is motivated by the following question: can we find a theory with a minimal degree of interpretation for which $\textsf {G1}$ holds. To approach this question, we first examine the following question: is there a theory T such that Robinson’s $\mathbf {R}$ interprets T but T does not interpret $\mathbf {R}$ and (...) $\textsf {G1}$ holds for T? In this paper, we show that there are many such theories based on Jeřábek’s work using some model theory. We prove that for each recursively inseparable pair $\langle A,B\rangle $, we can construct a r.e. theory $U_{\langle A,B\rangle }$ such that $U_{\langle A,B\rangle }$ is weaker than $\mathbf {R}$ w.r.t. interpretation and $\textsf {G1}$ holds for $U_{\langle A,B\rangle }$. As a corollary, we answer a question from Albert Visser. Moreover, we prove that for any Turing degree $\mathbf {0}< \mathbf {d}<\mathbf {0}^{\prime }$, there is a theory T with Turing degree $\mathbf {d}$ such that $\textsf {G1}$ holds for T and T is weaker than $\mathbf {R}$ w.r.t. Turing reducibility. As a corollary, based on Shoenfield’s work using some recursion theory, we show that there is no theory with a minimal degree of Turing reducibility for which $\textsf {G1}$ holds. (shrink)

Countries that abolished donor anonymity have imposed age limits for access to certain types of information by donor offspring. In the UK and the Netherlands, a debate has started on whether these age limits should be lowered or abolished all together. This article presents some arguments against lowering the age limits as a general rule for all donor children. The focus is on whether one should give a child the right to obtain the identity of the donor at an earlier (...) age than is presently stipulated. The first argument is that there is no evidence that a change in age will increase the total well-being of the donor offspring as a group. The second argument stresses that the rights language used for the donor-conceived child isolates the child from his or her family and this is unlikely to be in the best interest of the child. Finally, lowering the age limit reintroduces the genetic father in the family and expresses the bionormative ideology that contradicts gamete donation as a practice. (shrink)

In his speech at the University of Dakar in July 2007, the French president Nicolas Sarkozy referred to Africa as the continent that has not yet fully entered history. This article takes this obvious reference to Hegel as its starting point and examines the current significance of ‘Hegel’s Africa’. Through a close reading of The Philosophy of History and The Phenomenology of Spirit, it shows that Hegel’s remarks on Africa are by no means incidental. They constitute rem(a)inders of a modernity (...) that is based on the construction of Africa as its own limit. The return of Hegel’s Africa, the article concludes, can thus not be restricted to a problem of the new European right. It is part of an understanding of modernity that remains haunted by the specters of racism. (shrink)

We argue against claims that the classical ℏ → 0 limit is “singular” in a way that frustrates an eliminative reduction of classical to quantum physics. We show one precise sense in which quantum mechanics and scaling behavior can be used to recover classical mechanics exactly, without making prior reference to the classical theory. To do so, we use the tools of strict deformation quantization, which provides a rigorous way to capture the ℏ → 0 limit. We then (...) use the tools of category theory to demonstrate one way that this reduction is explanatory: it illustrates a sense in which the structure of quantum mechanics determines that of classical mechanics. (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 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)

The sciences occasionally generate discoveries that undermine their own assumptions. Two such discoveries are characterized here: the discovery of apophenia by cognitive psychology and the discovery that physical systems cannot be locally bounded within quantum theory. It is shown that such discoveries have a common structure and that this common structure is an instance of Priest’s well-known Inclosure Schema. This demonstrates that science itself is dialetheic: it generates limit paradoxes. How science proceeds despite this fact is briefly discussed, as (...) is the connection between our results and the realism-antirealism debate. We conclude by suggesting a position of epistemic modesty. (shrink)

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)

Work in the setting of the recursively enumerable sets and their Turing degrees. A set X is low if X', its Turning jump, is recursive in $\varnothing'$ and high if X' computes $\varnothing''$ . Attempting to find a property between being low and being recursive, Bickford and Mills produced the following definition. W is deep, if for each recursively enumerable set A, the jump of $A \bigoplus W$ is recursive in the jump of A. We prove that there are no (...) deep degrees other than the recursive one. Given a set W, we enumerate a set A and approximate its jump. The construction of A is governed by strategies, indexed by the Turning functionals Φ. Simplifying the situation, a typical strategy converts a failure to recursively compute W into a constraint on the enumeration of A, so that $(W \bigoplus A)'$ is forced to disagree with Φ(-; A'). The conversion has some ambiguity; in particular, A cannot be found uniformly from W. We also show that there is a "moderately" deep degree: There is a low nonzero degree whose join with any other low degree is not high. (shrink)

Some conditions are given to ensure that for a jump homogeneous Markov process $\{X(t),t\ge 0\}$ the law of the integral functional of the process $T^{-1/2} \int^T_0\varphi(X(t))dt$ converges to the normal law $N(0,\sigma^2)$ as $T\to \infty$, where $\varphi$ is a mapping from the state space $E$ into $\bbfR$.

How much value can our decisions create? We argue that unless our current understanding of physics is wrong in fairly fundamental ways, there exists an upper limit of value relevant to our decisions. First, due to the speed of light and the definition and conception of economic growth, the limit to economic growth is a restrictive one. Additionally, a related far larger but still finite limit exists for value in a much broader sense due to the physics (...) of information and the ability of physical beings to place value on outcomes. We discuss how this argument can handle lexicographic preferences, probabilities, and the implications for infinite ethics and ethical uncertainty. (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)

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 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)

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)

Our account of the problem of the classical limit of quantum mechanics involves two elements. The first one is self-induced decoherence, conceived as a process that depends on the own dynamics of a closed quantum system governed by a Hamiltonian with continuous spectrum; the study of decoherence is addressed by means of a formalism used to give meaning to the van Hove states with diagonal singularities. The second element is macroscopicity represented by the limit $\hbar \rightarrow 0$ : (...) when the macroscopic limit is applied to the Wigner transformation of the diagonal state resulting from decoherence, the description of the quantum system becomes equivalent to the description of an ensemble of classical trajectories on phase space weighted by their corresponding probabilities. (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.

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)

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)

The aim of this paper is to elucidate the question of whether Newtonian mechanics can be derived from relativity theory. Physicists agree that classical mechanics constitutes a limiting case of relativity theory. By contrast, philosophers of science like Kuhn and Feyerabend affirm that classical mechanics cannot be deduced from relativity theory because of the incommensurability between both theories; thus what we obtain when we take the limit c → ∞ in relativistic mechanics cannot be Newtonian mechanics sensu stricto. In (...) this paper I focus on the alleged change of reference of the term mass in the transition from one theory to the other. Contradicting Kuhn and Feyerabend, special relativity theory supports the view that the mass of an object is a characteristic property of the object, that it has the same value in whatever frame of reference it is measured, and that it does not depend on whether the object is in motion or at rest. Thus mass preserves the reference through the change of theory, and the existence of a Newtonian limit of relativity theory provides a good example of the rationality of theory change in mathematical physics. (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)

The implications of the repugnant conclusion for consequentialist theories, such as total utilitarianism, have been extensively discussed since the work of Derek Parfit. These discussions make the paradoxes of population ethics depend on welfarist conditions, like the dominance condition (or the Pareto Principle). Thus, one might think that the repugnant conclusion is not a practical problem for deontologists, who deny that we always ought to do what produces the most aggregate welfare. In this study, we offer two impossibility results using (...) what we call the limit aggregation property. This states that when welfaristic and non-welfaristic considerations conflict, there is a threshold number of persons such that the former can override the latter as long as more people than the threshold number can enjoy increases in well-being levels. We argue that this property should be accepted even by deontologists, insofar as they do not commit themselves to the implausible absolutist position that fails to assign any moral weight to aggregate welfare. Our results therefore state that any normative population theory that is not absolutist entails (a variant of) the repugnant conclusion or some other implausible conclusion. Therefore, the repugnant conclusion must be taken seriously even by non-absolutist deontologists, not just consequentialists. (shrink)

This contribution examines the relevance of the concept “limit situation” in relation to aging and old age in a geriatric psychotherapy setting. The idea is to bring together concepts from phenomenology and the philosophy of age with methods from the field of qualitative social research. Experiences of groundlessness are viewed through the lens of Karl Jaspers’ terminology, leading to conceptualizing a dynamic of stabilizing beliefs yielding in the context of aging and old age. The results promise to contribute to (...) psychotherapy research and explore new ways for employing phenomenological ideas in clinical practice and research. (shrink)

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)

‘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...

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)

LS Penrose was the first to propose a measure of voting power (which later came to be known as ‘the [absolute] Banzhaf index’). His limit theorem – which is implicit in Penrose (1952) and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely while the quota is pegged at half the total weight, then – under certain conditions – the ratio between the voting powers (as measured (...) by him) of any two voters converges to the ratio between their weights. We conjecture that the theorem holds, under rather general conditions, for large classes of variously defined weighted voting games, other values of the quota, and other measures of voting power. We provide proofs for some special cases. (shrink)

The aim of this paper is to elucidate the question of whether Newtonian mechanics can be derived from relativity theory. Physicists agree that classical mechanics constitutes a limiting case of relativity theory. By contrast, philosophers of science like Kuhn and Feyerabend affirm that classical mechanics cannot be deduced from relativity theory because of the incommensurability between both theories; thus what we obtain when we take the limit c in relativistic mechanics cannot be Newtonian mechanics sensu stricto. In this paper (...) I focus on the alleged change of reference of the term mass in the transition from one theory to the other. Contradicting Kuhn and Feyerabend, special relativity theory supports the view that the mass of an object is a characteristic property of the object, that it has the same value in whatever frame of reference it is measured, and that it does not depend on whether the object is in motion or at rest. Thus mass preserves the reference through the change of theory, and the existence of a Newtonian limit of relativity theory provides a good example of the rationality of theory change in mathematical physics. (shrink)

The first English translation of key texts by Georges Bataille pertaining to The Accursed Share that also map out his transition from "dissident surrealist" to systematic thinker.

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 this essay, I discuss the Chinese attitude towards caring for people within family first, using law only as a back-up. I demonstrate this both through negative/corrective applications of law, such as penal law, and positive/protective applications of law, such as those that protect human rights. I do not necessarily have a right to what is most beneficial to me, nor do I or the community necessarily benefit from the most fair punishment. In both cases, law protects fairness, while a (...) different kind of social care rooted in a smaller community enables a richer healing and nourishing of the person and community. With reference to Confucian philosophy and present scholarship, I address some differences between possessed rights and seeking a right way to care for people in situ, and between fairness and human potential. Instead of trying to show how the Chinese perspective has the seeds of a modern Western conception, I highlight a perpendicular value. (shrink)