The Loeb space construction in nonstandard analysis is applied to the theory of processes to reveal basic phenomena which cannot be treated using classical methods. An asymptotic interpretation of results established here shows that for a triangular array (or a sequence) of random variables, asymptotic uncorrelatedness or asymptotic pairwise independence is necessary and sufficient for the validity of appropriate versions of the law of large numbers. Our intrinsic characterization of almost sure pairwise independence leads to the equivalence of (...) various multiplicative properties of random variables. (shrink)

Adults increase the certainty of their inductive inferences by observing more diverse instances. However, most young children fail to do so. The present study tested the hypothesis that children's sensitivity to instance diversity is determined by three variables: ability to discriminate among instances ( Discrimination ); an intuition that large numbers of instances increase the strength of conclusion ( Monotonicity ); ability to detect subcategories and evaluate numerical differences between the subcategories, or Extraction . A total of 219 (...) Chinese children aged 6 to 11 were tested for sensitivity to diversity by means of Discrimination, Monotonicity, and Extraction. The results indicated that children at all ages were able to discriminate instances and attend to set size. However, only 9- and 11-year-olds demonstrated Extraction and sensitivity to diversity. Furthermore, among all children diversity scores increased linearly with the level of Extraction. These results suggest that the law of large numbers plays a role in children's diversity-based reasoning. (shrink)

This paper presents the metaphysics of liberal rights reasoning on one hand and that of demographic reasoning on the other, as exemplifying two worldviews that both compete and complement each other in the contemporary German public debate on demographic decline. First, this essay outlines the way in which liberal theorists of various outlooks, perfectionist and neutralist alike, assume that a wide range of rights serves not only the interests of those individuals who possess them, but that it constitutes the foundations (...) of a just and stable political order in general and therefore is to the advantage of everyone. Second, the essay explains how demographic reasoning questions the assumption of harmony shared by the liberal approaches. Third, it provides an impression of the way in which demographic arguments have been deployed in the public sphere in Germany in the last few years. These arguments associate the autonomy of women with the demise of Germany. They claim that by encouraging women to pursue self-realization as self-interested individuals, the modern secular ethos of Germany as a democratic welfare society may be self-destructive in the long run, since it leads to sub-replacement fertility. Finally, the essay stresses that liberal and demographic perspectives share a “blindness” of historical events. In response, the conclusion brings history back in, by historicizing both demographic reasoning and demographic developments in Germany, with the aim of defusing some of the anxieties that may have been aroused by the current debate. (shrink)

Maurice Merleau-Ponty argued that the seeing of things together (focal figure and background objects) accounted for the sense that things possess unseen depth: they are three-dimensional entities, not facades. I compare this idea to the law of large numbers. In both cases, single entities take on substance, depth, or meaning when assimilated into a large body of comparable instances. Thinking along these lines, Erwin Schrödinger proposed that living processes achieve order by virtue of the multiplicity of their (...) constituent parts, any of which, when considered individually, militate against perception and understanding. He further suggested that those parts take their place as things to be perceived even as they constitute our perceiving faculties, and this is why uncertainty occasions their reality. Thus he offers an instance of Merleau-Ponty’s notion of chiasmic intertwining, which allows for world-body interchange or reversibility beyond the reach of unequivocal apprehension. (shrink)

Maurice Merleau-Ponty argued that the seeing of things together (focal figure and background objects) accounted for the sense that things possess unseen depth: they are three-dimensional entities, not facades. I compare this idea to the law of large numbers. In both cases, single entities take on substance, depth, or meaning when assimilated into a large body of comparable instances. Thinking along these lines, Erwin Schrödinger proposed that living processes achieve order by virtue of the multiplicity of their (...) constituent parts, any of which, when considered individually, militate against perception and understanding. He further suggested that those parts take their place as things to be perceived even as they constitute our perceiving faculties, and this is why uncertainty occasions their reality. Thus he offers an instance of Merleau-Ponty’s notion of chiasmic intertwining, which allows for world-body interchange or reversibility beyond the reach of unequivocal apprehension. (shrink)

Von Mises defined a "physical" probability as a strict limit of the relative frequency of occurrence of an event in repeated trials. As a result of a number of criticisms of von Mises's approach, the more favored approach became the "propensity" interpretation. It is argued here that this interpretation is not compelling and that the only problem in von Mises's approach is the assumption that the relative frequency converges in a strict sense. This problem is then remedied by deducing the (...) axioms of probability theory from the assumption that the relative frequency converges only in the sense of the weak law of large numbers. (shrink)

Australia is second only to Israel in being the world’s most culturally diverse nation, based largely on high levels of immigration in the second part of the 20th century. From the 1970s onwards, Australia formally recognized the massive social changes brought about by postwar immigration, and provided legislation to incorporate cultural diversity into everyday lives. One such ‘legislative’ enactment saw the establishment of multicultural broadcasting in Australia, as arguably a world-first, both in its comprehensiveness and diversity. Today, Australia has a (...) public sector corporation, the Special Broadcasting Service, administering five radio services in 68 languages. Also, the Community Radio sector produces multicultural programming in 100 languages through a number of its 330 broadcast and 207 narrowcast stations. This article examines the relationship between radio and its communities. It argues that despite the ‘profile’ of SBS television, radio is much closer to its constituent communities, and therefore plays a greater role in enabling those communities to speak their own histories, beyond the confines of a consensual Anglophile paradigm. (shrink)

In the TACITUS project for using commonsense knowledge in the understanding of texts about mechanical devices and their failures, we have been developing various commonsense theories that are needed to mediate between the way we talk about the behavior of such devices and causal models of their operation. Of central importance in this effort is the axiomatization of what might be called commonsense metaphysics. This includes a number of areas that figure in virtually every domain of discourse, such as granularity, (...) scales, time, space, material, physical objects, shape, causality, functionality, and force. Our effort has been to construct core theories of each of these areas, and then to define, or at least characterize, a large number of lexical items in terms provided by the core theories. In this paper we discuss our methodological principles and describe the key ideas in the various domains we are investigating. (shrink)

This book details how quantification can serve both as evidence and as an instrument of government, whether when dealing with statistics on employment, occupational health and economic governance, or when developing public management or target-driven policies. In the process, it presents a thought-provoking homage to Alain Desrosières, who pioneered ways to study large numbers and the politics underlying them. It opens with a summary of Desrosières's contributions to the field in which several generations of researchers detail how this (...) statistician and historian profoundly influenced them. This tribute, based on personal testimonies, bears witness to the vitality of the school of thought and analytical framework Desrosières initiated. Next, a collection of essays explores the statistical argument in the neoliberal era, examining issues such as counting the homeless in Europe, measuring the performance of public services, and quantifying the effects of public action on the unemployed in France. The third part details the uses of quantification. It reveals that although statistics are frequently used to the advantage of those in power, they can also play a vital role in challenging and resisting both the conventions underlying the measurements as well as the measurements themselves.Featuring the work of economists, historians, political scientists, sociologists, and statisticians, this title provides readers with a thoughtful look at an influential figure in the history of statistics. It also shows how statistics are used to direct public policy, the degree of conflict that is possible in their production, and the disputes that can develop around their uses. (shrink)

In his [1937, 1938], Paul Dirac proposed his “Large Number Hypothesis” (LNH), as a speculative law, based upon what we will call the “Large Number Coincidences” (LNC’s), which are essentially “coincidences” in the ratios of about six large dimensionless numbers in physics. Dirac’s LNH postulates that these numerical coincidences reflect a deeper set of law-like relations, pointing to a revolutionary theory of cosmology. This led to substantial work, including the development of Dirac’s later [1969/74] cosmology, and (...) other alternative cosmologies, such as the Brans-Dicke modification of GTR, and to extensive empirical tests. We may refer to the generic hypothesis of “Large Number Relations” (LNR’s), as the proposal that there are lawlike relations of some kind between the dimensionless numbers, not necessarily those proposed in Dirac’s early LNH. Such relations would have a profound effect on our concepts of physics, but they remain shrouded in mystery. Although Dirac’s specific proposals for LNR theories have been largely rejected, the subject retains interest, especially among cosmologists seeking to test possible variations in fundamental constants, and to explain dark energy or the cosmological constant. In the first two sections here we briefly summarize the basic concepts of LNR’s. We then introduce an alternative LNR theory, using a systematic formalism to express variable transformations between conventional measurement variables and the true variables of the theory. We demonstrate some consistency results and review the evidence for changes in the gravitational constant G. The theory adopted in the strongest tests of Ġ/G, by the Lunar Laser Ranging (LLR) experiments, assumes: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m, as a fundamental relationship. Experimental measurements show the RHS to be close to zero, so it is inferred that significant changes in G are ruled out. However when the relation is derived in our alternative theory it gives: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m – (dR/dt)/R. The extra final term (which is the Hubble constant) is not taken into account in conventional derivations. This means the LLR experiments are consistent with our LNR theory (and others), and they do not really test for a changing value of G at all. This failure to transform predictions of LNR theories correctly is a serious conceptual flaw in current experiment and theory. (shrink)

Belief in the divine origin of the universe began to wane most markedly in the nineteenth century, when scientific accounts of creation by natural law arose to challenge traditional religious doctrines. Most of the credit - or blame - for the victory of naturalism has generally gone to Charles Darwin and the biologists who formulated theories of organic evolution. Darwinism undoubtedly played the major role, but the supporting parts played by naturalistic cosmogonies should also be acknowledged. Chief among these was (...) the nebular hypothesis proposed by Pierre Simon Laplace in 1796, which explained the origin of the solar system as a natural development over extended periods of time. Ronald Numbers focuses on Laplace's theory as it affected American scientific thought. he first traces the history of Laplace's cosmogony chronologically, from its European inception to its demise about 1900. the last three chapters explore some of the theological and scientific consequences resulting from the acceptance of this cosmogony. Most significant was the change in the status of supernatural doctrine. When the nebular hypothesis lost credence at the end of the nineteenth century, those who had before tried to accommodate natural theory with supernatural doctrine no longer felt compelled to do so when faced with succeeding theories. The nebular hypothesis, it seems, had established natural law in the heavens. (shrink)

Objectives: The mental health legislation of most developed countries includes either a dangerousness criterion or an obligatory dangerousness criterion (ODC). A dangerousness criterion holds that mentally ill people may be given treatment without consent if they are deemed to be a risk to themselves or others. An ODC holds that mentally ill people may be given treatment without consent only if they are deemed to be a risk to themselves or others. This paper argues that the dangerousness criterion is unnecessary, (...) unethical and, in the case of the ODC, potentially harmful to mentally ill people and to the rest of the community. Methods: We examine the history of the dangerousness criterion, and provide reasoned argument and empirical evidence in support of our position. Results: Dangerousness criteria are not required to balance the perceived loss of autonomy arising from mental health legislation. Dangerousness criteria unfairly discriminate against the mentally ill, as they represent an unreasonable barrier to treatment without consent, and they spread the burden of risk that any mentally ill person might become violent across large numbers of mentally ill people who will never become violent. Mental health legislation that includes an ODC is associated with a longer duration of untreated psychosis, and probably contributes to a poorer prognosis and an increase risk of suicide and violence in patients in their first episode of psychosis. Conclusions: Dangerousness criteria should be removed from mental health legislation and be replaced by criteria that focus on a patient’s capacity to refuse treatment. (shrink)

Let (leeway) incompatibilism be the thesis that causal determinism is incompatible with the freedom to do otherwise. Several prominent authors have claimed that incompatibilism alone can capture, or at least best captures, the intuitive appeal behind Jorge Luis Borges's famous “Garden of Forking Paths” metaphor. The thought, briefly, is this: the “single path” leading up to one's present decision represents the past; the forking paths that one must decide between represent those possible futures consistent with the past and the laws (...) of nature. But if determinism is true, there is only one possible future consistent with the past and the laws and, hence, only one path to choose from. That is, if determinism is true, then we are not free to do otherwise. In this paper, I argue that this understanding of the Garden of Forking Paths faces a number of problems and ought to be rejected even by incompatibilists. I then present an alternative understanding that not only avoids these problems but still supports incompatibilism. Finally, I consider how various versions of (leeway) compatibilism fit with the Garden of Forking Paths as well as the broader question of whether metaphors, however intuitive, have any dialectical force in the debates over freedom. (shrink)

Friedrich Nietzsche’s intellectual autobiography Ecce Homo has always been a controversial book. Nietzsche prepared it for publication just before he became incurably insane in early 1889, but it was held back until after his death, and finally appeared only in 1908. For much of the first century of its reception, Ecce Homo met with a sceptical response and was viewed as merely a testament to its author’s incipient madness. This was hardly surprising, since he is deliberately outrageous with the ‘megalomaniacal’ (...) self-advertisement of his chapter titles, and brazenly claims ‘I am not a man, I am dynamite’ as he attempts to explode one preconception after another in the Western philosophical tradition. In recent decades there has been increased interest in the work, especially in the English-speaking world, but the present volume is the first collection of essays in any language devoted to the work. Most of the essays are selected from the proceedings of an international conference held in London to mark the centenary of the first publication of Ecce Homo in 2008. They are supplemented by a number of specially commissioned essays. Contributors include established and emerging Nietzsche scholars from the UK and USA, Germany and France, Portugal, Sweden and the Netherlands. (shrink)

Kant argues against the ontological argument for the existence of God but replaces it with a moral theism. This article analyses Kant’s moral proof with emphasis on the Critique of the Power of Judgement, and his historical and political writings. It argues that at the heart of this argument is the idea of progress. The concrete content of the moral law is the idea of a just world. Such a just world would be impossible without the idea of God, since (...) there would be no harmony between nature and freedom. It contrasts Kant’s concept of time and history with Heidegger’s. The difference between them is a reversal of modality. For Kant, actuality determines possibility. If I cannot imagine a just word as actual, then I would fall into moral despair. The idea of God grounds this actuality. For Heidegger, possibility is higher than actuality. Since history has no teleology, then no idea of God is required. (shrink)

The question of whether there are laws in ecology is important for a number of reasons. If, as some have suggested, there are no ecological laws, this would seem to distinguish ecology from other branches of science, such as physics. It could also make a difference to the methodology of ecology. If there are no laws to be discovered, ecologists would seem to be in the business of merely supplying a suite of useful models. These models would need to be (...) assessed for their empirical adequacy but not for their ability to capture fundamental truths, or the like. If, on the other hand, ecology does have laws, this prompts further questions about what these laws are and why even the best candidates for ecological laws fall short of what might be expected of laws. (shrink)

The vast majority of Biblical historians believe there is evidence sufficient to place Jesus’ existence beyond reasonable doubt. Many believe the New Testamentdocuments alone suffice firmly to establish Jesus as an actual, historical figure. I question these views. In particular, I argue (i) that the three most popular criteria by which various non-miraculous New Testament claims made about Jesus are supposedly corroborated are not sufficient, either singly or jointly, to place his existence beyond reasonable doubt, and (ii) that a prima (...) facie plausible principle concerning how evidence should be assessed—a principle I call the contamination principle—entails that, given the large proportion of uncorroborated miracle claims made about Jesus in the New Testament documents, we should, in the absence of good independent evidence for an historical Jesus, remain sceptical about his existence. (shrink)

Human rights discourse has been likened to a global lingua franca, and in more ways than one, the analogy seems apt. Human rights discourse is a language that is used by all yet belongs uniquely to no particular place. It crosses not only the borders between nation-states, but also the divide between national law and international law: it appears in national constitutions and international treaties alike. But is it possible to conceive of human rights as a global language or lingua (...) franca not just in a figurative or metaphorical sense, but in a literal or linguistic sense as a legal dialect defined by distinctive patterns of word choice and usage? Does there exist a global language of human rights that transcends not only national borders, but also the divide between domestic and international law? Empirical analysis suggests that the answer is yes, but this global language comes in at least two variants or dialects. New techniques for performing automated content analysis enable us to analyze the bulk of all national constitutions over the last two centuries, together with the world’s leading regional and international human rights instruments, for patterns of linguistic similarity and to evaluate how much language, if any, they share in common. Specifically, we employ a technique known as topic modeling that disassembles texts into recurring verbal patterns. The results highlight the existence of two species or dialects of rights talk—the universalist dialect and the positive-rights dialect—both of which are global in reach and rising in popularity. The universalist dialect is generic in content and draws heavily on the type of language found in international and regional human rights instruments. It appears in particularly large doses in the constitutions of transitional states, developing states, and states that have been heavily exposed to the influence of the international community. The positive-rights dialect, by contrast, is characterized by its substantive emphasis on positive rights of a social or economic variety, and by its prevalence in lengthier constitutions and constitutions from outside the common law world, especially those of the Spanish-speaking world. Both dialects of rights talk are truly transnational, in the sense that they appear simultaneously in national, regional, and international legal instruments and transcend the distinction between domestic and international law. Their existence attests to the blurring of the boundary between constitutional law and international law. (shrink)

This is an article that explores the question "what is the meaning of life?" particularly with respect to humanism and theism. It defends a humanist position, and refutes a number of arguments for the conclusion that a meaningful human existence requires the existence of God.

In the epigraph, Fisher is blaming two generations of theoretical biologists, from Darwin on, for ignoring Quetelet's statistical techniques and hence harboring confusions about evolution and natural selection. He is right to imply that Darwin and his contemporaries were aware of the core of Quetelet's work. Quetelet's seminal monograph, Sur L'homme, was widely discussed in Darwin's academic circles. We know that Darwin owned a copy (Schweber 1977). More importantly, we have in Darwin's notebooks two entries referring to Quetelet's work on (...) the cause of a large-scale global phenomenon where each year more boys were born than girls. The first entry is written sometime between April and July 1838. Darwin writes "Find out from the Statistical Society—where M. Quetelet has published his laws about sexes relative to age of Marriages" (C 268, Barrett et al., 1987, p. 324). The second is written sometime after October 16, 1838: "In the Atheneum Numbers 406, 407, 409, Quetelet papers are given, & I think facts there mentioned about proportion of sexes, at birth & causes" (Ibid, p. 379). So, even if Darwin did not read Sur L'homme directly it is likely (though not certain) that he read its review in the Atheneum. There is no doubt that Darwin eventually became familiar with Quetelet's work in statistics. The smoking gun is an essay that Darwin writes in 1874, entitled, "On the Males and Complemental Males of Certain Cirripedes, and on Rudimentary Structures" where he discusses Quetelet's laws of variation. (shrink)

The ArgumentIn this we explore some of the ways in which a state scientific laboratory (Daresbury SERC) reacted to the rtetoric and forces of the marketpace in the 1980s. We describe laboratory attempts to create what we call “good customers” while converting itself into a “good seller” by developing a particulat set of costing practicting that were closely related to the implementation of a management accounting system. Finally, we consider how Daresbury response to “market forces” influenced scintific and organzational practice, (...) and arsponse that the social technologies of governmentality performed by accountancy — but also by scientific and bureaucratic practice are complex, discursively heterogeneou, and used in context-sensitive ways. This means, or so we suggest, that it is difficult to mount general argunents about “science” and “the market,” and that the use of such large-scale institions impedes impedes analysis. (shrink)

The aim of the article is to intervene in debates about the digital and, in particular, framings that imagine the digital in terms of epochal shifts or as redefining life. Instead, drawing on recent developments in digital methods, we explore the lively, productive and performative qualities of the digital by attending to the specificities of digital devices and how they interact, and sometimes compete, with older devices and their capacity to mobilize and materialize social and other relations. In doing so, (...) our aim is to explore the implications of digital devices and data for reassembling social science methods or what we call the social science apparatuses that assemble digital devices and data to ‘know’ the social and other relations. Building on recent work at CRESC on the social life of methods, we recommend a genealogical approach that is alive to the ways in which digital devices are simultaneously shaped by social worlds, and can in turn become agents that shape those worlds. This calls for attending to the specificities of digital devices themselves, how they are varied and composed of diverse socio-technical arrangements, and are enrolled in the creation of new knowledge spaces, institutions and actors. Rather than exploring what large-scale changes can be revealed and understood through the digital, we argue for explorations of how digital devices themselves are materially implicated in the production and performance of contemporary sociality. To that end we offer the following nine propositions about the implications of digital data and devices and argue that these demand rethinking the theoretical assumptions of social science methods: transactional actors; heterogeneity; visualization; continuous time; whole populations; granularity; expertise; mobile and mobilizing; and non-coherence. (shrink)

This chapter looks at a range of objections to theism that one might class as “logical.” Some of these objections aim to show that theism involves an internal logical contradiction. Others aim to show that theism is at least logically incompatible with other beliefs to which the theist is also typically committed. Also included are objections grounded in the thought that theism is nonsensical or meaningless. The chapter provides both an overview of this broad terrain, including a map of possible (...) responses to different kinds of objection, and then a number of examples. (shrink)

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words—thousand, million, billion—to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position (...) and response time are expected near the boundaries between categories. In contrast to previous work that suggested only that a minority of college undergraduates employed categorical boundaries, we find that discontinuities near category boundaries occur in most or all participants, but that accurate and inaccurate participants respond in opposite ways to category boundaries. Accurate participants highlight contrasts within a category, whereas inaccurate participants adjust their responses toward category centers. (shrink)

This brief position paper is stimulated from the continued need to define and redefine the area of transpersonal psychology. Understandably, being able to articulate what ‘transpersonal psychology’ is enables discussions within the wider academic and public community, yet all existing definitions are complex, conveying a number of inherent meanings in their definition, which in turn, can cloud others’ perceptions on the area.

The best philosophical account of human rights regards them as protections of the values we attach to human agency. The international law of human rights is embodied in a large number of declarations, conventions, covenants, charters, and judicial decisions. There are many discrepancies between the lists of human rights that emerge from these two authoritative sources. This lecture explores the significance of these discrepancies.

The best philosophical account of human rights regards them as protections of the values we attach to human agency. The international law of human rights is embodied in a large number of declarations, conventions, covenants, charters, and judicial decisions. There are many discrepancies between the lists of human rights that emerge from these two authoritative sources. This lecture explores the significance of these discrepancies.

The best philosophical account of human rights regards them as protections of the values we attach to human agency. The international law of human rights is embodied in a large number of declarations, conventions, covenants, charters, and judicial decisions. There are many discrepancies between the lists of human rights that emerge from these two authoritative sources. This lecture explores the significance of these discrepancies.

In lieu of an abstract, here is a brief excerpt of the content:176 Reviews c:\users\ken\documents\type3402\rj 3402 050 red.docx 2015-02-04 9:19 PM THE GRUNDGESETZE Nicholas Griffin Russell Research Centre / McMaster U. Hamilton, on, Canada l8s 4l6 [email protected] Gottlob Frege. Basic Laws of Arithmetic. Derived Using Concept-script. Volumes i and ii. Translated and edited by Philip A. Ebert and Marcus Rossberg with Crispin Wright. Oxford: Oxford U. P., 2013. Pp. xxxix + xxxii + 253 + xv + 285 + A–42 + (...) i–11. isbn 978-0-19-928174-9. £60; us$110. iven the steadily rising interest in Frege’s work since the 1950s, it is surprising that his Grundgesetze der Arithmetik, the work he thought would be the crowning achievement of his career, has not previously been fully translated into English. Other Frege works have long been available in English. The earlier Grundlagen der Arithmetik was nicely, if not always entirely accurately, translated by J. L. Austin and published in 1950.1 Translations of Frege’s other philosophical writings began to appear in influential editions about the same time,2 initially a small corpus that has been gradually added to over the years to include works from his Nachlass and letters from his correspondence.3 Somewhat later, the Begriffsschrift, Frege’s momentous first 1 The Foundations of Arithmetic (Oxford: Blackwell, 1950; 2nd edn. 1953). The later translation under the same title by Dale Jacquette (London: Longman, 2007) is much less satisfactory. 2 The first importance source for these was Peter Geach and Max Black’s Translations from the Philosophical Writing of Gottlob Frege (1952; 2nd edn. 1960; 3rd edn. 1980), though it included reprints of some much earlier translations. 3 The two most comprehensive English sources for the shorter writings are now Brian d= Reviews 177 c:\users\ken\documents\type3402\rj 3402 050 red.docx 2015-02-04 9:19 PM contribution to modern logic, the work which Quine 4 said had made logic a great subject, was translated in full despite the difficulties of Fregean notation.5 But through all this the Grundgesetze remained largely (though not entirely ) untranslated. The view seems, for a long time, to have been that Frege’s contributions to logic were to be found in the Begriffsschrift and his contributions to philosophy in the Grundlagen and a small number of seminal articles. The Grundgesetze, on the other hand, was widely thought not to have added much to these magni ficent achievements, but to have employed them in a project that was doomed by the discovery of Russell’s paradox; namely, the attempt to show that arithmetic could be rigorously derived from purely logical principles. In the bleak aftermath of Russell’s paradox it came to seem as if whatever was of value in the Grundgesetze had already been published elsewhere, while what was new in it was mistaken.6 That assessment of the book’s value, combined with the huge difficulties of typesetting Frege’s idiosyncratic two-dimensional notation, and the sheer scale of the work (even without the anticipated third volume, which was abandoned in the face of Russell’s paradox, it was, by far, Frege’s largest work) made it seem as though a translation of the whole Grundgesetze was not only a prohibitively large undertaking, but also one which was not really necessary. And so, through much of the twentieth century, the Grundgesetze vied with Principia Mathematica as the world’s bestknown but least-read philosophical book. But this understanding of the Grundgesetze’s importance could not withstand the development of neo-logicism, brought to prominence by Crispin Wright’s Frege’s Conception of Numbers as Objects.7 The key insight of neoMcGuinness, ed., Frege, Collected Papers on Mathematics, Logic, and Philosophy (1984); and Michael Beaney, ed., The Frege Reader (1997). 4 At least in early editions of Mathematical Logic. The remark was removed in later ones in deference to Boole. 5 By Stefan Bauer-Mengelberg in Jean van Heijenoort, ed., From Frege to Gödel (1967), pp. 5–82. 6 Not surprisingly the one part of the Grundgesetze which has appeared most frequently in translation is the “Nachwort” responding to Russell’s paradox which Frege added as the book was in press. Geach... (shrink)

We present statistical analyses of the large‐scale structure of 3 types of semantic networks: word associations, WordNet, and Roget's Thesaurus. We show that they have a small‐world structure, characterized by sparse connectivity, short average path lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale‐free pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many connections. These (...) regularities have also been found in certain other complex natural networks, such as the World Wide Web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or high‐dimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate small‐world statistics and power‐law connectivity distributions, and it also suggests one possible mechanistic basis for the effects of learning history variables (age of acquisition, usage frequency) on behavioral performance in semantic processing tasks. (shrink)

I extract some philosophical morals from some aspects of Lagrangian mechanics. One main moral concerns methodology: Lagrangian mechanics provides a level of description of phenomena which has been largely ignored by philosophers, since it falls between their accustomed levels---``laws of nature'' and ``models''. Another main moral concerns ontology: the ontology of Lagrangian mechanics is both more subtle and more problematic than philosophers often realize. The treatment of Lagrangian mechanics provides an introduction to the subject for philosophers, and is technically elementary. (...) In particular, it is confined to systems with a finite number of degrees of freedom, and for the most part eschews modern geometry. (shrink)

Both the theory that traumatic childhood memories can be repressed, and the reliability of the techniques used to retrieve these memories are challenged in this paper. Questions are raised about the robustness of the theory and the literature that purports to provide scientific evidence for it. Evidence to this end is provided by the demographic and qualitative results of a research study conducted by the authors which surveyed New Zealand families in which one member had accused another (or others) of (...) sexual abuse on the basis of recovered memories. It is shown that a number of these allegations involve very low probability events. Since memory repression theory is not currently scientifically substantiated it is argued that care needs to be taken in the mental health, legal and insurance compensation arenas. Memories recalled during therapy may be treated as metaphorical but, in the absence of corroborative evidence, should not be considered factually true. Clinicians who wish to use memory recovery techniques should inform patients of their experimental and controversial nature, point out potential adverse effects, and obtain consent before proceeding. (shrink)

Both the theory that traumatic childhood memories can be repressed, and the reliability of the techniques used to retrieve these memories are challenged in this paper. Questions are raised about the robustness of the theory and the literature that purports to provide scientific evidence for it. Evidence to this end is provided by the demographic and qualitative results of a research study conducted by the authors which surveyed New Zealand families in which one member had accused another (or others) of (...) sexual abuse on the basis of recovered memories. It is shown that a number of these allegations involve very low probability events. Since memory repression theory is not currently scientifically substantiated it is argued that care needs to be taken in the mental health, legal and insurance compensation arenas. Memories recalled during therapy may be treated as metaphorical but, in the absence of corroborative evidence, should not be considered factually true. Clinicians who wish to use memory recovery techniques should inform patients of their experimental and controversial nature, point out potential adverse effects, and obtain consent before proceeding. (shrink)

We present statistical analyses of the large‐scale structure of 3 types of semantic networks: word associations, WordNet, and Roget's Thesaurus. We show that they have a small‐world structure, characterized by sparse connectivity, short average path lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale‐free pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many connections. These (...) regularities have also been found in certain other complex natural networks, such as the World Wide Web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or high‐dimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate small‐world statistics and power‐law connectivity distributions, and it also suggests one possible mechanistic basis for the effects of learning history variables (age of acquisition, usage frequency) on behavioral performance in semantic processing tasks. (shrink)

A number of high-profile campaigns relating to diversity have focussed on the large law firm sector since the mid-2000s. Reflecting on what has been called the 'diversity approach' to equality management, they have emphasised voluntary action based on business case reasoning. This paper considers the impact of these campaigns in practice, focusing on the dynamics of diversity policy-making within firms. Drawing upon empirical work conducted in large law firms, it explores the perspective of newly appointed diversity staff who (...) have day to day responsibility for diversity policies in the majority of large law firms. It discusses research findings that show while certain policies were being implemented across the large law firm sector, much turns on the position of diversity staff within firms and their ability to conduct in-house negotiations effectively, to compromise and downplay the potential for disruption to the status quo. On the basis of this research I consider the ongoing debates about holding law firms to account with respect to the diversity of their workforce. While the strategy of pressuring firms to disclose 'diversity data' is gathering pace, the paper recommends an open discussion about the goals of diversity policy-making as a pre-condition of greater accountability. (shrink)

The main objective of the paper is to propose a frequentist interpretation of probability in the context of model-based induction, anchored on the Strong Law of Large Numbers (SLLN) and justifiable on empirical grounds. It is argued that the prevailing views in philosophy of science concerning induction and the frequentist interpretation of probability are unduly influenced by enumerative induction, and the von Mises rendering, both of which are at odds with frequentist model-based induction that dominates current practice. The (...) differences between the two perspectives are brought out with a view to defend the model-based frequentist interpretation of probability against certain well-known charges, including [i] the circularity of its definition, [ii] its inability to assign ‘single event’ probabilities, and [iii] its reliance on ‘random samples’. It is argued that charges [i]–[ii] stem from misidentifying the frequentist ‘long-run’ with the von Mises collective. In contrast, the defining characteristic of the long-run metaphor associated with model-based induction is neither its temporal nor its physical dimension, but its repeatability (in principle); an attribute that renders it operational in practice. It is also argued that the notion of a statistical model can easily accommodate non-IID samples, rendering charge [iii] simply misinformed. (shrink)

We present statistical analyses of the large‐scale structure of 3 types of semantic networks: word associations, WordNet, and Roget's Thesaurus. We show that they have a small‐world structure, characterized by sparse connectivity, short average path lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale‐free pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many connections. These (...) regularities have also been found in certain other complex natural networks, such as the World Wide Web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or high‐dimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate small‐world statistics and power‐law connectivity distributions, and it also suggests one possible mechanistic basis for the effects of learning history variables (age of acquisition, usage frequency) on behavioral performance in semantic processing tasks. (shrink)

The strong law of large numbers and considerations concerning additional information strongly suggest that Beauty upon awakening has probability 1/3 to be in a heads-awakening but should still believe the probability that the coin landed heads in the Sunday toss to be 1/2. The problem is that she is in a heads-awakening if and only if the coin landed heads. So, how can she rationally assign different probabilities or credences to propositions she knows imply each other? This is (...) the problem I address in this article. I suggest that ‘p whenever q and vice versa’ may be consistent with p and q having different probabilities if one of them refers to a sample space containing ordinary possible worlds and the other to a sample space containing centred possible worlds, because such spaces may fail to combine into one composite probability space and, as a consequence, ‘whenever’ may not be well defined; such is the main contribution of this article. 1The Sleeping Beauty Game2Groisman’s and Peter Lewis’s Approaches3Discussing Beauty’s Credences4The Principle of Equivalence's Failure5Making Sense of the Principle of Equivalence's Failure6Elga’s and Lewis’s Approaches7ConclusionAppendix. (shrink)

Both the theory that traumatic childhood memories can be repressed, and the reliability of the techniques used to retrieve these memories are challenged in this paper. Questions are raised about the robustness of the theory and the literature that purports to provide scientific evidence for it. Evidence to this end is provided by the demographic and qualitative results of a research study conducted by the authors which surveyed New Zealand families in which one member had accused another of sexual abuse (...) on the basis of recovered memories. It is shown that a number of these allegations involve very low probability events. Since memory repression theory is not currently scientifically substantiated it is argued that care needs to be taken in the mental health, legal and insurance compensation arenas. Memories recalled during therapy may be treated as metaphorical but, in the absence of corroborative evidence, should not be considered factually true. Clinicians who wish to use memory recovery techniques should inform patients of their experimental and controversial nature, point out potential adverse effects, and obtain consent before proceeding. (shrink)

This study examines the socioeconomic and familial background of Irish Catholic priests born between 1867 and 1911. Previous research has hypothesized that lack of marriage opportunities may influence adoption of celibacy as part of a religious institution. The present study traced data from Irish seminary registries for 46 Catholic priests born in County Limerick, Ireland, using 1901 Irish Census returns and Land Valuation records. Priests were more likely to originate from landholding backgrounds, and with landholdings greater in size and wealth (...) than the local average. Priests were found to originate from families with more sons than the national average, but with similar numbers of daughters. These findings are discussed in relation to competition for resources and lineage survival strategies. (shrink)

In recent years, foreign language learning has been proposed as a possible cognitive intervention for older adults. However, the brain network and cognitive functions underlying FLL has remained largely unconfirmed in older adults. In particular, older and younger adults have markedly different cognitive profile—while older adults tend to exhibit decline in most cognitive domains, their semantic memory usually remains intact. As such, older adults may engage the semantic functions to a larger extent than the other cognitive functions traditionally considered the (...) most important. Using anatomical measurements and a cognitive test battery, the present study examined this hypothesis in twenty cognitively normal older adults, who participated in a two-month Italian learning programme. Results showed that the immediate learning success and long-term retention of Italian vocabularies were most consistently predicted by the anatomical measures of the left pars orbitalis and left caudal middle frontal cortex, which are implicated in semantic and episodic memory functions. Convergent evidence was also found based on the pattern of cognitive associations. Our results are consistent with a prominent role of semantic and episodic memory functions in vocabulary learning in older learners. (shrink)

An overview of what Frege accomplishes in Part II of Grundgesetze, which contains proofs of axioms for arithmetic and several additional results concerning the finite, the infinite, and the relationship between these notions. One might think of this paper as an extremely compressed form of Part II of my book Reading Frege's Grundgesetze.