Kripke has argued that definitions of units of measurements provide examples of statements that are both contingent and a priori. In this paper I argue that definitions of units of measurement are intended to be stipulations of what Kripke calls "theoretical identities": a stipulation that two terms will have the same rigid designation. Hence such a definition is both a priori and necessary. The necessity arises because such definitions appeal to natural kind properties only, which on Kripke's account are necessary.

The thesis that numbers are ratios of quantities has recently been advanced by a number of philosophers. While adequate as a definition of the natural numbers, it is not clear that this view suffices for our understanding of the reals. These require continuous quantity and relative to any such quantity an infinite number of additive relations exist. Hence, for any two magnitudes of a continuous quantity there exists no unique ratio. This problem is overcome by defining ratios, and hence (...) real numbers, as binary relations between infinite standard sequences. This definition leads smoothly into a new definition of measurement consonant with the traditional view of measurement as the discovery or estimation of numerical relations. The traditional view is further strengthened by allowing that the additive relations internal to a quantity are distinct from relations observed in the behaviour of objects manifesting quantities. In this way the traditional theory can accommodate the theory of conjoint measurement. This is worth doing because the traditional theory has one great strength lacked by its rivals: measurement statements and quantitative laws are able to be understood literally. 1 This paper was completed in 1990-1. while the author was a visiting scholar at the Irvine Research Unit in Mathematical Behavioral Sciences. University of California. Irvine. The author wishes to thank the Director. Professor R. D. Luce, for the generous provision of space and facilities within the Unit and for his critical comments upon some of the ideas expressed herein: Professor L. Narens. for his trenchant criticisms: and the University of Sydney, for granting Special Study Leave and financial assistance to make the visit possible. (shrink)

The quality of doctoral-level biochemistry (N=139), botany (N=83), cellular/molecular biology (N=89), microbiology (N=134), physiology (N=101), and zoology (N=70) programs at United States universities was assessed, using 16 measures. These measures focused on variables related to: (1) program size; (2) characteristics of graduates; (3) reputational factors (scholarly quality of faculty, effectiveness of programs in educating research scholars/scientists, improvement in program quality during the last 5 years); (4) university library size; (5) research support; and (6) publication records. Chapter I discusses prior attempts (...) to assess quality in graduate education, development of the study plans, and the selection of disciplines and programs to be evaluated. Chapter II discusses the methodology used, focusing on each of the assessment measures. Chapters III to VIII present, respectively, findings from the analyses of the biochemistry, botany, cellular/molecular biology, microbiology, physiology, and zoology programs. Chapter IX includes a summary of results, correlations among measures, several additional analyses, and suggestions for future studies. Among the findings reported are those indicating that cellular/molecular biology programs had, on the average, the largest number of faculty and that students in cellular/molecular biology, biology, biochemistry, microbiology, and physiology received a relatively high fraction of financial support. (Survey instruments and supporting documentation are included in appendices.) (JN). (shrink)

The quality of doctoral-level chemistry (N=145), computer science (N=58), geoscience (N=91), mathematics (N=115), physics (N=123), and statistics/biostatistics (N=64) programs at United States universities was assessed, using 16 measures. These measures focused on variables related to: program size; characteristics of graduates; reputational factors (scholarly quality of faculty, effectiveness of programs in educating research scholars/scientists, improvement in program quality during the last 5 years); university library size; research support; and publication records. Chapter I discusses prior attempts to assess quality in graduate education, (...) development of the study plans, and the selection of disciplines and programs to be evaluated. Chapter II discusses the methodology used, focusing on each of the assessment measures. Chapters III to VIII present, respectively, findings from the analyses of the chemistry, computer science, geoscience, mathematics, physics, and statistics/biostatistics programs. Chapter IX includes a summary of results, correlations among measures, several additional analyses, and suggestions for future studies. Among the findings reported are those indicating that mathematics programs had, on the average, the largest number of faculty (N=33) in December 1980 followed closely by physics (N=28) and chemistry (N=23), and that 80 percent of computer science students had job commitments by graduation. (Survey instruments and supporting documentation are included in appendices.) (JN). (shrink)

000000001. Introduction Call a theory of the good—be it moral or prudential—aggregative just in case (1) it recognizes local (or location-relative) goodness, and (2) the goodness of states of affairs is based on some aggregation of local goodness. The locations for local goodness might be points or regions in time, space, or space-time; or they might be people, or states of nature.1 Any method of aggregation is allowed: totaling, averaging, measuring the equality of the distribution, measuring the minimum, etc.. Call (...) a theory of the good finitely additive just in case it is aggregative, and for any finite set of locations it aggregates by adding together the goodness at those locations. Standard versions of total utilitarianism typically invoke finitely additive value theories (with people as locations). A puzzle can arise when finitely additive value theories are applied to cases involving an infinite number of locations (people, times, etc.). Suppose, for example, that temporal locations are the locus of value, and that time is discrete, and has no beginning or end.2 How would a finitely additive theory (e.g., a temporal version of total utilitarianism) judge the following two worlds? Goodness at Locations (e.g. times) w1:..., 2, 2, 2, 2, 2, 2, 2, 2, 2, ..... w2:..., 1, 1, 1, 1, 1, 1, 1, 1, 1, ..... Example 1 At each time w1 contains 2 units of goodness and w2 contains only 1. Intuitively, we claim, if the locations are the same in each world, finitely additive theorists will want to claim that w1 is better than w2. But it's not clear how they could coherently hold this view. For using standard mathematics the sum of each is the same infinity, and so there seems to be no basis for claiming that one is better than the other.3 (Appealing to Cantorian infinities is of no help here, since for any Cantorian infinite N, 2xN=1xN.). (shrink)

The wrong version of my article ‘Aspects of the Infinite in Kant’ was printed in the last issue of Mind (pp. 205–23). I should like to correct an error that thereby appeared on page 207. In A430–2/B458–60 of the Critique of Pure Reason Kant does not deny that what is (mathematically) infinite should be what I called an actual measurable totality—if, by its measure, we mean ‘the multiplicity of given units which it contains’. His point is simply (...) that what makes it infinite cannot be the fact that its measure is the greatest possible; for there is no such thing. What he has in mind here can be illustrated as follows. Take the infinite multiplicity of hours that have elapsed up to a given moment; then the multiplicity of minutes that have elapsed, and indeed the multiplicity of hours that will have elapsed an hour later, are both greater. No multiplicity is so great that it cannot be increased in this way. (Of course, standard contemporary formal work on the infinite has superseded Kant here. A modern mathematician would want either to quarrel with this or at least to refine it.) He also refuses to allow that an infinite multiplicity is a number (cf. BIII and A526–7/B554–5). In the end, he thinks, there is no saying what it is for something to be (mathematically) infinite without falling back on ‘the true transcendental concept of infinitude,’ namely ‘that the successive synthesis of units required for the enumeration of a quantum can never be completed’. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Convention for Protection of Human Rights and Dignity of the Human Being with Regard to the Application of Biology and Biomedicine: Convention on Human Rights and BiomedicineCouncil of EuropePreambleThe Member States of the Council of Europe, the other States and the European Community signatories hereto,Bearing in mind the Universal Declaration of Human Rights proclaimed by the General Assembly of the United Nations on 10 December 1948;Bearing in mind the (...) Convention for the Protection of Human Rights and Fundamental Freedoms of 4 November 1950;Bearing in mind the European Social Charter of 18 October 1961;Bearing in mind the International Covenant on Civil and Political Rights and the International Covenant on Economic, Social and Cultural Rights of 16 December 1966;Bearing in mind the Convention for the Protection of Individuals with Regard to Automatic Processing of Personal Data of 28 January 1981;Bearing also in mind the Convention on the Rights of the Child of 20 November 1989;Considering that the aim of the Council of Europe is the achievement of a greater unity between its members and that one of the methods by which that aim is to be pursued is the maintenance and further realisation of human rights and fundamental freedoms;Conscious of the accelerating developments in biology and medicine;Convinced of the need to respect the human being both as an individual and as a member of the human species and recognising the importance of ensuring the dignity of the human being; [End Page 277]Conscious that the misuse of biology and medicine may lead to acts endangering human dignity;Affirming that progress in biology and medicine should be used for the benefit of present and future generations;Stressing the need for international co-operation so that all humanity may enjoy the benefits of biology and medicine;Recognising the importance of promoting a public debate on the questions posed by the application of biology and medicine and the responses to be given thereto;Wishing to remind all members of society of their rights and responsibilities;Taking account of the work of the Parliamentary Assembly in this field, including Recommendation 1160 (1991) on the preparation of a Convention on bioethics;Resolving to take such measures as are necessary to safeguard human dignity and the fundamental rights and freedoms of the individual with regard to the application of biology and medicine;Have agreed as follows:Chapter IGeneral provisionsArticle 1. (Purpose and object)Parties to this Convention shall protect the dignity and identity of all human beings and guarantee everyone, without discrimination, respect for their integrity and other rights and fundamental freedoms with regard to the application of biology and medicine.Each Party shall take in its internal law the necessary measures to give effect to the provisions of this Convention.Article 2. (Primacy of the human being)The interests and welfare of the human being shall prevail over the sole interest of society or science.Article 3. (Equitable access to health care)Parties, taking into account health needs and available resources, shall take appropriate measures with a view to providing, within their jurisdiction, equitable access to health care of appropriate quality. [End Page 278]Article 4. (Professional standards)Any intervention in the health field, including research, must be carried out in accordance with relevant professional obligations and standards.Chapter IIConsentArticle 5. (General rule)An intervention in the health field may only be carried out after the person concerned has given free and informed consent to it.This person shall beforehand be given appropriate information as to the purpose and nature of the intervention as well as on its consequences and risks.The person concerned may freely withdraw consent at any time.Article 6. (Protection of persons not able to consent)1. Subject to Articles 17 and 20 below, an intervention may only be carried out on a person who does not have the capacity to consent, for his or her direct benefit.2. Where, according to law, a minor does not have the capacity to consent to an intervention, the intervention may only be carried out with the authorisation of his or her representative or an authority or a person or... (shrink)

The quantum information introduced by quantum mechanics is equivalent to a certain generalization of classical information: from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The “qubit”, can be interpreted as that generalization of “bit”, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time (...) after measurement. The quantity of quantum information is the transfinite ordinal number corresponding to the infinity series in question. The transfinite ordinal numbers can be defined as ambiguously corresponding “transfinite natural numbers” generalizing the natural numbers of Peano arithmetic to “Hilbert arithmetic” allowing for the unification of the foundations of mathematics and quantum mechanics. (shrink)

This work provides the means for re-establishing the unity of science by interpreting the whole of modern experimental science from the perspective of analogous transfer of the metaphysical principle of unity rather than in terms of efficient causality.

Cantor’s theory of cardinal numbers offers a way to generalize arithmetic from finite sets to infinite sets using the notion of one-to-one association between two sets. As is well known, all countable infinite sets have the same ‘size’ in this account, namely that of the cardinality of the natural numbers. However, throughout the history of reflections on infinity another powerful intuition has played a major role: if a collectionAis properly included in a collectionBthen the ‘size’ ofAshould be less (...) than the ‘size’ ofB(part–whole principle). This second intuition was not developed mathematically in a satisfactory way until quite recently. In this article I begin by reviewing the contributions of some thinkers who argued in favor of the assignment of different sizes to infinite collections of natural numbers (Thabit ibn Qurra, Grosseteste, Maignan, Bolzano). Then, I review some recent mathematical developments that generalize the part–whole principle to infinite sets in a coherent fashion (Katz, Benci, Di Nasso, Forti). Finally, I show how these new developments are important for a proper evaluation of a number of positions in philosophy of mathematics which argue either for the inevitability of the Cantorian notion of infinite number (Gödel) or for the rational nature of the Cantorian generalization as opposed to that, based on the part–whole principle, envisaged by Bolzano (Kitcher). (shrink)

Dealing with the metaphysical foundations of modern physical science, this book demonstrates that not only is classical metaphysics not in conflict with the principles of modern experimental science but that, when analogously transferred to the different divisions of modern science, the metaphysical principle of unity makes intelligible all the laws of modern science. This revolutionary book provides the means for reestablishing the unity of science by interpreting the whole of modern experimental science from the perspective of an analogous transfer of (...) the metaphysical principle of unity rather than in terms of efficient causality. (shrink)

This entry discusses the notion of a unit of normativity. This notion may be understood in two distinct ways. One way to understand a unit of normativity is as some particular type of assignment of normative status, e.g., a requirement, an ought, a reason, or a permission. A second way to understand a unit of normativity is as a measure of a quantity of normativity, perhaps associated with the numerical assignment given to the strength of reasons. This entry outlines (...) some basic differences among units of normativity in the first sense, noting that they vary slightly depending on whether one is talking about normativity in a more general or more robust sense. This entry also discusses in more detail the question of whether there might be a unit of normativity in the second sense. It discusses the relevant metaphysical questions. It also provides an explanation of why reasons can be assigned numerical strengths, even if there are no units of normativity in the sense of measurements of quantities of normativity. (shrink)

The problem of how to rationally aggregate probability measures occurs in particular when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and when an individual whose belief system is compatible with several probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory. We investigate this problem by first recalling some negative results from preference and judgment (...) aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s :410–414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms à la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed. (shrink)

It has been suggested that we ought to idealize the apparatus used to measure quantum systems as consisting of an infinite number of particles. Various authors have claimed that if we do so we do not need to take seriously the limitations on measurement incorporated into the Wigner-Araki-Yanase quantum theory of measurement. Bub and claims we can solve the measurement problem if we make this assumption. I argue against both claims on the basis of differences between the role (...) of such idealizations in classical and quantum mechanics. (shrink)

It has been suggested that the measuring apparatus used to measure quantum systems ought to be idealized as consisting of an infinite number of quantum systems. Let us call this the infinity assumption. The suggestion that we ought to make the infinity assumption has been made in connection with two closely related but distinct problems. One is the problem of determining the importance of the limitations on measurement incorporated into the Wigner-Araki-Yanase quantum theory of measurement. The other is (...) the measurement problem. These problems are not internal to the quantum mechanical formalism. They arise when we obtain particular formal results in applying the quantum mechanical formalism to measurement interactions. The formal results are problematic because they resist explanation. Various authors have claimed that by making the infinity assumption we can neglect the limitations on measurement. Bub (1988) and (1989) claims it allows us to solve the measurement problem. I will argue that both claims are unjustified. (shrink)

This article investigates National Defense Education Act and National Defense Education Act-related calls in the late 1950s for the training of guidance counselors, an emergent profession that was to play an instrumental role in both the measuring and placement of students in schools by “intelligence” or academic “ability”. In analyzing this mid-century push for more guidance counseling in schools, this article will first explore a foundational argument for the fairness of intelligence testing made by Educational Testing Service psychometrician William Turnbull (...) in 1951, and then later taken up and employed by other National Defense Education Act-era advocates of testing and grouping. Secondly, this analysis will proceed to National Defense Education Act expert testimony, examining here assertions of the necessity of guidance counseling in schools, and an emergent and shared vision articulating the role guidance counseling was supposed to play in school life. A pattern or structure to this vision emerges here. According to its advocates, guidance counseling would not only inform the self-understanding of the measured individual, but it would also work to condition the ideology of individual intelligence across numerous layers of social life around the student: through peer group, through teachers and school administrators, and finally through home, family, and the wider community. (shrink)

We prove that if $$\mathcal {A}$$ A is an infinite Boolean algebra in the ground model V and $$\mathbb {P}$$ P is a notion of forcing adding any of the following reals: a Cohen real, an unsplit real, or a random real, then, in any $$\mathbb {P}$$ P -generic extension V[G], $$\mathcal {A}$$ A has neither the Nikodym property nor the Grothendieck property. A similar result is also proved for a dominating real and the Nikodym property.

We consider how to represent the measurable sets in an infinite measure space. We use sequences of simple measurable sets converging under metrics to represent general measurable sets. Then we study the computability of the measure and the set operators of measurable sets with respect to such representations.

The nature of measurement is a topic of central concern in the philosophy of science and, indeed, measurement is the essential link between science and mathematics. Professor Ellis's book, originally published in 1966, is the first general exposition of the philosophical and logical principles involved in measurement since N. R. Campbell's Principles of Measurement and Calculation, and P. W. Bridgman's Dimensional Analysis. Professor Ellis writes from an empiricist standpoint. His object is to distinguish and define the basic concepts in measurement, (...) for example: scale, quantity, unit. dimension, number and probability. He discusses the problem of classifying scales of measurement and the special logical problems associated with each kind of scale. A translation of mach's Critique on the Concept of Temperature, which gives his views on the nature of measurement more fully than in any of his other works, is given as an appendix. (shrink)

By compiling an experimental method combining both dialectic and rhetoric, 'Dialectic, Rhetoric and Contrast: The Infinite Middle of Meaning' demonstrates how singular meanings can be rendered in a spectrum of 12 repeating concepts that are in a continuum, gradated and symmetrical. The ability to arrange meaning into this pattern opens enquiry into its ontology, and presents meaning as closer to the sensation of colours or musical notes than the bivalent oppositions depicted in classical logic. However, the experiment does not (...) assert that this pattern suggests some sort of constant or absolute principle; instead, it theorises on the ways in which meaning can be considered to be recursive. To explain this, the book explores the concept of contrast itself. No exactitude on the precise existence of contrast can ever be struck because the answer varies infinitely depending upon the scale of measurement used to gauge the meeting point. This characteristic of contrast helps to define a whole new dimension from which sensation, meaning, cognition and consciousness can be analogised to the infinite forms between forms. At a time when the widest consensus in philosophy is the exhaustion of its central themes, the significance of such a hypothesis provides fresh impetus to revise some of the key meanings and concepts underpinning contemporary thought. To do this, the method explores the opposing themes of idealism and realism that run throughout western philosophy from Plato to the Speculative turn. This book will be of interest to professional academic audiences in the humanities and social sciences, from graduates to senior scholars. It will also be an interesting read to anyone wishing to keep abreast of developments in continental philosophy, epistemology, metaphysics, and the sociology of knowledge. (shrink)

The nature of measurement is a topic of central concern in the philosophy of science and, indeed, measurement is the essential link between science and mathematics. Professor Ellis's book, originally published in 1966, is the first general exposition of the philosophical and logical principles involved in measurement since N. R. Campbell's Principles of Measurement and Calculation, and P. W. Bridgman's Dimensional Analysis. Professor Ellis writes from an empiricist standpoint. His object is to distinguish and define the basic concepts in measurement, (...) for example: scale, quantity, unit. dimension, number and probability. He discusses the problem of classifying scales of measurement and the special logical problems associated with each kind of scale. A translation of mach's Critique on the Concept of Temperature, which gives his views on the nature of measurement more fully than in any of his other works, is given as an appendix. (shrink)

Issues of measure and measurement, and their relation to value and values, are of concern in several major threads in contemporary social theory and social research. In this article, the notion of ‘measure–value environments’ is introduced as a theoretical lens through which the life of measures can be better understood. A number of points are made which represent both a continuation and a slight change in emphasis vis-à-vis the existing scholarship. First, it is argued that the relation between (...) measure and value is necessarily circular – better, entangled. Second, a conceptualization of measures as territorializing devices is advanced. Third, importance is given to the fact that measures are not simply tools in our hands, they are also environments in which we live. Fourth, attention is drawn to the fact that the unit is not just a quantitative happening among others, but is qualitatively distinct. (shrink)

In this paper, I shall discuss the issue whether the standard meter in Paris is in fact one meter long. Whether one could meaningfully assert this proposition depends on how the unit of length a meter is defined. I would like to suggest three conceivable definitions. One meter long is everything that has the same length as an arbitrary chosen rod S now has. According to the second definition one meter long is everything that coincides in the endpoints with the (...) rod S when placed alongside. The third definition states that one meter long is-in a literal sense-the rod S solely. Other objects are one meter long-although in a derived sense-if they coincide in the endpoints with S when placed alongside. The first definition is in essence the standpoint of Kripke, the second one can be attributed to Wittgenstein, the last definition is the proposal I would like to advocate here. In particular, I hold that the third definition can be attributed to Wittgenstein as well. A language-game of measuring presupposes a preparatory game of fixing a unit of measure. The meaning of the expression "standard meter" must thus be derived from this preparatory game. Therefore with all other objects, one can say only in a derived sense that they are one meter long or not. (shrink)

The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time (...) after measurement. The quantity of quantum information is the ordinal corresponding to the infinity series in question. Number and being (by the meditation of time), the natural and artificial turn out to be not more than different hypostases of a single common essence. This implies some kind of neo-Pythagorean ontology making related mathematics, physics, and technics immediately, by an explicit mathematical structure. (shrink)

According to the realist interpretation, measurement commits us not just to the logically independent existence of things in space and time, but also to the existence of quantitatively structured properties and relations, and to the existence of real numbers, understood as relations of ratio between specific levels of such attributes. Measurement is defined as the estimation of numerical relations (or ratios) between magnitudes of a quantitative attribute and a unit. The history of scientific measurement, from antiquity to the present may (...) be interpreted as revealing a progressive deepening in the understanding of this position. First, the concept of ratio was broadened to include ratios between incommensurable magnitudes; second, the concept of a quantitative attribute was broadened to include non-extensive quantities; third, quantitative structure and its relations to ratios and real numbers were elaborated; and finally, the issue of empirically distinguishing between quantitative and non-quantitative structures was addressed. This interpretation of measurement understands it in a way that is continuous with scientific investigation in general, i.e., as an attempt to discover independently existing facts. (shrink)

We investigate in the frame of TTE the computability of functions of the measurable sets from an infinite computable measure space such as the measure and the four kinds of set operations. We first present a series of undecidability and incomputability results about measurable sets. Then we construct several examples of computable topological spaces from the abstract infinite computable measure space, and analyze the computability of the considered functions via respectively each of the standard representations (...) of the computable topological spaces constructed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Walking the Bodhisattva Path/Walking the Christ PathU.S. Conference of Catholic BishopsCatholics and Buddhists brought together by Dharma Realm Buddhist Association, the San Francisco Zen Center, and the United States Conference of Catholic Bishops (USCCB) met 20-23 March 2003 in the first of an anticipated series of four annual dialogues. Abbot Heng Lyu, the monks and nuns, and members of the Dharma Realm Buddhist Association hosted the dialogue at the (...) City of Ten Thousand Buddhas in Talmage, California. The community had transformed their Confucius Hall into a chapel, with a large, newly constructed wooden cross on a wall above an altar facing out from a raised platform, so the Catholic delegation would have a space for worship. A special poster announcing the theme of the conference, "Walking the Bodhisattva Path/Walking the Christ Path," showing a Buddhist dharma wheel at one foot of a bridge and a Celtic cross at the other foot, had been created by the hosting community.The daily schedule for the dialogue did not interfere with the monastic routine at the City of Ten Thousand Buddhas, which included early morning chanting (4:00-5:00 am), daily rituals in the Buddha Hall, and the single large meal for monastics before noon to which all participants were invited. Catholics and Buddhists meeting in the dialogue began each day with an optional forty-five minutes of quiet sitting together in the monastery meditation hall, each following their own form of meditation and prayer. There was a Eucharist on Friday and Saturday evenings for the Catholics and to which the Buddhists were invited, and additional meals of breakfast and supper throughout the meeting at the City's Jyun Kang Restaurant.Fourteen Buddhists and fourteen Catholics participated in the formal discussions. Each participant spoke on what it means to them to follow Christ or the way of the Bodhisattvas or enlightened beings. In addition to speaking, each participant distributed a short passage, usually from a traditional text, on this topic. Several passages from Master Dogen's Shobogenzo and the Gospel of John were among those shared by the group. Other passages shared were taken from the Avatamsaka Sutra and the Shurangama Sutra and from the other gospels and the writings of Zen master HakuinZenji, the Dalai Lama, Korean Zen Master I-sahn Hye-yeon, the teachings of Master [End Page 247] Hsuan Hua, Shantideva, Origen, St. Ignatius, St. Benedict, the author of The Cloud of Unknowing, St. John of the Cross, and Chiara Lubich. A minute of silence separated the fifteen-minute segments for each presentation. With so large a group, most of the time in the formal sessions involved listening to series of presentations; however, during discussion periods the participants asked several challenging questions of one another.Some participants noted the tension they felt between belonging to a particular religious group and the need to let go of any consequential narrowness. The goal of the discussion was to promote understanding of the differences and similarities between Christianity and Buddhism. At one point, the participants noted several concerns about mutual enrichment: whether Buddhist methods can be separated from Buddhism and Christian methods from Christianity, and what specific aspects of Christian practice truly enrich Buddhists and which Buddhist practices likewise enrich Christians. Several times participants discussed their understanding of terms such as transformation, grace, the incarnation and the passion of Jesus, discernment of spirits, prayer, Buddha-nature, and related terms. There was consensus that Buddhists and Catholics can practically help one another regarding mental cultivation and religious precepts. They expressed this consensus in their choice of the topic forthe next dialogue, "Transformation of Hearts and Minds: Chan/Zen-Catholic Approaches to Precepts."The group agreed to reconvene in 2004 to respond to six presentations, three from each side, on different aspects of this topic.Chairing the sessions were Rev. Heng Sure for the Dharma Realm Buddhist Association, Rev. Taigen Dan Leighton for the San Francisco Zen Center, and Bishop John Webster for the United States Conference of Catholic Bishops. Their three organizations are the sponsors of the Northern California Chan/Zen-Catholic Dialogue. Chan and Zen are respectively the Chinese and Japanese terms for the meditation school... (shrink)

This most unusual book consists of a 35 page prescript by the editor followed by the text in which the author seeks to show that the International System of Units, which is under the supervision of the International Bureau of Weights and Measures, depends upon Aristotelian-Thomistic philosophy.

Based on an extensive review of the literature and field surveys, the paper proposes a conceptualization and operationalization of corporate citizenship meaningful in two countries: the United States and France. A survey of 210 American and 120 French managers provides support for the proposed definition of corporate citizenship as a construct including the four correlated factors of economic, legal, ethical, and discretionary citizenship. The managerial implications of the research and directions for future research are discussed.

The recently developed technique of Bohrification associates to a (unital) C*-algebra Athe Kripke model, a presheaf topos, of its classical contexts;in this Kripke model a commutative C*-algebra, called the Bohrification of A;the spectrum of the Bohrification as a locale internal in the Kripke model. We propose this locale, the ‘state space’, as a (n intuitionistic) logic of the physical system whose observable algebra is A.We compute a site which externally captures this locale and find that externally its points may be (...) identified with partial measurement outcomes. This prompts us to compare Scott-continuity on the poset of contexts and continuity with respect to the C*-algebra as two ways to mathematically identify measurement outcomes with the same physical interpretation. Finally, we consider the not-not-sheafification of the Kripke model on classical contexts and obtain a space of measurement outcomes which for commutative C*-algebras coincides with the spectrum. The construction is functorial on the category of C*-algebras with commutativity reflecting maps. (shrink)

This volume examines a selection of late medieval works devoted to the intensive infinite in order to draw a comprehensive picture of the context, character and ...

Pollock (2004) argues in favour of Wittgenstein’s (1953) claim that the standard metre bar in Paris has no metric length: Because the standard retains a special status in the system of measurement, it cannot be applied to itself. However, we argue that Pollock is mistaken regarding the feature of the standard metre which supports its special status. While the unit markings were arbitrarily designated, the constitution, preservation and application of the bar have been scientifically developed to optimize stability, and hence (...) predictive accuracy. We argue that it is the ‘hard to improve’ quality of stability that supports the standard’s value in measurement, not any of its arbitrary features. And because the special status of the prototype is tied to its ability to meet this external criterion, the possibility always exists of identifying an alternative, more stable, standard, thereby allowing the original standard to be measured. (shrink)

In this study, we tested the feasibility of conducting quantitative assessments of patients’ experiences with care in the intensive care unit (ICU), in regard to treatment with respect and dignity. Patients completed the Patient Dignity Inventory, Collaborate, and selected domains from the Hospital Consumer Assessment of Health Providers and Systems Survey. Family members were additionally surveyed using the Family Satisfaction in ICU Care questionnaire. Overall, patients reported high levels of satisfaction in terms of nurses and doctors treating them with courtesy (...) and respect; however, physical aspects of care were reported to be more problematic. While this pilot study suggests some target areas for improving treatment with respect and dignity, the findings are limited since many patients were unable to participate in the survey. Future work should be directed at developing new measures that are easier to administer in this setting. (shrink)

It is possible that a fair coin tossed infinitely many times will always land heads. So the probability of such a sequence of outcomes should, intuitively, be positive, albeit miniscule: 0 probability ought to be reserved for impossible events. And, furthermore, since the tosses are independent and the probability of heads (and tails) on a single toss is half, all sequences are equiprobable. But Williamson has adduced an argument that purports to show that our intuitions notwithstanding, the probability of an (...) infinite sequence is 0. In this paper, I rebut his argument.No Abstract. (shrink)

Einstein’s razor, a corollary of Ockham’s razor, is often paraphrased as follows: make everything as simple as possible, but not simpler. This rule of thumb describes the challenge that designers of a legal system face—to craft simple laws that produce desired ends, but not to pursue simplicity so far as to undermine those ends. Complexity, simplicity’s inverse, taxes cognition and increases the likelihood of suboptimal decisions. In addition, unnecessary legal complexity can drive a misallocation of human capital toward comprehending and (...) complying with legal rules and away from other productive ends. While many scholars have offered descriptive accounts or theoretical models of legal complexity, most empirical research to date has been limited to simple measures of size, such as the number of pages in a bill. No extant research rigorously applies a meaningful model to real data. As a consequence, we have no reliable means to determine whether a new bill, regulation, order, or precedent substantially effects legal complexity. In this paper, we begin to address this need by developing a proposed empirical framework for measuring relative legal complexity. This framework is based on “knowledge acquisition”, an approach at the intersection of psychology and computer science, which can take into account the structure, language, and interdependence of law. We then demonstrate the descriptive value of this framework by applying it to the U.S. Code’s Titles, scoring and ranking them by their relative complexity. We measure various features of a title including its structural size, the net flow of its intra-title citations and its linguistic entropy. Our framework is flexible, intuitive, and transparent, and we offer this approach as a first step in developing a practical methodology for assessing legal complexity. (shrink)

Introduction. The problems of state and local governance in sparsely populated and rural areas is relevant for the Russian Federation due to the presence of depressed areas, depopulation of the countryside, small towns, monotowns, migration of the rural population to large cities, regional capitals, other regions and abroad. These processes are typical for many other modern states. Solving the problems of rural and sparsely populated areas includes providing socially significant services, protecting the health and safety of residents, developing education, creating (...) and maintaining social infrastructure, and creating jobs. The purpose of the article is to identify the most important management problems in rural and sparsely populated areas and reveal possible solutions to these problems using the example of Great Britain. Methods. The research is based on a systematic approach to management in rural and sparsely populated areas. Analysis of factual data, legal sources, published survey results, foreign Internet sources. Comparative analysis of problems and measures of state policy in different states. Scientific novelty of the research. The author highlights the current measures taken in the UK at the central, local levels in order to overcome the problems of rural and sparsely populated areas. These activities as a basis for developing practical recommendations may be important for solving similar problems in Russian regions, including in the context of the COVID-19 epidemic and economic problems in the near future. Results. As a result the author identifies problems in the field of management in rural and sparsely populated and hard-to-reach areas, as well as possible directions of state policy in the UK and Russia to overcome these problems. Conclusions. The most important direction of state policy for solving the problems highlighted in the study is the development of local interests of the community, the integration of state support measures and local events. As measures aimed at solving social and infrastructural problems of sparsely populated areas in the UK, one can single out government programs implemented at the national and regional levels with the participation of industrial enterprises and businesses, a grant mechanism for the implementation of financial support, combined with the empowerment of local communities. There is no such policy in Russia yet. (shrink)

We study the model-theoretic aspects of a probability logic suited for talking about measure spaces. This nonclassical logic has a model theory rather different from that of classical predicate logic. In general, not every satisfiable set of sentences has a countable model, but we show that one can always build a model on the unit interval. Also, the probability logic under consideration is not compact. However, using ultraproducts we can prove a compactness theorem for a certain class of weak (...) models. (shrink)

Based on an extensive review of the literature and field surveys, the paper proposes a conceptualization and operationalization of corporate citizenship meaningful in two countries: the United States and France. A survey of 210 American and 120 French managers provides support for the proposed definition of corporate citizenship as a construct including the four correlated factors of economic, legal, ethical, and discretionary citizenship. The managerial implications of the research and directions for future research are discussed.

Name der Zeitschrift: Journal of Ancient History Jahrgang: 5 Heft: 2 Seiten: 280-303.