Glenn Gould was Canada's greatest musician. From his home in Toronto, he rose to be a world-famous concert pianist and recording artist of the very top rank. Gould's eccentric attitudes and behaviours were well known, but the musical world was astonished when, in his mid-20s, he announced that he had permanently retired from the concert hall. Instead, Gould focused on the recording studio, on radio and television, and on exploring his fascination with the relation between audience (...) and performer. Through wide and innovative use of electronic technologies, he was able to reach enormous audiences before his untimely death. Glenn Gould: Music & Mind focuses not on the details of Gould's life but on his ideas, offering unique insights into this remarkable Canadian and his life's work. Includes bibliographies and discographies of Gould's work. (shrink)

A provocative account of pianist Glenn Gould's philosophy which argues that music is not only a reflection of social dynamics, but can also be a tool for a betterment of society.

In A Thousand Plateaus, Deleuze and Guattari refer to Glenn Gould as an illustration of the third principle of the rhizome, that of multiplicity: ‘When Glenn Gould speeds up the performance of a piece, he is not just displaying virtuosity, he is transforming the musical points into lines, he is making the whole piece proliferate’ (1987: 8). In an attempt to make sensible their ostensibly modest statement, I proliferate the relationships between Glenn Gould's philosophy (...) of sound recording, Deleuze's theory of passive synthesis, and Deleuze and Guattari's concept of the stutter. I argue, ultimately, that Glenn Gould's radical recording practice stutters and deterritorialises the temporality of the recorded performance. More generally, the Deleuzian perspective broadens the scope of Gould's aesthetic practices that highlights the importance of aesthetic acts in the redistribution of sensory experience. But the study serves a broader purpose than celebrating a pianist/recordist that Deleuze admired. Rather, while his contemporaries began to use the studio as a compositional element in sound recording, Gould bypassed such a step towards the informational logics of recording studios. Thus, it is inappropriate to think of Gould as having immersed himself in ‘technology’ than the broader concept of a complex, one that redistributed the striated listening space of the concert hall. (shrink)

This paper explores the meaning of interpretation in the works of Hans-Georg Gadamer and Glenn Gould, the Canadian pianist and intellectual. As a performing art, music illustrates the cognitive and practical dimensions of interpretation. While emphasizing the pre-interpreted character of musical reception and performance, both authors point to the fact that difference, alterity, and negativity lie at the heart of creative interpretation, cultivation and self-knowledge. The notion of ecstasy, understood as a type of self-forgetfulness that represents a radical (...) form of encounter with alterity, provides the basis for a conception of subjectivity as grounded on linguistic, historical and cultural conditions, albeit not reducible to them. I maintain that the notion of ecstatic subjects is a powerful alternative to both the self-centred notion of subjectivity and its anti-humanistic counterpart in accounting for human agency. (shrink)

En la página 52 de su autobiografía Mi vida en la música Daniel Barenboin afirma no compartir la filosofía de Glenn Gould para quien la grabación es la única manera de producir música en el futuro. Baremboin define a su filosofía de la música un ¿naturalismo¿ para el que la música es sinónimo de vida, y lo que la singulariza es el tiempo, y el tiempo es lo que se pierde y jamás vuelve. El tiempo es lo que (...) se pretende expulsar de una sala de grabación. La música es tiempo y, por lo tanto no repetición, el metrónomo sólo repite la medida. A las notas las sigue el silencio sin el cual no existirían, y la duración del sonido es por eso intermitente, finita, mortal. Este efecto de vacío es también marcado en el mundo del lenguaje. Foucault decía que desde el punto de vista ¿arqueológico¿ los discursos son escasos, que lo que primero debe llamarnos la atención es la rareza de su existencia. Por eso mismo el sentido es también escaso, no constituye una abundancia que los hermeneutas deben interpretar. Así como hay más palabras que sentido, hay menos palabras que cosas, y en este orden de las carencias no olvidemos la primera lección de la economía política que define al ¿bien¿ por su rareza. El sonido es, entonces, una isla en un mar de silencio. Pero no fue sin duda este pequeño parágrafo en el libro de Barenboin lo que me marcó un interrogante llamado Gould. Hubo, además, una mención en la misma página referida a la muerte de Gould que le había impedido comparar las distintas versiones de sus Variaciones de Goldberg. Es posible que una cierta curiosidad por los espíritus trágicos haya detenido mi atención. (shrink)

What are we to make of Western Buddhism? Glenn Wallis argues that in aligning their tradition with the contemporary self-help industry, Western Buddhists evade the consequences of Buddhist thought. This book shows that with concepts such as vanishing, nihility, extinction, contingency, and no-self, Buddhism, like all potent systems of thought, articulates a notion of the "real." Raw, unflinching acceptance of this real is held by Buddhism to be at the very core of human "awakening." Yet these preeminent human truths (...) are universally shored up against in contemporary Buddhist practice, which contradicts the very heart of Buddhism. The author's critique of Western Buddhism is threefold. It is immanent, in emerging out of Buddhist thought but taking it beyond what it itself publicly concedes; negative, in employing the "democratizing" deconstructive methods of François Laruelle's non-philosophy; and re-descriptive, in applying Laruelle's concept of philofiction. Through applying resources of Continental philosophy to Western Buddhism, A Critique of Western Buddhism suggests a possible practice for our time, an "anthropotechnic", or religion transposed from its seductive, but misguiding, idealist haven. (shrink)

Degrees of belief; Dempster's rule of combination; Simple and separable support functions; The weights of evidence; Compatible frames of discernment; Support functions; The discernment of evidence; Quasi support functions; Consonance; Statistical evidence; The dual nature of probable reasoning.

Responses to the COVID-19 pandemic prompted people and institutions to turn to online virtual environments for a wide variety of social gatherings. In this perspectives article, we draw upon our previous work and interviews with Ghanaian Christian leaders to consider implications of this shift. Specifically, we propose that the shift from physical to virtual interactions mimics and amplifies the neoliberal individualist experience of abstraction from place associated with Eurocentric modernity. On the positive side, the shift from physical to virtual environments (...) liberates people to selectively pursue the most fulfilling interactions, free from constraints of physical distance. On the negative side, the move from physical to virtual space necessitates a shift from material care and tangible engagement with the local community to the psychologization of care and pursuit of emotional intimacy in relations of one’s choosing—a dynamic that further marginalizes people who are already on the margins. The disruptions of the pandemic provide an opportunity to re-set social relations, to design ways of being that better promote sustainable collective well-being rather than fleeting personal fulfillment. (shrink)

: A central component of Bernard Williams' political realism is the articulation of a standard of legitimacy from within politics itself: LEG. This standard is presented as basic, inherent in all political orders and the best way to underwrite fundamental liberal principles particular to the modern state, including basic human rights. It does not require, according to Williams, a wider set of liberal values. In the following, I show that where Williams restricts LEG to generating only minimal political protections, seeking (...) to isolate his account of political legitimacy from a range of liberal principles, this is neither internal to, nor necessarily demanded by, the specifically political account of LEG. Instead, the limitation depends upon his wider ethical thought. (shrink)

An account of the conflict between our positive and negative emotional relationships to the Earth and how they will be resolved for the Symbiocene, the next period in the history of the Earth.

In most forms of evaluation the benefits of preventive health care are narrowly defined in terms of reductions in future morbidity and mortality. Thus it is normally assumed that it is the final health gains alone which bear utility. This discounts the possibility that individuals may derive utility from the process of health care and other outcomes as well as the end health states. Attributes such as anxiety, reassurance, autonomy, regret and hope provide potential benefits or disbenefits in addition to (...) health gains. This paper explores the concept of process utility in the specific context of preventive goods. Characteristics such as information, awareness and autonomy are examined for two preventive goods—hip protectors and mammographic screening. If individuals trade off process attributes for final health outcomes, then to ignore process utility may lead to a sub-optimal allocation of resources. (shrink)

Conceived as a solution to clinical dilemmas, and now required by organizations for hospital accreditation, ethics committees have been subject only to small-scale studies. The wide use of ethics committees and the diverse roles they play compel study. In 1999 the University of Pennsylvania Ethics Committee Research Group (ECRG) completed the first national survey of the presence, composition, and activities of U.S. healthcare ethics committees (HECs). Ethics committees are relatively young, on average seven years in operation. Eighty-six percent of ethics (...) committees report that they play a role in ongoing clinical decision making through clinical ethics consultation. All are engaged in developing institutional clinical policy. Although 4.5% of HECs write policy on managed care, 50% of HEC chairs feel inadequately prepared to address managed care. The power and activity of ethics committees parallels the composition of those committees and the relationship of members to their institutions. The role of ethics committees across the nation in making policies about clinical care is greater than was known, and ethics committees will likely continue to play an important role in the debate and resolution of clinical cases and clinical policies. (shrink)

Are there no new ideas to be invented? Are today's ideas really just borrowed from previous times? Postmodernism says this is so, and it's one of the hottest philosophies of today. The book provides an indispensable guide to this often-demanding terrain for readers encountering theories of postmodernism for the first time and places the subject in a broad context. It introduces a wide range of ideas, thinkers, and views yet maintains the readers' focus by linking theory with concrete examples from (...) both "high" and "popular" culture. After completing Teach Yourself Postmodernism , readers will never look at their world the same way again. (shrink)

Borrowing from evolutionary biology, existentialism, developmental psychology, and social learning theory, an integrated model of human behavior is applied to several forms of self-destructive behavior, to include anorexia nervosa, suicide, substance abuse, and pathological gambling. It is argued that self-destructive behavior is a function of how the individual psychologically construes survival and copes with perceptions of isolation and separation from the environment. The paradox of self-destructive behavior in organisms motivated by self-preservation is resolved by taking note of the fact that (...) self-destruction stems from peopleís efforts to survive psychologically and resolve the subjectóobject duality, even when this places their physical well-being in jeopardy. (shrink)

This article examines the argument that biodiversity is crucial for well-functioning ecosystems and that such ecosystems provide important goods and services to our human societies, in short the ecosystem services argument (ESA). While the ESA can be a powerful argument for nature preservation, we argue that its dominant functionalist interpretation is confronted with three significant problems. First, the ESA seems unable to preserve the nature it claims to preserve. Second, the ESA cannot explain why those caring about nature want to (...) preserve it. Third, the ESA might undermine its own goal because it potentially decreases environmental motivations. (shrink)

The present article is a contribution to a particularly urgent issue that is unfolding in Buddhist circles in North America andEurope. Although this issue is framed in various ways, it revolves around a single question; namely, what form will contemporary reconfigurations of Buddhism take in the twenty-first century West? The most influential groups in this discussion to date are those that style themselves secular-, progressive-, atheist-, agnostic-, liberal-, and post-traditional Buddhist. As these groups gain adherents in the West, traditional organizations, (...) such as the various Zens, Tibetans, Vipassanas, etc., are stating their claim to “Buddhism” with increasingly vehement proprietorship. The present article, however, is not yet another attempt to reformulate or reform (in any sense of the term) “Buddhism.” Neither is it concerned with ameliorating traditional Buddhism's relationship with contemporary western secular values. In performing its first task, however, my emerging theory, called “speculative non-buddhism,” can contribute to the current debate in a decisive way by showing that all forms of Buddhism are identical. What makes them so is that they are all governed by what I call “buddhistic decision:” the syntactical structure that constitutes all things, discourse, and people, “Buddhist.” Decision thus constitutes both the ideological nature, and the ideological constant, of “Buddhism.”. (shrink)

Glenn Alexander Magee's controversial book argues that Hegel was decisively influenced by the Hermetic tradition, a body of thought with roots in Greco-Roman ...

Numerous searches have failed to identify a single co-occurrence of total blindness and schizophrenia. Evidence that blindness causes loss of certain NMDA-receptor functions is balanced by reports of compensatory gains. Connections between visual and anterior cingulate NMDA-receptor systems may help to explain how blindness could protect against schizophrenia.

This article analyzes business power in the context of noisy politics by comparing business involvement in two British referendum campaigns: one about membership in the European Communities in 1975, and the Brexit referendum about European Union membership in 2016. By exploring these two contexts, the article seeks to identify the conditions under which business elites can and cannot be effective in a context of noisy politics. Three key factors are identified as determinants of business influence during periods of noisy politics: (...) the incentives to get directly involved in noisy politics; the legitimacy of business involvement; and, finally, the capacity to act in a cohesive way. The article shows that these factors have changed substantially over the last four decades because of wider changes in the nature of capitalism, and their impact on business power in the United Kingdom and more generally is discussed. (shrink)

The sense of embodiment is vital for self recognition. An examination of anosognosia for hemiplegia—the inability to recognise that one is paralysed down one side of one’s body—suggests the existence of ‘online’ and ‘offline’ representations of the body. Online representations of the body are representations of the body as it is currently, are newly constructed moment by moment and are directly “plugged into” current perception of the body. In contrast, offline representations of the body are representations of what the body (...) is usually like, are relatively stable and are constructed from online representations. This distinction is supported by an analysis of phantom limb—the feeling that an amputated limb is still present—phenomena. Initially it seems that the sense of embodiment may arise from either of these types of representation; however, an integrated representation of the body seems to be required. It is suggested information from vision and emotions is involved in generating these representations. A lack of access to online representations of the body does not necessarily lead to a loss in the sense of embodiment. An integrated offline representation of the body could account for the sense of embodiment and perform the functions attributed to this sense. (shrink)

In this paper, I reinterpret the conflict between rewilders and those who want to preserve traditional agricultural landscapes. By showing that underlying both positions is a common outlook in which nature preservation can be described as a primarily interpretative act geared towards the preservation of meaning by establishing a successful contact with external reality, I hope to refocus the debate away from the current stalemate. Too often, the debate ends in a dispute about what counts as 'real nature'. By interpreting (...) nature preservation - whether it is directed at rewilding or at preserving old agricultural landscapes - as an act that is a response to nature's meanings, we will refocus attention on the real issue underlying preservation: articulating the ways nature is meaningful to us. (shrink)

This article examines Bernard Lonergan's account of the meaning, functions, and importance of art, focusing on the chapter on art in his Topics in Education (volume 10 of The Collected Works of Bernard Lonergan), the text derived from his 1959 Cincinnati lectures on philosophy of education. The essay begins by identifying important parallels between Lonergan s analysis of art and selected elements in the philosophies of Aristotle, Saint Augustine, Kant, Hegel, Tolstoy, Collingwood, and Heidegger. It then focuses upon Lonergan's particular (...) emphasis on artistic creation and appreciation as an exercise of human liberty, and as a testimony to the freedom of human consciousness. Developing this theme, it explores how Lonergan's analysis answers three critical questions: 1) what does art liberate us from? 2) what does art liberate us for? and, 3) why is art always about freedom? /// O presente artigo constitui uma análise da posição de Bernard Lonergan acerca do sentido, das funções, e da importância da arte, análise esta centrada no capítulo sobre a arte que se encontra na obra Topics in Education (volume 10 das Collected Works of Bernard Lonergan), texto este derivado das conferências pronunciadas pelo filósofo canadiano, em 1959, em Cincinnati, sobre Filosofia da Educação. O artigo começa com o estabelecimento de importantes paralelos entre as análises de Lonergan acerca da arte e alguns elementos escolhidos nas filosofias de Aristóteles, Santo Agostinho, Kant, Hegel, Tolstoi, Collingwood, e Martin Heidegger. Seguidamente, o artigo concentra-se na ênfase dada por Lonergan à criatividade e avaliação artísticas, mostrando de que modo uma e outra constituem exercícios maiores da liberdade humana, e, nessa medida, devem ser vistas como testemunhas privilegiadas da liberdade da consciência humana. Assim, ao desenvolver este tema, o artigo explora o modo como a análise de Lonergan responde às seguintes três questões críticas fundamentais: 1) de que coisas nos liberta a arte? 2) para que coisas nos liberta a arte? e 3) por que razão tem a arte sempre a ver com a liberdade? (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Nomadic Turns:Epistemology, Experience, and Women University Band DirectorsElizabeth GouldMusic education occupations in the U.S. have been segregated by gender and race for decades. While women are most likely to teach young students in classroom settings, men are most likely to teach older students in all settings, but most particularly in wind/percussion ensembles.1 Despite gender-affirmative employment practices, men constitute a large majority among band directors at all levels.2 At the (...) postsecondary level in the U.S., women constitute less than 10%.3 In all cases and all levels, the vast majority of band directors are white. Occupational segregation inhibits the development of individuals' careers as well as the development of the profession as individuals choose or are hired for positions based on their gender and/or race rather than their abilities.In terms of women university band directors, researchers have investigated employment trends,4 personal and occupational characteristics,5 occupational role models, and professional identity.6 Their findings generally have supported the hypotheses that historical precedent, traditional socialization, discrimination, segregation, and lack of role models contribute to their persistently low percentage as band directors. Longitudinal studies7 demonstrate that the percentage of women band directors has not increased significantly, and may be actually [End Page 147] declining after thirty years of enforcing affirmative action laws, which would suggest that these interventions have not provided the basis for enacting change in the profession. Further, change does not seem possible if members of the profession do not understand what causes the situation to persist. For example, while the College Band Directors National Association has supported the Linda A. Hartley and Deborah A. Sheldon study,8 their concern seems to be in only identifying the extent of the situation with the intention of increasing the number of women and non-white individuals who are band directors within the profession as it currently is constructed. This empirical approach is inadequate because it addresses neither the values held by members of the profession, nor its structure, which as previous research indicates, is poorly understood and must change to make possible meaningful increases in the number of women and non-white people.The profession of conducting university bands exists within the profession of music education in general, which, of course, exists within the profession of music. Clearly, one cannot be adequately understood without placing it in the context of the others. What is needed, then, are richer, more substantive, and meaningful understandings of the professions in general and of specific questions within them in particular, as they may provide the basis on which change can be possible. In addition to addressing the issue of persistent occupational gender and racial segregation, questions that may be addressed include positionalities9 of bands in the music education profession, the relationship of performance/conducting to the music profession, and the role of the musician in society in general. In order to accomplish this, I propose an analytical method that is both postmodern and feminist, and in which the philosophical figuration of the nomad, as explicated by Rosi Braidotti,10 is central.Postmodern/Feminist AnalysisDescribed variously as a "philosophical perspective,"11 a "sensibility,"12 and a historical moment,13 postmodernism resists definition. It may be understood as a way of perceiving the world that accepts and even embraces contradictions and uncertainties while rejecting commonly accepted cultural beliefs and practices, including humanist understandings of identity, representation, and the subject. This is a "postmodernism of resistance"14 that interrogates cultural practices, focusing on what is unexpected, marginalized, and silenced, opening spaces for change. In contrast, analysis based on modernism is constrained by binary oppositions that inscribe the positionalities of social groups. These oppositions are exemplified by Subject/Other (for example, male/female, reason/emotion) and consist of asymmetrical power relations in which the former is privileged over the latter, and the latter is defined in terms of not-the former. Postmodern analysis [End Page 148] reveals what these dualisms exclude, distort, or obscure, and provides flexibility for research from a variety of perspectives. Braidotti describes it as a "new kind of theoretical style"15 in terms of thinking, design, and analysis of research, a style... (shrink)

Over the past several decades, philosophers have grown to recognize the role played by frameworks and models in the construction of human knowledge. Further, they have paid increasing attention to the origins of knowing processes in social and historical contexts of human practical activities, and to social transformation of the frameworks over time. In a series of original essays by prominent philosophers, Constructivism and Practice advances the understanding of the role of construction and model creation, reflects on the relationship of (...) these models to social practices, and considers whether our modes of knowing themselves have a history. These questions are thoughtfully considered in the light of the 'historical epistemology' first developed by Marx Wartofsky. Contributions by Joseph Margolis; Tom Rockmore; Lisa Dolling; Jaakko Hintikka; Anton Alterman; Stephen Toulmin; Michel Paty; John Stachel; Gregg Horowitz; Michael Kelly; Tom Huhn; Barbara Savedoff; Saul Fisher; Sybil Schwarzenbach; John Pittman; Raphael Sassower; and MaryAnn Cutter. (shrink)

They are correct that punctuated equilibria apply to sexually reproducing organisms and that morphological evolutionary change is regarded as largely (if not exclusively) correlated with speciation events. However, they err in suggesting that we attribute stasis strictly to "developmental constraints," which represent only one of a set of possible mechanisms that we have suggested for the causes of stasis. Others include habitat tracking and the internal structure of species themselves [for example, (2)].

In this paper, I defend a pluralistic view of phenomenological method which will provide evidence for particular accounts of experience without relying exclusively on the reflective method or on intuition as a criterion for truth. To this end, I discuss the prospects for indirect phenomenology. I argue that phenomenology ought to be defined by its object of investigation, first-person experience, and not by any particular method of gaining access to this object of investigation. On this view, an integration of naturalized (...) phenomenology into the cognitive sciences is far more feasible than we might have expected. (shrink)

I offer a new metacognitive account of the feeling of agency over bodily actions. On this model the feeling of agency is the metacognitive monitoring of two cues: i) smoothness of action: done via monitoring the output of the comparison between actual and predicted sensory consequences of action and ii) action outcome: done via monitoring the outcome of action and its success relative to a prior intention. Previous research has shown that the comparator model offers a powerful explanation of the (...) feeling of agency. However, within the literature there is a growing sense of unease with the model; a consensus seems to be building that the model is not up to the task of explaining all of the new discoveries made regarding the feeling of agency since its inception. Most problematically there are paradigms which deeply challenge the comparator model by suggesting that a weak feeling of agency can be elicited even when no motor prediction is formed. The new account offered here inherits the explanatory power of the comparator model whilst avoiding this problem. (shrink)

Gottfried Wilhelm Leibniz was one of the central figures of seventeenth-century philosophy, and a huge intellectual figure in his age. This book from Glenn A. Hartz is an advanced study of Leibniz's metaphysics. Hartz analyzes a very complicated topic, widely discussed in contemporary commentaries on Leibniz, namely the question of whether Leibniz was a metaphysical idealist, realist, or whether he tried to reconcile both trends in his mature philosophy. Because Leibniz is notoriously unclear about this, much has been written (...) on the subject. In recent years, the debate has centered on whether it is possible to maintain compatibility between the two trends. In this controversial book, Hartz demonstrates that it is not possible to maintain compatibility of idealist and realist views - they must be understood as completely separate theories. As the first major work on realism in Leibniz's metaphysics, this key text will interest international Leibniz scholars, as well as students at the graduate level. (shrink)

The sense of agency, that is the sense that one is the agent of one’s bodily actions, is one component of our self-consciousness. Recently, Wegner and colleagues have developed a model of the causal history of this sense. Their model takes it that the sense of agency is elicited for an action when one infers that one or other of one’s mental states caused that action. In their terms, the sense of agency is elicited by the inference to apparent mental (...) state causation. Here, I argue that this model is inconsistent with data from developmental psychology that suggests children can identify the agent behind an action without being capable of understanding the relationship between their intentions and actions. Furthermore, I argue that this model is inconsistent with the preserved sense of agency in autism. In general, the problem is that there are cases where subjects can experience themselves as the agent behind their actions despite lacking the resources to make the inference to apparent mental state causation. (shrink)

THE ART OF CAUSAL CONJECTURE Glenn Shafer Table of Contents Chapter 1. Introduction........................................................................................ ...........1 1.1. Probability Trees..........................................................................................3 1.2. Many Observers, Many Stances, Many Natures..........................................8 1.3. Causal Relations as Relations in Nature’s Tree...........................................9 1.4. Evidence............................................................................................ ...........13 1.5. Measuring the Average Effect of a Cause....................................................17 1.6. Causal Diagrams..........................................................................................20 1.7. Humean Events............................................................................................23 1.8. Three Levels of Causal Language................................................................27 1.9. An Outline of the Book................................................................................27 Chapter 2. Event Trees............................................................................................... .....31 2.1. Situations and Events...................................................................................32 2.2. The Ordering of Situations and Moivrean Events.......................................35 2.3. Cuts................................................................................................ ..............39 2.4. Humean Events............................................................................................43 (...) 2.5. Moivrean Variables......................................................................................49 2.6. Humean Variables........................................................................................53 2.7. Event Trees for Stochastic Processes...........................................................54 2.8. Timing in Event Trees.................................................................................56 2.9. Intersecting Event Trees...............................................................................60 2.10. Notes on the Literature...............................................................................61 Chapter 3. Probability Trees...........................................................................................63 3.1. Some Types of Probability Trees.................................................................64 ii 3.2. Axioms for the Probabilities of Moivrean Events.......................................68 3.3. Zero Probabilities....................................................................................... ..70 3.4. A Sample-Space Analysis of the Event-Tree Axioms.................................72 3.5. Probabilities and Expected Values for Variables.........................................74 3.6. Martingales......................................................................................... .........79 3.7. The Expectation of a Variable in a Cut........................................................83 3.8. Conditional Expected Value and Conditional Expectation.........................87 Chapter 4. The Meaning of Probability...........................................................................91 4.1. The Interpretation of Expected Value..........................................................92 4.2. The Interpretation of Expectation................................................................95 4.3. The Long Run..............................................................................................98 4.4. Changes in Belief.........................................................................................101 4.5. The Empirical Validation of Probability......................................................106 4.6. The Diversity of Uses of Probability...........................................................108 4.7. Notes on the Literature.................................................................................110 Chapter 5. Independent Events.......................................................................................113 5.1. Independence........................................................................................ .......114 5.2. Weak Independence.....................................................................................118 5.3. The Principle of the Common Cause...........................................................121 5.4. Conditional Independence............................................................................128 5.5. Notes on the Literature.................................................................................133 Chapter 6. Events Tracking Events.................................................................................135 6.1. Tracking............................................................................................ ...........137 6.2. Tracking and Conditional Independence.....................................................142 6.3. Stochastic Subsequence...............................................................................143 6.4. Singular Diagrams for Stochastic Subsequence...........................................147 6.5. Conjunctive and Interactive Forks...............................................................149 Chapter 7. Events as Signs of Events..............................................................................153 iii 7.1. Sign................................................................................................ ..............154 7.2. Weak Sign................................................................................................ ....159 7.3. The Ethics of Causal Talk............................................................................160 7.4. Screening Off...............................................................................................16 2 Chapter 8. Independent Variables...................................................................................167 8.1. Unconditional Independence........................................................................170 8.2. Conditional Independence............................................................................175 8.3. Independence for Partitions.........................................................................177 8.4. Independence for Families of Variables......................................................182 8.5. Individual Properties of the Independence Relations...................................186 Chapter 9. Variables Tracking Variables........................................................................189 9.1. Tracking and Conditional Independence: A Summary...............................190 9.2. Strong Tracking............................................................................................ 192 9.3. Strong Tracking and Conditional Independence..........................................198 9.4. Stochastic Subsequence...............................................................................201 9.5. Functional Dependence................................................................................203 9.6. Tracking in Mean.........................................................................................204 9.7. Linear Tracking............................................................................................ 207 9.8. Tracking by Partitions..................................................................................210 9.9. Tracking by Families of Variables...............................................................212 Chapter 10. Variables as Signs of Variables...................................................................215 10.1. Sign................................................................................................ ............219 10.2. Linear Sign................................................................................................ .222 10.3. Scored Sign................................................................................................ 225 10.4. Families of Variables.................................................................................227 Chapter 11. AnTheory of Event Trees.............................................................229 11.1. Event Trees as Sets of Sets........................................................................230 11.2. Event Trees as Partially Ordered Sets........................................................232 iv 11.3. Regular Event Trees...................................................................................240 11.4. The Resolution of Moivrean Variables......................................................244 11.5. Humean Events and Variables...................................................................246 Chapter 12. Martingale Trees..........................................................................................247 12.1. Examples of Decision Trees......................................................................249 12.2. The Meaning of Probability in a Decision Tree.........................................253 12.3. Martingales......................................................................................... .......257 12.4. The Structure of Martingale Trees.............................................................261 12.5. Probability and Causality...........................................................................265 12.6. Lower and Upper Probability.....................................................................269 12.7. The Law of Large Numbers.......................................................................272 12.8. Notes on the Literature...............................................................................274 Chapter 13. Refining............................................................................................ ...........275 13.1. Examples of Refinement............................................................................277 13.2. A Constructive Definition of Finite Refinement.......................................281 13.3. Axioms for Refinement..............................................................................282 13.4. Lifting Moivrean Events and Variables.....................................................288 13.5. Refining Martingale Trees.........................................................................288 13.6. Grounding........................................................................................... .......294 Chapter 14. Principles of Causal Conjecture..................................................................299 14.1. The Diversity of Causal Explanation.........................................................302 14.2. The Mean Effect of the Happening of a Moivrean Event..........................305 14.3. The Effect of a Humean Variable..............................................................311 14.4. Attribution and Generality.........................................................................316 14.5. The Statistical Measurement of the Effect of a Cause...............................319 14.6. Measurement by Experiment.....................................................................320 14.7. Using Our Knowledge of How Things Work............................................322 v 14.8. Sampling Error...........................................................................................329 14.9. The Sampling Frame..................................................................................329 14.10. Notes on the Literature.............................................................................330 Chapter 15. Causal Models.............................................................................................3 31 15.1. The Causal Interpretation of Statistical Prediction....................................333 15.2. Generalizing to a Family of Exogenous Variables....................................337 15.3 Some Joint Causal Diagrams......................................................................339 15.4. Causal Path Diagrams................................................................................342 15.5. Causal Relevance Diagrams.......................................................................346 15.6. The Meaning of Latent Variables..............................................................352 15.7. Notes on the Literature...............................................................................357 Chapter 16. Representing Probability Trees...................................................................359 16.1. Three Graphical Representations...............................................................361 16.2. Skeletal Simplifications.............................................................................368 16.3. Martingale Trees in Type Theory...............................................................371 Appendix A. Huygens’s Probability Trees.....................................................................379 Huygens’s Manuscript in Translation..................................................................380 Appendix B. Some Elements of Graph Theory..............................................................385 B1. Undirected Graphs........................................................................................385 B2. Directed Graphs............................................................................................38 6 Appendix C. Some Elements of Order Theory...............................................................393 C1. Partial and Quasi Orderings.........................................................................393 C2. Singular and Joint Diagrams for Binary Relations.......................................394 C3. Lattices............................................................................................ .............395 C4. The Lattice of Partitions of a Set..................................................................396 Appendix D. The Sample-Space Framework for Probability.........................................399 D1. Probability Measures....................................................................................399 D2. Variables........................................................................................... ...........400 vi D3. Families of Variables...................................................................................401 D4. Expected Value............................................................................................402 D5. The Law of Large Numbers.........................................................................405 D6. Conditional Probability................................................................................406 D7. Conditional Expected Value........................................................................407 Appendix E. Prediction in Probability Spaces................................................................409 E1. Conditional Distribution...............................................................................411 E2. Regression on a Single Variable...................................................................412 E3. Regression on a Partition or a Family of Variables......................................415 E4. Linear Regression on a Single Variable.......................................................418 E5. Linear Regression on a Family of Variables................................................422 Appendix F. Sample-Space Concepts of Independence.................................................425 F1. Overview............................................................................................ ...........426 F2. Independence Proper.....................................................................................432 F3. Unpredictability in Mean..............................................................................434 F4. Simple Uncorrelatedness..............................................................................437 F5. Mixed Uncorrelatedness...............................................................................438 F6. Partial Uncorrelatedness...............................................................................440 F7. Independence for Partitions..........................................................................442 F8. Independence for Families of Variables.......................................................445 F9. The Basic Role of Uncorrelatedness.............................................................448 F10. Dawid’s Axioms.........................................................................................449 Appendix G. Prediction Diagrams..................................................................................453 G1. Path Diagrams............................................................................................ ..454 G2. Generalized Path Diagrams..........................................................................462 G3. Relevance Diagrams.....................................................................................466 G4. Bubbled Relevance Diagrams......................................................................475 Appendix H. Abstract Stochastic Processes...................................................................479 vii H1. Probability Conditionals and Probability Distributions...............................477 H2. Abstract Stochastic Processes......................................................................479 H3. Embedding Variables and Processes in a Sample Space.............................480 References.......................................................................................... ..............................491. (shrink)