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

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

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

How should the definition of “minimal risk” in the federal research regulations be interpreted in regard to pregnant women and fetuses? Surprisingly, there has been little discussion of this question. There is, after all, a substantial amount of published work addressing the question of how “minimal risk” should be interpreted. Similarly, there is a large body of literature on the ethics of research involving pregnant women and fetuses, particularly maternal-fetal surgery. However, in neither of these bodies of work can (...) one find an analysis of minimal risk in regard to fetuses or pregnant women.The concept of minimal risk is defined in the regulations as follows:Minimal risk means that the probability and magnitude of harm or discomfort anticipated in the research are not greater in and of themselves than those ordinarily encountered in daily life or during the performance of routine physical or psychological examinations or tests. (shrink)

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

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

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

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

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

Since the first draft of the human genome was published in 2001, DNA sequencing technology has advanced at a remarkable pace. Launched in 1990, the Human Genome Project sought to sequence all three billion base pairs of the haploid human genome, an endeavor that took more than a decade and cost nearly three billion dollars. The subsequent development of so-called “next generation” sequencing methods has raised the possibility that real-time, affordable genome sequencing will soon be widely available. Currently, NGS methods (...) can be used to sequence up to 60 billion base pairs per day. Whole-genome sequencing costs an estimated $5,000-10,000, with that number predicted to fall to $1000 in the near future.In the past few years, the availability of high-throughput NGS methods has led to a proliferation of potential and actual clinical applications for NGS. NGS therefore has the potential to usher in the long-awaited era of personalized medicine. (shrink)

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

We show that in the setting of fair-coin measure on the power set of the natural numbers, each sufficiently random set has an infinite subset that computes no random set. That is, there is an almost sure event [Formula: see text] such that if [Formula: see text] then X has an infinite subset Y such that no element of [Formula: see text] is Turing computable from Y.

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

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

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

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

A moderately risk averse person may turn down a 50/50 gamble that either results in her winning $200 or losing $100. Such behaviour seems rational if, for instance, the pain of losing $100 is felt more strongly than the joy of winning $200. The aim of this paper is to examine an influential argument that some have interpreted as showing that such moderate risk aversion is irrational. After presenting an axiomatic argument that I take to be the strongest case for (...) the claim that moderate risk aversion is irrational, I show that it essentially depends on an assumption that those who think that risk aversion can be rational should be skeptical of. Hence, I conclude that risk aversion need not be irrational. (shrink)

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

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

Let be n events in a probability space, and suppose that we have only partial information about the distribution: The probabilites of the events themselves, and their pair intersections. With this partial information we cannot, usually, deternine the probability of an event B in the algebra generated by the 's, but we can obtain lower and upper bounds. This is done by a linear program related to the correlation polytope c(n), a structure introduced in [3], [4]. In the first part (...) of the paper I demonstrate how laws of large numbers (for sequences of events which are not necessarily independent) can be proved, using only the duality theorem of linear programming. These include the weak law of large numbers (necessary and sufficient condition) and various sufficient conditions for strong laws. The connection between these laws and the facet structure of the correlation polytope is established. In the second part of the paper I consider a more general case. Assume that our information consists of the values of the probabilities of all intersections of the 's up to size k, k < n. The techniques of linear programming lead naturally to an application of the theory of polynomial approximation in estimating the size of various events. In particular, I prove an approximate version of the central limit theorem. (shrink)

We study whether the probabilistic postulate could be derived from basic principles. Through the analysis of the Strong Law of Large Numbers and its formulation in quantum mechanics, we show, contrary to the claim of the many-worlds interpretation defenders and the arguments of some other authors, the impossibility of obtaining the probabilistic postulate by means of the frequency analysis of an ensemble of infinite copies of a single system. It is shown, though, how the standard form of (...) the probability as the square of the scalar product follows from Gleason's theorem. (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)

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

Starting with the Born interpretation of quantum mechanics, we show that the quantum theory of measurement, supplemented by the strong law of large numbers, leads to a measurement statistics interpretation of quantum mechanics. A probabilistic characterization of the spectrum of a physical quantity is given, and an analysis of the notions of possible values and possible measurement results is carried out.

Laws of nature are merely expressions of the powers possessed by various kinds of things, and counterfactual conditionals are grounded in the powers and tendencies of the entities involved in the counterfactual supposition together with their counterfactual surroundings. There are two versions of Strong Powerism. One takes the truthmakers for causal laws to be universals (a 'Realist' version). The second takes the truthmakers for causal laws to be the particulars that fall under the laws (a 'Nominalist' version). This chapter (...) focuses on how Powerism compares to other views about the laws. Neo‐Humeism has the leanest metaphysical theory, since its class of fundamental truths includes no conditionals, laws of nature or attributions of power. Metaphysically, Nomism is burdened with a large number of brute necessities, linking laws with actual patterns of particular fact. The chapter talks about the causal theory of properties: causal structuralism. (shrink)

This paper addresses and rejects claims that one can demonstrate experimentally that most untutored subjects are systematically and incurably irrational in their probability judgements and in some deductive reasoning tasks. From within a strongly subjectivist theory of probability, it develops the notions of resiliency —a measure of stability of judgements—and robustness —a measure of expected stability. It then becomes possible to understand subjects' behaviour in the Wason selection task, in examples which have been claimed to involve a 'base-rate fallacy', in (...) appearing to ignore laws of large numbers and to overestimate their own success rate as entirely rational: a matter of combining first-order probability assignments with judgements about the robustness of those assignments. (shrink)

Can it be rational to be risk-averse? It seems plausible that the answer is yes—that normative decision theory should accommodate risk aversion. But there is a seemingly compelling class of arguments against our most promising methods of doing so. These long-run arguments point out that, in practice, each decision an agent makes is just one in a very long sequence of such decisions. Given this form of dynamic choice situation, and the (Strong) Law of Large Numbers, they (...) conclude that those theories which accommodate risk aversion end up delivering the same verdicts as risk-neutral theories in nearly all practical cases. If so, why not just accept a simpler, risk-neutral theory? The resulting practical verdicts seem to be much the same. In this paper, I show that these arguments do not in fact condemn those risk-aversion-accommodating theories. Risk aversion can indeed survive the long run. (shrink)

Don Marquis has put forward a non-religious argument against abortion based on what he claims is a morally relevant similarity between killing adult human beings and killing fetuses. He asserts that killing adults is wrong because it deprives them of their valuable futures. He points out that a fetus’s future includes everything that is in an adult’s future, given that fetuses naturally develop into adults. Thus, according to Marquis, killing a fetus deprives it of the same sort of valuable future (...) that an adult is deprived of in being killed and this makes abortion seriously wrong. Commentators have raised a number of objections to Marquis’s argument, to which he has satisfactorily responded. In this paper, difficulties with Marquis’s argument that have not been considered by previous commentators are pointed out. A main thesis of this paper is that Marquis does not adequately defend his argument against several important objections that he himself has raised. These new considerations support the view that Marquis’s argument is unsuccessful. (shrink)

Casuistic methods of reasoning in medical ethics have been criticized by a number of authors. At least five main objections to casuistry have been put forward: (1) it requires a uniformity of views that is not present in contemporary pluralistic society; (2) it cannot achieve consensus on controversial issues; (3) it is unable to examine critically intuitions about cases; (4) it yields different conclusions about cases when alternative paradigms are chosen; and (5) it cannot articulate the grounds of its conclusions. (...) Two main versions of casuistry have been put forward, and the responses to these objections depend in part on which version one is defending. Jonsen has advocated a version modeled on the approach to casuistry used by moral theologians in the 15th and 16th century, involving comparison of the case at hand with a single paradigm and a lineup of cases. The present author has advocated another version, drawn from experience with cases in clinical ethics, which involves comparing the case at hand with two or more paradigms. Four of the five objections are unsuccessful when directed against Jonsen'sapproach, and all of them are unsuccessful when directed against the approach involving comparison with two or more paradigms. (shrink)

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

A central argument of the _Leviathan_ has to do with the political importance of education. Hobbes wants his book to be taught in universities and expounded much in the manner that Scripture was. Only thus will citizens realize what is in their hearts as to the nature of good political order. Glory affects this process in two ways. The pursuit of glory _by a citizen_ leads to political chaos and disorder. On the other hand, _God’s_ glory is such that one (...) can do nothing but acquiesce to it. The Hobbesian sovereign shares some of the effects of glory that God has naturally; this, however, has to be supplemented by awe and that but fear. (shrink)

Several methods have been reported for extracting sperm from a man after he dies or enters a persistent vegetative state. Although such sperm retrieval could be performed for nonprocreative purposes, such as research, in this paper I focus on cases involving procreative intent. Since 1980, more than ninety cases have occurred in which family members requested sperm retrieval from patients who died or were irreversibly unconscious, with the intent that a wife, girlfriend, or other woman would be inseminated. Recently, the (...) first report of pregnancy and birth following postmortem sperm retrieval appeared in the media.In these cases, death or PVS typically is caused by anoxic injuries, trauma, or rapidly progressing infections. (shrink)

Several methods have been reported for extracting sperm from a man after he dies or enters a persistent vegetative state. Although such sperm retrieval could be performed for nonprocreative purposes, such as research, in this paper I focus on cases involving procreative intent. Since 1980, more than ninety cases have occurred in which family members requested sperm retrieval from patients who died or were irreversibly unconscious, with the intent that a wife, girlfriend, or other woman would be inseminated. Recently, the (...) first report of pregnancy and birth following postmortem sperm retrieval appeared in the media.In these cases, death or PVS typically is caused by anoxic injuries, trauma, or rapidly progressing infections. (shrink)

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

The apparent liberalism of Raymond Aron's thought can be understood only in the context of the questions asked by the "continental" philosophical tradition. Aron contends that the strong neo-Kantian and existentialist trends which came together in Weber's work serve to split man off from meaningful intercourse with the social world. Aron intends to re-establish that intercourse. He attempts to show precisely what the consequences and responsibilities of making choices are for a man "thrown" into the world. Politics becomes focused (...) around the choice of values in a world delineated only in negative terms. Aron's program yields a low number of generalizable empirical conclusions and policy recommendations, and this is instructive to those who wish to practice "good" social science. (shrink)

Ethical controversy over transplantation of human fetal tissue has arisen because the source of tissue is induced abortions. Opposition to such transplants has been based on various arguments, including the following: rightful informed consent cannot be obtained for use of fetal tissue from induced abortions, and fetal tissue transplantation might result in an increase in the number of abortions. These arguments were not accepted by the National Institutes of Health (NIH) Human Fetal Tissue Transplantation Research Panel. The majority opinion of (...) the panel stated that abortion and fetal tissue use are entirely separate issues, and that tissue use is ethically acceptable because it can be morally insulated from the issue of abortion. In support of this view, panel members and others have replied to the arguments put forward by opponents of fetal tissue use. However, replies to the two arguments mentioned above have been unsatisfactory, and the shortcomings of those replies are identified herein. Examination of the arguments pro and con suggests that fetal tissue use cannot be completely insulated from the issue of abortion. Thus, in seeking an ethical justification for fetal tissue transplantation we must consider reasons other than those put forward by the NIH panel. In this paper it is argued that whatever wrong is involved in using fetal tissue from induced abortions must be balanced against the benefits for patients, and it is on this basis that fetal tissue transplantation can be ethically justified. (shrink)

ABSTRACT In previous articles I discussed the ethics of human reproductive cloning, focusing on a possible future scenario in which reproductive cloning can be accomplished without an elevated risk of anomalies to the children who are created. I argued that in such a scenario it would be ethically permissible for infertile couples to use cloning as a way to have genetically related children and that such use should not be prohibited. In ‘Reproductive Cloning and a (Kind of) Genetic Fallacy’, Neil (...) Levy and Mianna Lotz raise objections to my conclusions. They disagree with the view, for which I argued, that some couples can have defensible reasons for desiring genetically related children. They also offer several new arguments against reproductive cloning, including an argument that it would diminish the number of adoptions, thereby adversely affecting the welfare of children who need to be adopted. In this paper I point out that Levy and Lotz's criticisms misconstrue my arguments and that there are serious problems with their arguments for prohibiting infertile couples from using cloning, including their argument from adoption. (shrink)

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

The situated potentials for action between material things in the world and the interactional processes thereby afforded need to be seen as not only constituting the possibility of agency, but thereby also comprising it. Eo ipso, agency must be de-fused from any local, "contained" subject and be understood as a situational property in which subjects and objects can both participate. Any technological artifact should thus be understood as a complex of agential capacities that function relative to any number of social (...) and material factors. Keeping in mind that we are co-constituted by webs of relations involving increasingly complex collections of artefacts, networks, niches, and communities of practice, our investigation will be guided by interrogating the functional potential of a thing that in the last fifteen years has seamlessly worked its way into the everyday life of millions of human agents. This "thing," the smartphone, is merely a nodal point in a highly complex network. Recognizing this massive "collective," we nevertheless want to show some of the ways in which something as seemingly mundane as a smartphone can reflexively alter the range of actions available to a cognitive agent (Latour 1994). Specifically, we hope to shed light on some of the social-cognitive consequences of technological mediation by looking at the complementary, if not mutually implied, domains of memory and knowledge. (shrink)