I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.

IBE ('Inference to the best explanation' or abduction) is a popular and highly plausible theory of how we should judge the evidence for claims of past events based on present evidence. It has been notably developed and supported recently by Meyer following Lipton. I believe this theory is essentially correct. This paper supports IBE from a probability perspective, and argues that the retrodictive probabilities involved in such inferences should be analysed in terms of predictive probabilities and a priori (...) class='Hi'>probability ratios of initial events. The key point is to separate these two features. Disagreements over evidence can be traced to disagreements over either the a priori probability ratios or predictive conditional ratios. In many cases, in real science, judgements of the former are necessarily subjective. The principles of iterated evidence are also discussed. The Sceptic's position is criticised as ignoring iteration of evidence, and characteristically failing to adjust a priori probability ratios in response to empirical evidence. (shrink)

When probability discounting (or probability weighting), one multiplies the value of an outcome by one's subjective probability that the outcome will obtain in decision-making. The broader import of defending probability discounting is to help justify cost-benefit analyses in contexts such as climate change. This chapter defends probability discounting under risk both negatively, from arguments by Simon Caney (2008, 2009), and with a new positive argument. First, in responding to Caney, I argue that small costs (...) and benefits need to be evaluated, and that viewing practices at the social level is too coarse-grained. Second, I argue for probability discounting using a distinction between causal responsibility and moral responsibility. Moral responsibility can be cashed out in terms of blameworthiness and praiseworthiness, while causal responsibility obtains in full for any effect which is part of a causal chain linked to one's act. With this distinction in hand, unlike causal responsibility, moral responsibility can be seen as coming in degrees. My argument is, given that we can limit our deliberation and consideration to that which we are morally responsible for and that our moral responsibility for outcomes is limited by our subjective probabilities, our subjective probabilities can ground probability discounting. (shrink)

The late scholastic era was, among others, contemporary to the “emergence of probability”, the German academic philosophy from Leibniz to Kant, and the introduction of Newtonian physics. Within this era, two branches of the late-scholastic analysis of induction can be identified, one which can be thought of as a continual development of earlier scholastic approaches, while the other one absorbed influences of early modern philosophy, mathematics, and physics. Both branches of scholastic philosophy share the terminology of modalities, probability, (...) and forms of arguments. Furthermore, induction was commonly considered valid as a result of being a covert syllogism. Last but not least, there appears to be a difference in emphasis between the two traditions’ analyses of induction: while Tolomei discussed the theological presuppositions of induction, Amort’s “leges contingentium” exemplify the principles of induction by aleatory phenomena and Boscovich’s rules for inductive arguments are predominately concerned with the generalisation of macro-level observations to the micro-level. (shrink)

Stanovich & West analyze individual differences with respect to response output (e.g., participants' numerical estimates). They do not analyze the underlying cognitive processes that led to the outputs; they thereby probably misclassify some non-normative responses as normative. Using base rate neglect and overconfidence as examples, I demonstrate the advantages of analyzing cognitive processes further.

Using probability functions defined over a simple language as models of states of belief, my goal in this article has been to analyse contractions and revisions of beliefs. My first strategy was to formulate postulates for these processes. Close parallels between the postulates for contractions and the postulates for revisions have been established - the results in Section 5 show that contractions and revisions are interchangeable. As a second strategy, some suggestions for more or less explicit constructive definitions of (...) the revision process (and indirectly also of the contraction process) were then presented. However, the results in Section 6 are less conclusive than in the earlier ones. This problem area still awaits further development. (shrink)

In this paper a new use case for legal argumentation support tools is considered: supporting discussions about analyses of complex criminal cases with the help of Bayesian probability theory. By way of a case study, two actual discussions between experts in court cases are analysed on their argumentation structure. In this study the usefulness of several recognised argument schemes is confirmed, a new argument scheme for arguments from statistics are proposed, and an analysis is given of debates between (...) experts about the validity of their arguments. From a practical point of view the case study yields insights into the design of support software for discussions about Bayesian analyses of complex criminal cases. (shrink)

How are we to understand the use of probability in Popper’s corroboration function? Popper says logically, but this raises a problem that becomes apparent when his views on logical probability are compared with those of Keynes. Specifically, Popper does not make it clear how we could have access to, or even calculate, probability values in a logical sense. For first, he would likely want to deny the Keynesian distinction between primary and secondary propositions, and the underlying notion (...) of knowledge-by-acquaintance with Neo-Platonic entities. Second, he would presumably reject not only the notion of non-numerical probabilities, but also the claim that the principle of indifference is aught other than a heuristic, given paradoxes such as Bertrand’s. An attempt might be made to solve this problem by appeal to semantic or possible world analyses over the relative truth-values of statements, but this seems to fail due to concerns relating to infinity: if the set of possible worlds in which p is true is infinite, and the set of possible worlds in which q is true is infinite, then no numerical value for P can be reasonably determined by a comparison between those worlds. As such, an all-too-familiar sort of criticism of Popper’s view of science seems to loom large: if the corroboration function only makes sense when the probabilities employed therein are subjective, then what counts as impressive evidence for a theory might seem to be a matter of convention, or even whim. However, we now have a new interpretation of probability at our disposal: the intersubjective interpretation, recently championed by Gillies, according to which probabilities can lie on a spectrum between the aleatory and the epistemic. Might we employ this to preserve the corroboration function, and deliver ourselves from Bayesianism, without succumbing to radical subjectivism? (shrink)

Self-taught mathematician and father of Boolean algebra, George Boole (1815-1864) published An Investigation of the Laws of Thought in 1854. In this highly original investigation of the fundamental laws of human reasoning, a sequel to ideas he had explored in earlier writings, Boole uses the symbolic language of mathematics to establish a method to examine the nature of the human mind using logic and the theory of probabilities. Boole considers language not just as a mode of expression, but as a (...) system one can use to understand the human mind. In the first 12 chapters, he sets down the rules necessary to represent logic in this unique way. Then he analyses a variety of arguments and propositions of various writers from Aristotle to Spinoza. One of history's most insightful mathematicians, Boole is compelling reading for today's student of intellectual history and the science of the mind. (shrink)

The contributions to this special collection concern issues and problems discussed in or related to the work of Wesley C. Salmon. Salmon has long been noted for his important work in the philosophy of science, which has included research on the interpretation of probability, the nature of explanation, the character of reasoning, the justification of induction, the structure of space/time and the paradoxes of Zeno, to mention only some of the most prominent. During a time of increasing preoccupation with (...) historical and sociological approaches to under standing science (which characterize scientific developments as though they could be adequately analysed from the perspective of political movements, even mistaking the phenomena of conversion for the rational appraisal of scientific theories), Salmon has remained stead fastly devoted to isolating and justifying those normative standards distinguishing science from non-science - especially through the vindi cation of general principles of scientific procedure and the validation of specific examples of scientific theories - without which science itself cannot be (even remotely) adequately understood. In this respect, Salmon exemplifies and strengthens a splendid tradi tion whose most remarkable representatives include Hans Reichenbach, Rudolf Carnap and Carl G. Hempel, all of whom exerted a profound influence upon his own development. (shrink)

The contributions to this special collection concern issues and problems discussed in or related to the work of Wesley C. Salmon. Salmon has long been noted for his important work in the philosophy of science, which has included research on the interpretation of probability, the nature of explanation, the character of reasoning, the justification of induction, the structure of space/time and the paradoxes of Zeno, to mention only some of the most prominent. During a time of increasing preoccupation with (...) historical and sociological approaches to under standing science (which characterize scientific developments as though they could be adequately analysed from the perspective of political movements, even mistaking the phenomena of conversion for the rational appraisal of scientific theories), Salmon has remained stead fastly devoted to isolating and justifying those normative standards distinguishing science from non-science - especially through the vindi cation of general principles of scientific procedure and the validation of specific examples of scientific theories - without which science itself cannot be (even remotely) adequately understood. In this respect, Salmon exemplifies and strengthens a splendid tradi tion whose most remarkable representatives include Hans Reichenbach, Rudolf Carnap and Carl G. Hempel, all of whom exerted a profound influence upon his own development. (shrink)

Today philosophical discussion on indicative conditionals is dominated by the so called Lewis Triviality Results, according to which, tehere is no binary connective '-->' (let alone truth-functional) such that the probability of p --> q equals the probability of q conditionally on p, so that P(p --> q)= P(q|p). This tenet, that suggests that conditonals lack truth-values, has been challenged in 1991 by Goodman et al. who show that using a suitable three-valued logic the above equation may be (...) restored. In this paper it is first analysed a long neglected paper by Bruno de Finetti, written in 1935, where the essentials of Goodman's theory was clearly outlined. It is also stressed that de Finetti anticipated Kleene's as well as Bochvar and Blamey ideas. In the second part of the paper it is argued that the de Finetti-Goodman's original theory is defective and leads to absurd results. However, a new semantics, called semantics of hypervaluations, is here defined, that avoids the defects of the original theory. This appears to be a powerful challenge to Lewis Triviality results and to the thesis by which conditionals lack truth-values as well. (shrink)

Probability is increasingly important for our understanding of the world. What is probability? How do we model it, and how do we use it? Timothy Childers presents a lively introduction to the foundations of probability and to philosophical issues it raises. He keeps technicalities to a minimum, and assumes no prior knowledge of the subject.

A lot of research in cognition and decision making suffers from a lack of formalism. The quantum probability program could help to improve this situation, but we wonder whether it would provide even more added value if its presumed focus on outcome models were complemented by process models that are, ideally, informed by ecological analyses and integrated into cognitive architectures.

The aim of this paper is to present and analyse Bruno de Finetti's view that the axiom of countable additivity of the probability calculus cannot be justified in terms of the subjective interpretation of probability. After presenting the core of the subjective theory of probability and the main de Finetti's argument against the axiom of countable additivity (the so called de Finetti's infinite lottery) I argue against de Finetti's view. In particular, I claim that de Finetti does (...) not prove the impossibility of using Dutch Book argument for the axiom of countable additivity. Consequently, we can use Dutch Book argument for the justification of the axiom of countable additivity and regard de Finetti's lottery as a special case when the axiom does not hold, or we can justify countable additivity by Dutch Book argument and reject de Finetti's lottery as irrational. The second strategy, represented especially by Jon Williamson, is much more compatible with the idea of subjective interpretation of probability. (shrink)

Evidential reasoning is hard, and errors can lead to miscarriages of justice with serious consequences. Analytic methods for the correct handling of evidence come in different styles, typically focusing on one of three tools: arguments, scenarios or probabilities. Recent research used Bayesian networks for connecting arguments, scenarios, and probabilities. Well-known issues with Bayesian networks were encountered: More numbers are needed than are available, and there is a risk of misinterpretation of the graph underlying the Bayesian network, for instance as a (...) causal model. The formalism presented here models presumptive arguments about coherent hypotheses that are compared in terms of their strength. No choice is needed between qualitative or quantitative analytic styles, since the formalism can be interpreted with and without numbers. The formalism is applied to key concepts in argumentative, scenario and probabilistic analyses of evidential reasoning, and is illustrated with a fictional crime investigation example based on Alfred Hitchcock’s film ‘To Catch A Thief’. (shrink)

The book was planned and written as a single, sustained argument. But earlier versions of a few parts of it have appeared separately. The object of this book is both to establish the existence of the paradoxes, and also to describe a non-Pascalian concept of probability in terms of which one can analyse the structure of forensic proof without giving rise to such typical signs of theoretical misfit. Neither the complementational principle for negation nor the multiplicative principle for conjunction (...) applies to the central core of any forensic proof in the Anglo-American legal system. There are four parts included in this book. Accordingly, these parts have been written in such a way that they may be read in different orders by different kinds of reader. (shrink)

Largely due to the difficulty of observing behavior, empirical business ethics research relies heavily on the scenario methodology. While not disputing the usefulness of the technique, this paper highlights the importance of a careful assessment of the fit between the context of the situation described in the scenario and the knowledge and experience of the respondents. Based on a study of online auctions, we provide evidence that even respondents who have direct knowledge of the situation portrayed in the scenario may (...) develop significantly different assessments of the level of unethical behavior. Further, those assessments may be conditioned in different ways by the same moderating variables. We conclude that care should be exercised when recruiting respondents to choose only those who can be expected to understand the scenario in its true context and that separate analyses should be conducted for groups of respondents who have different perspectives within that context. (shrink)

Largely due to the difficulty of observing behavior, empirical business ethics research relies heavily on the scenario methodology. While not disputing the usefulness of the technique, this paper highlights the importance of a careful assessment of the fit between the context of the situation described in the scenario and the knowledge and experience of the respondents. Based on a study of online auctions, we provide evidence that even respondents who have direct knowledge of the situation portrayed in the scenario may (...) develop significantly different assessments of the level of unethical behavior. Further, those assessments may be conditioned in different ways by the same moderating variables. We conclude that care should be exercised when recruiting respondents to choose only those who can be expected to understand the scenario in its true context and that separate analyses should be conducted for groups of respondents who have different perspectives within that context. (shrink)

The contribution of Bayes to statistical inference has been much discussed, whereas his evaluations of the beta probability integral have received little attention, and Price's improvements of these results have never been analysed in detail. It is the purpose of the present paper to redress this state of affairs and to show that the Bayes-Price approximation to the two-sided beta probability integral is considerably better than the normal approximation, which became popular under the influence of Laplace, although it (...) had been stated by Price. The Bayes-Price results are obtained by approximating the skew beta density by a symmetric beta density times a factor tending to unity for n → ∞, the two functions having the same maximum and the same points of inflection. Since the symmetric beta density converges to the normal density, all the results of Laplace based on the normal distribution can be obtained as simple limits of the results of Bayes and Price. This fact was not observed either by Laplace or by Todhunter. (shrink)

A presentation showing how the statements which relate to microphysical objects as they are different from the statements of classical mechanics is made. The determinism of classical and of quantum-mechanical theories is qualified. A (crucial) distinction between causality and determinism is given. Detailed analyses of diffraction as a result of single and double-slit demonstrations point to paradoxes arising from the use of particle or wave models, respectively, for photons and electrons. The compromising wave-packet model is underscored. The meanings for (...) the Psi-function and for |ψ|2 are presented, with an explanation of the limitations that arise from giving an interpretation of |ψ|2 as a probability. The meaning of ψ -waves is analyzed. A case is made for the ψ -function's describing a well-ordered list of betting odds, based on previous statistical experiences, for the different results of specific experiments of a microscopic object of study with macroscopic apparatus. The Schrödinger wave equation is evaluated for meaning and judged as a deterministic expression. (shrink)

This paper is a re-examination of Popper’s propensity interpretation of probability in respect of its potential methodological value in social science. A long standing problem for the frequency interpretation of probability is that whilst it is able to treat both aggregate and individual phenomena as having measurable properties, it cannot explain the ontological relationship between such concrete individual cases and aggregates. Popper’s interpretation treats single cases as both real, but also as realisations of a propensity to occur. The (...) frequency and propensity interpretations are compared and whilst some common objections raised must be upheld, they do not devalue the importance of the propensity interpretation as at least a metaphysical basis for probabilistic claims in social science. However the value of the approach may also lie in its methodological potential. Here I sugest that single case probabilities must be analysed in terms of the anterior probabilities of prior constituent events. In this I move beyond Popper’s own programme, but suggest that such a move is theoretically compatible with recent complexity approaches in social science and goes some way toward meeting anti-naturalist concerns about intentionality. (shrink)

Analyses of singular causation often make use of the idea that a cause increases the probability of its effect. Of particular salience in such accounts are the values of the probability function of the effect, conditional on the presence and absence of the putative cause, analysed around the times of the events in question: causes are characterized by the effect’s probability function being greater when conditionalized upon them. Put this way, it becomes clearer that the ‘behaviour’ (...) of probability functions in small intervals about the times in question ought to be of concern. In this article, I make an extended case that causal theorists employing the ‘probability raising’ idea should pay attention to the continuity question. Specifically, if the probability functions are ‘jumping about’ in ways typical of discontinuous functions, then the stability of the relevant probability increase is called into question. The rub, however, is that sweeping requirements for either continuity or discontinuity are problematic and, as I argue, this constitutes a ‘continuity bind’. Hence more subtle considerations and constraints are needed, two of which I consider: utilizing discontinuous first derivatives of continuous probability functions, and abandoning point probability for imprecise probability. _1_ Introduction _2_ Probability Trajectories and Continuity _2.1_ Probability trajectories _2.2_ Causation as discontinuous jumps _2.3_ Against systematic discontinuity _3_ Broader Discontinuity Concerns _4_ The Continuity Bind _4.1_ Retaining continuity with discontinuous first derivatives _4.2_ Imprecise probability trajectories _5_ Concluding Remarks Appendix. (shrink)

Report on analysis of ” pergamene sigillata“ from Delos This paper presents the results of the analysis of twenty samples of ” pergamene sigillata” from destruction layers of Delian living quarter, which can be dated to 69 BC. The programme included petrographical and chemical analysis, as well as MGR (Matrix Group by Refiring) method. The results show that the samples belong to several groups, among which some could be identified by comparison with chemical reference groups. Two samples were produced in (...) the Ketios valley workshops, four come from the Çandarlı area, and four others probably from the Pergamon region, from workshops not yet identified. The rest of the samples do not originate from that region, and were produced in other Asia Minor centers (six of them come from Ephesos, the rest from unidentified workshops). (shrink)

A conception of probability as an irreducible feature of the physical world is outlined. Propensity analyses of probability are examined and rejected as both formally and conceptually inadequate. It is argued that probability is a non-dispositional property of trial-types; probabilities are attributed to outcomes as event-types. Brier's Rule in an objectivist guise is used to forge a connection between physical and subjective probabilities. In the light of this connection there are grounds for supposing physical probability (...) to obey some standard set of axioms. However, there is no a priori reason why this should be the case. (shrink)

Understanding probabilities as something other than point values has often been motivated by the need to find more realistic models for degree of belief, and in particular the idea that degree of belief should have an objective basis in “statistical knowledge of the world.” I offer here another motivation growing out of efforts to understand how chance evolves as a function of time. If the world is “chancy” in that there are non-trivial, objective, physical probabilities at the macro-level, then the (...) chance of an event e that happens at a given time is \ until it happens. But whether the chance of e goes to one continuously or not is left open. Discontinuities in such chance trajectories can have surprising and troubling consequences for probabilistic analyses of causation and accounts of how events occur in time. This, coupled with the compelling evidence for quantum discontinuities in chance’s evolution, gives rise to a “continuity bind” with respect to chance probability trajectories. I argue that a viable option for circumventing the continuity bind is to understand the probabilities “imprecisely,” that is, as intervals rather than point values. I then develop and motivate an alternative kind of continuity appropriate for interval-valued chance probability trajectories. (shrink)

Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilised in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual combinations are compositional, and so can be considered as a function of the semantics of the constituent concepts, or not. While the systematicity and productivity of language provide a strong argument in favor of assuming compositionality, this very assumption is still regularly questioned in both cognitive science and philosophy. (...) Additionally, the principle of semantic compositionality is underspecifi ed, which means that notions of both "strong" and "weak" compositionality appear in the literature. Rather than adjudicating between different grades of compositionality, the framework presented here contributes formal methods for determining a clear dividing line between compositional and non-compositional semantics. In addition, we suggest that the distinction between these is contextually sensitive. Compositionality is equated with a joint probability distribution modeling how the constituent concepts in the combination are interpreted. Marginal selectivity is introduced as a pivotal probabilistic constraint for the application of the Bell/CH and CHSH systems of inequalities. Non-compositionality is equated with a failure of marginal selectivity, or violation of either system of inequalities in the presence of marginal selectivity. This means that the conceptual combination cannot be modeled in a joint probability distribution, the variables of which correspond to how the constituent concepts are being interpreted. The formal analysis methods are demonstrated by applying them to an empirical illustration of twenty-four non-lexicalised conceptual combinations. (shrink)

Gelman and Loken (2013, 2014) proposed that when researchers base their statistical analyses on the idiosyncratic characteristics of a specific sample (e.g., a nonlinear transformation of a variable because it is skewed), they open up alternative analysis paths in potential replications of their study that are based on different samples (i.e., no transformation of the variable because it is not skewed). These alternative analysis paths count as additional (multiple) tests and, consequently, they increase the probability of making a (...) Type I error during hypothesis testing. The present article considers this forking paths problem and evaluates four potential solutions that might be used in psychology and other fields: (a) adjusting the prespecified alpha level, (b) preregistration, (c) sensitivity analyses, and (d) abandoning the Neyman-Pearson approach. It is concluded that although preregistration and sensitivity analyses are effective solutions to p-hacking, they are ineffective against result-neutral forking paths, such as those caused by transforming data. Conversely, although adjusting the alpha level cannot address p-hacking, it can be effective for result-neutral forking paths. Finally, abandoning the Neyman-Pearson approach represents a further solution to the forking paths problem. (shrink)

An analysis of indefinite probability statements has been offered by Jackson and Pargetter (1973). We accept that this analysis will assign the correct probability values for indefinite probability claims. But it does so in a way which fails to reflect the epistemic state of a person who makes such a claim. We offer two alternative analyses: one employing de re (epistemic) probabilities, and the other employing de dicto (epistemic) probabilities. These two analyses appeal only to (...) probabilities which are accessible to a person who makes an indefinite probability judgment, and yet we prove that the probabilities which either of them assigns will always be equivalent to those assigned by the Jackson and Pargetter analysis. (shrink)

The papers collected here are, with three exceptions, those presented at a conference on probability and causation held at the University of California at Irvine on July 15-19, 1985. The exceptions are that David Freedman and Abner Shimony were not able to contribute the papers that they presented to this volume, and that Clark Glymour who was not able to attend the conference did contribute a paper. We would like to thank the National Science Foundation and the School of (...) Humanities of the University of California at Irvine for generous support. WILLIAM HARPER University of Western Ontario BRIAN SKYRMS University of California at Irvine VII INTRODUCTION TO CAUSATION, CHANCE, AND CREDENCE The search for causes is so central to science that it has sometimes been taken as the defining attribute of the scientific enterprise. Yet even after twenty-five centuries of philosophical analysis the meaning of "cause" is still a matter of controversy, among scientists as well as philosophers. Part of the problem is that the servicable concepts of causation built out of Necessity, Sufficiency, Locality, and Temporal Precedence were constructed for a deterministic world-view which has been obsolete since the advent of quantum theory. A physically credible theory of causation must be, at basis, statistical. And statistical analyses of caus­ ation may be of interest even when an underlying deterministic theory is assumed, as in classical statistical mechanics. (shrink)

Randomized controlled clinical trials play an important role in the development of new medical therapies. There is, however, an ethical issue surrounding the use of randomized treatment allocation when the patient is suffering from a life threatening condition and requires immediate treatment. Such patients can only benefit from the treatment they actually receive and not from the alternative therapy, even if it ultimately proves to be superior. We discuss a novel new way to analyse data from such clinical trials based (...) on the use of the recently developed theory of imprecise probabilities. This work draws an explicit distinction between the related but nevertheless distinct questions of inference and decision in clinical trials. The traditional question of scientific interest asks 'Which treatment offers the greater chance of success?' and is the primary reason for conducting the clinical trial. The question of decision concerns the welfare of the patients in the clinical trial, asking whether the accumulated evidence favours one treatment over the other to such an extent that the next patient should decline randomization and instead express a preference for one treatment. Consideration of the decision question within the framework of imprecise probabilities leads to a mathematical definition of equipoise and a method for governing the randomization protocol of a clinical trial. This paper describes in detail the protocol for the conduct of clinical trials based on this new method of analysis, which is illustrated in a retrospective analysis of data from a clinical trial comparing the anti-emetic drugs ondansetron and droperidol in the treatment of postoperative nausea and vomiting. The proposed methodology is compared quantitatively using computer simulation studies with conventional clinical trial designs and is shown to maintain high statistical power with reduced sample sizes, at the expense of a high type I error rate that we argue is irrelevant in some specific circumstances. Particular emphasis is placed on describing the type of medical conditions and treatment comparisons where the new methodology is expected to provide the greatest benefit. (shrink)

A complete probability guide of Hold'em Poker, this guide covers all possible gaming situations. The author focuses on the practical side of the presentation and use of the probabilities involved in Hold'em, while taking into account the subjective side of the probability-based criteria of each player's strategy.

James Forbes' critical examination of the probabilistic reasoning, which led John Michell to infer a physical connection between optically double and multiple stars, is analysed. It is argued that despite the interpretations of its nineteenth-century defenders, Michell's reasoning has some force which does not depend upon questionable Bayesian principles. Attention is drawn to some of the ambiguities concerning the notion of randomness, and it is shown that these ambiguities render Forbes' objections less than conclusive.

My object in this paper is to consider what relevance, if any, current analyses of probability have to problems of religious belief. There is no doubt that words such as ‘probable’ are used in this context; what is doubtful is that this use can be analysed as other major uses of such words can. I shall conclude that this use cannot be so analysed and hence, given the preponderance of the other uses that can, that it is misleading.

Information, entropy, probability: these three terms are closely interconnected in the prevalent understanding of statistical mechanics, both when this field is taught to students at an introductory level and in advanced research into the field’s foundations. This paper examines the interconnection between these three notions in light of recent research in the foundations of statistical mechanics. It disentangles these concepts and highlights their differences, at the same time explaining why they came to be so closely linked in the literature. (...) In the literature the term ‘information’ is often linked to entropy and probability in discussions of Maxwell’s Demon and its attempted exorcism by the Landauer-Bennett thesis, and in analyses of the spin echo experiments. The direction taken in the present paper is a different one. Here we discuss the statistical mechanical underpinning of the notions of probability and entropy, and this constructive approach shows that information plays no fundamental role in these concepts, although it can be conveniently used in a sense that we shall specify. (shrink)

Causal inference is perhaps the most important form of reasoning in the sciences. A panoply of disciplines, ranging from epidemiology to biology, from econometrics to physics, make use of probability and statistics to infer causal relationships. The social and health sciences analyse population-level data using statistical methods to infer average causal relations. In diagnosis of disease, probabilistic statements are based on population-level causal knowledge combined with knowledge of a particular person’s symptoms. For the physical sciences, the Salmon-Dowe account develops (...) an analysis of causation based on the notion of process and interaction. In artificial intelligence, the development of graphical methods has leant impetus to a probabilistic analysis of causality. The biological sciences use probabilistic methods to look for evolutionary causes of the state of a current species and to look for genetic causal factors. This variegated situation raises at least two fundamental philosophical issues: about the relation between causality and probability, and about the interpretation of probability in causal analysis. In this book we bring philosophers and scientists together to discuss the relation between causality and probability, and the applications of these concepts within the sciences. (shrink)