The purpose of this paper is to provide a systematic defense of the single-case propensity account of probabilistic explanation from the criticisms advanced by Hanna and by Humphreys and to offer a critical appraisal of the aleatory conception advanced by Humphreys and of the deductive-nomological-probabilistic approach Railton has proposed. The principal conclusion supported by this analysis is that the Requirements of Maximal Specificity and of Strict Maximal Specificity afford the foundation for completely objective explanations of probabilistic (...) explananda, so long as they are employed on the basis of propensity criteria of explanatory relevance. (shrink)

This paper argues that if the world is irreducibly stochastic, then both Salmon's S-R model of explanation and Fetzer's C-R model of explanation have the following undesirable consequence: the objective probability (associated with the model's relevance condition) of any actual macro-event is either undefined or else, if defined, it equals one--so that the event is not even a candidate for a probabilistic explanation. This result follows from the temporal ambiguity of ontic probability in an irreducibly stochastic (...) world. It is argued further that an analogous difficulty faces those theories of probabilistic causality which depend upon the notions of contributing and counteracting causes. Because of the problem of temporal ambiguity, it is not possible to objectively label a particular event as a contributing (or a counteracting) cause of some subsequent event. The argument is carried through in detail for a recent theory of probabilistic causality proposed by Paul Humphreys. (shrink)

It has been the dominant view that probabilistic explanations of particular facts must be inductive in character. I argue here that this view is mistaken, and that the aim of probabilistic explanation is not to demonstrate that the explanandum fact was nomically expectable, but to give an account of the chance mechanism(s) responsible for it. To this end, a deductive-nomological model of probabilistic explanation is developed and defended. Such a model has application only when the (...) probabilities occurring in covering laws can be interpreted as measures of objective chance, expressing the strength of physical propensities. Unlike inductive models of probabilistic explanation, this deductive model stands in no need of troublesome requirements of maximal specificity or epistemic relativization. (shrink)

A consistent finding in research on conditional reasoning is that individuals are more likely to endorse the valid modus ponens (MP) inference than the equally valid modus tollens (MT) inference. This pattern holds for both abstract task and probabilistic task. The existing explanation for this phenomenon within a Bayesian framework (e.g., Oaksford & Chater, 2008) accounts for this asymmetry by assuming separate probability distributions for both MP and MT. We propose a novel explanation within a computational-level Bayesian (...) account of reasoning according to which “argumentation is learning”. We show that the asymmetry must appear for certain prior probability distributions, under the assumption that the conditional inference provides the agent with new information that is integrated into the existing knowledge by minimizing the Kullback-Leibler divergence between the posterior and prior probability distribution. We also show under which conditions we would expect the opposite pattern, an MT-MP asymmetry. (shrink)

The article is a reappraisal of the requirement of maximal specificity (RMS) proposed by the author as a means of avoiding "ambiguity" in probabilistic explanation. The author argues that RMS is not, as he had held in one earlier publication, a rough substitute for the requirement of total evidence, but is independent of it and has quite a different rationale. A group of recent objections to RMS is answered by stressing that the statistical generalizations invoked in probabilistic (...) explanations must be lawlike, and by arguing that predicates fit for occurrence in lawlike statistical probability statements must meet two conditions, at least one of which is violated in each of the counterexamples adduced in the objections. These considerations suggest the conception that probabilistic-statistical laws concern the long-run frequency of some characteristic within a reference class as characterized by some particular "description" or predicate expression, and that replacement of such a description by a coextensive one may turn a statement that is lawlike into another that is not. Finally, to repair a defect noted by Grandy, the author's earlier formulation of RMS is replaced by a modified version. (shrink)

In many ways, entropy and probability are two concepts that complement each other. But it has been argued that there is no ‘straightforward connection’ between them with a no-go thesis from Kevin D...

One aim of this article is to explore the connection between the Knobe effect and the epistemic side-effect effect (ESEE). Additionally, we report evidence about a further generalization regarding probability judgments. We demonstrate that all effects can be found within German material, using ‘absichtlich’ [intentionally], ‘wissen’ [know] and ‘wahrscheinlich’ [likely]. As the explanations discussed with regard to the Knobe effect do not suffice to explicate the ESEE, we survey whether the characteristic asymmetry in knowledge judgments is caused by a differing (...) perception of probabilities concerning the occurrence of the side-effects. Our findings show that a negative side-effect is judged more probable, even if the objective probabilities would suggest otherwise. We argue that the best explanation for these results is that the Knobe effect applies to the perception of probabilities as well: a probabilistic side-effect effect. (shrink)

Salmon has argued that science provides explanations by describing a causal nexus: For Salmon, this nexus is a network of processes and interactions. I argue that this picture of the causal nexus is insufficient for an account of scientific explanation: a taxonomy of causal relevance is also needed. ;Probabilistic theories of causation seem to provide such a taxonomy in their dichotomy between promoting and inhibiting causes. However, standard probabilistic theories are beset by a difficulty called the problem (...) of disjunctive factors. According to such theories, an effect is more probable in the presence of a cause than in its absence . But there are many ways in which a particular cause may come about, and many in which it may be absent; these ways need not confer the same probabilities upon the effect. Thus, there is no direct comparison of two probabilities to be made. My solution is to abandon the oversimplified dichotomy between promoting and inhibiting causes. Causal claims convey qualitative information about more complex probabilistic relationships. Interestingly, this picture of causation meshes naturally with extant theories of explanation. ;I show how this framework may be employed in resolving several outstanding problems in the theories of causation and explanation, such as the relationship between singular and general causal claims, and the role of contrastive stress in causal and explanatory claims. ;Finally, I show how my account of causal explanation can be connected with the semantic conception of scientific theories. According to this conception, a theory is characterized in terms of a class of mathematical models. I describe the relationship between these mathematical models and the probabilistic relationships that are described by causal explanations. These ideas are illustrated in an extended discussion of causation and explanation in evolutionary theory. (shrink)

Standard models of statistical explanation face two intractable difficulties. In his 1984 Salmon argues that because statistical explanations are essentially probabilistic we can make sense of statistical explanation only by rejecting the intuition that scientific explanations are contrastive. Further, frequently the point of a statistical explanation is to identify the etiology of its explanandum, but on standard models probabilistic explanations often fail to do so. This paper offers an alternative conception of statistical explanations on which (...) explanations of the frequency of a property consist in the derivation of that frequency from a statistical specification of the mechanism by which instances of the relevant property are produced. Such explanations are contrastive precisely because they identify the determinate causal etiologies of their explananda. (shrink)

Carl Hempel (1965) argued that probabilistic hypotheses are limited in what they can explain. He contended that a hypothesis cannot explain why E is true if the hypothesis says that E has a probability less than 0.5. Wesley Salmon (1971, 1984, 1990, 1998) and Richard Jeffrey (1969) argued to the contrary, contending that P can explain why E is true even when P says that E’s probability is very low. This debate concerned noncontrastive explananda. Here, a view of contrastive (...) causal explanation is described and defended. It provides a new limit on what probabilistic hypotheses can explain; the limitation is that P cannot explain why E is true rather than A if P assign E a probability that is less than or equal to the probability that P assigns to A. The view entails that a true deterministic theory and a true probabilistic theory that apply to the same explanandum partition are such that the deterministic theory explains all the true contrastive propositions constructable from that partition, whereas the probabilistic theory often fails to do so. (shrink)

Words are the essence of communication: They are the building blocks of any language. Learning the meaning of words is thus one of the most important aspects of language acquisition: Children must first learn words before they can combine them into complex utterances. Many theories have been developed to explain the impressive efficiency of young children in acquiring the vocabulary of their language, as well as the developmental patterns observed in the course of lexical acquisition. A major source of disagreement (...) among the different theories is whether children are equipped with special mechanisms and biases for word learning, or their general cognitive abilities are adequate for the task. We present a novel computational model of early word learning to shed light on the mechanisms that might be at work in this process. The model learns word meanings as probabilistic associations between words and semantic elements, using an incremental and probabilistic learning mechanism, and drawing only on general cognitive abilities. The results presented here demonstrate that much about word meanings can be learned from naturally occurring child-directed utterances (paired with meaning representations), without using any special biases or constraints, and without any explicit developmental changes in the underlying learning mechanism. Furthermore, our model provides explanations for the occasionally contradictory child experimental data, and offers predictions for the behavior of young word learners in novel situations. (shrink)

Carl Hempel argued that probabilistic hypotheses are limited in what they can explain. He contended that a hypothesis cannot explain why E is true if the hypothesis says that E has a probability less than 0.5. Wesley Salmon and Richard Jeffrey argued to the contrary, contending that P can explain why E is true even when P says that E’s probability is very low. This debate concerned noncontrastive explananda. Here, a view of contrastive causal explanation is described and (...) defended. It provides a new limit on what probabilistic hypotheses can explain; the limitation is that P cannot explain why E is true rather than A if P assign E a probability that is less than or equal to the probability that P assigns to A. The view entails that a true deterministic theory and a true probabilistic theory that apply to the same explanandum partition are such that the deterministic theory explains all the true contrastive propositions constructable from that partition, whereas the probabilistic theory often fails to do so. (shrink)

This article considers the popular thesis that a more proportional relationship between a cause and its effect yields a more abstract causal explanation of that effect, which in turn produces a deeper explanation. This thesis is taken to have important implications for choosing the optimal granularity of explanation for a given explanandum. In this article, I argue that this thesis is not generally true of probabilistic causal relationships. In light of this finding, I propose a pragmatic, (...) interest-relative measure of explanatory depth. This measure uses a decision-theoretic model of information pricing to determine the optimal granularity of explanation for a given explanandum, agent, and decision problem. (shrink)

This paper describes the development of theories of scientific explanation since Hempel's earliest models in the 1940ies. It focuses on deductive and probabilistic whyexplanations and their main problems: lawlikeness, explanation-prediction asymmetries, causality, deductive and probabilistic relevance, maximal specifity and homogenity, the height of the probability value. For all of these topic the paper explains the most important approaches as well as their criticism, including the author's own accounts. Three main theses of this paper are: (1) Both (...) deductive and probabilistic explanations are important in science, not reducible to each other. (2) One must distinguish between (cause giving) explanations and (reason giving) justifications and predictions. (3) The adequacy of deductive as well as probabilistic explanations is relative to a pragmatically given background knowledge-which does not exclude, however, the possibility of purely semantic models. (shrink)

The explanatory role of natural selection is one of the long-term debates in evolutionary biology. Nevertheless, the consensus has been slippery because conceptual confusions and the absence of a unified, formal causal model that integrates different explanatory scopes of natural selection. In this study we attempt to examine two questions: (i) What can the theory of natural selection explain? and (ii) Is there a causal or explanatory model that integrates all natural selection explananda? For the first question, we argue that (...) five explananda have been assigned to the theory of natural selection and that four of them may be actually considered explananda of natural selection. For the second question, we claim that a probabilistic conception of causality and the statistical relevance concept of explanation are both good models for understanding the explanatory role of natural selection. We review the biological and philosophical disputes about the explanatory role of natural selection and formalize some explananda in probabilistic terms using classical results from population genetics. Most of these explananda have been discussed in philosophical terms but some of them have been mixed up and confused. We analyze and set the limits of these problems. (shrink)

Remarkable progress in the mathematics and computer science of probability has led to a revolution in the scope of probabilistic models. In particular, ‘sophisticated’ probabilistic methods apply to structured relational systems such as graphs and grammars, of immediate relevance to the cognitive sciences. This Special Issue outlines progress in this rapidly developing field, which provides a potentially unifying perspective across a wide range of domains and levels of explanation. Here, we introduce the historical and conceptual foundations of (...) the approach, explore how the approach relates to studies of explicit probabilistic reasoning, and give a brief overview of the field as it stands today. (shrink)

The main aim of this paper is to provide some probabilistic notions on causality proposed to be applied to the nomic statements which intend to give account of the indeterministic processes within the domain of a scientific theory. In general, such statements are, in more or less extent, idealized statements which rest on a variety of unrealistic suppositions. I try to show how the probability distribution over the final states of an indeterministic process changes accordingly as the nomic statement (...) in question is de-idealized by means of addition of the causally relevant factors. In order to illustrate the study I take few nomic statements from population genetics. Besides, in the course, I attempt to contrast the ideas embraced here with some of the notions of Humphreys´ ontic conceptions of causality and explanation, which are contrary to the epistemic view adopted here about those subjects. (shrink)

The notions of psychological similarity and probabilistic learning are key posits in cognitive, computational, and developmental psychology and in machine learning. However, their explanatory relationship is rarely made explicit within and across these research fields. This opinionated review critically evaluates how these notions can mutually inform each other within computational cognitive science. Using probabilistic models of concept learning as a case study, I argue that two notions of psychological similarity offer important normative constraints to guide modelers’ interpretations of (...) representational primitives. In particular, the two notions furnish probabilistic models of cognition with meaningful interpretations of what the associated subjective probabilities in the model represent and how they attach to experiences from which the agent learns. Similarity representations thereby provide probabilistic models with cognitive, as opposed to purely mathematical, content. (shrink)

According to a standard assumption in epistemology, if one only partially believes that p , then one cannot thereby have knowledge that p. For example, if one only partially believes that that it is raining outside, one cannot know that it is raining outside; and if one only partially believes that it is likely that it will rain outside, one cannot know that it is likely that it will rain outside. Many epistemologists will agree that epistemic agents are capable of (...) partial beliefs in addition to full beliefs and that partial beliefs can be epistemically assessed along some dimensions. However, it has been generally assumed that such doxastic attitudes cannot possibly amount to knowledge. In Probabilistic Knowledge, Moss challenges this standard assumption and provides a formidable defense of the claim that probabilistic beliefs—a class of doxastic attitudes including credences and degrees of beliefs—can amount to knowledge too. Call this the probabilistic knowledge claim . Throughout the book, Moss goes to great lengths to show that probabilistic knowledge can be fruitfully applied to a variety of debates in epistemology and beyond. My goal in this essay is to explore a further application for probabilistic knowledge. I want to look at the role of probabilistic knowledge within a “knowledge-centered” psychology—a kind of psychology that assigns knowledge a central stage in explanations of intentional behavior. My suggestion is that Moss’s notion of probabilistic knowledge considerably helps further both a knowledge-centered psychology and a broadly intellectualist picture of action and know-how that naturally goes along with it. At the same time, though, it raises some interesting issues about the notion of explanation afforded by the resulting psychology. (shrink)

There has been a probabilistic turn in contemporary cognitive science. Far and away, most of the work in this vein is Bayesian, at least in name. Coinciding with this development, philosophers have increasingly promoted Bayesianism as the best normative account of how humans ought to reason. In this paper, we make a push for exploring the probabilistic terrain outside of Bayesianism. Non-Bayesian, but still probabilistic, theories provide plausible competitors both to descriptive and normative Bayesian accounts. We argue (...) for this general idea via recent work on explanationist models of updating, which are fundamentally probabilistic but assign a substantial, non-Bayesian role to explanatory considerations. (shrink)

The turn from deterministic to probabilistic explanations has been used to argue that social science does not explain human action in ways that are incompatible with free will, since, according to some accounts of probabilism, causal factors merely influence actions without determining them. I argue that the notion of nondetermining causal influence is a multifaceted and problematic idea, which notably is unclear about whether the probability is objective or subjective, whether it applies to individual occurrences or merely to sets (...) of occurrences, and whether it is possible for an occurrence to be "almost determined.". (shrink)

Los's probability semantics are used to identify the appropriate probability conditional for use in probabilistic explanations. This conditional is shown to have applications to probabilistic reasoning in expert systems. The reasoning scheme of the system MYCIN is shown to be probabilistically invalid; however, it is shown to be "close" to a probabilistically valid inference scheme.

Probabilistic reasoning is traditionally represented by inferences of the following form (also called probabilistic explanations):where A and B are one-place predicates in a first order language, P(A | B) is the conditional probability of observing A among individuals having property B, and q is close to one.This argument is not logically valid, as the premises may be true while the conclusion is false. Moreover, as it stands, the premises do not even make the conclusion plausible. It may be (...) the case that 90% of the population dies before the age of 85, and that individual j is a member of the population, but this in itself does not make it plausible that individual j will die before the age of 85. (shrink)

It is shown that the probabilistic theories of coherence proposed up to now produce a number of counter-intuitive results. The last section provides some reasons for believing that no probabilistic measure will ever be able to adequately capture coherence. First, there can be no function whose arguments are nothing but tuples of probabilities, and which assigns different values to pairs of propositions {A, B} and {A, C} if A implies both B and C, or their negations, and if (...) P(B)=P(C). But such sets may indeed differ in their degree of coherence. Second, coherence is sensitive to explanatory relations between the propositions in question. Explanation, however, can hardly be captured solely in terms of probability. (shrink)

Wesley Salmon is renowned for his seminal contributions to the philosophy of science. He has powerfully and permanently shaped discussion of such issues as lawlike and probabilistic explanation and the interrelation of explanatory notions to causal notions. This unique volume brings together twenty-six of his essays on subjects related to causality and explanation, written over the period 1971-1995. Six of the essays have never been published before and many others have only appeared in obscure venues. The volume (...) includes a section of accessible introductory pieces, as well as more advanced and technical pieces, and will make essential work in the philosophy of science readily available to both scholars and students. (shrink)

All extant purely probabilistic measures of explanatory power satisfy the following technical condition: if Pr(E | H1) > Pr(E | H2) and Pr(E | ∼H1) < Pr(E | ∼H2), then H1’s explanatory power with respect to E is greater than H2’s explanatory power with respect to E. We argue that any measure satisfying this condition faces three serious problems—the Problem of Temporal Shallowness, the Problem of Negative Causal Interactions, and the Problem of Nonexplanations. We further argue that many such (...) measures face a fourth problem—the Problem of Explanatory Irrelevance. (shrink)

Larry Wright and others have advanced causal accounts of functional explanation, designed to alleviate fears about the legitimacy of such explanations. These analyses take functional explanations to describe second order causal relations. These second order relations are conceptually puzzling. I present an account of second order causation from within the framework of Eells' probabilistic theory of causation; the account makes use of the population-relativity of causation that is built into this theory.

In their article 'Causes and Explanations: A Structural-Model Approach. Part I: Causes', Joseph Halpern and Judea Pearl draw upon structural equation models to develop an attractive analysis of 'actual cause'. Their analysis is designed for the case of deterministic causation. I show that their account can be naturally extended to provide an elegant treatment of probabilistic causation.

Coherence is a measure of how much our beliefs hang together. Understanding is achieved when we see that something is not just a brute, isolated fact. This suggests that it might be possible to use the extant probabilistic measures of coherence to formulate a measure of understanding. We attempt to do so, but it turns out that a coherence theory runs into trouble with the asymmetry of understanding. We identify four difficulties and show how they have been solved by (...) a unification approach to explanation. We also identify four advantages of the coherence approach, and assess the possibilities of reconciling the strengths of the two approaches.La coherencia es una medida sobre cuanta interdependencia hay entre nuestras creencias. La comprension se obtiene cuando vemos que algo no es un hecho bruto, aislado. Esto sugiere la posibilidad de usar las medidas probabilisticas de coherencia al uso para elaborar una medida de la comprension. Explorare esta posibilidad, a pesar de que una teoria de la coherencia tropieza con problemas aqui dado el caracter asimetrico de la comprension. Identifico cuatro dificultades al respecto y muestro como han sido resueltas mediante un enfoque de la explicacion basado en la nocion de unificacion. Tambien identifico cuatro ventajas en la aproximacion desde la coherencia y examino que perspectivas hay de reconciliar los puntos fuertes de ambos planteamientos. (shrink)

Several philosophers propose probabilistic measures of how well a potential scientific explanation would explain the given evidence. These measures could elaborate “best” in “inference to the best explanation”. This paper argues that none of these measures succeeds. The paper considers the various rival explanations that scientists proposed for the parallelogram of forces. Scientists regarded various features of these proposals as making them more or less “lovely”. None of these probabilistic measures of loveliness can reflect these features. (...) The paper concludes by considering the kinds of probabilities that could reflect these features. (shrink)

On explanationist accounts of genealogical debunking, roughly, a belief is debunked when its explanation is not suitably related to its content. We argue that explanationism cannot accommodate cases in which beliefs are explained by factors unrelated to their contents but are nonetheless independently justified. Justification-specific versions of explanationism face an iteration of the problem. The best account of debunking is a probabilistic account according to which subject S’s justification J for their belief that P is debunked when S (...) learns that J is no more likely to be true on the hypothesis that P than on the hypothesis that ¬P. The probabilistic criterion is fully general, applying not only to cases where the learned undercutting defeater is a proposition about our beliefs or other mental states but to any case of undercutting defeat, providing the grounds for a debunking argument against the existence of a special, metacognitive debunking principle. (shrink)

The idea that good explanations come with strong changes in probabilities has been very common. This criterion is called probabilistic difference-making. Since it is an intuitive criterion and has a long tradition in the literature on scientific explanation, it comes as a surprise that probabilistic difference-making is rarely discussed in the context of interventionist causal explanation. Specificity, proportionality, and stability are usually employed to measure explanatory power instead. This paper is a first step into the larger (...) project of connecting difference-making to the interventionist debate, and it starts by investigating whether probabilistic difference-making is contained in the notion of specificity. The choice of specificity is motivated by the observation that both probabilistic difference-making and specificity build on similar underlying intuitions. When comparing measures for both specificity and probabilistic difference-making, it turns out that the measures are not strictly correlated, and so the thesis that probabilistic difference-making is encoded within specificity has to be rejected. Some consequences of this result are discussed as well. (shrink)

When surprising events occur, people naturally try to generate explanations of them. Such explanations usually involve hypothesizing causes that have the events as effects. Reasoning from effects to prior causes is found in many domains, including: Social reasoning: when friends are acting strange, we conjecture about what might be bothering them. Legal reasoning: when a crime has been committed, jurors must decide whether the prosecution's case gives a convincing explanation of the evidence. Medical diagnosis: given a set of symptoms, (...) a physician tries to decide what disease or diseases produced them. Fault diagnosis in manufacturing: when a piece of equipment breaks down, a trouble shooter must try to determine the cause of the breakdown. Scientific theory evaluation: scientists seek an acceptable theory to explain experimental evidence. What is the nature of such reasoning? (shrink)

Explanation and understanding are intimately connected notions, but the nature of that connection has generally not been considered a topic worthy of serious philosophical investigation. Most authors have avoided making reference to the notion of understanding in their accounts of explanation because they fear that any mention of the epistemic states of the individuals involved compromises the objectivity of explanation. Understanding is a pragmatic notion, they argue, and pragmatics should be kept at a safe distance from the (...) universal features of explanation. My main contention in this dissertation is that there is a sense in which it is meaningful and useful to talk about objective understanding, and that to characterize this notion it is necessary to formulate an account of objective explanation that makes reference to the beliefs and epistemic goals of the participants in a cognitive enterprise. ;My account of explanation is based on the belief-doubt model of inquiry first proposed by Peirce. Using the tools provided by decision theory, and the models of belief revision developed by Isaac Levi and by Alchourron, Gardenfors, and Makinson, I analyze the objective and pragmatic conditions that a piece of information must fulfill to be both explanatory and epistemically useful to an inquiring agent. The objective basis for an explanation is provided by the relation of probabilistic relevance that the fact described by the explanans bares to the fact described by the explanandum. But an explanation is much more than its foundation. As an epistemological notion, a potential explanation can only be a bona fide explanation if it becomes part of inquiry, that is, if an agent or a group of agents can see any value in it for their cognitive purposes. I provide a way to evaluate an explanation in terms of its credibility, its content, and its explanatory value. I argue that although an objective measure of the credibility and content of an explanation can be established, in many cases a complete determination of its explanatory value will ultimately depend on the interests and goals of the individual inquirers. (shrink)

A recent development in the philosophy of religion has been the attempt to justify belief in God using Bayesian confirmation theory. My dissertation critically discusses two prominent spokesmen for this approach--Richard Swinburne and J. L. Mackie. Using probabilistic confirmation theory, these philosophers come to wildly divergent conclusions with respect to the hypothesis of theism; Swinburne contends that the evidence raises the overall probability of the hypothesis of theism, whereas Mackie argues that the evidence disconfirms the existence of God. After (...) a careful analysis of the individual authors, this dissertation critically examines the assumptions of the project. The authors consider arguments for the existence of God separately--the cosmological argument, the argument from design, apparent miracles, the problem of evil, and arguments from religious experience--and then conjoin them to assess the cumulative effect of the arguments. The assumptions are that the probability calculus may be interpreted for a successful inductive argument for or against the existence of God, that inference to best explanation is applicable to the justification of religious belief, that the justification of belief in God is analogous to the justification of a scientific theory, and that a classical foundationalist conception of rationality is correct. It is the contention of this dissertation that all of these assumptions are incorrect. All of the major interpretations of the probability calculus are examined and it is argued that there are either no interpretations for the probability assignments or no interpretations which will advance an argument for or against the existence of God. It is also argued that the usual methods for interpreting the explanatory power of theism will not determine any non-zero probabilities; however, density measuring will provide a non-zero interpretation. In the final chapter it is argued that a subjective Bayesian conception of rationality is neither a necessary nor a sufficient condition of rationality and that classical foundationalism is self-referentially inconsistent. An alternative approach to the rationality of religious belief is offered that proceeds along Reidian and Plantingan lines, belief in God is properly basic. (shrink)

Existing definitions of relevance relations are essentially ambiguous outside the binary case. Hence definitions of probabilistic causality based on relevance relations, as well as probability values based on maximal specificity conditions and homogeneous reference classes are also not uniquely specified. A 'neutral state' account of explanations is provided to avoid the problem, based on an earlier account of aleatory explanations by the author. Further reasons in support of this model are given, focusing on the dynamics of explanation. It (...) is shown that truth in explanation need not entail maximal specificity and that probabilistic explanations should not contain a specification of probability values. (shrink)

Approaches to explanation -- Causal and explanatory relevance -- The kairetic account of /D making -- The kairetic account of explanation -- Extending the kairetic account -- Event explanation and causal claims -- Regularity explanation -- Abstraction in regularity explanation -- Approaches to probabilistic explanation -- Kairetic explanation of frequencies -- Kairetic explanation of single outcomes -- Looking outward -- Looking inward.

I advance a new theory of causal relevance, according to which causal claims convey information about conditional probability functions. This theory is motivated by the problem of disjunctive factors, which haunts existing probabilistic theories of causation. After some introductory remarks, I present in Section 3 a sketch of Eells's (1991) probabilistic theory of causation, which provides the framework for much of the discussion. Section 4 explains how the problem of disjunctive factors arises within this framework. After rejecting three (...) proposed solutions, I offer in Section 6 a new approach to causation that avoids the problem. Decision-theoretic considerations also support the new approach. Section 8 develops the consequences of the new theory for causal explanation. The resulting theory of causal explanation incorporates the new insights while respecting important work on scientific explanation by Salmon (1971), Railton (1981), and Humphreys (1989). My conclusions are enumerated in Section 9. (shrink)

In this paper I argue that economic theories have never been able to provide a coherent explanation of the causation requirement in tort law. The economic characterization of this requirement faces insurmountable difficulties, because discourse on tort liability cannot be reduced to a cost-benefit analysis without a loss of meaning. More seriously, I try to show that by describing causation in economic terms, economic theories offer an image of the practice in which the participants incur in logical contradictions and (...) develop patterns of inference that are far from intuitive. For this reason, efficiency cannot be the fundamental principle underlying tort law. Finally, I suggest that economic analysis of law can provide a genuine explanation of certain aspects of legal practice if it relinquishes its reductionist claims. (shrink)

A procedure is given for the transformation of quantum mechanical operator equations into stochastic equations. The stochastic equations reveal a simple correlation between quantum mechanics and classical mechanics: Quantum mechanics operates with “optimal estimations,” classical mechanics is the limit of “complete information.” In this connection, Schrödinger's substitution relationsp x → -iħ ∂/∂x, etc, reveal themselves as exact mathematical transformation formulas. The stochastic version of quantum mechanical equations provides an explanation for the difficulties in correlating quantum mechanics and the theory (...) of relativity: In physics “time” is always thought of as a numerical parameter; but in the present formalism of physics “time” is described by two formally totally different quantities. One of these two “times” is a numerical parameter and the other a random variable. This last concept of time shows all the properties required by the theory of relativity and is therefore to be considered as the relativistic time. (shrink)

Several philosophers have used the framework of means/ends reasoning to explain the methodological choices made by scientists and mathematicians (see, e.g., Goldman 1999, Levi 1962, Maddy 1997). In particular, they have tried to identify the epistemic objectives of scientists and mathematicians that will explain these choices. In this paper, the framework of means/ends reasoning is used to study an important methodological choice made by mathematicians. Namely, mathematicians will only use deductive proofs to establish the truth of mathematical claims. In this (...) paper, I argue that none of the epistemic objectives of mathematicians that are currently on the table provide a satisfactory explanation of this rejection of probabilistic proofs. (shrink)

Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of IBE. My argument focuses (...) on cases in which we are concerned with multiple levels of explanation of some phenomenon. I show that in many such cases, following IBE as an inference rule for full beliefs leads to deductively inconsistent beliefs, and following IBE as a non-Bayesian updating rule for degrees of belief leads to probabilistically incoherent degrees of belief. (shrink)