This paper considers a puzzling conflict between two positions that are each compelling: it is irrational for an agent to pay to avoid `free' evidence before making a decision, and rational agents may have imprecise beliefs and/or desires. Indeed, we show that Good's theorem concerning the invariable choice-worthiness of free evidence does not generalise to the imprecise realm, given the plausible existing decision theories for handling imprecision. A key ingredient in the analysis, and a potential source of controversy, is the (...) general approach taken for resolving sequential decision problems { we make explicit what the key alternatives are and defend our own approach. Furthermore, we endorse a resolution of the aforementioned puzzle { we privilege decision theories that merely permit avoiding free evidence over decision theories for which avoiding free evidence is uniquely admissible. Finally, we situate this particular result about free evidence within the broader `dynamic-coherence' literature. (shrink)

In a recent paper, Pettigrew reports a generalization of the celebrated accuracy-dominance theorem due to Predd et al., but Pettigrew’s proof is incorrect. I will explain the mistakes and provide a correct proof.

In this article, I explain how a variant of David Miller's argument concerning the language dependence of the accuracy of predictions can be applied to Joyce's notion of the accuracy of “estimates of numerical truth-values”. This leads to a potential problem for Joyce's accuracy-dominance-based argument for the conclusion that credences should obey the probability calculus.

Probabilistic belief contraction has been a much neglected topic in the field of probabilistic reasoning. This is due to the difficulty in establishing a reasonable reversal of the effect of Bayesian conditionalization on a probabilistic distribution. We show that indifferent contraction, a solution proposed by Ramer to this problem through a judicious use of the principle of maximum entropy, is a probabilistic version of a full meet contraction. We then propose variations of indifferent contraction, using both the Shannon entropy measure (...) as well as the Hartley entropy measure, with an aim to avoid excessive loss of beliefs that full meet contraction entails. (shrink)

Dutch Book Arguments. B is susceptibility to sure monetary loss (in a certain betting set-up), and F is the formal role played by non-Pr b’s in the DBT and the Converse DBT. Representation Theorem Arguments. B is having preferences that violate some of Savage’s axioms (and/or being unrepresentable as an expected utility maximizer), and F is the formal role played by non-Pr b’s in the RT.

- In decision theory, an agent is deciding how to value a gamble that results in different outcomes in different states. Each outcome gets a utility value for the agent.

'The Probabilistic Mind' is a follow-up to the influential and highly cited 'Rational Models of Cognition'. It brings together developments in understanding how, and how far, high-level cognitive processes can be understood in rational terms, and particularly using probabilistic Bayesian methods.

Probabilistic epistemology holds that probability is an essential ingredient of science and human knowledge at large, and that induction is a necessary constituent of the scientific method. Developed in some detail by a number of authors including Patrick Suppes, Richard Jeffrey and Brian Skyrms, this view has been embraced by so many, as to gradually become predominant. While probabilistic epistemology has been growing, awareness of its origins was somehow left behind. Probabilistic epistemology is usually seen as a product of the (...) encounter of logical empiricism with American pragmatism. Without denying the impact of such an encounter, it is argued that the probabilistic approach was already part of the European scenario before the dissolution of logical empiricism in the late 1930s. Notably, such an approach is not linked to a particular interpretation of probability, having been endorsed by upholders of different probability notions, including Janina Hosiasson, Frank Plumpton Ramsey, Bruno de Finetti, Harold Jeffreys, and Hans Reichenbach, to mention only those authors whose contribution is addressed here. The list could extend to the French probabilists Émile Borel and Maurice Fréchet, and others not considered in this survey. The work of so many authors operating at the four corners of Europe in the first decades of the 19th century reflects a European tradition in probabilistic epistemology, somewhat overshadowed in the literature by the attention paid to logical empiricism. (shrink)

We investigate an approach for drawing logical inference from inconsistent premisses. The main idea in this approach is that the inconsistencies in the premisses should be interpreted as uncertainty of the information. We propose a mechanism, based on Kinght’s [14] study of inconsistency, for revising an inconsistent set of premisses to a minimally uncertain, probabilistically consistent one. We will then generalise the probabilistic entailment relation introduced in [15] for propositional languages to the first order case to draw logical inference from (...) a probabilistic set of premisses. We will show how this combination can allow us to limit the effect of uncertainty introduced by inconsistent premisses to only the reasoning on the part of the premise set that is relevant to the inconsistency. (shrink)

Should Probabilistic Design Replace Safety Factors? Content Type Journal Article Pages 151-168 DOI 10.1007/s13347-010-0003-6 Authors Neelke Doorn, Department of Technology, Policy and Management, Delft University of Technology, PO Box 5015, 2600 GA Delft, The Netherlands Sven Ove Hansson, Department of Philosophy and the History of Technology, Royal Institute of Technology, Teknikringen 78 B, 100 44 Stockholm, Sweden Journal Philosophy & Technology Online ISSN 2210-5441 Print ISSN 2210-5433 Journal Volume Volume 24 Journal Issue Volume 24, Number 2.

This study presents a probabilistic model of melody perception, which infers the key of a melody and also judges the probability of the melody itself. The model uses Bayesian reasoning: For any “surface” pattern and underlying “structure,” we can infer the structure maximizing P(structure|surface) based on knowledge of P(surface, structure). The probability of the surface can then be calculated as ∑ P(surface, structure), summed over all structures. In this case, the surface is a pattern of notes; the structure is a (...) key. A generative model is proposed, based on three principles: (a) melodies tend to remain within a narrow pitch range; (b) note‐to‐note intervals within a melody tend to be small; and (c) notes tend to conform to a distribution (or key profile) that depends on the key. The model is tested in three ways. First, it is tested on its ability to identify the keys of a set of folksong melodies. Second, it is tested on a melodic expectation task in which it must judge the probability of different notes occurring given a prior context; these judgments are compared with perception data from a melodic expectation experiment. Finally, the model is tested on its ability to detect incorrect notes in melodies by assigning them lower probabilities than the original versions. (shrink)

The aim of the paper is to develop general criteria of argumentative validity and adequacy for probabilistic arguments on the basis of the epistemological approach to argumentation. In this approach, as in most other approaches to argumentation, proabilistic arguments have been neglected somewhat. Nonetheless, criteria for several special types of probabilistic arguments have been developed, in particular by Richard Feldman and Christoph Lumer. In the first part (sects. 2-5) the epistemological basis of probabilistic arguments is discussed. With regard to the (...) philosophical interpretation of probabilities a new subjectivist, epistemic interpretation is proposed, which identifies probabilities with tendencies of evidence (sect. 2). After drawing the conclusions of this interpretation with respect to the syntactic features of the probability concept, e.g. one variable referring to the data base (sect. 3), the justification of basic probabilities (priors) by judgements of relative frequency (sect. 4) and the justification of derivative probabilities by means of the probability calculus are explained (sect. 5). The core of the paper is the definition of '(argumentatively) valid derivative probabilistic arguments', which provides exact conditions for epistemically good probabilistic arguments, together with conditions for the adequate use of such arguments for the aim of rationally convincing an addressee (sect. 6). Finally, some measures for improving the applicability of probabilistic reasoning are proposed (sect. 7). (shrink)

The debate on probabilistic measures of coherence flourishes for about 15 years now. Initiated by papers that have been published around the turn of the millennium, many different proposals have since then been put forward. This contribution is partly devoted to a reassessment of extant coherence measures. Focusing on a small number of reasonable adequacy constraints I show that (i) there can be no coherence measure that satisfies all constraints, and that (ii) subsets of these adequacy constraints motivate two different (...) classes of coherence measures. These classes do not coincide with the common distinction between coherence as mutual support and coherence as relative set-theoretic overlap. Finally, I put forward arguments to the effect that for each such class of coherence measures there is an outstanding measure that outperforms all other extant proposals. One of these measures has recently been put forward in the literature, while the other one is based on a novel probabilistic measure of confirmation. (shrink)

In this paper, it is shown that an event E can be the cause of an event E* even if there is a less than 100% likelihood that, given an arbitrary E-similar event, an E*-similar event will ensue.

In the two-envelope problem, a reasoner is offered two envelopes, one containing exactly twice the money in the other. After observing the amount in one envelope, it can be traded for the unseen contents of the other. It appears that it should not matter whether the envelope is traded, but recent mathematical analyses have shown that gains could be made if trading was a probabilistic function of amount observed. As a problem with a purely probabilistic solution, it provides a potentially (...) interesting way to test people's consistency with probabilistic models. Three experiments did this by varying the size of both the observed and maximum amounts, and their possible distribution. The results showed that trading decisions were affected by where the observed amount in the opened envelope fell in the distribution, though its size did not always do so. This suggests that participants’ trade decisions could be affected by the perceived probabilities of different observed amounts, which is consistent with the pro.. (shrink)

How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain or (...) an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are sigma-algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we compare our results with existing results on binary judgment aggregation and Arrovian preference aggregation. This paper is the first of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

The central problem with Bayesian philosophy of science is that it cannot take account of the relevance of simplicity and unification to confirmation, induction, and scientific inference. The standard Bayesian folklore about factoring simplicity into the priors, and convergence theorems as a way of grounding their objectivity are some of the myths that Earman's book does not address adequately. 1Review of John Earman: Bayes or Bust?, Cambridge, MA. MIT Press, 1992, £33.75cloth.

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)

Participants were asked to draw inferences about correlation from single x,y observations. In Experiment 1 statistically sophisticated participants were given the univariate characteristics of distributions of x and y and asked to infer whether a single x, y observation came from a correlated or an uncorrelated population. In Experiment 2, students with a variety of statistical backgrounds assigned posterior probabilities to five possible populations based on single x, y observations, again given knowledge of the univariate statistics. In Experiment 3, statistically (...) naïve participants were given a problem analogous to that given in Experiment 1, framed verbally. Experiment 4 replicated Experiment 3 but added an “impossible to determine” response option. Models that rely on computing sample correlations make no predictions about these investigations. From a Bayesian perspective, participants’ inferences in all four experiments tended to make probabilistically valid inferences as long as the single datum was directional. The results are discussed in light of the Brunswikian notion of vicarious functioning. (shrink)

This paper attempts to set up a probabilistic framework for understanding the notion of causal necessity. What results is a relaxed and relativized probabilistic theory of epsilon-Causal necessity and an explicit attempt to avoid deterministic assumptions. The theory developed emphasizes the notions of partial cause, Causal contribution, And the degree of contribution. Implications for causal overdetermination, Causal preemption, And causal discourse are discussed.

Are probabilism and special relativity compatible? Dieks argues that they are. But the possible universe he specifies, designed to exemplify both probabilism and special relativity, either incorporates a universal “now”, or amounts to a many world universe, or fails to have any one definite overall Minkowskian-type space-time structure. Probabilism and special relativity appear to be incompatible after all. What is at issue is not whether “the flow of time” can be reconciled with special relativity, but rather whether (...) explicitly probabilistic versions of quantum theory should be rejected because of incompatibility with special relativity. (shrink)

While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches to probabilistic logic into a simple unifying framework: logically complex evidence can be used to associate probability intervals or probabilities with sentences.

The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions p τ (t) at a given time t obtain by integrating out the past and future. We discuss all-time probability distributions that realize a unitary time evolution as described by rotations of the real wave function $q_{\tau}(t)=\pm \sqrt{p_{\tau}(t)}$ . We establish a map to quantum physics and the Schrödinger equation. Suitable classical observables are mapped to quantum operators. The non-commutativity of the operator product is (...) traced back to the incomplete statistics of the local-time subsystem. Our investigation of classical statistics is based on two-level observables that take the values one or zero. Then the wave functions can be mapped to elements of a Grassmann algebra. Quantum field theories for fermions arise naturally from our formulation of probabilistic time. (shrink)

Probabilistic methods are providing new explanatory approaches to fundamental cognitive science questions of how humans structure, process and acquire language. This review examines probabilistic models defined over traditional symbolic structures. Language comprehension and production involve probabilistic inference in such models; and acquisition involves choosing the best model, given innate constraints and linguistic and other input. Probabilistic models can account for the learning and processing of language, while maintaining the sophistication of symbolic models. A recent burgeoning of theoretical developments and online (...) corpus creation has enabled large models to be tested, revealing probabilistic constraints in processing, undermining acquisition arguments based on a perceived poverty of the stimulus, and suggesting fruitful links with probabilistic theories of categorization and ambiguity resolution in perception. (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)

Developments in the Academy from the time of Arcesilaus to that of Carneades and his successors tend to be classified under two heads: scepticism and probabilism. Carneades was principally responsible for the Academy's view of the latter subject, and our sources credit him with an elaborate discussion of it. The evidence furnished by those sources is, however, frequently confusing and sometimes self-contradictory. My aim in this paper is to extract a coherent account of Carneades' theory of probability from the (...) testimony with a further end in view, namely to understand better the uses to which that theory was put by the Academy in its debate with the Stoa. Though it is not its principal object, the investigation should also help make clear how the Academy's scepticism and its probabilism were related to each other as parts of a single consistent practice of philosophy. (shrink)

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model- theoretic probabilistic reasoning and to default reasoning in System . In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System (...) . That is, we provide a new probabilistic semantics for System , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System , and they give new insight into default reasoning with conditional objects. (shrink)

A probabilistic theory of causation is a theory which holds that the central feature of causation is that causes raise the probability of their effects. In this dissertation, I defend Hans Reichenbach's original version of the probabilistic theory of causation, which analyses causal relations in terms of a three place statistical betweenness relation. Unlike most discussions of this theory, I hold that the statistical relation should be taken as a sufficient, but not as a necessary , condition for causal betweenness. (...) With this difference in interpretation, Reichenbach's theory is shown to be immune to all of the criticisms which have been raised against it in the last fifty years. ;Reichenbach's main purpose in defending a probabilistic theory of causation was to use it in giving an analysis of the direction of time. I defend this view, arguing that the arrow of causation is more basic than any of the other arrows of time---metaphysical, psychological or physical. In particular, I argue against the popular view that the direction of time is given by the physical fact that entropy only increases in one direction. I further show that the probabilistic theory of causation is particularly suited to the task of analysing the various arrows of time. In my final chapter, I also suggest that the probabilistic theory of causation may be fruitfully applied to the analysis of some important puzzles in the interpretation of quantum mechanics. (shrink)

This work is in two parts. The main aim of part 1 is a systematic examination of deductive, probabilistic, inductive and purely inductive dependence relations within the framework of Kolmogorov probability semantics. The main aim of part 2 is a systematic comparison of (in all) 20 different relations of probabilistic (in)dependence within the framework of Popper probability semantics (for Kolmogorov probability semantics does not allow such a comparison). Added to this comparison is an examination of (in all) 15 purely inductive (...) dependence relations. ————Part 1 leads in an axiomatic step-by-step development from the elementary classical truth value semantics of a sentential-logical language, called ‘L’, (chapter 1) to the elementary Kolmogorov probability semantics of L (chapter 2), which is then extended to four axiomatic semantical theories of dependence relations between the formulae of L. First the elementary Kolmogorov probability semantics of L is extended to a theory, called ‘Kdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 3). Then Kdd is extended to a theory, called ‘Kpd1’, of the degree to which formulae of L probabilistically depend on each other in regard to a given probability distribution on the set of all formulae of L (chapter 4). Kpd1, in its turn, gets extended to a theory, called ‘Kpd2’, of the relations of probabilistic dependence and independence, relativized to unary Kolmogorov probability functions defined on L (chapter 5). Then Kpd2 is extended to a theory, called ‘Kid’, of the relations of inductive dependence and inductive independence, again relativized to unary Kolmogorov probability functions defined on L (chapter 6). Finally, Kid is extended to a theory, called ‘Kpid’, of the relations of purely inductive positive and negative dependence, relativized to unary Kolmogorov probability functions defined on L (chapter 7). ——Chapter 1, which deals with the familiar notions of truth value functions, tautologies, consequence relations and relations of logical opposition, is naturally the shortest chapter of part 1.——In chapter 2, the elementary classical semantics of L is extended to the elementary Kolmogorov probability semantics of L, i.e. to an axiomatic theory of unary and of binary Kolmogorov probability functions defined on the set of formulae of L. Because of the elementary character of this theory, chapter 2 is also rather short.——Chapter 3 introduces the first theory on dependence relations, to wit: Kdd, the theory of deductive (in)dependence between formulae of L. I follow here the well-known idea of Popper and Miller, who have used it in a famous discussion on the nature of probabilistic support for their arguments that probabilistic support is deductive, not inductive. I develop Kdd in the form of about 100 theorems, making ample use of the fact that deductive independence is nothing but subcontrary opposition, and close with a remark on the fundamental difference between deductive and logical dependence—two relations the ideas of which are all too easily mixed up.——Chapters 4 and 5 deal extensively with the traditional ideas of probabilistic (in)dependence, applied to formulae rather than to events. As always, I proceed axiomatically in a step-by-step process under systematic viewpoints and obtain about 300 theorems in this way. In the formulation of the theorems, I took special care to state clearly and expressly so-called tacit assumptions, especially those concerning the probability values of the formulae said to be dependent on each other. These assumptions are usually missing in the literature, due either to economy of writing or to sloppiness of thinking. Presumably, both chapters contain little that is new, their value lying more in the systematic grouping and organic development of the theorems than in the newness of these.——In chapter 6, I extend the axiomatic theory about probabilistic (in)dependence which has been elaborated in chapter 5, to an axiomatic theory of inductive (in)dependence by requiring of the relation of inductive (in)dependence that it be probabilistic (in)dependence, but not also logical implication or logical opposition. I point out the differences between probabilistic and inductive (in)dependence by means of some 60 theorems and close my examination of inductive (in)dependence by considering its relationship to the notion of support in the philosophy of science.——Finally, in chapter 7, the last of part 1, I take the step from inductive dependence to what I call ‘purely inductive dependence’ by combining the idea of inductive dependence with that of deductive independence in a way which is suggested by writings of Popper and Miller. I arrive at two noteworthy theorems. Firstly, there is indeed no purely inductive support. But secondly, and perhaps amazingly, countersupport is purely inductive.————Whereas the probabilistic framework of part 1 of the present work is Kolmogorov probability semantics, the framework of part 2 is Popper probability semantics, which is not only worth examining as a fascinating alternative to orthodox Kolmogorov probability semantics, but also allows us to examine dependence relations more deeply, than Kolmogorov probability semantics does. Part 2 leads—again in an axiomatic step-by-step development—from the basic Popper probability semantics of L, called ‘Pb’, (chapter 8) via a probabilistic theory of logical attributes, called ‘Ps’, (chapter 9) to four axiomatic semantical theories of dependence relations between the formulae of L. First, Ps is extended to a theory, called ‘Pdd’, of the relations of deductive dependence and deductive independence between formulae of L (chapter 10). Then Pdd is extended to a theory, called ‘Ppd’, of (in all) 20 relations of probabilistic (in)dependence, relativized to binary Popper probability functions defined on L (chapter 11). Ppd, in its turn, is extended to a theory, called ‘Pid’, of (in all) 10 relations of inductive dependence, again relativized to binary Popper probability functions defined on L (first part of chapter 12). Finally, Pid is extended to a theory, called ‘Ppid’, of (in all) 15 relations of purely inductive positive and negative dependence, relativized to binary Popper probability functions defined on L (second part of chapter 12).——Chapter 8, the first chapter of part 2 of the present work, is entirely preparatory. It introduces the axioms and about 180 theorems (150 of them together with their proofs) of basic Popper probability semantics in order to set this kind of semantics under way.——Then, in chapter 9, basic Popper probability semantics is extended to a probabilistic theory of logical properties of and relations between the formulae of L. Although I think that the way I did this extension is of some interest in itself, the main task of chapter 9 is again a preparatory one: to yield the indispensable lemmata (about 90 in number) for the theorems concerning probabilistic dependence relations in chapter 11 and concerning inductive dependence relations in chapter 12.——Chapter 10 brings the extension of Ps to the theory Pdd of deductive (in)dependence. Only half a dozen theorems are noted here for later use in the Pdd-extensions Ppd and Ppid. In view of the over 100 theorems already gained on this topic in the Kolmogorovian framework (cf. chapter 3), a similar extensive elaboration of Pdd would have been superfluous.——Chapter 11 is the most important one of part 2. It consists of a systematic comparison of 20 probabilistic (in)dependence concepts by means of about 230 theorems, obtained within the axiomatic theory Ppd, which is built up as an extension of Pdd. The main points of comparison were: differences in logical strength; reflexivity and symmetry; behaviour under the condition that the probability values of the formulae in question are extreme. It turned out that each of the examined concepts violates a strong and straightforward version of the intuitive requirement that probabilistic dependence should go with logical dependence. Whereas the corresponding chapter 5 in part 1 of the present work may not have led to new theorems, chapter 11 yields dozens of them in the process of comparison of concepts of dependence and independence which had—as far as I know—never before been treated in a single theoretical framework. With Popper probability semantics, this framework has become available, and here I have simply made full use of it.——In chapter 12, I extend the theory Ppd of probabilistic (in)dependence to the theories Pid and Ppid of inductive and purely inductive dependence, in a way very similar to that in which I have extended the theory Kpd2 to the theories Kid and Kpid in chapters 6 and 7. The first main result of Kpid (roughly: there is no purely inductive support) could be repeated for four of the five purely inductive positive dependence relations considered in chapter 12, whereas the second main result of Kpid (roughly: there is purely inductive countersupport ) could be repeated for each of the five examined purely inductive negative dependence relations. Chapter 12 closes with a brief recapitulation and critical discussion of the main results. (shrink)

In this important book, Ellery Eells explores and refines philosophical conceptions of probabilistic causality. In a probabilistic theory of causation, causes increase the probability of their effects rather than necessitate their effects in the ways traditional deterministic theories have specified. Philosophical interest in this subject arises from attempts to understand population sciences as well as indeterminism in physics. Taking into account issues involving spurious correlation, probabilistic causal interaction, disjunctive causal factors, and temporal ideas, Professor Eells advances the analysis of what (...) it is for one factor to be a positive causal factor for another. A salient feature of the book is a theory of token level probabilistic causation in which the evolution of the probability of a later event from an earlier event is central. This will be a book of crucial significance to philosophers of science and metaphysicians; it will also prove stimulating to many economists, psychologists, and physicists. (shrink)

For certain methodological and historical reasons, the science of probability (probabilistics) had never been constructed before as a single whole, and it has basically split into probability theory and into statistics. One of the reasons was the neglect of an extremely important methodological principle which reads: It is necessary to distinguish strictly between concrete objects and abstract objects. This principle is displayed and exemplified. Its use has made it possible to discover the basic phenomenon of probalilistics and to construct the (...) science, whose outlines are given. The application of probabilistics to physics gives rise to probabilistic physics, whose particular domains are, among others, both classical statistical physics and quantum physics. The actual meaning of quantum physics becomes quite clear and no artificial interpretation of it proves to be necessary. (shrink)

According to Nancy Cartwright, a causal law holds just when a certain probabilistic condition obtains in all test situations which in turn satisfy a set of background conditions. These background conditions are shown to be inconsistent and, on separate account, logically incoherent. I offer a corrective reformulation which also incorporates a strategy for problems like Hesslow's thrombosis case. I also show that Cartwright's recent argument for modifying the condition to appeal to singular causes fails.Proposed modifications of the theory's probabilistic condition (...) to handle effects with extreme probabilities (0 or 1) are found unsatisfactory. I propose a unified solution which also handles extreme causes. Undefined conditional probabilities give rise to three good, but non-equivalent, ways of formulating the theory. Various formulations appear in the literature. I give arguments to eliminate all but one candidate. Finally, I argue for a crucial new condition clause, and show how to extend the results beyond a simple probabilistic framework. (shrink)

We often have some reason to do actions insofar as they promote outcomes or states of affairs, such as the satisfaction of a desire. But what is it to promote an outcome? I defend a new version of 'probabilism about promotion'. According to Minimal Probabilistic Promotion, we promote some outcome when we make that outcome more likely than it would have been if we had done something (anything) else. This makes promotion easy and reasons cheap.

Let E be a set of n propositions E1, ..., En. We seek a probabilistic measure C(E) of the ‘degree of coherence’ of E. Intuitively, we want C to be a quantitative, probabilistic generalization of the (deductive) logical coherence of E. So, in particular, we require C to satisfy the following..

Four experiments investigated the effects of probability manipulations on the indicative four card selection task (Wason, 1966, 1968). All looked at the effects of high and low probability antecedents (p) and consequents (q) on participants' data selections when determining the truth or falsity of a conditional rule, if p then q . Experiments 1 and 2 also manipulated believability. In Experiment 1, 128 participants performed the task using rules with varied contents pretested for probability of occurrence. Probabilistic effects were observed (...) which were partly consistent with some probabilistic accounts but not with non-probabilistic approaches to selection task performance. No effects of believability were observed, a finding replicated in Experiment 2 which used 80 participants with standardised and familiar contents. Some effects in this experiment appeared inconsistent with existing probabilistic approaches. To avoid possible effects of content, Experiments 3 (48 participants) and 4 (20 participants) used abstract material. Both experiments revealed probabilistic effects. In the Discussion we examine the compatibility of these results with the various models of selection task performance. (shrink)

Over the years several non-equivalent probabilistic measures of coherence have been discussed in the philosophical literature. In this paper we examine these measures with respect to their empirical adequacy. Using test cases from the coherence literature as vignettes for psychological experiments we investigate whether the measures can predict the subjective coherence assessments of the participants. It turns out that the participants’ coherence assessments are best described by Roche’s coherence measure based on Douven and Meijs’ average mutual support approach and the (...) conditional probability. (shrink)

According to probabilistic theories of reasoning in psychology, people's degree of belief in an indicative conditional `if A, then B' is given by the conditional probability, P(B|A). The role of language pragmatics is relatively unexplored in the new probabilistic paradigm. We investigated how consequent relevance a ects participants' degrees of belief in conditionals about a randomly chosen card. The set of events referred to by the consequent was either a strict superset or a strict subset of the set of events (...) referred to by the antecedent. We manipulated whether the superset was expressed using a disjunction or a hypernym. We also manipulated the source of the dependency, whether in long-term memory or in the stimulus. For subset-consequent conditionals, patterns of responses were mostly conditional probability followed by conjunction. For superset-consequent conditionals, conditional probability responses were most common for hypernym dependencies and least common for disjunction dependencies, which were replaced with responses indicating inferred consequent irrelevance. Conditional probability responses were also more common for knowledge-based than stimulus-based dependencies. We suggest. (shrink)

This article provides an overview of a probabilistic constraints framework for thinking about language acquisition and processing. The generative approach attempts to characterize knowledge of language (i.e., competence grammar) and then asks how this knowledge is acquired and used. Our approach is performance oriented: the goal is to explain how people comprehend and produce utterances and how children acquire this skill. Use of language involves exploiting multiple probabilistic constraints over various types of linguistic and nonlinguistic information. Acquisition is the process (...) of accumulating this information, which begins in infancy. The constraint satisfaction processes that are central to language use are the same as the bootstrapping processes that provide entry to language for the child. Framing questions about acquisition in terms of models of adult performance unifies the two topics under a set of common principles and has important consequences for arguments concerning language learnability. (shrink)

Probabilistic realism and syntactical positivism were two among outdated theories that Feigl criticised on account of their semantical poverty. In this paper, I argue that a refined version of probabilistic realism, which relies on what Feigl specified as the pragmatic description of the symbolic behaviour of scientists’ estimations and foresight, is defendable. This version of statistical realism does not need to make the plausibility of realist thesis dependent on the conventional acceptance of a constructed semantic metalanguage. I shall rely on (...) the Prediction Error Minimisation theory to support my probabilistic version of realism with a scientifically-informed and naturalistically plausible statistical account of the theories-world relationship which has a pragmatic ring to it. (shrink)

This paper discusses Simpson's paradox and the problem of positive relevance in probabilistic causality. It is argued that Cartwright's solution to Simpson's paradox fails because it ignores one crucial form of the paradox. After clarifying different forms of the paradox, it is shown that any adequate solution to the paradox must allow a cause to be both a negative cause and a positive cause of..

In mathematics, any form of probabilistic proof obtained through the application of a probabilistic method is not considered as a legitimate way of gaining mathematical knowledge. In a series of papers, Don Fallis has defended the thesis that there are no epistemic reasons justifying mathematicians’ rejection of probabilistic proofs. This paper identifies such an epistemic reason. More specifically, it is argued here that if one adopts a conception of mathematical knowledge in which an epistemic subject can know a mathematical proposition (...) based solely on a probabilistic proof, one is then forced to admit that such an epistemic subject can know several lottery propositions based solely on probabilistic evidence. Insofar as knowledge of lottery propositions on the basis of probabilistic evidence alone is denied by the vast majority of epistemologists, it is concluded that this constitutes an epistemic reason for rejecting probabilistic proofs as a means of acquiring mathematical knowledge. (shrink)

Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of (...) pooling functions (most of them classic, but one new) and argue that linear pooling can be justified procedurally, but not epistemically, while the other two pooling methods can be justified epistemically. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. We conclude by mentioning a number of other pooling methods. (shrink)

In this paper I expound an argument which seems to establish that probabilism and special relativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole.