In earlier work we proposed an account of information grounded in counterfactual conditionals rather than probabilities, and argued that it might serve philosophical needs that more familiar probabilistic alternatives do not. Demir [2008] and Scarantino [2008] criticize the counterfactual approach by contending that its alleged advantages are illusory and that it fails to secure attractive desiderata. In this paper we defend the counterfactual account from these criticisms, and suggest that it remains a useful account of information.

This paper is a response to Tyler Wunder’s ‘The modality of theism and probabilistic natural theology: a tension in Alvin Plantinga's philosophy’ (this journal). In his article, Wunder argues that if the proponent of the Evolutionary Argument Against Naturalism (EAAN) holds theism to be non-contingent and frames the argument in terms of objective probability, that the EAAN is either unsound or theism is necessarily false. I argue that a modest revision of the EAAN renders Wunder’s objection irrelevant, and (...) that this revision actually widens the scope of the argument. (shrink)

In earlier work we proposed an account of information grounded in counterfactual conditionals rather than probabilities, and argued that it might serve philosophical needs that more familiar probabilistic alternatives do not. Demir [2008] and Scarantino [2008] criticize the counterfactual approach by contending that its alleged advantages are illusory and that it fails to secure attractive desiderata. In this paper we defend the counterfactual account from these criticisms, and suggest that it remains a useful account of information.

This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability is a mode of judgment. Written by one of the greatest figures in the field of probability theory, the book is both a summation and synthesis of a lifetime of wrestling with these problems and issues. After an introduction to basic probability theory, there are chapters on scientific hypothesis-testing, on changing your mind in response to generally (...) uncertain observations, on expectations of the values of random variables, on de Finetti's dissolution of the so-called problem of induction, and on decision theory. (shrink)

In his constructive and well-informed commentary, Andrei Khrennikov acknowledges a privileged status of classical probability theory with respect to statistical analysis. He also sees advantages offered by the Contextuality-by-Default theory, notably, that it “demystifies quantum mechanics by highlighting the role of contextuality,” and that it can detect and measure contextuality in inconsistently connected systems. He argues, however, that classical probability theory may have difficulties in describing empirical phenomena if they are described entirely in terms of observable events. We (...) disagree: contexts in which random variables are recorded are as observable as the variables’ values. Khrennikov also argues that the Contextuality-by-Default theory suffers the problem of non-uniqueness of couplings. We disagree that this is a problem: couplings are all possible ways of imposing counterfactual joint distributions on random variables that de facto are not jointly distributed. The uniqueness of modeling experiments by means of quantum formalisms brought up by Khrennikov is achieved for the price of additional, substantive assumptions. This is consistent with our view of quantum theory as a special-purpose generator of classical probabilities. Khrennikov raises the issue of “mental signaling,” by which he means inconsistent connectedness in behavioral systems. Our position is that it is as inherent to behavioral systems as their stochasticity. (shrink)

The response mode bias, in which subjects exhibit different risk attitudes when assessing certainty equivalents versus indifference probabilities, is a well-known phenomenon in the assessment of utility functions. In this empirical study, we develop and apply a cardinal measure of risk attitudes to analyze not only the existence, but also the strength of this phenomenon. Since probability levels involved in decision problems are already known to have a strong impact on behavior, we use this approach to study the (...) impact of probabilities on the extent of the response mode bias. We find that the direction in which probabilities influence measured risk aversion is the opposite in the certainty equivalence (CE) method versus in the probability equivalence (PE) method. Utilizing the CE elicitation approach leads to an increase of risk seeking for gambles involving high probabilities. For the PE method, subjects tend to behave risk averse with gambles of high probabilities. This behavior is reversed in the gain domain. This “tailwhip” effect is consistently replicated in several experiments, involving both loss and gain domains of lotteries. (shrink)

The rejection of an infinitesimal solution to the zero-fit problem by A. Elga ([2004]) does not seem to appreciate the opportunities provided by the use of internal finitely-additive probability measures. Indeed, internal laws of probability can be used to find a satisfactory infinitesimal answer to many zero-fit problems, not only to the one suggested by Elga, but also to the Markov chain (that is, discrete and memory-less) models of reality. Moreover, the generalization of likelihoods that Elga has in (...) mind is not as hopeless as it appears to be in his article. In fact, for many practically important examples, through the use of likelihoods one can succeed in circumventing the zero-fit problem. 1 The Zero-fit Problem on Infinite State Spaces 2 Elga's Critique of the Infinitesimal Approach to the Zero-fit Problem 3 Two Examples for Infinitesimal Solutions to the Zero-fit Problem 4 Mathematical Modelling in Nonstandard Universes? 5 Are Nonstandard Models Unnatural? 6 Likelihoods and Densities A Internal Probability Measures and the Loeb Measure Construction B The (Countable) Coin Tossing Sequence Revisited C Solution to the Zero-fit Problem for a Finite-state Model without Memory D An Additional Note on ‘Integrating over Densities’ E Well-defined Continuous Versions of Density Functions. (shrink)

Probabilistic reasoning is heavily investigated in decision research. Violations of probability theory have been demonstrated numerously, for instance, the tendency to overestimate the joint probab...

I present a straightforward objection to the view that what we know has epistemic probability 1: when combined with Bayesian decision theory, the view seems to entail implausible conclusions concerning rational choice. I consider and reject three responses. The first holds that the fault is with decision theory, rather than the view that knowledge has probability 1. The second two try to reconcile the claim that knowledge has probability 1 with decision theory by appealing to contextualism and (...) sensitive invariantism, respectively. I argue that each response fails, and that we can hold on to much of what was attractive in the responses while denying that what we know has probability 1. (shrink)

In a recent article on the interpretation of probability in evidence-based medical practice, Jonathan Fuller argues that we should interpret probabilities as credences in individual cases because this avoids some important problems. In this article, I argue that Fuller misidentifies the real issue and so fails to offer a meaningful solution to it. The real problem with making probability judgments in individual cases is deciding which objective considerations ought to constrain our formation of credences. This leads us to (...) the reference class problem, which, as Alan Hajek argues, is a problem for any interpretation of probability. (shrink)

In response to Smith, I argue that probabilities cannot be rationally neglected. I show that Smith’s proposal for ignoring low-probability outcomes must, on pain of violating dominance reasoning, license taking arbitrarily high risk for arbitrarily little reward.

Most accounts of responsibility focus on one type of responsibility, moral responsibility, or address one particular aspect of moral responsibility such as agency. This article outlines a broader framework to think about responsibility that includes causal responsibility, relational responsibility, and what I call “narrative responsibility” as a form of “hermeneutic responsibility”, connects these notions of responsibility with different kinds of knowledge, disciplines, and perspectives on human being, and shows how this framework is helpful for mapping and analysing how artificial intelligence (...) (AI) challenges human responsibility and sense-making in various ways. Mobilizing recent hermeneutic approaches to technology, the article argues that next to, and interwoven with, other types of responsibility such as moral responsibility, we also have narrative and hermeneutic responsibility—in general and for technology. For example, it is our task as humans to make sense of, with and, if necessary, against AI. While from a posthumanist point of view, technologies also contribute to sense-making, humans are the experiencers and bearers of responsibility and always remain in charge when it comes to this hermeneutic responsibility. Facing and working with a world of data, correlations, and probabilities, we are nevertheless condemned to make sense. Moreover, this also has a normative, sometimes even political aspect: acknowledging and embracing our hermeneutic responsibility is important if we want to avoid that our stories are written elsewhere—through technology. (shrink)

In response to cases that involve tiny probabilities of huge payoffs, some argue that we ought to discount small probabilities down to zero. However, this paper shows that doing so violates Independence and Continuity, and as a result of these violations, those who discount small probabilities can be exploited by money pumps. Various possible ways of avoiding exploitation will be discussed. This paper concludes that the money pump for Independence undermines the plausibility of discounting small probabilities. Much of the (...) discussion on Independence generalizes to other views that also violate Independence. (shrink)

The article shows, using elementary examples, that risk assessment depends both on the probability of future events and on their results. Various approaches to the integration of probabilities and numerical estimates of possible outcomes are shown and analyzed. The subjective nature of risk is substantiated. An interdisciplinary definition of risk is proposed, not associated with any science or group of sciences. The definition is based on the idea that risk is a consequence of decisions made by the subject, who (...) evaluates their consequences. The question is raised about responsibility for decisions under risk conditions. (shrink)

A. J. Ayer was one of the foremost analytical philosophers of the twentieth century, and was known as a brilliant and engaging speaker. In essays based on his influential Dewey Lectures, Ayer addresses some of the most critical and controversial questions in epistemology and the philosophy of science, examining the nature of inductive reasoning and grappling with the issues that most concerned him as a philosopher. This edition contains revised and expanded versions of the lectures and two additional essays. Ayer (...) begins by considering Hume's formulation of the problem of induction and then explores the inferences on which we base our beliefs in factual matters. In other essays, he defines the three kinds of probability that inform inductive reasoning and examines the various criteria for verifiability and falsifiability. In his extensive introduction, Graham Macdonald discusses the arguments in _Probability and Evidence_, how they relate to Ayer's other works, and their influence in contemporary philosophy. He also provides a brief biographical sketch of Ayer, and includes a bibliography of works about and in response to _Probability and Evidence_. (shrink)

Classical probability models of incentive response are inadequate in where the dimensions of relative risk and the dimensions of similarity in outcome comparisons typically differ. Quantum probability models for choice in large worlds may be motivated pragmatically or metaphysically: statistical processing in the brain adapts to the true scale-relative structure of the universe.

For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of the possible posteriors. (...) Furthermore, this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion. 1 Introduction2 Alternative Updating Policies3 Modelling the Situation for Normal Updating4 Tracking: A Criterion for Updating Policies5 Tracking: Precise Formulation and Relation to Convexity6 The Spanning Criterion7 Non-Bayesian Policies that Satisfy the Spanning and Tracking Criteria8 Policies that Violate the Spanning and Tracking Criteria AppendixAppendix. (shrink)

ABSTRACT For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of the possible (...) posteriors. Furthermore, this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion. _1_ Introduction _2_ Alternative Updating Policies _3_ Modelling the Situation for Normal Updating _4_ Tracking: A Criterion for Updating Policies _5_ Tracking: Precise Formulation and Relation to Convexity _6_ The Spanning Criterion _7_ Non-Bayesian Policies that Satisfy the Spanning and Tracking Criteria _8_ Policies that Violate the Spanning and Tracking Criteria Appendix Appendix. (shrink)

We describe a computational model of two central aspects of people's probabilistic reasoning: descriptive probability estimation and inferential probability judgment. This model assumes that people's reasoning follows standard frequentist probability theory, but it is subject to random noise. This random noise has a regressive effect in descriptive probability estimation, moving probability estimates away from normative probabilities and toward the center of the probability scale. This random noise has an anti-regressive effect in inferential judgement, however. (...) These regressive and anti-regressive effects explain various reliable and systematic biases seen in people's descriptive probability estimation and inferential probability judgment. This model predicts that these contrary effects will tend to cancel out in tasks that involve both descriptive estimation and inferential judgement, leading to unbiased responses in those tasks. We test this model by applying it to one such task, described by Gallistel et al. ). Participants' median responses in this task were unbiased, agreeing with normative probability theory over the full range of responses. Our model captures the pattern of unbiased responses in this task, while simultaneously explaining systematic biases away from normatively correct probabilities seen in other tasks. (shrink)

This collection of essays is on the relation between probabilities, especially conditional probabilities, and conditionals. It provides negative results which sharply limit the ways conditionals can be related to conditional probabilities. There are also positive ideas and results which will open up areas of research. The collection is intended to honour Ernest W. Adams, whose seminal work is largely responsible for creating this area of inquiry. As well as describing, evaluating, and applying Adams's work the contributions extend his ideas in (...) directions he may or may not have anticipated, but that he certainly inspired. In addition to a wide range of philosophers of science, the volume should interest computer scientists and linguists. (shrink)