My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...) problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)

This paper examines the preference-based approach to the identification of beliefs. It focuses on the main problem to which this approach is exposed, namely that of state-dependent utility. First, the problem is illustrated in full detail. Four types of state-dependent utility issues are distinguished. Second, a comprehensive strategy for identifying beliefs under state-dependent utility is presented and discussed. For the problem to be solved following this strategy, however, preferences need to extend beyond choices. We claim that this a necessary feature (...) of any complete solution to the problem of state-dependent utility. We also argue that this is the main conceptual lesson to draw from it. We show that this lesson is of interest to both economists and philosophers. (shrink)

Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work in neuroscience and (...) behavioral psychology. The repercussions of the view for how we conceive of many ordinary instances of subjective probability, and how it relates to more traditional conceptions of subjective probability, are discussed in some detail. (shrink)

Starting from the sixties of the past century theory change has become a main concern of philosophy of science. Two of the best known formal accounts of theory change are the post-Popperian theories of verisimilitude (PPV for short) and the AGM theory of belief change (AGM for short). In this paper, we will investigate the conceptual relations between PPV and AGM and, in particular, we will ask whether the AGM rules for theory change are effective means for approaching the truth, (...) i.e., for achieving the cognitive aim of science pointed out by PPV. First, the key ideas of PPV and AGM and their application to a particular kind of propositional theories - the so called "conjunctive propositions" - will be illustrated. Afterwards, we will prove that, as far as conjunctive propositions are concerned, AGM belief change is an effective tool for approaching the truth. (shrink)

Both the quantity of information and the informational content of a signal are defined in the context of signaling games. Informational content is a generalization of standard philosophical notions of propositional content. It is shown how signals that initially carry no information may spontaneously acquire informational content by evolutionary or learning dynamics. It is shown how information can flow through signaling chains or signaling networks.

This essay addresses the methodology of philosophy of science and illustrates how formal and empirical methods can be fruitfully combined. Special emphasis is given to the application of experimental methods to confirmation theory and to recent work on the conjunction fallacy, a key topic in the rationality debate arising from research in cognitive psychology. Several other issue can be studied in this way. In the concluding section, a brief outline is provided of three further examples.

The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt of providing a satisfactory account of the phenomenon has proven challenging. Here, we elaborate the suggestion (first discussed by Sides et al., 2001) that in standard conjunction problems the fallacious probability judgments experimentally observed are typically guided by sound assessments of confirmation relations, meant in terms of contemporary Bayesian confirmation theory. Our main formal result is (...) a confirmation-theoretic account of the conjuntion fallacy which is proven robust (i.e., not depending on various alternative ways of measuring degrees of confirmation). The proposed analysis is shown distinct from contentions that the conjunction effect is in fact not a fallacy and is compared with major competing explanations of the phenomenon, including earlier references to a confirmation-theoretic account. (shrink)

Almost everything Turing wrote is now accessible on-line in some form, much of it in the Turing Digital Archive, which makes available scanned versions of the physical papers held in the archive at King's College, Cambridge University. See..

Crupi et al. (2008) offer a confirmation-theoretic, Bayesian account of the conjunction fallacy—an error in reasoning that occurs when subjects judge that Pr( h 1 & h 2 | e ) > Pr( h 1 | e ). They introduce three formal conditions that are satisfied by classical conjunction fallacy cases, and they show that these same conditions imply that h 1 & h 2 is confirmed by e to a greater extent than is h 1 alone. Consequently, they suggest (...) that people are tracking this confirmation relation when they commit conjunction fallacies. I offer three experiments testing the merits of Crupi et al.’s account specifically and confirmation-theoretic accounts of the conjunction fallacy more generally. The results of Experiment 1 show that, although Crupi et al.’s conditions do seem to be causally linked to the conjunction fallacy, they are not necessary for it; there exist cases that do not meet their three conditions in which subjects still tend to commit the fallacy. The results of Experiments 2 and 3 show that Crupi et al.’s conditions, and those offered by other confirmation-theoretic accounts of the fallacy, are not sufficient for the fallacy either; there exist cases that meet all three of CFT’s conditions in which subjects do not tend to commit the fallacy. Additionally, these latter experiments show that such confirmation-theoretic conditions are at best only weakly causally relevant to the presence of the conjunction fallacy. Given these findings, CFT’s account specifically, and any general confirmation-theoretic account more broadly, falls short of offering a satisfying explanation of the presence of the conjunction fallacy. (shrink)

The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt to provide a satisfactory account of the phenomenon has proved challenging. Here we elaborate the suggestion (first discussed by Sides, Osherson, Bonini, & Viale, 2002) that in standard conjunction problems the fallacious probability judgements observed experimentally are typically guided by sound assessments of _confirmation_ relations, meant in terms of contemporary Bayesian confirmation theory. Our main formal (...) result is a confirmation-theoretic account of the conjunction fallacy, which is proven _robust_ (i.e., not depending on various alternative ways of measuring degrees of confirmation). The proposed analysis is shown distinct from contentions that the conjunction effect is in fact not a fallacy, and is compared with major competing explanations of the phenomenon, including earlier references to a confirmation-theoretic account. (shrink)

Rational analysis (Anderson 1990, 1991a) is an empiricalprogram of attempting to explain why the cognitive system isadaptive, with respect to its goals and the structure of itsenvironment. We argue that rational analysis has two importantimplications for philosophical debate concerning rationality. First,rational analysis provides a model for the relationship betweenformal principles of rationality (such as probability or decisiontheory) and everyday rationality, in the sense of successfulthought and action in daily life. Second, applying the program ofrational analysis to research on human reasoning (...) leads to a radicalreinterpretation of empirical results which are typically viewed asdemonstrating human irrationality. (shrink)

A theory of information is developed in which the informational content of a signal (structure, event) can be specified. This content is expressed by a sentence describing the condition at a source on which the properties of a signal depend in some lawful way. Information, as so defined, though perfectly objective, has the kind of semantic property (intentionality) that seems to be needed for an analysis of cognition. Perceptual knowledge is an information-dependent internal state with a content corresponding to the (...) information producing it. This picture of knowledge captures most of what makes knowledge an important cpistcmological notion. It also avoids many of the problems infecting traditional justificational accounts of knowledge (knowledge as [justified, true belief those (unlike knowledge) having a content that can be either true or false (e.g., belief) – are described in terms of the way internal (presumably neural) structures acquire during learning a certain information-carrying role. The content of these structures (whether true or false) is identified with the kind of information they were developed to carry. (shrink)

This dissertation looks at a set of interconnected questions concerning the foundations of probability, and gives a series of interconnected answers. At its core is a piece of old-fashioned philosophical analysis, working out what probability is. Or equivalently, investigating the semantic question of what is the meaning of ‘probability’? Like Keynes and Carnap, I say that probability is degree of reasonable belief. This immediately raises an epistemological question, which degrees count as reasonable? To solve that in its full generality would (...) mean the end of human inquiry, so that won’t be attempted here. Rather I will follow tradition and merely investigate which sets of partial beliefs are coherent. -/- The standard answer to this question, what is commonly called the Bayesian answer, says that degrees of belief are coherent iff they form a probability function. I disagree with the way this is usually justified, but subject to an important qualification I accept the answer. The important qualification is that degrees of belief may be imprecise, or vague. Part one of the dissertation, chapters 1 to 6, looks largely at the consequences of this qualification for the semantic and epistemological questions already mentioned. It turns out that when we allow degrees of belief to be imprecise, we can discharge potentially fatal objections to some philosophically attractive theses. Two of these, that probability is degree of reasonable belief and that the probability calculus provides coherence constraints on partial beliefs, have been mentioned. Others include the claim, defended in chapter 4, that chance is probability given total history. -/- As well as these semantic and epistemological questions, studies of the foundations of probability usually include a detailed discussion of decision theory. For reasons set out in chapter 2, I deny we can gain epistemological insights from decision theory. Nevertheless, it is an interesting field to study on its own, and it might be expected that there would be decision theoretic consequences of allowing imprecise degrees of belief. As I show in part two, this expectation seems to be mistaken. Chapter 9 shows that there aren’t interesting consequences of this theory for decision theory proper, and chapters 10 and 11 show that Keynes’s attempt to use imprecision in degrees of belief to derive a distinctive theory of interest rates is unsound. -/- Chapters 7 and 8 provide a link between these two parts. In chapter 7 I look at some previous philosophical investigations into the effects of imprecision. In chapter 8 I develop what I take to be the best competitor to the theory defended here – a constructivist theory of probability. On this view degrees of belief are precise, but the relevant coherence constraint is a constructivist probability calculus. This view is, I think, mistaken, but the calculus has some intrinsic interest, and there are at least enough arguments for it to warrant a chapter-length examination. (shrink)

Theories of rational decision making often abstract away from computational and other resource limitations faced by real agents. An alternative approach known as resource rationality puts such matters front and center, grounding choice and decision in the rational use of finite resources. Anticipated by earlier work in economics and in computer science, this approach has recently seen rapid development and application in the cognitive sciences. Here, the theory of rationality plays a dual role, both as a framework for normative assessment (...) and as a source of scientific hypotheses about how mental processes in fact work. The latter project, often called rational analysis, depends for its success on a fine-grained characterization of the computational problem facing a decision maker, which may in turn depend on realistic assumptions about what the relevant agent is like. As a consequence, resource rationality involves a delicate, but often fruitful interplay between the normative and the descriptive. (shrink)

By “Propensities” I mean the kind of probabilities that figure in laws of nature. Propensities might be (i) relative frequencies, finite or long run, de facto or modalized, or (ii) reflections of our epistemic probabilities or (iii) sui generus theoretical notions. I believe that the whole family of relative frequency proposals (i) are inadequate. As an alternative I wish to suggest (ii) an epistemic account of propensities and of nomic force in general, in the spirit of Hume, Mill, DeFinetti, Ayer, (...) Suppes and Jeffrey. Whether accounts of the third kind differ in substance or in name only from the sort of account that I am proposing is a nice question, to which. I will devote some brief closing remarks. (shrink)

This dissertation proposes and defends a hybrid view I call Hybrid Impermissivism, which combines the following two theses: Moderate Uniqueness and Credal Permissivism. Moderate Uniqueness says that no evidence could justify both believing a proposition and its negation. However, on Moderate Uniqueness, evidence could justify both believing and suspending judgement on a proposition (hence the adjective “Moderate”). And Credal Permissivism says that more than one credal attitude could be justified on the evidence. Hybrid Impermissisim is developed into a precise theory (...) by using normative bridge principles on how rational belief and credence ought to interact. My overall conclusion is that Hybrid Impermissivism is a coherent, plausible, and conciliatory position and provides a correct characterisation of the requirements of evidence on doxastic attitudes . (shrink)

Evidential support is often equated with confirmation, where evidence supports hypothesis H if and only if it increases the probability of H. This article argues against this received view. As the author shows, support is a comparative notion in the sense that increase-in-probability is not. A piece of evidence can confirm H, but it can confirm alternatives to H to the same or greater degree; and in such cases, it is at best misleading to conclude that the evidence supports H. (...) The author puts forward an alternative view that defines support in terms of measures of degree of confirmation. The proposed view is both sufficiently comparative and able to accommodate the increase-in-probability aspect of support. The author concludes that the proposed measure-theoretic approach to support provides a superior alternative to the standard confirmatory approach. (shrink)

Why is it good to be less, rather than more incoherent? Julia Staffel, in her excellent book “Unsettled Thoughts,” answers this question by showing that if your credences are incoherent, then there is some way of nudging them toward coherence that is guaranteed to make them more accurate and reduce the extent to which they are Dutch-bookable. This seems to show that such a nudge toward coherence makes them better fit to play their key epistemic and practical roles: representing the (...) world and guiding action. In this paper, I argue that Staffel’s strategy needs a small tweak. While she identifies appropriate measures of epistemic value, she does not identify appropriate measures of practical value. Staffel measures practical value using Dutchbookability scores. But credences have practical value in virtue of recommending actions that produce as much utility as possible. And while susceptibility to a Dutch book is a surefire sign that one’s credences are needlessly bad at this task, one’s degree of Dutch-bookability is not itself a good measure of how well they recommend practically valuable actions. Strictly proper scoring rules, I argue, are the right tools for measuring both epistemic and practical value. I show that we can rerun Staffel’s strategy swapping in strictly proper scoring rules for Dutch-bookability measures. So long as one’s epistemic scoring rule and practical scoring rule are “sufficiently similar,” there is some way of nudging incoherent credences toward coherence that is guaranteed to yield more of both types of value. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

We explore the question of whether cost-free uncertain evidence is worth waiting for in advance of making a decision. A classical result in Bayesian decision theory, known as the value of evidence theorem, says that, under certain conditions, when you update your credences by conditionalizing on some cost-free and certain evidence, the subjective expected utility of obtaining this evidence is never less than the subjective expected utility of not obtaining it. We extend this result to a type of update method, (...) a variant of Judea Pearl’s virtual conditionalization, where uncertain evidence is represented as a set of likelihood ratios. Moreover, we argue that focusing on this method rather than on the widely accepted Jeffrey conditionalization enables us to show that, under a fairly plausible assumption, gathering uncertain evidence not only maximizes expected pragmatic utility, but also minimizes expected epistemic disutility. (shrink)

Confirmation is a graded notion: evidence can confirm a hypothesis to a greater or lesser degree. There has been debate about how to measure degree of confirmation. Starting from the observation that we would like evidence to be a discriminating indicator of truth, we conduct computer simulations to determine how well the various known measures of confirmation predict the extent to which a given piece of evidence fulfills that role, given a hypothesis of interest. The outcomes show that some measures (...) are markedly better indicators of truth than others. (shrink)

This paper defends a novel sceptical response to the fine-tuning argument for the existence of God (FTA). According to this response, even if FTA can establish, what I call, the confirmation proposition: ‘fine-tuning confirms the God hypothesis’, there is no reason to think that a strengthening of FTA can establish the evidence-favouring proposition: ‘fine-tuning favours the God hypothesis over its competitors’. My argument is that, any criteria for the explanation of fine-tuning that permit us to take the God hypothesis seriously (...) ought to make us sceptical that fine-tuning favours the God hypothesis over its competitors. As taking the God hypothesis seriously requires us to give a fair hearing to all sorts of non-theistic explanations, including the so-called weird sorts of atheism. (shrink)

Policymakers who seek to make scientifically informed decisions are constantly confronted by scientific uncertainty and expert disagreement. This thesis asks: how can policymakers rationally respond to expert disagreement and scientific uncertainty? This is a work of non-ideal theory, which applies formal philosophical tools developed by ideal theorists to more realistic cases of policymaking under scientific uncertainty. I start with Bayesian approaches to expert testimony and the problem of expert disagreement, arguing that two popular approaches— supra-Bayesianism and the standard model of (...) expert deference—are insufficient. I develop a novel model of expert deference and show how it can deal with many of these problems raised for them. I then turn to opinion pooling, a popular method for dealing with disagreement. I show that various theoretical motivations for pooling functions are irrelevant to realistic policymaking cases. This leads to a cautious recommendation of linear pooling. However, I then show that any pooling method relies on value judgements, that are hidden in the selection of the scoring rule. My focus then narrows to a more specific case of scientific uncertainty: multiple models of the same system. I introduce a particular case study involving hurricane models developed to support insurance decision-making. I recapitulate my analysis of opinion pooling in the context of model ensembles, confirming that my hesitations apply. This motivates a shift of perspective, to viewing the problem as a decision theoretic one. I rework a recently developed ambiguity theory, called the confidence approach, to take input from model ensembles. I show how it facilitates the resolution of the policymaker’s problem in a way that avoids the issues encountered in previous chapters. This concludes my main study of the problem of expert disagreement. In the final chapter, I turn to methodological reflection. I argue that philosophers who employ the mathematical methods of the prior chapters are modelling. Employing results from the philosophy of scientific models, I develop the theory of normative modelling. I argue that it has important methodological conclusions for the practice of formal epistemology, ruling out popular moves such as searching for counterexamples. (shrink)

In a recent survey of the literature on the relation between information and confirmation, Crupi and Tentori claim that the former is a fruitful source of insight into the latter, with two well-known measures of confirmation being definable purely information-theoretically. I argue that of the two explicata of semantic information which are considered by the authors, the one generating a popular Bayesian confirmation measure is a defective measure of information, while the other, although an admissible measure of information, generates a (...) defective measure of confirmation. Some results are proved about the representation of measures on consequence-classes. (shrink)

Probability ratio and likelihood ratio measures of inductive support and related notions have appeared as theoretical tools for probabilistic approaches in the philosophy of science, the psychology of reasoning, and artificial intelligence. In an effort of conceptual clarification, several authors have pursued axiomatic foundations for these two families of measures. Such results have been criticized, however, as relying on unduly demanding or poorly motivated mathematical assumptions. We provide two novel theorems showing that probability ratio and likelihood ratio measures can be (...) axiomatized in a way that overcomes these difficulties. (shrink)

The so‐called problem of irrelevant conjunction has been seen as a serious challenge for theories of confirmation. It involves the consequences of conjoining irrelevant statements to a hypothesis that is confirmed by some piece of evidence. Following Hawthorne and Fitelson, we reconstruct the problem with reference to Bayesian confirmation theory. Then we extend it to the case of conjoining irrelevant statements to a hypothesis that is dis confirmed by some piece of evidence. As a consequence, we obtain and formally present (...) a novel and more troublesome problem of irrelevant conjunction. We conclude by indicating a possible solution based on a measure‐sensitive approach and by critically discussing a major alternative way to address the problem. *Received December 2008; revised August 2009. †To contact the authors, please write to: Department of Philosophy, University of Turin, via Sant'Ottavio 20, 10124 Turin, Italy; e‐mail: [email protected] ; [email protected] or [email protected]. (shrink)

Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for ten different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.

The so-called "non-commutativity" of probability kinematics has caused much unjustified concern. When identical learning is properly represented, namely, by identical Bayes factors rather than identical posterior probabilities, then sequential probability-kinematical revisions behave just as they should. Our analysis is based on a variant of Field's reformulation of probability kinematics, divested of its (inessential) physicalist gloss.

Recently, natural language pragmatics started to make use of decision-, game-, and information theoretical tools to determine the usefulness of questions and assertions in a quantitative way. In the first part of this paper several of these notions are related with each other. It is shown that under particular natural assumptions the utility of questions and answers reduces to their informativity, and that the ordering relation induced by utility sometimes even reduces to the logical relation of entailment. The second part (...) of the paper shows how different proposals (using either protocols or likelihood functions) to measure the relevance/utility of non-partitional questions come down to the same thing. (shrink)

It is argued that models of H. Jeffreys' axioms of probability (Jeffreys [1939] 1967) are not monotone even with I. J. Good's proposed modification (Good 1950). Hence the additivity axiom seems essential to a theory of probability as it is with Kolmogorov's system (Kolmogorov 1950).

Plausibly, when we adopt a probabilistic standpoint any measure Cb of the degree to which evidence e confirms hypothesis h relative to background knowledge b should meet these five desiderata: Cb > 0 when P > P < 0 when P < P; Cb = 0 when P = P. Cb is some function of the values P and P assume on the at most sixteen truth-functional combinations of e and h. If P < P and P = P then (...) Cb ≤ Cb; if P = P and P < P then Cb ≥ Cb. Cb – Cb is fully determined by Cb and Cbe – Cbe; if Cb = 0 then Cb + Cbe = 0. If P = P then Cb = Cb. (shrink)

While orthodox (Neyman-Pearson) statistical tests enjoy widespread use in science, the philosophical controversy over their appropriateness for obtaining scientific knowledge remains unresolved. I shall suggest an explanation and a resolution of this controversy. The source of the controversy, I argue, is that orthodox tests are typically interpreted as rules for making optimal decisions as to how to behave--where optimality is measured by the frequency of errors the test would commit in a long series of trials. Most philosophers of statistics, however, (...) view the task of statistical methods as providing appropriate measures of the evidential-strength that data affords hypotheses. Since tests appropriate for the behavioral-decision task fail to provide measures of evidential-strength, philosophers of statistics claim the use of orthodox tests in science is misleading and unjustified. What critics of orthodox tests overlook, I argue, is that the primary function of statistical tests in science is neither to decide how to behave nor to assign measures of evidential strength to hypotheses. Rather, tests provide a tool for using incomplete data to learn about the process that generated it. This they do, I show, by providing a standard for distinguishing differences (between observed and hypothesized results) due to accidental or trivial errors from those due to systematic or substantively important discrepancies. I propose a reinterpretation of a commonly used orthodox test to make this learning model of tests explicit. (shrink)

This paper attempts to define Exploratory Data Analysis (EDA) more precisely than usual, and to produce the beginnings of a philosophy of this topical and somewhat novel branch of statistics. A data set is, roughly speaking, a collection of k-tuples for some k. In both descriptive statistics and in EDA, these k-tuples, or functions of them, are represented in a manner matched to human and computer abilities with a view to finding patterns that are not "kinkera". A kinkus is a (...) pattern that has a negligible probability of being even partly potentially explicable. A potentially explicable pattern is one for which there probably exists a hypothesis of adequate "explicativity", which is another technical probabilistic concept. A pattern can be judged to be probably potentially explicable even if we cannot find an explanation. The theory of probability understood here is one of partially ordered (interval-valued), subjective (personal) probabilities. Among other topics relevant to a philosophy of EDA are the "reduction" of data; Francis Bacon's philosophy of science; the automatic formulation of hypotheses; successive deepening of hypotheses; neurophysiology; and rationality of type II. (shrink)

I examine the concept of granting for the sake of the argument in the context of explanatory reasoning. I discuss a situation where S wishes to argue for H1 as a true explanation of evidence E and also decides to grant, for the sake of the argument, that H2 is an explanation of E. S must then argue that H1 and H2 jointly explain E. When H1 and H2 compete for the force of E, it is usually a bad idea (...) for S to grant H2 for the sake of the argument. If H1 and H2 are not positively dependent otherwise, there is a key argumentative move that he will have to make anyway in order to retain a place at the table for H1 at all—namely, arguing that the probability of E given H2 alone is low. Some philosophers of religion have suggested that S can grant that science has successfully provided natural explanations for entities previously ascribed to God, while not admitting that theism has lost any probability. This move involves saying that the scientific explanations themselves are dependent on God. I argue that this “granting” move is not an obvious success and that the theist who grants these scientific successes may have to grant that theism has lost probability. (shrink)

Everyday life reasoning and argumentation is defeasible and uncertain. I present a probability logic framework to rationally reconstruct everyday life reasoning and argumentation. Coherence in the sense of de Finetti is used as the basic rationality norm. I discuss two basic classes of approaches to construct measures of argument strength. The first class imposes a probabilistic relation between the premises and the conclusion. The second class imposes a deductive relation. I argue for the second class, as the first class is (...) problematic if the arguments involve conditionals. I present a measure of argument strength that allows for dealing explicitly with uncertain conditionals in the premise set. (shrink)

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty and the (...) reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma–Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information‐theoretic formalism. (shrink)

This paper discusses two senses in which a hypothesis may be said to unify evidence. One is the ability of the hypothesis to increase the mutual information of a set of evidence statements; the other is the ability of the hypothesis to explain commonalities in observed phenomena by positing a common origin for them. On Bayesian updating, it is only mutual information unification that contributes to the incremental support of a hypothesis by the evidence unified. This poses a challenge for (...) the view that explanation is a confirmatory virtue that contributes to such incremental support; its advocates must ground it in some relevant difference between humans and a Bayesian agent. (shrink)

Garber (1983) and Jeffrey (1991, 1995) have both proposed solutions to the old evidence problem. Jeffrey's solution, based on a new probability revision method called reparation, has been generalized to the case of uncertain old evidence and probabilistic new explanation in Wagner 1997, 1999. The present paper reformulates some of the latter work, highlighting the central role of Bayes factors and their associated uniformity principle, and extending the analysis to the case in which an hypothesis bears on a countable family (...) of evidentiary propositions. This extension shows that no Garber-type approach is capable of reproducing the results of generalized reparation. (shrink)

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is (...) a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the explanation of cognition; and re-evaluate the empirical case for Bayesian rationality. (shrink)