How do we go about weighing evidence, testing hypotheses, and making inferences? According to the model of _Inference to the Best Explanation_, we work out what to infer from the evidence by thinking about what would actually explain that evidence, and we take the ability of a hypothesis to explain the evidence as a sign that the hypothesis is correct. In _Inference to the Best Explanation_, Peter Lipton gives this important and influential idea the development and assessment it deserves. The (...) second edition has been substantially enlarged and reworked, with a new chapter on the relationship between explanation and Bayesianism, and an extension and defence of the account of contrastive explanation. It also includes an expanded defence of the claims that our inferences really are guided by diverse explanatory considerations, and that this pattern of inference can take us towards the truth. This edition of _Inference to the Best Explanation_ has also been updated throughout and includes a new bibliography. (shrink)

There is currently no viable alternative to the Bayesian analysis of scientific inference, yet the available versions of Bayesianism fail to do justice to several aspects of the testing and confirmation of scientific hypotheses. Bayes or Bust? provides the first balanced treatment of the complex set of issues involved in this nagging conundrum in the philosophy of science. Both Bayesians and anti-Bayesians will find a wealth of new insights on topics ranging from Bayes’s original paper to contemporary formal learning theory.In (...) a paper published posthumously in 1763, the Reverend Thomas Bayes made a seminal contribution to the understanding of "analogical or inductive reasoning." Building on his insights, modem Bayesians have developed an account of scientific inference that has attracted numerous champions as well as numerous detractors. Earman argues that Bayesianism provides the best hope for a comprehensive and unified account of scientific inference, yet the presently available versions of Bayesianisin fail to do justice to several aspects of the testing and confirming of scientific theories and hypotheses. By focusing on the need for a resolution to this impasse, Earman sharpens the issues on which a resolution turns. John Earman is Professor of History and Philosophy of Science at the University of Pittsburgh. (shrink)

This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves (...) a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available. (shrink)

A collection of 13 papers by David Lewis, written on a variety of topics including causation, counterfactuals and indicative conditionals, the direction of time, subjective and objective probability, explanation, perception, free will, and rational decision. The conclusions reached include the claim that time travel is possible, that counterfactual dependence is asymmetrical, that events are properties of spatiotemporal regions, that the Prisoners’ Dilemma is a Newcomb problem, and that causation can be analyzed in terms of counterfactual dependence between events. These papers (...) can be seen as a “prolonged campaign” for a philosophical position Lewis calls “Humean supervenience,” according to which “all there is to the world is a vast mosaic of local matters of particular fact,” with all global features of the world thus supervening on the spatiotemporal arrangement of local qualities. (shrink)

Are people rational? This question was central to Greek thought and has been at the heart of psychology and philosophy for millennia. This book provides a radical and controversial reappraisal of conventional wisdom in the psychology of reasoning, proposing that the Western conception of the mind as a logical system is flawed at the very outset. It argues that cognition should be understood in terms of probability theory, the calculus of uncertain reasoning, rather than in terms of logic, the calculus (...) of certain reasoning. (shrink)

Conditional sentences are among the most intriguing and puzzling features of language, and analysis of their meaning and function has important implications for, and uses in, many areas of philosophy. Jonathan Bennett, one of the world's leading experts, distils many years' work and teaching into this book, making it the fullest and most authoritative treatment of the subject.

The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. _Philosophical Theories of Probability_ is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.

Inference to the Best Explanation (IBE) and Bayesianism are our two most prominent theories of scientific inference. Are they compatible? Van Fraassen famously argued that they are not, concluding that IBE must be wrong since Bayesianism is right. Writers since then, from both the Bayesian and explanationist camps, have usually considered van Fraassen’s argument to be misguided, and have plumped for the view that Bayesianism and IBE are actually compatible. I argue that van Fraassen’s argument is actually not so misguided, (...) and that it causes more trouble for compatibilists than is typically thought. Bayesianism in its dominant, subjectivist form, can only be made compatible with IBE if IBE is made subservient to conditionalization in a way that robs IBE of much of its substance and interest. If Bayesianism and IBE are to be fit together, I argue, a strongly objective Bayesianism is the preferred option. I go on to sketch this objectivist, IBE-based Bayesianism, and offer some preliminary suggestions for its development. (shrink)

I defend the view that the truth conditions of the ordinary indicative conditional are those of the material conditional. This is done via a discussion of assertability and by appeal to conventional implicature rather than conversational implicature.

Recent work on inference to the best explanation has come to an impasse regarding the proper way to coordinate the theoretical virtues in explanatory inference with probabilistic confirmation theory, and in particular with aspects of Bayes's Theorem. I argue that the theoretical virtues are best conceived heuristically and that such a conception gives us the resources to explicate the virtues in terms of ceteris paribus theorems. Contrary to some Bayesians, this is not equivalent to identifying the virtues with likelihoods or (...) priors per se; the virtues may be more accessible epistemically than likelihoods or priors. I then prove a ceteris paribus theorem regarding theoretical consilience, use it to correct a recent application of Reichenbach's common cause principle, and apply it to a test case of scientific reasoning. Explanation and confirmation The heuristic conception of theoretical virtues Abduction and the accessibility of explanatory power Evidential and theoretical consilience A test case: gravitational lensing Conclusion Thus natural science appears completely to lose from sight the large and general questions; but all the more splendid is the success when, groping in the thicket of special questions, we suddenly find a small opening that allows a hitherto undreamt of outlook on the whole. (L. Boltzmann, Theoretical Physics and Philosophical Problems). (shrink)

A study is reported testing two hypotheses about a close parallel relation between indicative conditionals, if A then B , and conditional bets, I bet you that if A then B . The first is that both the indicative conditional and the conditional bet are related to the conditional probability, P(B|A). The second is that de Finetti's three-valued truth table has psychological reality for both types of conditional— true , false , or void for indicative conditionals and win , lose (...) , or void for conditional bets. The participants were presented with an array of chips in two different colours and two different shapes, and an indicative conditional or a conditional bet about a random chip. They had to make judgements in two conditions: either about the chances of making the indicative conditional true or false or about the chances of winning or losing the conditional bet. The observed distributions of responses in the two conditions were generally related to the conditional probability, supporting the first hypothesis. In addition, a majority of participants in further conditions chose the third option, “void”, when the antecedent of the conditional was false, supporting the second hypothesis. (shrink)

Among the many philosophers who hold that causal facts1 are to be explained in terms of—or more ambitiously, shown to reduce to—facts about what happens, together with facts about the fundamental laws that govern what happens, the clear favorite is an approach that sees counterfactual dependence as the key to such explanation or reduction. The paradigm examples of causation, so advocates of this approach tell us, are examples in which events c and e— the cause and its effect— both occur, (...) but: had c not occurred, e would not have occurred either. From this starting point ideas proliferate in a vast profusion. But the remarkable disparity among these ideas should not obscure their common foundation. Neither should the diversity of opinion about the prospects for a philosophical analysis of causation obscure their importance. For even those philosophers who see these prospects as dim—perhaps because they suffer post-Quinean queasiness at the thought of any analysis of any concept of interest—can often be heard to say such things as that causal relations among events are somehow “a matter of” the patterns of counterfactual dependence to be found in them. (shrink)

According to so-called epistemic theories of conditionals, the assertability/acceptability/acceptance of a conditional requires the existence of an epistemically significant relation between the conditional’s antecedent and its consequent. This paper points to some linguistic data that our current best theories of the foregoing type appear unable to explain. Further, it presents a new theory of the same type that does not have that shortcoming. The theory is then defended against some seemingly obvious objections.

Inference to the Best Explanation has become the subject of a livelydebate in the philosophy of science. Scientific realists maintain, while scientificantirealists deny, that it is a compelling rule of inference. It seems that anyattempt to settle this debate empirically must beg the question against theantirealist. The present paper argues that this impression is misleading. A methodis described that, by combining Glymour's theory of bootstrapping and Hacking'sarguments from microscopy, allows us to test IBE without begging any antirealistissues.

A paper on how to adapt your probabilisitc beliefs when learning a conditional.

The two main psychological theories of the ordinary conditional were designed to account for inferences made from assumptions, but few premises in everyday life can be simply assumed true. Useful premises usually have a probability that is less than certainty. But what is the probability of the ordinary conditional and how is it determined? We argue that people use a two stage Ramsey test that we specify to make probability judgements about indicative conditionals in natural language, and we describe experiments (...) that support this conclusion. Our account can explain why most people give the conditional probability as the probability of the conditional, but also why some give the conjunctive probability. We discuss how our psychological work is related to the analysis of ordinary indicative conditionals in philosophical logic. (shrink)

The present chapter describes a probabilistic framework of human reasoning. It is based on probability logic. While there are several approaches to probability logic, we adopt the coherence based approach.

Richard Jeffrey espoused an antifoundationalist variant of Bayesian thinking that he termed ‘Radical Probabilism’. Radical Probabilism denies both the existence of an ideal, unbiased starting point for our attempts to learn about the world and the dogma of classical Bayesianism that the only justified change of belief is one based on the learning of certainties. Probabilistic judgment is basic and irreducible. Bayesian conditioning is appropriate when interaction with the environment yields new certainty of belief in some proposition but leaves one’s (...) conditional beliefs untouched (the ‘Rigidity’ condition). Although Richard Jeffrey denied the general applicability of this condition, one of his main contributions to probabilistic thinking is a form of belief updating—now typically called ‘Jeffrey conditioning’ or ‘probability kinematics’—that is appropriate in circumstances in which Rigidity is satisfied, but where the interaction causes one to reevaluate one’s probability judgments over some partition of the possibility space without conferring certainty on any particular element. The most familiar occasion for Jeffrey conditioning is receipt of uncertain evidence: things partially perceived or remembered. But it also serves to illuminate belief updating occasioned by a change in one’s degrees of conditional belief, a kind of belief change largely ignored by classical Bayesianism. I argue that such changes in conditional belief can also be basic (in the sense of not being analyzable as a consequence of conditioning on factual information) and offer a kinematical model for a particular kind change in conditional belief. Both are applied to changes in preference. Finally, I argue that Rigidity can fail when changes of belief give inferential grounds for changes in conditional belief (and vice versa). These failures show that conditioning methods are properly regarded, not as valid rules of inference, but as tools in the ‘art of judgment’. (shrink)

A substantial body of evidence shows that people tend to rely too heavily on explanations when trying to justify an opinion. Some research suggests these errors may arise from an inability to distinguish between explanations and the evidence that bears upon them. We examine an alternative account, that many people do distinguish between explanations and evidence, but rely more heavily on unsubstantiated explanations when evidence is scarce or absent. We examine the philosophical and psychological distinctions between explanation and evidence, and (...) show that participants use explanations as a substitute for missing evidence. Experiment 1 replicates the results of other researchers, but further shows that participants generate more evidence when they are not constrained by their lack of data. Merely mentioning a source of data can alter both their evaluation (Experiment 2) and their production (Experiment 3) of explanations and evidence. In Experiment 4, we show that participants can explicitly consider the availability of evidence and other pragmatic factors when evaluating arguments. Finally, we consider the implications of using explanations to replace missing evidence as a strategy in argument. (shrink)

According to Stalnaker’s Hypothesis, the probability of an indicative conditional, $\Pr(\varphi \rightarrow \psi),$ equals the probability of the consequent conditional on its antecedent, $\Pr(\psi | \varphi)$ . While the hypothesis is generally taken to have been conclusively refuted by Lewis’ and others’ triviality arguments, its descriptive adequacy has been confirmed in many experimental studies. In this paper, we consider some possible ways of resolving the apparent tension between the analytical and the empirical results relating to Stalnaker’s Hypothesis and we argue (...) that none offer a satisfactory resolution. (shrink)

This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicative conditionals has been subject to severe criticism. The majority view is now apparently in favour of a subjective conditional probability interpretation. A comparative model fitting (...) exercise is presented that shows that a conditional probability model can explain as much of the data on abstract indicative conditional reasoning tasks as psychological theories that supplement material implication with various rationally unjustified processing assumptions. Consequently, when people are asked to solve laboratory reasoning tasks, they can be seen as simply generalising their everyday probabilistic reasoning strategies to this novel context. (shrink)

Most philosophers agree that abduction (in the sense of Inference to the Best Explanation) is a type of inference that is frequently employed, in some form or other, both in everyday and in scientific reasoning. However, the exact form as well as the normative status of abduction are still matters of controversy. This entry contrasts abduction with other types of inference; points at prominent uses of it, both in and outside philosophy; considers various more or less precise statements of it; (...) discusses its normative status; and highlights possible connections between abduction and Bayesian confirmation theory. (shrink)

Section 1 briefly examines three theories of indicative conditionals. The Suppositional Theory is defended, and shown to be incompatible with understanding conditionals in terms of truth conditions. Section 2 discusses the psychological evidence about conditionals reported by Over and Evans (this volume). Section 3 discusses the syntactic grounds offered by Haegeman (this volume) for distinguishing two sorts of conditional.

To save antirealism from Fitch's Paradox, Tennant has proposed to restrict the scope of the antirealist principle that all truths are knowable to truths that can be consistently assumed to be known. Although the proposal solves the paradox, it has been accused of doing so in an ad hoc manner. This paper argues that, first, for all Tennant has shown, the accusation is just; second, a restriction of the antirealist principle apparently weaker than Tennat's yields a non-ad hoc solution to (...) Fitch's Paradox; and third, the alternative is only apparently weaker than, and even provably equivalent to, Tennant's. It is thereby shown that the latter is not ad hoc after all. (shrink)

Adams famously suggested that the acceptability of any indicative conditional whose antecedent and consequent are both factive sentences amounts to the subjective conditional probability of the consequent given the antecedent. The received view has it that this thesis offers an adequate partial explication of Ramsey’s test, which characterizes graded acceptability for conditionals in terms of hypothetical updates on the antecedent. Some results in van Fraassen may raise hope that this explicatory approach to Ramsey’s test is extendible to left-nested conditionals, that (...) is, conditionals whose antecedent is itself conditional in form. We argue that this interpretation of van Fraassen’s results is to be rejected. Specifically, we provide an argument from material inadequacy against a generalization of Adams’ thesis for left-nested conditionals. (shrink)

This book makes a significant contribution to the standard decision theory, that is, the theory of choice built around the principle of maximizing expected utility, both to its causal version and to the more traditional noncausal approach. The author’s success in clarifying the foundations of the standard decision theory in general, and causal decision theory in particular, also makes the book uniquely suitable for a person whose research in philosophy has led her to want to learn about contemporary decision theory. (...) The book presupposes some mathematical sophistication, and it contains more philosophical and mathematical argumentation per page than may be suitable for an undergraduate level course; but it stands out as an ideal textbook for a graduate-level course focused on the foundations of the standard decision theory. (shrink)