Probabilistic models have much to offer to philosophy. We continually receive information from a variety of sources: from our senses, from witnesses, from scientific instruments. When considering whether we should believe this information, we assess whether the sources are independent, how reliable they are, and how plausible and coherent the information is. Bovens and Hartmann provide a systematic Bayesian account of these features of reasoning. Simple Bayesian Networks allow us to model alternative assumptions about the nature of the information sources. (...) Measurement of the coherence of information is a controversial matter: arguably, the more coherent a set of information is, the more confident we may be that its content is true, other things being equal. The authors offer a new treatment of coherence which respects this claim and shows its relevance to scientific theory choice. Bovens and Hartmann apply this methodology to a wide range of much discussed issues regarding evidence, testimony, scientific theories, and voting. Bayesian Epistemology is an essential tool for anyone working on probabilistic methods in philosophy, and has broad implications for many other disciplines. (shrink)

According to Bayesian confirmation theory, evidence E (incrementally) confirms (or supports) a hypothesis H (roughly) just in case E and H are positively probabilistically correlated (under an appropriate probability function Pr). There are many logically equivalent ways of saying that E and H are correlated under Pr. Surprisingly, this leads to a plethora of non-equivalent quantitative measures of the degree to which E confirms H (under Pr). In fact, many non-equivalent Bayesian measures of the degree to which E confirms (or (...) supports) H have been proposed and defended in the literature on inductive logic. I provide a thorough historical survey of the various proposals, and a detailed discussion of the philosophical ramifications of the differences between them. I argue that the set of candidate measures can be narrowed drastically by just a few intuitive and simple desiderata. In the end, I provide some novel and compelling reasons to think that the correct measure of degree of evidential support (within a Bayesian framework) is the (log) likelihood ratio. The central analyses of this research have had some useful and interesting byproducts, including: (i ) a new Bayesian account of (confirmationally) independent evidence, which has applications to several important problems in con- firmation theory, including the problem of the (confirmational) value of evidential diversity, and (ii ) novel resolutions of several problems in Bayesian confirmation theory, motivated by the use of the (log) likelihood ratio measure, including a reply to the Popper-Miller critique of probabilistic induction, and a new analysis and resolution of the problem of irrelevant conjunction (a.k.a., the tacking problem). (shrink)

We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wason's selection paradigm for subjects who have had (...) no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain. (shrink)

What counts as human rationality: reasoning processes that embody content-independent formal theories, such as propositional logic, or reasoning processes that are well designed for solving important adaptive problems? Most theories of human reasoning have been based on content-independent formal rationality, whereas adaptive reasoning, ecological or evolutionary, has been little explored. We elaborate and test an evolutionary approach, Cosmides' social contract theory, using the Wason selection task. In the first part, we disentangle the theoretical concept of a “social contract” from that (...) of a “cheater-detection algorithm”. We demonstrate that the fact that a rule is perceived as a social contract — or a conditional permission or obligation, as Cheng and Holyoak proposed — is not sufficient to elicit Cosmides' striking results, which we replicated. The crucial issue is not semantic, but pragmatic: whether a person is cued into the perspective of a party who can be cheated. In the second part, we distinguish between social contracts with bilateral and unilateral cheating options. Perspective change in contracts with bilateral cheating options turns P & not-Q responses into not-P & Q responses. The results strongly support social contract theory, contradict availability theory, and cannot be accounted for by pragmatic reasoning schema theory, which lacks the pragmatic concepts of perspectives and cheating detection. (shrink)

Addresses ‘too-odd-not-to-be-true’ reasoning in the assessment of testimony. This is the curious phenomenon that an initially less plausible report from multiple independent witnesses may elicit more confidence than an initially more plausible report.

The literature on the theory of social choice has grown considerably beyond the few items in existence at the time the first edition of this book appeared in 1951. Some of the new literature has dealt with the technical, mathematical aspects, more with the interpretive. My own thinking has also evolved somewhat, although I remain far from satisfied with present formulations. The exhaustion of the first edition provides a convenient time for a selective and personal stocktaking in the form of (...) an appended commentary entitled, 'Notes on the Theory of Social Choice, 1963, ' containing reflections on the text and its omissions and on some of the more recent literature. This form has seemed more appropriate than a revision of the original text, which has to some extent acquired a life of its own. (shrink)

Kuhn’s famous thesis that there is ‘no unique algorithm’ for choosing between rival scientific theories is analysed using the machinery of social choice theory. It is shown that the problem of theory choice as posed by Kuhn is formally identical to a standard social choice problem. This suggests that analogues of well-known results from the social choice literature, such as Arrow’s impossibility theorem, may apply to theory choice. If an analogue of Arrow’s theorem does hold for theory choice this would (...) refute Kuhn’s thesis, but it would also pose a threat to the rationality of science, a threat that is if anything more worrying than that posed by Kuhn. Various possible ‘escape routes’ from Arrow’s impossibility result are examined, in particular Amartya Sen’s idea of ‘enriching the informational basis’. It is shown that Sen’s idea can be applied to the problem of theory choice in science. This in turn sheds light on two well-known approaches to inductive inference in philosophy of science: Bayesianism and statistical model selection. (shrink)

The study of deductive reasoning has been a major paradigm in psychology for approximately the past 40 years. Research has shown that people make many logical errors on such tasks and are strongly influenced by problem content and context. It is argued that this paradigm was developed in a context of logicist thinking that is now outmoded. Few reasoning researchers still believe that logic is an appropriate normative system for most human reasoning, let alone a model for describing the process (...) of human reasoning, and many use the paradigm principally to study pragmatic and probabilistic processes. It is suggested that the methods used for studying reasoning be reviewed, especially the instructional context, which necessarily defines pragmatic influences as biases. (shrink)

The detailed analysis of a particular quasi-historical numerical example is used to illustrate the way in which a Bayesian personalist approach to scientific inference resolves the Duhemian problem of which of a conjunction of hypotheses to reject when they jointly yield a prediction which is refuted. Numbers intended to be approximately historically accurate for my example show, in agreement with the views of Lakatos, that a refutation need have astonishingly little effect on a scientist's confidence in the ‘hard core’ of (...) a successful research programme even when a comparable confirmation would greatly enhance that confidence. Timeo Danaos et dona ferentis. (shrink)

A platitude that took hold with Kuhn is that there can be several equally good ways of balancing theoretical virtues for theory choice. Okasha recently modelled theory choice using technical apparatus from the domain of social choice: famously, Arrow showed that no method of social choice can jointly satisfy four desiderata, and each of the desiderata in social choice has an analogue in theory choice. Okasha suggested that one can avoid the Arrow analogue for theory choice by employing a strategy (...) used by Sen in social choice, namely, to enhance the information made available to the choice algorithms. I argue here that, despite Okasha’s claims to the contrary, the information-enhancing strategy is not compelling in the domain of theory choice. (shrink)

This paper examines the standard Bayesian solution to the Quine–Duhem problem, the problem of distributing blame between a theory and its auxiliary hypotheses in the aftermath of a failed prediction. The standard solution, I argue, begs the question against those who claim that the problem has no solution. I then provide an alternative Bayesian solution that is not question-begging and that turns out to have some interesting and desirable properties not possessed by the standard solution. This solution opens the way (...) to a satisfying treatment of a problem concerning ad hoc auxiliary hypotheses. (shrink)

In a recent article, Okasha challenges Kuhn’s claim that there is no ‘neutral’ algorithm for theory choice. He argues using Arrow’s ‘impossibility’ theorem that — except under certain favourable conditions concerning the measurability and comparability of theoretical values — there are no theory choice algorithms at all, neutral or otherwise. But Okasha’s argument does not apply to important theory choice problems, among them the case of Copernican and Ptolemaic astronomy that much occupied Kuhn. The reason is that Kuhn’s choice criteria (...) can rank rival theories in only a few ways, which makes the analogue of Arrow’s domain assumption inappropriate. It is hard to see any consequences for Kuhn’s claim, or threat to the rationality of science. (shrink)

Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.

An analogue of Arrow’s theorem has been thought to limit the possibilities for multi-criterial theory choice. Here, an example drawn from Toy Science, a model of theories and choice criteria, suggests that it does not. Arrow’s assumption that domains are unrestricted is inappropriate in connection with theory choice in Toy Science. There are, however, variants of Arrow’s theorem that do not require an unrestricted domain. They require instead that domains are, in a technical sense, ‘rich’. Since there are rich domains (...) in Toy Science, such theorems do constrain theory choice to some extent—certainly in the model and perhaps also in real science. (shrink)

Kuhn claimed that several algorithms can be defended to select the best theory based on epistemic values such as simplicity, accuracy, and fruitfulness. In a recent paper, Okasha :83–115, 2011) argued that no theory choice algorithm exists which satisfies a set of intuitively compelling conditions that Arrow had proposed for a consistent aggregation of individual preference orderings. In this paper, we put forward a solution to avoid this impossibility result. Based on previous work by Gaertner and Xu, we suggest to (...) view the theory choice problem in a cardinal context and to use a general scoring function defined over a set of qualitative verdicts for every epistemic value. This aggregation method yields a complete and transitive ranking and the rule satisfies all Arrovian conditions appropriately reformulated within a cardinal setting. We also propose methods that capture the aggregation across different scientists. (shrink)

Wulf Gaertner provides a comprehensive account of an important and complex issue within social choice theory: how to establish a social welfare function while restricting the spectrum of individual preferences in a sensible way. Gaertner's starting point is K. J. Arrow's famous 'Impossibility Theorem', which showed that no welfare function could exist if an unrestricted domain of preferences is to be satisfied together with some other appealing conditions. A number of leading economists have tried to provide avenues out of this (...) 'impossibility' by restricting the variety of preferences: here, Gaertner provides a clear and detailed account, using standardized mathematical notation, of well over forty theorems associated with domain conditions. Domain Conditions in Social Choice Theory will be an essential addition to the library of social choice theory for scholars and their advanced graduate students. (shrink)

In a recent article I compared the problem of theory choice, in which scientists must choose between competing theories, with the problem of social choice, in which society must choose between competing social alternatives. I argued that the formal machinery of social choice theory can be used to shed light on the problem of theory choice in science, an argument that has been criticized by Michael Morreau and Jacob Stegenga. This article replies to Morreau’s and Stegenga’s criticisms.

Juries, committees and experts panels commonly appraise things of one kind or another on the basis of grades awarded by several people. When everybody's grading thresholds are known to be the same, the results sometimes can be counted on to reflect the graders’ opinion. Otherwise, they often cannot. Under certain conditions, Arrow's ‘impossibility’ theorem entails that judgements reached by aggregating grades do not reliably track any collective sense of better and worse at all. These claims are made by adapting the (...) Arrow–Sen framework for social choice to study grading in groups. (shrink)

The inaugural volume of the Pitt-Konstanz series, devoted to the work of philosopher Adolf Grünbaum, encompasses the philosophical problems of space, time, and cosmology, the nature of scientific methodology, and the foundations of psychoanalysis.