There is a tension between normative and descriptive elements in the theory of rational belief. This tension has been reflected in work in psychology and decision theory as well as in philosophy. Canons of rationality should be tailored to what is humanly feasible. But rationality has normative content as well as descriptive content.A number of issues related to both deductive and inductive logic can be raised. Are there full beliefs – statements that are categorically accepted? Should statements be accepted when (...) they become overwhelmingly probable? What is the structure imposed on these beliefs by rationality? Are they consistent? Are they deductively closed? What parameters, if any, does rational acceptance depend on? How can accepted statements come to be rejected on new evidenceShould degrees of belief satisfy the probability calculus? Does conformity to the probability calculus exhaust the rational constraints that can be imposed on partial beliefs? With the acquisition of new evidence, should beliefs change in accord with Bayes' theorem? Are decisions made in accord with the principle of maximizing expected utility? Should they be?A systematic set of answers to these questions is developed on the basis of a probabilistic rule of acceptance and a conception of interval-valued logical probability according to which probabilities are based onknownfrequencies. This leads to limited deductive closure, a demand for only limited consistency, and the rejection of Bayes' theorem as universally applicable to changes of belief. It also becomes possible, given new evidence, to reject previously accepted statements. (shrink)

Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a contextual “cautiousness” threshold, there (...) is but one way of determining the extension of the concept of belief that does the job. The qualitative concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing qualitative belief to assignments of resiliently high degrees of belief and a “cautiousness” threshold, qualitative and quantitative belief turn out to be governed by one unified theory that offers the prospects of a huge range of applications. Within that theory, logic and probability theory are not opposed to each other but go hand in hand. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

Bayesian confirmation theory—abbreviated to in these notes—is the predominant approach to confirmation in late twentieth century philosophy of science. It has many critics, but no rival theory can claim anything like the same following. The popularity of the Bayesian approach is due to its flexibility, its apparently effortless handling of various technical problems, the existence of various a priori arguments for its validity, and its injection of subjective and contextual elements into the process of confirmation in just the places where (...) critics of earlier approaches had come to think that subjectivity and sensitivity to context were necessary. (shrink)

This paper takes as its point of departure two striking incongruities between scientiªc practice and trends in modern history and philosophy of science. (1) Many modern historians of science are so preoccupied with local scientiªc practices that they fail to recognize important non-local elements. (2) Many modern philosophers of science make a sharp distinction between explanation and evidence, whereas in scientiªc practice explanatory power is routinely used as evidence for scientiªc claims. I draw attention to one speciªc way in..

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)

The growing range of methods for statistical model selection is inspiring new debates about how to handle the potential for conflicting results when different methods are applied to the same data. While many factors enter into choosing a model selection method, we focus on the implications of disagreements among scientists about whether, and in what sense, the true probability distribution is included in the candidate set of models. While this question can be addressed empirically, the data often provide inconclusive results (...) in practice. In such cases, we argue that differences in prior metaphysical views about the local adequacy of the models can produce underdetermination of results, even for the same data and candidate models. As a result, data alone are sometimes insufficient to settle rational beliefs about nature. (shrink)

Going back at least to Duhem, there is a tradition of thinking that crucial experiments are impossible in science. I analyse Duhem's arguments and show that they are based on the excessively strong assumption that only deductive reasoning is permissible in experimental science. This opens the possibility that some principle of inductive inference could provide a sufficient reason for preferring one among a group of hypotheses on the basis of an appropriately controlled experiment. To be sure, there are analogues to (...) Duhem's problems that pertain to inductive inference. Using a famous experiment from the history of molecular biology as an example, I show that an experimentalist version of inference to the best explanation (IBE) does a better job in handling these problems than other accounts of scientific inference. Furthermore, I introduce a concept of experimental mechanism and show that it can guide inferences from data within an IBE-based framework for induction. 1. Introduction2. Duhem on the Logic of Crucial Experiments3. ‘The Most Beautiful Experiment in Biology’4. Why Not Simple Elimination?5. Severe Testing6. An Experimentalist Version of IBE 6.1. Physiological and experimental mechanisms6.2. Explaining the data6.3. IBE and the problem of untested auxiliaries6.4. IBE-turtles all the way down7. Van Fraassen's ‘Bad Lot’ Argument8. IBE and Bayesianism9. Conclusions. (shrink)

This paper places formal learning theory in a broader philosophical context and provides a glimpse of what the philosophy of induction looks like from a learning-theoretic point of view. Formal learning theory is compared with other standard approaches to the philosophy of induction. Thereafter, we present some results and examples indicating its unique character and philosophical interest, with special attention to its unified perspective on inductive uncertainty and uncomputability.

This paper is an examination of evidential holism, a prominent position in epistemology and the philosophy of science which claims that experiments only ever confirm or refute entire theories. The position is historically associated with W.V. Quine, and it is at once both popular and notorious, as well as being largely under-described. But even though there’s no univocal statement of what holism is or what it does, philosophers have nevertheless made substantial assumptions about its content and its truth. Moreover they (...) have drawn controversial and important conclusions from these assumptions. In this paper I distinguish three types of evidential holism and argue that the most oft-cited and controversial thesis is entirely unmotivated. The other two theses are much overlooked, but are well-motivated and free from controversial implications. (shrink)

I argue that the Bayesian Way of reconstructing Duhem's problem fails to advance a solution to the problem of which of a group of hypotheses ought to be rejected or "blamed" when experiment disagrees with prediction. But scientists do regularly tackle and often enough solve Duhemian problems. When they do, they employ a logic and methodology which may be called error statistics. I discuss the key properties of this approach which enable it to split off the task of testing auxiliary (...) hypotheses from that of appraising a primary hypothesis. By discriminating patterns of error, this approach can at least block, if not also severely test, attempted explanations of an anomaly. I illustrate how this approach directs progress with Duhemian problems and explains how scientists actually grapple with them. (shrink)

has proposed an interesting and novel Bayesian analysis of the Quine-Duhem (Q–D) problem (i.e., the problem of auxiliary hypotheses). Strevens's analysis involves the use of a simplifying idealization concerning the original Q–D problem. We will show that this idealization is far stronger than it might appear. Indeed, we argue that Strevens's idealization oversimplifies the Q–D problem, and we propose a diagnosis of the source(s) of the oversimplification. Some background on Quine–Duhem Strevens's simplifying idealization Indications that (I) oversimplifies Q–D Strevens's argument (...) for the legitimacy of (I). (shrink)

Models are a principle instrument of modern science. They are built, applied, tested, compared, revised and interpreted in an expansive scientific literature. Throughout this paper, I will argue that models are also a valuable tool for the philosopher of science. In particular, I will discuss how the methodology of Bayesian Networks can elucidate two central problems in the philosophy of science. The first thesis I will explore is the variety-of-evidence thesis, which argues that the more varied the supporting evidence, the (...) greater the degree of confirmation for a given hypothesis. However, when investigated using Bayesian methodology, this thesis turns out not to be sacrosanct. In fact, under certain conditions, a hypothesis receives more confirmation from evidence that is obtained from one rather than more instruments, and from evidence that confirms one rather than more testable consequences of the hypothesis. The second challenge that I will investigate is scientific theory change. This application highlights a different virtue of modeling methodology. In particular, I will argue that Bayesian modeling illustrates how two seemingly unrelated aspects of theory change, namely the (Kuhnian) stability of (normal) science and the ability of anomalies to over turn that stability and lead to theory change, are in fact united by a single underlying principle, in this case, coherence. In the end, I will argue that these two examples bring out some metatheoretical reflections regarding the following questions: What are the differences between modeling in science and modeling in philosophy? What is the scope of the modeling method in philosophy? And what does this imply for our understanding of Bayesianism? (shrink)

On the basis of an analysis of a single paper on plate tectonics, a paper whose actual content is nowhere in evidence, Frederick Suppe concludes that no standard model of confirmation—hypothetico-deductive, Bayesian-inductive, or inference to the best explanation—can account for the structure of a scientific paper that reports an experimental result. He further argues on the basis of a survey of scientific papers, a survey whose data and results are also absent, that papers which have a rather stringent length limit, (...) such as the one on plate tectonics, are typical of science. Thus, he concludes that no standard confirmation scheme is capable of dealing with scientific practice. Suppe also requires that an adequate model of philosophical testing should be able to account for everything in such scientific papers, in which space is at a premium. (shrink)

Fitch’s paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch’s result while still offering all that antirealists should care for.

In applying Bayes’s theorem to the history of science, Bayesians sometimes assume – often without argument – that they can safely ignore very implausible theories. This assumption is false, both in that it can seriously distort the history of science as well as the mathematics and the applicability of Bayes’s theorem. There are intuitively very plausible counter-examples. In fact, one can ignore very implausible or unknown theories only if at least one of two conditions is satisfied: (i) one is certain (...) that there are no unknown theories which explain the phenomenon in question, or (ii) the likelihood of at least one of the known theories used in the calculation of the posterior is reasonably large. Often in the history of science, a very surprising phenomenon is observed, and neither of these criteria is satisfied. (shrink)

In a recent paper Samir Okasha has suggested an application of Arrow’s impossibility theorem to theory choice. When epistemic virtues are interpreted as ‘voters’ in charge of ranking competing theories, and there are more than two theories at stake, the final ordering is bound to coincide with the one proposed by one of the voters, provided a number of seemingly reasonable conditions are in place. In a similar spirit, Jacob Stegenga has shown that Arrow’s theorem applies to the amalgamation of (...) evidence; the ‘voters’ here are the different sources of evidence. As with Okasha’s proposal, it is not clear how to avoid Arrow’s pessimistic conclusion.In this paper we develop a novel argument that purports to show that, in typical examples, Arrow’s result does not obtain when dealing with evidence amalgamation. The reason is that we cannot escape the well-known Duhem problem: the evidence actually confirms complex conjunctions that include various auxiliary hypotheses. We argue that confirmational holism induces us to restrict the domain of a reasonable amalgamation function, thus violating one of Arrow’s conditions. The upshot is that we are now able to see the Duhem problem under a different, positive light – namely, as a phenomenon that makes the aggregation of the evidence possible in the first place, when there are at least three options on the table. (shrink)

Many philosophers have claimed that Bayesianism can provide a simple justification for hypothetico-deductive inference, long regarded as a cornerstone of the scientific method. Following up a remark of van Fraassen, we analyze a problem for the putative Bayesian justification of H-D inference in the case where what we learn from observation is logically stronger than what our theory implies. Firstly, we demonstrate that in such cases the simple Bayesian justification does not necessarily apply. Secondly, we identify a set of sufficient (...) conditions for the mismatch in logical strength to be justifiably ignored as a "harmless idealization''. Thirdly, we argue, based upon scientific examples, that the pattern of H-D inference of which there is a ready Bayesian justification is only rarely the pattern that one actually finds at work in science. Whatever the other virtues of Bayesianism, the idea that it yields a simple justification of a pervasive pattern of scientific inference appears to have been oversold. (shrink)

When the results of an experiment appears to disconfirm a hypothesis, how does one know whether it’s the hypothesis, or rather some auxiliary hypothesis or assumption, that is at fault? Philosophers’ answers to this question, now known as “Duhem’s problem,” have differed widely. Despite these differences, we affirm Duhem’s original position that the logical structure of this problem alone does not allow a solution. A survey of philosophical approaches to Duhem’s problem indicates that what allows any philosopher, or scientists for (...) that matter, to solve this problem is the addition of epistemic information that guides their assignment of praise and blame after a negative test. We therefore advocate a distinction between the logical and epistemic formulations of Duhem’s problem, the latter relying upon additional relevant information about the system being tested. Recognition of the role of this additional information suggests that some proposed solutions to the epistemic form of Duhem’s problem are preferable over others. (shrink)

Abstract The Duhem?Quine thesis is generally presented as the radical underdetermi? nation of a theory by experimental evidence. But there is a much?neglected second aspect, i.e. the coherence or interrelatedness of the conceptual components of a theory. Although both Duhem and Quine recognised this aspect, they failed to see its consequences: it militates against the idea of radical underdetermination. Because scientific theories are coherent conceptual systems, empirical evidence penetrates, as it were, the periphery and allows the localisation of central, not (...) just peripheral hypotheses. There is then no reason to deny the existence of crucial experiments. Both these ideas are denied in the Quine?Duhem thesis. A discussion of the famous Stem?Gerlach experiment and the role of fundamental physical constants shows, however, that localisation is not only possible but essential for the validity of scientific theories. Quine's famous ?latitude of choice? turns out to be severely restricted. (shrink)

Knowledge of residual perturbations in the orbit of Uranus in the early 1840s did not lead to the refutation of Newton's law of gravitation but instead to the discovery of Neptune in 1846. Karl Popper asserts that this case is atypical of science and that the law of gravitation was at least prima facie falsified by these perturbations. I argue that these assertions are the product of a false, a priori methodological position I call, 'Weak Popperian Falsificationism'. Further, on the (...) evidence the law was not prima facie false and was not generally considered so by astronomers at the time. Many of Popper's commentators presuppose WPF and their views on this case and its implications for scientific rationality and method suffer from this same defect. (shrink)

En este trabajo hago una comparación sistemática entre las dos teorías de la confirmación más populares en la actualidad: el método hipotético-deductivo y el bayesianismo. En primer lugar, enumero los cinco problemas fundamentales de la teoría hipotético-deductivista. Estos son el problema de las hipótesis estadísticas, el del grado de confirmación, el de la conjunción irrelevante, el del holismo epistemológico y el de las hipótesis alternativas. Luego, hago una presentación general de la epistemología bayesiana y muestro de qué manera estos problemas (...) resultan tratables en el marco bayesiano. Finalmente, concluyo que los tres primeros admiten una solución satisfactoria, sobre la base de algunos supuestos razonables. Los dos últimos, en cambio, todavía son problemas abiertos para la teoría bayesiana de la confirmación. Bayesians often affirm they have produced the best available theory of confirmation. In particular, they claim to have superseded the venerable hypothetico-deductive method. In this paper I intend to assess that claim by making a systematic comparison between both theories of confirmation. I begin by listing the main problems of hypothetico-deductive confirmation. I then show that this conception is incompatible with Hempel's conditions of adequacy for qualitative confirmation. I expound the Bayesian theory of confirmation with some detail in order to show that this theory is able to solve three out of the five fundamental problems of hypothetico-deductive confirmation. largue that the remaining two problems are still open questions for the Bayesians. (shrink)

in this paper i assess Pierre Duhem’s criticism of crucial experiments, and argue that we have reasons to vindicate their existence. i then analize the experiments carried out by Fizeau and Foucault in 1850, and criticize Duhem’s interpretation of their results. i contend that the results of crucial experiences can be described in terms that are neutral with respect to the competing theories. For that reason an experimental result is relatively stable and open to different interpretations in the light of (...) new theories. i conclude by distinguishing successful crucial experiments from decisive experiments. The former are meant to provide evidence that confirms one theory and disconfirms its rivals, but not necessarily to provide sufficient reasons for accepting or rejecting one of those theories. (shrink)

Richard Jeffrey has labelled his philosophy of probability radical probabilism and qualified this position as Bayesian, nonfoundational and anti-rationalist. This paper explores the roots of radical probabilism, to be traced back to the work of Frank P. Ramsey and Bruno de Finetti.

Against Hellman's (1997) recent claims, I argue that Bayesianism is unable to explain the value of generally successful aspects of scientific methodology, viz., deflecting blame from well-confirmed theories onto auxiliaries and preferring more-varied data. Such an explanation would require not just objectification of priors, but a reason to believe priors will generally fall on values that justify the practice. Given the track record on the objectification problem, adding further conditions on priors merely makes the Bayesian's problems even worse.

In the first half of this dissertation, I develop a heuristic methodology for analyzing scientific solutions to the problem of underdetermination. Heuristics are rough-and-ready procedures used by scientists to construct models, design experiments, interpret evidence, etc. But as powerful as they are, heuristics are also error-prone. Therefore, I argue that they key to prudently using a heuristic is the articulation of meta-heuristics---guidelines to the kinds of problems for which a heuristic is well- or ill-suited. Given that heuristics will introduce certain (...) errors into our scientific investigations, I emphasize the importance of a particular category of meta-heuristics involving the search for robust evidence. Robustness is understood to be the epistemic virtue bestowed by agreement amongst multiple modes of determination. The more modes we have at our disposal, and the more these confirm the same result, the more confident can we be that a result is not a mere artifact of some heuristic simplification. Through an analysis of case-studies in the philosophy of biology and clinical trials, I develop a principled method for modeling and evaluating heuristics and robustness claims in a qualitative problem space. The second half of the dissertation deploys the heuristic methodology to address ethical and epistemological issues in the science of clinical trials. To that end, I develop a network model for the problem space of clinical research, capable of representing the various kinds of experiments, epistemic relationships, and ethical justifications intrinsic to the domain. I then apply this model to ongoing research with the antibacterial agent, moxifloxacin, for the treatment of tuberculosis, tracking its development from initially successful and promising in vitro and animal studies to its disappointing and discordant performance across five human efficacy trials. Given this failure to find a robust result with moxifloxacin across animal and human studies, what should researchers now do? While my final analysis of this case does not definitively answer that question, I demonstrate how my methodology, unlike a statistical meta-analysis, helps to clarify the directions for further research. (shrink)

Scientific principles can undergo various developments. While philosophers of science have acknowledged that such changes occur, there is no systematic account of the development of scientific principles. Here we propose a template for analyzing the development of scientific principles called the ‘life cycle’ of principles. It includes a series of processes that principles can go through: prehistory, elevation, formalization, generalization, and challenge. The life cycle, we argue, is a useful heuristic for the analysis of the development of scientific principles. We (...) illustrate this by discussing examples from foundational physics including Lorentz invariance, Mach’s principle, the naturalness principle, and the perfect cosmological principle. We also explore two applications of the template. First, we propose that the template can be employed to diagnose the quality of scientific principles. Second, we discuss the ramifications of the life cycle’s processes for the empirical testability of principles. (shrink)

In this paper we consider a Bayesian treatment of ‘Duhem's thesis’, the proposition that theories are never refuted on empirical grounds because they cannot be tested in isolation from auxiliary hypotheses about initial conditions or the operation of scientific instruments. Sawyer, Beed, and Sankey consider Duhem's thesis and its role in hypothesis testing, using four theories from economics and finance as examples. Here we consider Duhem's thesis in the context of theory choice, econometric results, and the ‘farm problem’ in agricultural (...) economics. This problem is defined as persistently low and highly variable prices, incomes, and returns in the agricultural sector as compared to the nonagricultural sector of the U.S. economy. The existence of the farm problem tends to refute an implication of general equilibrium theory — that resources flow to equate returns between sectors of the economy. We discuss Duhem's thesis in the context of demonstrating why evidence supporting the farm problem has not diminished the standing of general equilibrium theory among agricultural economists. (shrink)

In the four papers available on our web site (of which this is the first), we propose to develop an inductive logic. By “inductive logic” we mean a set of principles that distinguish between successful and unsuccessful strategies for scientific inquiry. Our logic will have a technical character, since it is built from the concepts and terminology of (elementary) model theory. The reader may therefore wish to know something about the kind of results on offer before investing time in definitions (...) and notation. Providing such an informal overview is the purpose of the present essay. We begin with discussion of the central concept under investigation, namely, theory acceptance. (shrink)