Any theory of confirmation must answer the following question: what is the purpose of its conception of confirmation for scientific inquiry? In this article, we argue that no Bayesian conception of confirmation can be used for its primary intended purpose, which we take to be making a claim about how worthy of belief various hypotheses are. Then we consider a different use to which Bayesian confirmation might be put, namely, determining the epistemic value of experimental outcomes, and thus to decide (...) which experiments to carry out. Interestingly, Bayesian confirmation theorists rule out that confirmation be used for this purpose. We conclude that Bayesian confirmation is a means with no end. 1 Introduction2 Bayesian Confirmation Theory3 Bayesian Confirmation and Belief4 Confirmation and the Value of Experiments5 Conclusion. (shrink)

Reichenbach’s use of ‘posits’ to defend his frequentistic theory of probability has been criticized on the grounds that it makes unfalsifiable predictions. The justice of this criticism has blinded many to Reichenbach’s second use of a posit, one that can fruitfully be applied to current debates within epistemology. We show first that Reichenbach’s alternative type of posit creates a difficulty for epistemic foundationalists, and then that its use is equivalent to a particular kind of Jeffrey conditionalization. We conclude that, under (...) particular circumstances, Reichenbach’s approach and that of the Bayesians amount to the same thing, thereby presenting us with a new instance in which chance and credence coincide. (shrink)

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)

Elliott Sober has suggested his criterion of contrastive testability as an improvement over previous criteria of empirical significance like falsifiability. I argue that his criterion renders almost any theory empirically significant because its restrictions on auxiliary assumptions are to weak. Even when the criterion is modified to avoid this trivialization, it fails to meet other conditions of adequacy for a criterion of empirical significance that follow from Sober's position. I suggest to define empirical significance as empirical non-equivalence to a tautology, (...) because this definition does meet the conditions of adequacy. Specifically, it is equivalent to the standard Bayesian criterion of empirical significance whenever all probabilities are defined and contains falsifiability as a special case. This latter feature is important because those conditions of adequacy that apply to criteria of deductive empirical significance single out falsifiability. (shrink)

Intuition is sometimes derided as an abstruse or esoteric phenomenon akin to crystal-ball gazing. Such derision appears to be fuelled primarily by the suggestion, evidently endorsed by traditional rationalists such as Plato and Descartes, that intuition is a kind of direct, immediate apprehension akin to perception. This paper suggests that although the perceptual analogy has often been dismissed as encouraging a theoretically useless metaphor, a quasi-perceptualist view of intuition may enable rationalists to begin to meet the challenge of supplying a (...) theoretically satisfying treatment of their favoured epistemic source. It is argued, first, that intuitions and perceptual experiences are at a certain level of abstraction the same type of mental state, presentations, which are distinct from beliefs, hunches, inclinations, attractions, and seemings. The notion of a presentation is given a positive explication, which identifies its characteristic features, accounts for several of its substantive psychological roles, and systematically locates it in a threefold division among types of contentful states. Subsequently, it is argued that presentations, intuitive no less than sensory, are by their nature poised to play a distinctive epistemic role. Specifically, in the case of intuition, we encounter an intellectual state that is so structured as to provide justification without requiring justification in turn—something which may, thus, be thought of as ‘given’. (shrink)

The main objective of the paper is to propose a frequentist interpretation of probability in the context of model-based induction, anchored on the Strong Law of Large Numbers (SLLN) and justifiable on empirical grounds. It is argued that the prevailing views in philosophy of science concerning induction and the frequentist interpretation of probability are unduly influenced by enumerative induction, and the von Mises rendering, both of which are at odds with frequentist model-based induction that dominates current practice. The differences between (...) the two perspectives are brought out with a view to defend the model-based frequentist interpretation of probability against certain well-known charges, including [i] the circularity of its definition, [ii] its inability to assign ‘single event’ probabilities, and [iii] its reliance on ‘random samples’. It is argued that charges [i]–[ii] stem from misidentifying the frequentist ‘long-run’ with the von Mises collective. In contrast, the defining characteristic of the long-run metaphor associated with model-based induction is neither its temporal nor its physical dimension, but its repeatability (in principle); an attribute that renders it operational in practice. It is also argued that the notion of a statistical model can easily accommodate non-IID samples, rendering charge [iii] simply misinformed. (shrink)

This dissertation consists of three parts. Part I is a defense of an artificial language methodology in philosophy and a historical and systematic defense of the logical empiricists' application of an artificial language methodology to scientific theories. These defenses provide a justification for the presumptions of a host of criteria of empirical significance, which I analyze, compare, and develop in part II. On the basis of this analysis, in part III I use a variety of criteria to evaluate the scientific (...) status of intelligent design, and further discuss confirmation, reduction, and concept formation. (shrink)

This target article presents a new computational theory of explanatory coherence that applies to the acceptance and rejection of scientific hypotheses as well as to reasoning in everyday life, The theory consists of seven principles that establish relations of local coherence between a hypothesis and other propositions. A hypothesis coheres with propositions that it explains, or that explain it, or that participate with it in explaining other propositions, or that offer analogous explanations. Propositions are incoherent with each other if they (...) are contradictory, Propositions that describe the results of observation have a degree of acceptability on their own. An explanatory hypothesis is acccpted if it coheres better overall than its competitors. The power of the seven principles is shown by their implementation in a connectionist program called ECHO, which treats hypothesis evaluation as a constraint satisfaction problem. Inputs about the explanatory relations are used to create a network of units representing propositions, while coherende and incoherence relations are encoded by excitatory and inbihitory links. ECHO provides an algorithm for smoothly integrating theory evaluation based on considerations of explanatory breadth, simplicity, and analogy. It has been applied to such important scientific cases as Lovoisier's argument for oxygen against the phlogiston theory and Darwin's argument for evolution against creationism, and also to cases of legal reasoning. The theory of explanatory coherence has implications for artificial intelligence, psychology, and philosophy. (shrink)

: For philosophers of science interested in elucidating the social character of science, an important question concerns the manner in which and degree to which the objectivity of scientific knowledge is socially constituted. We address this broad question by focusing specifically on philosophical theories of evidence. To get at the social character of evidence, we take an interdisciplinary approach informed by categories from argumentation studies. We then test these categories by exploring their applicability to a case study from high-energy physics. (...) Our central claim is that normative philosophy of science must move beyond abstract theories of justification, confirmation, or evidence conceived impersonally and incorporate a theoretical perspective that includes dialogical elements, either as adjuncts to impersonal theories of evidence or as intrinsic to the cogency of scientific argumentation. (shrink)

Reichenbach held that all scientific inference reduces, via probability calculus, to induction, and he held that induction can be justified. He sees scientific knowledge in a practical context and insists that any rational assessment of actions requires a justification of induction. Gaps remain in his justifying argument; for we can not hope to prove that induction will succeed if success is possible. However, there are good prospects for completing a justification of essentially the kind he sought by showing that while (...) induction may succeed, no alternative is a rational way of trying.Reichenbach's claim that probability calculus, especially via Bayes' Theorem, can help to exhibit the structure of inference to theories is a valuable insight. However, his thesis that the weighting of all hypotheses rests only on frequency data is too restrictive, especially given his scientific realism. Other empirical factors are relevant. Any satisfactory account of scientific inference must be deeply indebted to Reichenbach's foundation work. (shrink)

Deductive and inductive logic confront this skeptical challenge: we can justify any logical principle only by means of an argument but we can acquire justification by means of an argument only if we are already justified in believing some logical principle. We could solve this problem if probative arguments do not require justified belief in their corresponding conditionals. For if not, then inferential justification would not require justified belief in any logical principle. So even arguments whose corresponding conditionals are epistemically (...) dependent upon their conclusions--epistemically self-supporting arguments--need not be viciously circular. R. B. Braithwaite and James Van Cleve use internalist and externalist versions of this strategy in their proposed solutions to the problem of induction. Unfortunately, their arguments for self-support are unsound and any theory of inferential justification that does not require justified belief in the corresponding conditionals of justification-affording arguments is unacceptably arbitrary. So self-supporting arguments cannot be justification-creating. (shrink)

Bayesian confirmation theory, as traditionally interpreted, treats the temporal relationship between the formulation of a hypothesis and the confirmation (or recognition) of evidence entailed by that hypothesis merely as a component of the psychology of discovery and acceptance of a hypothesis. The temporal order of these events is irrelevant to the logic of rational theory choice. A few years ago Richmond Campbell and Thomas Vinci offered a reinterpretation of Bayes' Theorem in defense of the view that the temporal relationship between (...) hypothesis and evidence really does matter. More specifically, they advocated the thesis that successful predictions implied by scientific hypothesis H will increase the degree of confirmation of H only if they are novel predictions in the following sense; Evidence E is heuristically novel with respect to hypothesis H if and only if H was not deliberately designed to explain E (if E has already been corroborated) or in anticipation of E (if E is regarded as likely to be corroborated at some future date). Campbell and Vinci argue that the traditional interpretation of Bayes' Theorem misconstrues the significance of predictive novelty by ignoring heuristic novelty. In this paper I review the formal component of their preferred interpretation and demonstrate that it fails to establish that heuristic novelty has any special effect on theory confirmation. That is, even on their revisionist interpretation, regardless of whether H was deliberately designed to explain known evidence E (or in anticipation of suspected E), or whether H was designed without any awareness of the entailment relationship between H and E, Bayes' Theorem will generate the same epistemic probability for hypothesis H. Cases where new evidence was not foreseen at the time a hypothesis first emerged do not carry any more epistemic weight than they would have if such evidence had been foreseen. * Research on this paper was supported by an NEH summer grant. My thanks also to Richmond Campbell and Thomas Vinci for their reply to my initial evaluation of their position (in private correspondence), which compelled me to reconsider their arguments more carefully. (shrink)

Richmond Campbell and Thomas Vinci have recently presented a Bayesian theory of confirmation by novel evidence (Campbell and Vinci [1983]). I shall review their theory as briefly as possible and present three objections to it.

After delineating the distinguishing features of pragmatism, and noting the resources that pragmatists have available to respond effectively as pragmatists to the two major objections to pragmatism, I examine and critically evaluate the various proposals that pragmatists have offered as a solution to the problem of induction, followed by a discussion of the pragmatic positions on the status of theoretical entities. Thereafter I discuss the pragmatic posture toward the nature of explanation in science. I conclude that pragmatism has (a) a (...) generally compelling solution to Hume's problem of induction; (b) no specific position on the status of theoretical entities, although something like the non-realism of the sort developed by van Fraassen seems a defensible candidate for most pragmatists in general, even though there are non-trivial objections to van Fraassen's position; and (c) central to the pragmatic conception of scientific explanation is the abandonment of our common conception of truth as a necessary condition for sentences to provide adequate explanations, and a drift in the direction of a contextualist account of explanation. (shrink)

: Some feminist epistemologists make the radical claim that there are varieties of epistemically valid warrant that agents access only through having lived particular types of contingent history, varieties of epistemic warrant to which, moreover, the confirmation-theoretic accounts of warrant favored by some traditional epistemologists are inapplicable. I offer Aristotelian virtue as a model for warrant of this sort, and use loosely Aristotelian vocabulary to express, and begin to evaluate, a range of feminist epistemological positions.

Events between which we have no epistemic reason to discriminate have equal epistemic probabilities. Bertrand’s chord paradox, however, appears to show this to be false, and thereby poses a general threat to probabilities for continuum sized state spaces. Articulating the nature of such spaces involves some deep mathematics and that is perhaps why the recent literature on Bertrand’s Paradox has been almost entirely from mathematicians and physicists, who have often deployed elegant mathematics of considerable sophistication. At the same time, the (...) philosophy of probability has been left out. In particular, left out entirely are the philosophical ground of the principle of indifference, the nature of the principle itself, the stringent constraint this places on the mathematical representation of the principle needed for its application to continuum sized event spaces, and what these entail for rigour in developing the paradox itself. This book puts the philosophy and its entailments back in and in so doing casts a new light on the paradox, giving original analyses of the paradox, its possible solutions, the source of the paradox, the philosophical errors we make in attempting to solve it and what the paradox proves for the philosophy of probability. The book finishes with the author’s proposed solution—a solution in the spirit of Bertrand’s, indeed—in which an epistemic principle more general than the principle of indifference offers a principled restriction of the domain of the principle of indifference. (shrink)

Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the thermodynamic arrow of time can be grounded on typicality within statistical mechanics. This account, which I will call typicality frequentism, will evade the major criticisms raised against previous forms of frequentism. In this theory, probabilities arise within a physical theory from statistical (...) behavior of almost all initial conditions. The main advantage of typicality frequentism is that it shows which kinds of probabilities (that also have empirical relevance) can be derived from physics. Although one cannot recover all probability talk in this account, this is rather a virtue than a vice, because it shows which types of probabilities can in fact arise from physics and which types need to be explained in different ways, thereby opening the path for a pluralistic account of probabilities. (shrink)

Putnam construed the aim of Carnap’s program of inductive logic as the specification of a “universal learning machine,” and presented a diagonal proof against the very possibility of such a thing. Yet the ideas of Solomonoff and Levin lead to a mathematical foundation of precisely those aspects of Carnap’s program that Putnam took issue with, and in particular, resurrect the notion of a universal mechanical rule for induction. In this paper, I take up the question whether the Solomonoff–Levin proposal is (...) successful in this respect. I expose the general strategy to evade Putnam’s argument, leading to a broader discussion of the outer limits of mechanized induction. I argue that this strategy ultimately still succumbs to diagonalization, reinforcing Putnam’s impossibility claim. (shrink)

This paper is concerned with the problem of experimental error. The prevalent view that experimental errors can be dismissed as a tiresome but trivial blemish on the method of experimentation is criticized. It is stressed that the occurrence of errors in experiments constitutes a permanent feature of the attempt to test theories in the physical world, and this feature deserves proper attention. It is suggested that a classification of types of experimental error may be useful as a heuristic device in (...) studying the nature of these errors. However, the standard classification of systematic and random errors is mathematically based does not focus on the causes of the errors, their origins, or the contexts in which they arise. A new typology of experimental errors is therefore proposed whose criterion is epistemological. This typology reflects the various stages that can be discerned in the execution of an experiment, each stage constituting a category of a certain type of experimental error. The proposed classification consists of four categories which are illustrated by historical cases. (shrink)

A consensus exists among contemporary philosophers of biology about the history of their field. According to the received view, mainstream philosophy of science in the 1930s, 40s, and 50s focused on physics and general epistemology, neglecting analyses of the 'special sciences', including biology. The subdiscipline of philosophy of biology emerged (and could only have emerged) after the decline of logical positivism in the 1960s and 70s. In this article, I present bibliometric data from four major philosophy of science journals (Erkenntnis, (...) Philosophy of Science, Synthese, and the British Journal for the Philosophy of Science), covering 1930-59, which challenge this view. (shrink)

Das Thema dieses Bandes ist die Frage, ob die Wissenschaftstheorie eine normative Disziplin ist. Zunächst überrascht die Frage, denn für viele Wissenschaftstheoretiker ist die Antwort ein klares „Ja“; sie halten es für einen Allgemeinplatz, dass die Wissenschaftstheorie ein normatives Unternehmen ist. Bei genauerem Hinsehen stellt sich jedoch heraus, dass die Frage unterschiedliche Interpretationen zulässt, die einzeln diskutiert werden müssen. Dies geschieht im ersten Abschnitt. Im zweiten Abschnitt suchen wir nach möglichen Erklärungen dafür, warum die Wissenschaftstheorie bisher bei dem Projekt, eine (...) allseits akzeptable Methodologie wissenschaftlichen Schließens zu formulieren und zu begründen, so wenig Erfolg hatte. Eine mögliche Erklärung für den ausbleibenden Erfolg ist der Partikularismus, wonach Methoden keine allgemeine, sondern nur eine lokale, bereichsabhängige Gültigkeit haben. Im dritten Abschnitt wollen wir an Hand des Bayesianismus zeigen, dass die Methodologie doch nicht so schlecht da steht, wie es zunächst den Anschein hat. Der Bayesianismus ist für viele Wissenschaftstheoretiker der aussichtsreichste Kandidat für eine allgemeine Theorie induktiven Räsonierens. Wir besprechen seine Vorzüge, stellen aber auch dar, welche Konzessionen er an den Partikularismus machen muss. (shrink)

This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.

The dilemma objection charges that ‘weak’ versions of the precautionary principle (PP) are vacuous while ‘strong’ ones are incoherent. I respond that the ‘weak’ versus ‘strong’ distinction is misleading and should be replaced with a contrast between PP as a meta-rule and PP proper. Meta versions of PP require that the decision-making procedures used for environmental policy not be susceptible to paralysis by scientific uncertainty. Such claims are substantive because they often recommend against basing environmental policy decisions on cost–benefit analysis. (...) I argue that the second horn of the dilemma fails as a result of disregarding the role of proportionality in applications of PP. (shrink)

I conceive of inductive logic as a project of explication. The explicandum is one of the meanings of the word `probability' in ordinary language; I call it inductive probability and argue that it is logical, in a certain sense. The explicatum is a conditional probability function that is specified by stipulative definition. This conception of inductive logic is close to Carnap's, but common objections to Carnapian inductive logic (the probabilities don't exist, are arbitrary, etc.) do not apply to this conception.

In a formal theory of induction, inductive inferences are licensed by universal schemas. In a material theory of induction, inductive inferences are licensed by facts. With this change in the conception of the nature of induction, I argue that the celebrated “problem of induction” can no longer be set up and is thereby dissolved. Attempts to recreate the problem in the material theory of induction fail. They require relations of inductive support to conform to an unsustainable, hierarchical empiricism.

Arguably no concept is more fundamental to science than that of causality, for investigations into cases of existence, persistence, and change in the natural world are largely investigations into the causes of these phenomena. Yet the metaphysics and epistemology of causality remain unclear. For example, the ontological categories of the causal relata have been taken to be objects (Hume 1739), events (Davidson 1967), properties (Armstrong 1978), processes (Salmon 1984), variables (Hitchcock 1993), and facts (Mellor 1995). (For convenience, causes and effects (...) will usually be understood as events in what follows.) Complicating matters, causal relations may be singular (Socrates’s drinking hemlock caused Socrates’s death) or general (Drinking hemlock causes death); hence the relata might be tokens (e.g., instances of properties) or types (e.g., types of events) of the category in question. Other questions up for grabs are: Are singular causes metaphysically and/or epistemologically prior to general causes or vice versa (or neither)? What grounds the intuitive asymmetry of the causal relation? Are macro-causal relations reducible to micro-causal relations? And perhaps most importantly: Are causal facts (e.g., the holding of causal relations) reducible to non-causal facts (e.g., the holding of certain spatiotemporal relations)? (shrink)

Proponents of Bayesian confirmation theory believe that they have the solution to a significant, recalcitrant problem in philosophy of science. It is the identification of the logic that governs evidence and its inductive bearing in science. That is the logic that lets us say that our catalog of planetary observations strongly confirms Copernicus’ heliocentric hypothesis; or that the fossil record is good evidence for the theory of evolution; or that the 3oK cosmic background radiation supports big bang cosmology. The definitive (...) solution to this problem would be a significant achievement. The problem is of central importance to philosophy of science, for, in the end, what distinguishes science from myth making is that we have good evidence for the content of science, or at least of mature sciences, whereas myths are evidentially ungrounded fictions. The core ideas shared by all versions of Bayesian confirmation theory are, at a good first approximation, that a scientist’s beliefs are or should conform to a probability measure; and that the incorporation of new evidence is through conditionalization using Bayes’ theorem. While the burden of this chapter will be to inventory why critics believe this theory may not be the solution after all, it is worthwhile first to summarize here the most appealing virtues of this simple account. There are three. First, the theory reduces the often nebulous notion of a logic of.. (shrink)

This paper describes the corner-stones of a means-ends approach to the philosophy of inductive inference. I begin with a fallibilist ideal of convergence to the truth in the long run, or in the 'limit of inquiry'. I determine which methods are optimal for attaining additional epistemic aims (notably fast and steady convergence to the truth). Means-ends vindications of (a version of) Occam's Razor and the natural generalizations in a Goodmanian Riddle of Induction illustrate the power of this approach. The paper (...) establishes a hierarchy of means-ends notions of empirical success, and discusses a number of issues, results and applications of means-ends epistemology. (shrink)

This paper rejects a traditional epistemic interpretation of conditional probability. Suppose some chance process produces outcomes X, Y,..., with probabilities P(X), P(Y),... If later observation reveals that outcome Y has in fact been achieved, then the probability of outcome X cannot normally be revised to P(X|Y) ['P&Y)/P(Y)]. This can only be done in exceptional circumstances - when more than just knowledge of Y-ness has been attained. The primary reason for this is that the weight of a piece of evidence varies (...) with the means by which it is provided, so knowledge of Y-ness does not have uniform impact on the probability of X. A better updating of the probability of X is provided by P(X|Y*), where Y* is not an outcome of the chance process being observed, but the sentence 'the outcome Y has been observed', an 'outcome' of the subsequent observation process. This alternative formula is widely endorsed in practice, but not well recognized in theory, where the oversight has generated some unsatisfactory consequences. (shrink)

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that it (...) is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (shrink)

Predictivism asserts that novel confirmations carry special probative weight. Epistemic pluralism asserts that the judgments of agents (about, e.g., the probabilities of theories) carry epistemic import. In this paper, I propose a new theory of predictivism that is tailored to pluralistic evaluators of theories. I replace the orthodox notion of use-novelty with a notion of endorsement-novelty, and argue that the intuition that predictivism is true has two roots. I provide a detailed Bayesian rendering of this theory and argue that pluralistic (...) theory evaluation pervades scientific practice. I compare my account of predictivism with those of Maher and Worrall. Introduction Why construction is a red herring for pluralist evaluators The unvirtuous accommodator Virtuous endorsers and the two roots of predictivism The two roots in Bayesian terms: the priors and background beliefs of endorsers Who are the pluralist evaluators? Two contemporary theories of predictivism 7.1 Maher: Reliable methods of theory construction 7.2 Worrall: The confirmation of core ideas Conclusion. (shrink)

The debates between Bayesian, frequentist, and other methodologies of statistics have tended to focus on conceptual justifications, sociological arguments, or mathematical proofs of their long run properties. Both Bayesian statistics and frequentist (“classical”) statistics have strong cases on these grounds. In this article, we instead approach the debates in the “Statistics Wars” from a largely unexplored angle: simulations of different methodologies’ performance in the short to medium run. We conducted a large number of simulations using a straightforward decision problem based (...) around tossing a coin with unknown bias and then placing bets. In this simulation, we programmed four players, inspired by Bayesian statistics, frequentist statistics, Jon Williamson’s version of Objective Bayesianism, and a player who simply extrapolates from observed frequencies to general frequencies. The last player functions as a benchmark: a statistical methodology should at least outperform a crude form of induction. We focused on the performance of these methodologies in guiding the players towards good decisions. Unlike an earlier simulation study of this type, we found no systematic difference in performance between the Bayesian and frequentist players, provided the Bayesian used a flat prior and the frequentist used a low confidence level. Unlike that study, we were able to use Big Data methods to mitigate problems of random error in the simulation results. The Williamsonian player, who is a novel element of our study, also had no systematic differences in their performance, provided that they use a low confidence level. These players performed similarly even in the very short run, when players were making different decisions. Our study indicates that all three methodologies should be taken seriously by philosophers and practitioners of statistics. However, the frequentist and Williamsonian performed poorly when their confidence levels were high, and the Bayesian was surprisingly harmed by biased priors, providing some unexpected lessons for these methodologies when facing this type of decision problem. (shrink)

John D. Norton’s “Material Theory of Induction” has been one of the most intriguing recent additions to the philosophy of induction. Norton’s account appears to be a notably natural account of actual inductive practices, although his theory has attracted considerable criticism. I detail several novel issues for his theory but argue that supplementing the Material Theory with a theory of direct inference could address these problems. I argue that if this combination is possible, a stronger theory of inductive reasoning emerges, (...) which has a more propitious answer to the Problem of Induction. (shrink)

The word ‘probability’ in ordinary language has two different senses, here called inductive and physical probability. This paper examines the concept of inductive probability. Attempts to express this concept in other words are shown to be either incorrect or else trivial. In particular, inductive probability is not the same as degree of belief. It is argued that inductive probabilities exist; subjectivist arguments to the contrary are rebutted. Finally, it is argued that inductive probability is an important concept and that it (...) is a mistake to try to replace it with the concept of degree of belief, as is usual today. (shrink)

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be made on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the data deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative, or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

SummaryAfter presumably cleaning science of induction, Karl Popper claims to offer a purely noninductivist theory of science. In critically evaluating this theory, I focus on the allegedly noninductive character of this theory. First, I defend and expand Wesley Salmon's charge that Popper's dismissal of induction renders science useless for practical purposes. Without induction practitioners have no grounds for believing that the predicted event will actually take place. Second, despite Popper's demands to the contrary, his theory of science is shown to (...) rest on induction. In particular, the function he attributes to background knowledge in testing a scientific hypothesis requires induction. (shrink)

In October 2009 I decided to stop doing philosophy. This meant, in particular, stopping work on the book that I was writing on the nature of probability. At that time, I had no intention of making my unfinished draft available to others. However, I recently noticed how many people are reading the lecture notes and articles on my web site. Since this draft book contains some important improvements on those materials, I decided to make it available to anyone who wants (...) to read it. That is what you have in front of you. The account of Laplace’s theory of probability in Chapter 4 is very different to what I said in my seminar lectures, and also very different to any other account I have seen; it is based on a reading of important texts by Laplace that appear not to have been read by other commentators. The discussion of von Mises’ theory in Chapter 7 is also new, though perhaps less revolutionary. And the final chapter is a new attempt to come to grips with the popular, but amorphous, subjective theory of probability. The material in the other chapters has mostly appeared in previous articles of mine but things are sometimes expressed differently here. I would like to say again that this is an incomplete draft of a book, not the book I would have written if I had decided to finish it. It no doubt contains poor expressions, it may contain some errors or inconsistencies, and it doesn’t cover all the theories that I originally intended to discuss. Apart from this preface, I have done no work on the book since October 2009. (shrink)