Objective Bayesianism is a methodological theory that is currently applied in statistics, philosophy, artificial intelligence, physics and other sciences. This book develops the formal and philosophical foundations of the theory, at a level accessible to a graduate student with some familiarity with mathematical notation.

Not since Ernest Nagel’s 1939 monograph on the theory of probability has there been a comprehensive elementary survey of the philosophical problems of probablity and induction. This is an authoritative and up-to-date treatment of the subject, and yet it is relatively brief and nontechnical. Hume’s skeptical arguments regarding the justification of induction are taken as a point of departure, and a variety of traditional and contemporary ways of dealing with this problem are considered. The author then sets forth his own (...) criteria of adequacy for interpretations of probability. Utilizing these criteria he analyzes contemporary theories of probability, as well as the older classical and subjective interpretations. (shrink)

This book is devoted to a different proposal--that the logical structure of the scientist's method should guarantee eventual arrival at the truth given the scientist's background assumptions.

Traditional analyses of the curve fitting problem maintain that the data do not indicate what form the fitted curve should take. Rather, this issue is said to be settled by prior probabilities, by simplicity, or by a background theory. In this paper, we describe a result due to Akaike [1973], which shows how the data can underwrite an inference concerning the curve's form based on an estimate of how predictively accurate it will be. We argue that this approach throws light (...) on the theoretical virtues of parsimoniousness, unification, and non ad hocness, on the dispute about Bayesianism, and on empiricism and scientific realism. * Both of us gratefully acknowledge support from the Graduate School at the University of Wisconsin-Madison, and NSF grant DIR-8822278 (M.F.) and NSF grant SBE-9212294 (E.S.). Special thanks go to A. W. F. Edwards.William Harper. Martin Leckey. Brian Skyrms, and especially Peter Turney for helpful comments on an earlier draft. (shrink)

A class of problems is called decidable if there is an algorithm which will give the answer to any problem of the class after a finite length of time. The purpose of this paper is to discuss the classes of problems that can be solved by infinitely long decision procedures in the following sense: An algorithm is given which, for any problem of the class, generates an infinitely long sequence of guesses. The problem will be said to be solved in (...) the limit if, after some finite point in the sequence, all the guesses are correct and the same. Functions, sets, and functionals which are decidable by such infinite algorithms will be calledlimiting recursive. These, together with classes of objects which can beidentified in the limit, are the subjects of this report.Without qualification,setwill mean set of numbers;functionwill mean number-theoretic function of 1 variable, possibly partial;functionalswill take numerical values and have any number of numerical and/or function variables, the latter ranging solely over total functions of 1 variable. Thus a function is a special case of a functional,xwill invariably stand for a numerical variable;φfor a function variable;gfor a guess ;nfor the numerical variable which indexes the guesses, referred to as thetime. (shrink)

Ockham’s razor is the characteristic scientific penchant for simpler, more testable, and more unified theories. Glymour’s early work on confirmation theory eloquently stressed the rhetorical plausibility of Ockham’s razor in scientific arguments. His subsequent, seminal research on causal discovery still concerns methods with a strong bias toward simpler causal models, and it also comes with a story about reliability—the methods are guaranteed to converge to true causal structure in the limit. However, there is a familiar gap between convergent reliability and (...) scientific rhetoric: convergence in the long run is compatible with any conclusion in the short run. For that reason, Carnap suggested that the proper sense of reliability for scientific inference should lie somewhere between short-run reliability and mere convergence in the limit. One natural such concept is straightest possible convergence to the truth, where straightness is explicated in terms of minimizing reversals of opinion and cycles of opinion prior to convergence. We close the gap between scientific rhetoric and scientific reliability by showing that Ockham’s razor is necessary for cycle-optimal convergence to the truth, and that patiently waiting for information to resolve conflicts among simplest hypotheses is necessary for reversal-optimal convergence to the truth. (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)

A Photcopy of Thinking Things Through, Princeton Univeresity Press, 1980.

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought. New preface and new footnotes to 1954 edition, with a supplementary 180-item annotated bibliography by author. Calculus, probability, statistics, and Boolean algebra are recommended.

Here is the usual way philosophers think about science and induction. Scientists do many things— aspire, probe, theorize, conclude, retract, and refine— but successful research culminates in a published research report that presents an argument for some empirical conclusion. In mathematics and logic there are sound deductive arguments that fully justify their conclusions, but such proofs are unavailable in the empirical domain because empirical hypotheses outrun the evidence adduced for them. Inductive skeptics insist that such conclusions cannot be justified. But (...) “justification” is a vague term— if empirical conclusions cannot be established fully, as mathematical conclusions are, perhaps they are justified in the sense that they are partially supported or confirmed by the available evidence. To respond to the skeptic, one merely has to explicate the concept of confirmation or partial justification in a systematic manner that agrees, more or less, with common usage and to observe that our scientific conclusions are confirmed in the explicated sense. This process of explication is widely thought to culminate in some version of Bayesian confirmation theory. (shrink)

The problem of theory choice and model selection is hard but still important when useful truths are underdetermined, perhaps not by all kinds of data but by the kinds of data we can have access to ethically or practicably—even if we have an infinity of such data. This article addresses a crucial instance of that problem: the problem of inferring causal structures from nonexperimental, nontemporal data without assuming the so-called causal Faithfulness condition or the like. A new account of epistemic (...) evaluation is developed to solve that problem and justify a standard practice of causal inference in data science. (shrink)

A U-shaped curve in a cognitive-developmental trajectory refers to a three-step process: good performance followed by bad performance followed by good performance once again. U-shaped curves have been observed in a wide variety of cognitive-developmental and learning contexts. U-shaped learning seems to contradict the idea that learning is a monotonic, cumulative process and thus constitutes a challenge for competing theories of cognitive development and learning. U-shaped behavior in language learning (in particular in learning English past tense) has become a central (...) topic in the Cognitive Science debate about learning models. Antagonist models (e.g., connectionism versus nativism) are often judged on their ability of modeling or accounting for U-shaped behavior. The prior literature is mostly occupied with explaining how U-shaped behavior occurs. Instead, we are interested in the necessity of this kind of apparently inefficient strategy. We present and discuss a body of results in the abstract mathematical setting of (extensions of) Gold-style computational learning theory addressing a mathematically precise version of the following question: Are there learning tasks that require U-shaped behavior? All notions considered are learning in the limit from positive data. We present results about the necessity of U-shaped learning in classical models of learning as well as in models with bounds on the memory of the learner. The pattern emerges that, for parameterized, cognitively relevant learning criteria, beyond very few initial parameter values, U-shapes are necessary for full learning power! We discuss the possible relevance of the above results for the Cognitive Science debate about learning models as well as directions for future research. (shrink)

The problem of induction reminds us that science cannot wait for empirical hypotheses to be verified and Duhem’s problem reminds us that we cannot expect full refutations either. We must settle for something less. The shape of this something less depends on which features of full verification and refutation we choose to emphasize. If we conceive of verification and refutation as arguments in which evidence entails the hypothesis or its negation, then the central problem of the philosophy of science is (...) to explicate a relation of confirmation or support that is weaker than full entailment but which serves, nonetheless, to justify empirical conclusions. (shrink)

The purpose of this paper is to explore a new deontic operator for representing what an agent ought to do; the operator is cast against the background of a modal treatment of action developed by Nuel Belnap and Michael Perlo, which itself relies on Arthur Prior's indeterministic tense logic. The analysis developed here of what an agent ought to do is based on a dominance ordering adapted from the decision theoretic study of choice under uncertainty to the present account of (...) action. It is shown that this analysis gives rise to a normal deontic operator, and that the result is superior to an analysis that identi es what an agent ought to do with what it ought to be that the agent does. (shrink)

Consider the problem of learning, from non-experimental data, the causal (Markov equivalence) structure of the true, unknown causal Bayesian network (CBN) on a given, fixed set of (categorical) variables. This learning problem is known to be very hard, so much so that there is no learning algorithm that converges to the truth for all possible CBNs (on the given set of variables). So the convergence property has to be sacrificed for some CBNs—but for which? In response, the standard practice has (...) been to design and employ learning algorithms that secure the convergence property for at least all the CBNs that satisfy the famous faithfulness condition, which implies sacrificing the convergence property for some CBNs that violate the faithfulness condition (Spirtes, Glymour, and Scheines, 2000). This standard design practice can be justified by assuming—that is, accepting on faith—that the true, unknown CBN satisfies the faithfulness condition. But the real question is this: Is it possible to explain, without assuming the faithfulness condition or any of its weaker variants, why it is mandatory rather than optional to follow the standard design practice? This paper aims to answer the above question in the affirmative. We first define an array of modes of convergence to the truth as desiderata that might or might not be achieved by a causal learning algorithm. Those modes of convergence concern (i) how pervasive the domain of convergence is on the space of all possible CBNs and (ii) how uniformly the convergence happens. Then we prove a result to the following effect: for any learning algorithm that tackles the causal learning problem in question, if it achieves the best achievable mode of convergence (considered in this paper), then it must follow the standard design practice of converging to the truth for at least all CBNs that satisfy the faithfulness condition—it is a requirement, not an option. (shrink)

In this first English translation the author has included all of the original text and has added new footnotes, preface, and 150 more pages of text. The new material is conveniently starred. A monumental work which develops the view Popper calls "deductivism" --the theory of the deductive method of testing.--J. E. M.