Scientific reasoning is—and ought to be—conducted in accordance with the axioms of probability. This Bayesian view—so called because of the central role it accords to a theorem first proved by Thomas Bayes in the late eighteenth ...

Attempts to show that the simplicity of a hypothesis can be measured by attending to how well it answers certain kinds of questions.

This text provides a critique of the subjective Bayesian view of statistical inference, and proposes the author's own error-statistical approach as an alternative framework for the epistemology of experiment. It seeks to address the needs of researchers who work with statistical analysis.

Attempts to show that the simplicity of a hypothesis can be measured by attending to how well it answers certain kinds of questions.

Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...) we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism. (shrink)

Leplin attempts to reinstate the common sense idea that theoretical knowledge is achievable, indeed that its achievement is part of the means to progress in empirical knowledge. He sketches the genesis of the skeptical position, then introduces his argument for Minimalist Scientific Realism -- the requirement that novel predicitons be explained, and the claim that only realism about scientific theories can explain the importance of novel prediction.

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 underdetermination of theory by evidence must be distinguished from holism. The latter is a doctrine about the testing of scientific hypotheses; the former is a thesis about empirically adequate logically incompatible global theories or "systems of the world". The distinction is crucial for an adequate assessment of the underdetermination thesis. The paper shows how some treatments of underdetermination are vitiated by failure to observe this distinction, and identifies some necessary conditions for the existence of multiple empirically equivalent global theories. (...) We consider how empiricists should respond to the possibility of such systems of the world. (shrink)

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)

Bayes's theorem is a tool for assessing how probable evidence makes some hypothesis. The papers in this volume consider the worth and applicability of the theorem. Richard Swinburne sets out the philosophical issues. Elliott Sober argues that there are other criteria for assessing hypotheses. Colin Howson, Philip Dawid and John Earman consider how the theorem can be used in statistical science, in weighing evidence in criminal trials, and in assessing evidence for the occurrence of miracles. David Miller argues for the (...) worth of the probability calculus as a tool for measuring propensities in nature rather than the strength of evidence. The volume ends with the original paper containing the theorem, presented to the Royal Society in 1763. (shrink)

We introduce a distinction, unnoticed in the literature, between four varieties of objective Bayesianism. What we call ' strong objective Bayesianism' is characterized by two claims, that all scientific inference is 'logical' and that, given the same background information two agents will ascribe a unique probability to their priors. We think that neither of these claims can be sustained; in this sense, they are 'dogmatic'. The first fails to recognize that some scientific inference, in particular that concerning evidential relations, is (...) not (in the appropriate sense) logical, the second fails to provide a non-question-begging account of 'same background information'. We urge that a suitably objective Bayesian account of scientific inference does not require either of the claims. Finally, we argue that Bayesianism needs to be fine-grained in the same way that Bayesians fine-grain their beliefs. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship (...) between simplicity of a theory and its predictive accuracy. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to BTC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that AIC approach (...) has shortcomings. We also discuss the relationship between Schwarz's Bayesian Information Criterion and BTC. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes’ theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory’s goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship (...) between simplicity of a theory and its predictive accuracy. (shrink)

Elliott Sober is both an empiricist and an instrumentalist. His empiricism rests on a principle called actualism, whereas his instrumentalism violates this. This violation generates a tension in his work. We argue that Sober is committed to a conflicting methodological imperative because of this tension. Our argument illuminates the contemporary debate between realism and empiricism which is increasingly focused on the application of scientific inference to testing scientific theories. Sober’s position illustrates how the principle of actualism drives a wedge between (...) two conceptions of scientific inference and at the same time brings to the surface a deep conflict between empiricism and instrumentalism. (shrink)

The notion of a severe test has played an important methodological role in the history of science. But it has not until recently been analyzed in any detail. We develop a generally Bayesian analysis of the notion, compare it with Deborah Mayo’s error-statistical approach by way of sample diagnostic tests in the medical sciences, and consider various objections to both. At the core of our analysis is a distinction between evidence and confirmation or belief. These notions must be kept separate (...) if mistakes are to be avoided; combined in the right way, they provide an adequate understanding of severity. Those who think that the weight of the evidence always enables you to choose between hypotheses “ignore one of the factors (the prior probability) altogether, and treat the other (the likelihood) as though it ...meant something other than it actually does. This is the same mistake as is made by someone who has scruples about measuring the arms of a balance (having only a tape measure at his disposal ...), but is willing to assert that the heavier load will always tilt the balance (thereby implicitly assuming, although without admitting it, that the arms are of equal length!). (Bruno de Finetti, Theory of Probability)2. (shrink)

This book offers a superbly clear analysis of the standard arguments for and against scientific realism. In surveying claims on both sides of the debate, Kukla organizes them in ways that expose unnoticed connections. He identifies broad patterns of error, reconciles seemingly incompatible positions, and discovers unoccupied positions with the potential to influence further debate. Kukla's overall assessment is that neither the realists nor the antirealists may claim a decisive victory.

This landmark collection of essays by six renowned philosophers explores the implications of the contentious realism/antirealism debate for epistemology. The essays examine issues such as whether epistemology needs to be realist, the bearing of a realist conception of truth on epistemology, and realism and antirealism in terms of a pragmatist conception of epistemic justification. Richard Rorty's essay provides a critical commentary on the other five.

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

Elliott Sober is one of the leading philosophers of science and is a former winner of the Lakatos Prize, the major award in the field. This new collection of essays will appeal to a readership that extends well beyond the frontiers of the philosophy of science. Sober shows how ideas in evolutionary biology bear in significant ways on traditional problems in philosophy of mind and language, epistemology, and metaphysics. Amongst the topics addressed are psychological egoism, solipsism, and the interpretation of (...) belief and utterance, empiricism, Ockham's razor, causality, essentialism, and scientific laws. The collection will prove invaluable to a wide range of philosophers, primarily those working in the philosophy of science, the philosophy of mind, and epistemology. (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.

This chapter introduces the definitions of the notion of a random sequence using the three main ideas described that have dominated algorithmic randomness. There are three key approaches for defining randomness in sequences: unpredictability, typicality, and incompressibility. A notion is set up notation for strings and sequences, the Cantor Space, which forms the basic framework for carrying out further discussions, and contains a brief and informal introduction to Lebesgue measure on the unit interval and the Cantor space, which one treats (...) as equivalent. Discussion of mathematical randomness defines a series of classical stochastic or frequency properties in an effort to distill out randomness. This chapter further forms the core material on algorithmic randomness: Von Mises randomness, Martin-Lof randomness, Kolmogorov complexity and randomness of finite strings, application to Godel incompleteness, and Schnorr's theorem. It forms an overview of other forms of related randomness notions that have been studied and indicates the current state of affairs. (shrink)

According to the underdetermination thesis, all evidence necessarily underdetermines any scientific theory. Thus it is often argued that our agreement on the content of mature scientific theories must be due to social and other factors. Drawing on a long standing tradition of criticism, I shall argue that the underdetermination thesis is little more than speculation based on an impoverished account of induction. A more careful look at accounts of induction does not support an assured underdetermination or the holism usually associated (...) with it. I also urge that the display of observationally equivalent theories is a self-defeating strategy for supporting the underdetermination thesis. The very fact that observational equivalence can be demonstrated by arguments brief enough to be included in a journal article means that we cannot preclude the possibility that the theories are merely variant formulations of the same theory. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the relationship (...) between simplicity of a theory and its predictive accuracy. (shrink)