Models are of central importance in many scientific contexts. The centrality of models such as inflationary models in cosmology, general-circulation models of the global climate, the double-helix model of DNA, evolutionary models in biology, agent-based models in the social sciences, and general-equilibrium models of markets in their respective domains is a case in point (the Other Internet Resources section at the end of this entry contains links to online resources that discuss these models). Scientists spend significant amounts of time building, (...) testing, comparing, and revising models, and much journal space is dedicated to interpreting and discussing the implications of models. In short, models are one of the principal instruments of modern science. (shrink)

The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

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 ...

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

Preface. I. BASICS OF LOGIC. Introduction. The Structure of Simple Statements. The Structure of Complex Statements. Simple and Complex Properties. Validity. 2. PROBABILITY AND INDUCTIVE LOGIC. Introduction. Arguments. Logic. Inductive versus Deductive Logic. Epistemic Probability. Probability and the Problems of Inductive Logic. 3. THE TRADITIONAL PROBLEM OF INDUCTION. Introduction. Hume’s Argument. The Inductive Justification of Induction. The Pragmatic Justification of Induction. Summary. IV. THE GOODMAN PARADOX AND THE NEW RIDDLE OF INDUCTION. Introduction. Regularities and Projection. The Goodman Paradox. The Goodman (...) Paradox, Regularity, and the Principle of the Uniformity of Nature. Summary. 5. MILL’S METHODS OF EXPERIMENTAL INQUIRY AND THE NATURE OF CAUSALITY. Introduction. Causality and Necessary and Sufficient Conditions. Mill’s Methods. The Direct Method of Agreement. The Inverse Method of Agreement. The Method of Difference. The Combined Methods. The Application of Mill’s Methods. Sufficient Conditions and Functional Relationships. Lawlike and Accidental Conditions. 6. THE PROBABILITY CALCULUS. Introduction. Probability, Arguments, Statements, and Properties. Disjunction and Negation Rules. Conjunction Rules and Conditional Probability. Expected Value of a Gamble. Bayes’ Theorem. Probability and Causality. 7. KINDS OF PROBABILITY. Introduction. Rational Degree of Belief. Utility. Ramsey. Relative Frequency. Chance. 8. PROBABILITY AND SCIENTIFIC INDUCTIVE LOGIC. Introduction. Hypothesis and Deduction. Quantity and Variety of Evidence. Total Evidence. Convergence to the Truth. ANSWERS TO SELECTED EXERCISES. INDEX. (shrink)

This paper is an essay review of Steven French and Harmke Kamminga (eds.), Correspondence, Invariance and Heuristics. Essays in Honour of Heinz Post (Dordrecht: Kluwer, 1993). I distinguish a varity of correspondence relations between scientific theories (exemplified by cases from the book under review) and examine how one can make sense of the the prevailing continuity in scientific theorizing.

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)

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

In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usual, on the probability but on the confirmation of a coherent set and its members. We show that, if evidence confirms a hypothesis, confirmation is “transmitted” to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson’s or Fitelson’s measure. Our findings have (...) implications for scientific methodology, as they provide a formal rationale for the method of indirect confirmation and the method of confirming theories by confirming their parts. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

In this pithy and highly readable book, Brian Skyrms, a recognised authority on game and decision theory, investigates traditional problems of the social contract in terms of evolutionary dynamics. Game theory is skilfully employed to offer new interpretations of a wide variety of social phenomena, including justice, mutual aid, commitment, convention and meaning. The author eschews any grand, unified theory. Rather, he presents the reader with tools drawn from evolutionary game theory for the purpose of analysing and coming to understand (...) the social contract. The book is not technical and requires no special background knowledge. As such, it could be enjoyed by students and professionals in a wide range of disciplines: political science, philosophy, decision theory, economics and biology. (shrink)

Models as Mediators discusses the ways in which models function in modern science, particularly in the fields of physics and economics. Models play a variety of roles in the sciences: they are used in the development, exploration and application of theories and in measurement methods. They also provide instruments for using scientific concepts and principles to intervene in the world. The editors provide a framework which covers the construction and function of scientific models, and explore the ways in which they (...) enable us to learn about both theories and the world. The contributors to the volume offer their own individual theoretical perspectives to cover a wide range of examples of modelling, from physics, economics and chemistry. These papers provide ideal case-study material for understanding both the concepts and typical elements of modelling, using analytical approaches from the philosophy and history of science. (shrink)

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)

The Tanner Lectures are a collection of educational and scientific discussions relating to human values. Conducted by leaders in their fields, the lectures are presented at prestigious educational facilities around the world.

Fundamental theories are hard to come by. But even if we had them, they would be too complicated to apply. Quantum chromodynamics is a case in point. This theory is supposed to govern all strong interactions, but it is extremely hard to apply and test at energies where protons, neutrons and ions are the effective degrees of freedom. Instead, scientists typically use highly idealized models such as the MIT Bag Model or the Nambu Jona-Lasinio Model to account for phenomena in (...) this domain, to explain them and to gain nderstanding. Based on these models, which typically isolate a single feature of QCD and disregard many others, scientists attempt to get a better understanding of the physics of strong interactions. But does this practice make sense? Is it justified to use these models for the purposes at hand? Interestingly, these models do not even provide an accurate description of the mass spectrum of protons, neutrons and pions and their lowest lying excitations well - despite several adjustable parameters. And yet, the models are heavily used. I'll argue that a qualitative story, which establishes an explanatory link between the fundamental theory and a model, plays an important role in model acceptance in these cases. (shrink)