Statistical Explanation and Statistical Relevance

University of Pittsburgh Pre
Free sample

According to modern physics, many objectively improbable events actually occur, such as the spontaneous disintegration of radioactive atoms. Because of high levels of improbability, scientists are often at a loss to explain such phenomena. In this main essay of this book, Wesley Salmon offers a solution to scientific explanation based on the concept of statistical relevance (the S-R model). In this vein, the other two essays herein discuss “Statistical Relevance vs. Statistical Inference,” and “Explanation and Information.”
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About the author

Wesley C. Salmon was University Professor of Philosophy at the University of Pittsburgh, past president of the Philosophy of Science Association, and the author of numerous books, including: Four Decades of Scientific Explanation; The Foundations of Scientific Inference; Space, Time, and Motion: A Philosophical Introduction; and Scientific Explanation.
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Additional Information

Publisher
University of Pittsburgh Pre
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Published on
Sep 15, 1971
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Pages
128
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ISBN
9780822974116
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Language
English
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Genres
Philosophy / General
Philosophy / Logic
Science / Philosophy & Social Aspects
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Content Protection
This content is DRM protected.
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In May of 1973 we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the University of Western Ontario. During the past four decades there have been striking formal advances in our understanding of logic, semantics and algebraic structure in probabilistic and statistical theories. These advances, which include the development of the relations between semantics and metamathematics, between logics and algebras and the algebraic-geometrical foundations of statistical theories (especially in the sciences), have led to striking new insights into the formal and conceptual structure of probability and statistical theory and their scientific applications in the form of scientific theory. The foundations of statistics are in a state of profound conflict. Fisher's objections to some aspects of Neyman-Pearson statistics have long been well known. More recently the emergence of Bayesian statistics as a radical alternative to standard views has made the conflict especially acute. In recent years the response of many practising statisticians to the conflict has been an eclectic approach to statistical inference. Many good statisticians have developed a kind of wisdom which enables them to know which problems are most appropriately handled by each of the methods available. The search for principles which would explain why each of the methods works where it does and fails where it does offers a fruitful approach to the controversy over foundations.
This work breaks new ground by carefully distinguishing the concepts of belief, confirmation, and evidence and then integrating them into a better understanding of personal and scientific epistemologies. It outlines a probabilistic framework in which subjective features of personal knowledge and objective features of public knowledge have their true place. It also discusses the bearings of some statistical theorems on both formal and traditional epistemologies while showing how some of the existing paradoxes in both can be resolved with the help of this framework.This book has two central aims: First, to make precise a distinction between the concepts of confirmation and evidence and to argue that failure to recognize this distinction is the source of certain otherwise intractable epistemological problems. The second goal is to demonstrate to philosophers the fundamental importance of statistical and probabilistic methods, at stake in the uncertain conditions in which for the most part we lead our lives, not simply to inferential practice in science, where they are now standard, but to epistemic inference in other contexts as well. Although the argument is rigorous, it is also accessible. No technical knowledge beyond the rudiments of probability theory, arithmetic, and algebra is presupposed, otherwise unfamiliar terms are always defined and a number of concrete examples are given. At the same time, fresh analyses are offered with a discussion of statistical and epistemic reasoning by philosophers. This book will also be of interest to scientists and statisticians looking for a larger view of their own inferential techniques.The book concludes with a technical appendix which introduces an evidential approach to multi-model inference as an alternative to Bayesian model averaging.
The Freakonomics of math—a math-world superstar unveils the hidden beauty and logic of the world and puts its power in our hands

The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.

Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?

How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.

Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
For over two decades Wesley Salmon has helped to shape the course of debate in philosophy of science. He is a major contributor to the philosophical discussion of problems associated with causality and the author of two influential books on scientific explanation. This long-awaited volume collects twenty- six of Salmon's essays, including seven that have never before been published and others difficult to find. Part I comprises five introductory essays that presuppose no formal training in philosophy of science and form a background for subsequent essays. Parts II and III contain Salmon's seminal work on scientific explanation and causality. Part IV offers survey articles that feature advanced material but remain accessible to those outside philosophy of science. Essays in Part V address specific issues in particular scientific disciplines, namely, archaeology and anthropology, astrophysics and cosmology, and physics. Clear, compelling, and essential, this volume offers a superb introduction to philosophy of science for nonspecialists and belongs on the bookshelf of all who carry out work in this exciting field. Wesley Salmon is renowned for his seminal contributions to the philosophy of science. He has powerfully and permanently shaped discussion of such issues as lawlike and probabilistic explanation and the interrelation of explanatory notions to causal notions. This unique volume brings together twenty-six of his essays on subjects related to causality and explanation, written over the period 1971-1995. Six of the essays have never been published before and many others have only appeared in obscure venues. The volume includes a section of accessible introductory pieces, as well as more advanced and technical pieces, and will make essential work in the philosophy of science readily available to both scholars and students.
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