An Introduction to Probability and Inductive Logic

The author gives admirable attention to clarity for the topics discussed in this book. As an introductory text, it's not reasonable to expect completeness for the more complex topics addressed. I highly recommend this book to anyone looking for an introduction to probability and inductive logic.

Maybe 1/3 of a college course in probability and statistics consists of a rapid trip, in math language, through basic conceptual ideas such as the interpretation of "probability", Bayes rule, significance tests and confidence intervals. This book, aimed at students of philosophy, treats this material and the associated math much more slowly and carefully -- relating probability to logic and philosophy, not just to math. For instance it has clear discussions of the principle of maximizing expected utility; the frequentist/Bayes philosophies and the coherence ideas emphasized by Bayesian apologists; the logic of significance tests and confidence intervals. Concepts are illustrated by creative selection of hypothetical story examples -- much more interesting than the usual math textbooks full of X's and Y's. The final 20 pages are a rather big jump toward technical philosophy -- arguing that both Bayesian and frequentist philosophies comprise "evasions" rather than "solutions" of "the problem of induction". For a textbook, rather than bedtime reading, on this material it is hard to imagine a better treatment. My only criticism -- perhaps a criticism of analytic philosophy in general -- is that it seems more concerned with teaching the reader how to critique other people's arguments that with teaching them how to say anything constructive about the real world.

This is a first rate introductory text prepared by a well known philosopher and expert on the logic and history of probability & statistics. The approach is disarmingly simple. Hacking avoids complicated math and proofs and teaches via the intuitive appeals to the underlying logic of these topics. Hacking begins with an intuitively based discussion of basic features of probability theory, expectation, Bayes rule, and decision analysis. This is followed by a particularly good exposition of the different senses of probability; belief-Bayesian and frequentist. Hacking shows how both approaches can be used fruitfully and rigorously in even mundane problems. These sections are followed by very nice chapters on the underlying logic of normal distributions, statistical hypothesis testing, and confidence intervals. This is the diametrical opposite of the cookbook approach used often in many statistics books and provides very nice understanding of key features of statistical methods. I never appreciated the strength of the confidence interval approach before reading this book. Hacking concludes with some concise but thoughtful chapters on the philosophical implications of these ideas, particularly as applied to the classic problem of induction. The quality of writing is excellent and the book features a large number of good examples and problems to work through. Strongly recommended to individuals who want to learn more about the basis of statistical methods.

Hacking's book is a job well done.He blends history,philosophy,logic,mathematics,statistics and science with wit and judicious scrutiny in general.Unfortunately,the book is slightly marred by inaccurate and/or incorrect statements about J. M. Keynes and/or his logical theory of probability.Describing Keynes as a"belief dogmatist"is way off the mark given Keynes's penchant for changing his mind as new and/or relevant information and analysis became available over his lifetime.Secondly,it is bizarre for Hacking to claim that Keynes had no use for frequency-type probability theories and jeered at the idea of relative frequency holding in the long run because in the long run we are all dead.(Hacking,pp.146-151).The only frequency theory Keynes ever rejected was that of John Venn.Keynes always considered frequency theories to be accurate and correct for some cases.However,they were not general in scope but limited in their applicability.The interested reader should consult chapter 8 of Keynes's A Treatise on Probability(1921).Finally, Keynes rejected the fallacy of long runism or conditional apriorism because of its unsound argument.The fact that in the long run some process may converge to a particular outcome in the limit offers no support to a do-nothing policy in the present.If the only available relevant evidence bearing on the probability of a proposition is frequency data then the logical probability is the same as the relative frequency estimate.The only caveat Keynes would add would be that the frequency data should have passed the Lexis Q Test for stability.

I would HIGHLY recommend this book for anyone (including business men) who must make decisions with incomplete information and under uncertainty. Instead of focusing on the mechanics of statistics, it focuses on how to think about risky propositions.I bought this book while working on a particular problem in machine learning, at a point where I had started realizing that I was losing clarity on my definition of probability. I was using the mechanics, but didn't clearly understand why the use was valid. This seemed an odd and embarrassing circumstance at the time, how could I not understand what "probability" means? As it turns out this confusion is one shared broadly in history of science, and in current applications of statistical mechanics.Prof Hacking's writing is clear and entertaining, clearly aimed at engaging the reading audience.