An Introduction to Probability and Inductive Logic

Rating:
Summary: Hacking gets everything right except for Keynes
Review: 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.

Rating:
Summary: For anyone, any thinker
Review: 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.

Rating:
Summary: For anyone, any thinker
Review: 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.

Rating:
Summary: What do you mean, "probably"?
Review: The best thing about this book is that it teachs basic probability theory while keeping the reader constantly aware of the on-going debate regarding what it means to talk in terms of probabilities, and of how that debate has shaped the development of probability theory. If you are a student taking a course in probability and statistics who would like to genuinely understand the conceptual basis of all those formulas they are teaching you, I suggest you read this book.

Some readers will be disappointed by this book. Since the book concentrates on the conceptual basis of probability and inductive logic, it does not give the reader enough technical tools to really do much applied mathematics. On the other hand, by the time Hacking gets around to discussing what students of philosophy will likely view as the big philosophical pay-off of probability theory (i.e. Bayesian and frequentist contributions to the problem of justifying induction) he devotes to them a mere 20 pages of not terribly deep discussion.