This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability is a mode of judgment. Written by one of the greatest figures in the field of probability theory, the book is both a summation and synthesis of a lifetime of wrestling with these problems and issues. After an introduction to basic probability theory, there are chapters on scientific hypothesis-testing, on changing your mind in response to generally uncertain observations, on expectations of (...) the values of random variables, on de Finetti's dissolution of the so-called problem of induction, and on decision theory. (shrink)
Richard Jeffrey is beyond dispute one of the most distinguished and influential philosophers working in the field of decision theory and the theory of knowledge. His work is distinctive in showing the interplay of epistemological concerns with probability and utility theory. Not only has he made use of standard probabilistic and decision theoretic tools to clarify concepts of evidential support and informed choice, he has also proposed significant modifications of the standard Bayesian position in order that it provide a better (...) fit with actual human experience. Probability logic is viewed not as a source of judgment but as a framework for explaining the implications of probabilistic judgments and their mutual compatability. This collection of essays spans a period of some 35 years and includes what have become some of the classic works in the literature. There is also one completely new piece, while in many instances Jeffrey includes afterthoughts on the older essays. (shrink)
Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a (...) simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual. (shrink)
Personalistic Bayesian decision theory provides a simple, roomy framework for hypothesis-testing and choice under uncertainty. Call the theory Bayesianism, for short. It’s the line that L. J. Savage made respectable among statisticians and economists. It’s the same thing as the expected utility hypothesis, in this form: preference does or should go by personal probabilistic expectation of utility. The question of whether to say “does” or “should” is the question of whether the theory is meant to be normative or descriptive.
This brief paperback is designed for symbolic/formal logic courses. It features the tree method proof system developed by Jeffrey. The new edition contains many more examples and exercises and is reorganized for greater accessibility.
In the social sciences norms are sometimes taken to play a key explanatory role. Yet norms differ from group to group, from society to society, and from species to species. How are norms formed and how do they change? This 'state-of-the-art' collection of essays presents some of the best contemporary research into the dynamic processes underlying the formation, maintenance, metamorphosis and dissolution of norms. The volume combines formal modelling with more traditional analysis, and considers biological and cultural evolution, individual learning, (...) and rational deliberation. In filling a significant gap in the current literature this volume will be of particular interest to economists, political scientists and sociologists, in addition to philosophers of the social sciences. (shrink)
The approach to decision theory floated in my 1965 book is reviewed (I), challenged in various related ways (II–V) and defended, firstad hoc (II–IV) and then by a general argument of Ellery Ells's (VI). Finally, causal decision theory (in a version sketched in VII) is exhibited as a special case of my 1965 theory, according to the Eellsian argument.
Logicism Lite counts number‐theoretical laws as logical for the same sort of reason for which physical laws are counted as as empirical: because of the character of the data they are responsible to. In the case of number theory these are the data verifying or falsifying the simplest equations, which Logicism Lite counts as true or false depending on the logical validity or invalidity of first‐order argument forms in which no numbertheoretical notation appears.
Isaac Levi and I have different views of probability and decision making. Here, without addressing the merits, I will try to answer some questions recently asked by Levi (1985) about what my view is, and how it relates to his.
The Sure Thing Principle (1), Dominance Principle (2), and Strong Independence Axiom (3) have been attacked and defended in various ways over the past 30 years. In the course of a survey of some of that literature, it is argued that these principles are acceptable iff suitably qualified.
From a point of view like de Finetti's, what is the judgmental reality underlying the objectivistic claim that a physical magnitude X determines the objective probability that a hypothesis H is true? When you have definite conditional judgmental probabilities for H given the various unknown values of X, a plausible answer is sufficiency, i.e., invariance of those conditional probabilities as your probability distribution over the values of X varies. A different answer, in terms of conditional exchangeability, is offered for use (...) when such definite conditional probabilities are absent. (shrink)