And this paper is an attempt to say precisely how, thus addressing a philosophical problem which is commonly taken to be a serious one. It does so, however, in quite an idiosyncratic way. It is based on the account of inductive schemes I have given in (1988) and (1990a) and on the conception of causation I have presented in (1980), (1983), and (1990b), and it intends to fill one of many gaps which have been left by these papers. Still, I (...) have tried to make this paper self-contained. Section 1 explains the philosophical question this paper is about; in more general terms it asks what might be meant by objectifying epistemic states or features of them and to which extent epistemic states can be objectified. The next sections introduce the basis I rely on with formal precision and some explanation; section 2 deals with induction and section 3 with causation. Within these confines, section 4 attempts to give an explication of the relevant sense of objectification and section 5 investigates the extent to which various features of epistemic states are objectifiable. The two most salient results are roughly that the relation "A is a reason for B" cannot be objectified at all and that the relation "A is a cause of B" can be objectified only under substantial, though reasonable restrictions. What has all of this to do with probability? A lot. The paper trades on a pervasive duality between probabilistic and deterministic epistemology, between a probabilistic representation of epistemic states together with a theory of probabilistic causation and another representation of epistemic states which I call deterministic because it lends itself, in a perfectly parallel fashion, to a theory of deterministic causation. Here I explicitly deal only with the deterministic side, but the duality should pave the way for further conclusions concerning objective probabilities and statistical laws. This outlook is briefly expanded in the final section 6. (shrink)

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

"The best book available for non-mathematicians." — Contemporary Psychology. Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.

The Novum Organum, (or Novum Organum Scientiarum - "New Instrument of Science"), is a philosophical work by Francis Bacon, originally published in 1620. The title is a reference to Aristotle's work Organon, which was his treatise on logic and syllogism. In Novum Organum, Bacon details a new system of logic he believes to be superior to the old ways of syllogism. This is now known as the Baconian method.

The Novum Organum, (or Novum Organum Scientiarum - "New Instrument of Science"), is a philosophical work by Francis Bacon, originally published in 1620. The title is a reference to Aristotle's work Organon, which was his treatise on logic and syllogism. In Novum Organum, Bacon details a new system of logic he believes to be superior to the old ways of syllogism. This is now known as the Baconian method.

In the middle of the 1980s, logical tools were discovered that make it possible to model changes in belief and knowledge in entirely new ways. These logical tools turned out to be applicable both to human beliefs and to the contents of databases. This is the first textbook in this new area. It contains both discursive chapters with a minimum of formalism and formal chapters in which proofs and proof methods are presented. By using different selections from the formal section (...) the book can be used on all levels of University education. (shrink)

This comprehensive discussion of the problem of rational belief develops the subject on the pattern of Bayesian decision theory. The analogy with decision theory introduces philosophical issues not usually encountered in logical studies and suggests some promising new approaches to old problems."We owe Professor Levi a debt of gratitude for producing a book of such excellence. His own approach to inductive inference is not only original and profound, it also clarifies and transforms the work of his predecessors. In short, the (...) book deserves to become a classic....There is a great deal of interest in the book besides these basic matters [forumlating rules of acceptance]. Some of the most interesting chapters are those that examine the implications of such rules. The discussions of probability, generalization, and various forms of inference are brilliant and enlightening. Indeed, the problems and methods elaborated by Professor Levi in his book serve as a new foundation for the study of inductive inference."--Keith Lehrer, Nous"Levi's book is an extremely interesting report on 'tentative and speculative first steps' toward a decision-theoretic approach to inductive inference....Professor Levi is to be congratulated on his ingenious development and application of this approach...."--Richard C. Jeffrey, The Journal of Philosophy. (shrink)

The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc. The truth-value set, , of FL is assumed to be generated by a context-free grammar, with a semantic rule providing a means of computing the meaning of each linguistic truth-value in as a (...) fuzzy subset of [0, 1].Since is not closed under the operations of negation, conjunction, disjunction and implication, the result of an operation on truth-values in requires, in general, a linguistic approximation by a truth-value in . As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very, quite, more or less, etc. (shrink)

Vagueness provides the first comprehensive examination of a topic of increasing importance in metaphysics and the philosophy of logic and language. Timothy Williamson traces the history of this philosophical problem from discussions of the heap paradox in classical Greece to modern formal approaches such as fuzzy logic. He illustrates the problems with views which have taken the position that standard logic and formal semantics do not apply to vague language, and defends the controversial realistic view that vagueness is a kind (...) of ignorance--that there really is a grain of sand whose removal turns a heap into a non-heap, but we cannot know which one it is. (shrink)

The characteristic difference between laws and accidental generalizations lies in our epistemic or inductive attitude towards them. This idea has taken various forms and dominated the discussion about lawlikeness in the last decades. Likewise, the issue about ceteris paribus conditions is essentially about how we epistemically deal with exceptions. Hence, ranking theory with its resources of defeasible reasoning seems ideally suited to explicate these points in a formal way. This is what the paper attempts to do. Thus it will turn (...) out that a law is simply the deterministic analogue of a sequence of independent, identically distributed random variables. This entails that de Finetti's representation theorems can be directly transformed into an account of confirmation of laws thus conceived. (shrink)

The paper is based on ranking theory, a theory of degrees of disbelief (and hence belief). On this basis, it explains enumerative induction, the confirmation of a law by its positive instances, which may indeed take various schemes. It gives a ranking theoretic explication of a possible law or a nomological hypothesis. It proves, then, that such schemes of enumerative induction uniquely correspond to mixtures of such nomological hypotheses. Thus, it shows that de Finetti's probabilistic representation theorems may be transformed (...) into an account of confirmation of possible laws and that enumerative induction is equivalent to such an account. The paper concludes with some remarks about the apriority of lawfulness or the uniformity of nature. (shrink)

The paper builds on the basically Humean idea that A is a cause of B iff A and B both occur, A precedes B, and A raises the metaphysical or epistemic status of B given the obtaining circumstances. It argues that in pursuit of a theory of deterministic causation this ‘status raising’ is best explicated not in regularity or counterfactual terms, but in terms of ranking functions. On this basis, it constructs a rigorous theory of deterministic causation that successfully deals (...) with cases of overdetermination and pre-emption. It finally indicates how the account's profound epistemic relativization induced by ranking theory can be undone. Introduction Variables, propositions, time Induction first Causation Redundant causation Objectivization. (shrink)

James Joyce's 'Nonpragmatic Vindication of Probabilism' gives a new argument for the conclusion that a person's credences ought to satisfy the laws of probability. The premises of Joyce's argument include six axioms about what counts as an adequate measure of the distance of a credence function from the truth. This paper shows that (a) Joyce's argument for one of these axioms is invalid, (b) his argument for another axiom has a false premise, (c) neither axiom is plausible, and (d) without (...) these implausible axioms Joyce's vindication of probabilism fails. (shrink)

_ Convention_ was immediately recognized as a major contribution to the subject and its significance has remained undiminished since its first publication in 1969. Lewis analyzes social conventions as regularities in the resolution of recurring coordination problems-situations characterized by interdependent decision processes in which common interests are at stake. Conventions are contrasted with other kinds of regularity, and conventions governing systems of communication are given special attention.

This book review describes and evaluates Issac Levi's views about belief revision.

This is a review of Marc Lange's _Natural Laws in Scientific Practice<D>.

It is often presumed that the laws of nature have special significance for scientific reasoning. But the laws' distinctive roles have proven notoriously difficult to identify--leading some philosophers to question if they hold such roles at all. This study offers original accounts of the roles that natural laws play in connection with counterfactual conditionals, inductive projections, and scientific explanations, and of what the laws must be in order for them to be capable of playing these roles. Particular attention is given (...) to laws of special sciences, levels of scientific explanation, natural kinds, ceteris-paribus clauses, and physically necessary non-laws. (shrink)

This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves (...) a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available. (shrink)

The pragmatic character of the Dutch book argument makes it unsuitable as an "epistemic" justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. To secure an appropriately epistemic justification for this conclusion, one must explain what it means for a system of partial beliefs to accurately represent the state of the world, and then show that partial beliefs that violate the laws of probability are invariably less accurate than they could be otherwise. (...) The first task can be accomplished once we realize that the accuracy of systems of partial beliefs can be measured on a gradational scale that satisfies a small set of formal constraints, each of which has a sound epistemic motivation. When accuracy is measured in this way it can be shown that any system of degrees of belief that violates the axioms of probability can be replaced by an alternative system that obeys the axioms and yet is more accurate in every possible world. Since epistemically rational agents must strive to hold accurate beliefs, this establishes conformity with the axioms of probability as a norm of epistemic rationality whatever its prudential merits or defects might be. (shrink)

This book makes a significant contribution to the standard decision theory, that is, the theory of choice built around the principle of maximizing expected utility, both to its causal version and to the more traditional noncausal approach. The author’s success in clarifying the foundations of the standard decision theory in general, and causal decision theory in particular, also makes the book uniquely suitable for a person whose research in philosophy has led her to want to learn about contemporary decision theory. (...) The book presupposes some mathematical sophistication, and it contains more philosophical and mathematical argumentation per page than may be suitable for an undergraduate level course; but it stands out as an ideal textbook for a graduate-level course focused on the foundations of the standard decision theory. (shrink)

This paper uses Popper's treatment of probability and an epistemic constraint on probability assignments to conditionals to extend the Bayesian representation of rational belief so that revision of previously accepted evidence is allowed for. Results of this extension include an epistemic semantics for Lewis' theory of counterfactual conditionals and a representation for one kind of conceptual change.

Using formal systems to represent and reason about uncertainty.

We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...) belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. (shrink)

The book was planned and written as a single, sustained argument. But earlier versions of a few parts of it have appeared separately. The object of this book is both to establish the existence of the paradoxes, and also to describe a non-Pascalian concept of probability in terms of which one can analyse the structure of forensic proof without giving rise to such typical signs of theoretical misfit. Neither the complementational principle for negation nor the multiplicative principle for conjunction applies (...) to the central core of any forensic proof in the Anglo-American legal system. There are four parts included in this book. Accordingly, these parts have been written in such a way that they may be read in different orders by different kinds of reader. (shrink)

Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues that the (...) transformations that made it possible for probability concepts to emerge have constrained all subsequent development of probability theory and determine the space within which philosophical debate on the subject is still conducted. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends. Ian Hacking is the winner of the Holberg International Memorial Prize 2009. (shrink)

Change, Choice and Inference develops logical theories that are necessary both for the understanding of adaptable human reasoning and for the design of intelligent systems. The book shows that reasoning processes - the drawing on inferences and changing one's beliefs - can be viewed as belonging to the realm of practical reason by embedding logical theories into the broader context of the theory of rational choice. The book unifies lively and significant strands of research in logic, philosophy, economics and artificial (...) intelligence. It elaborates on the relevant theories and provides a mathematically precise foundation for the thesis that large parts of theoretical reason can be subsumed under practical reason. (shrink)

SUGGESTED COURSES Introductory level A (Requires very little background in logic .): 4: -9 - - -7 -2 Introductory level B: -9,:+-+ -,2:+,2: -,3:20+-22+ -7 -2 ...

Degrees of belief; Dempster's rule of combination; Simple and separable support functions; The weights of evidence; Compatible frames of discernment; Support functions; The discernment of evidence; Quasi support functions; Consonance; Statistical evidence; The dual nature of probable reasoning.