A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.

Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur. If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur. And so on for other (...) kinds of probability, such as evidential probability. The formal analogue of this picture is the regularity constraint: a probability distribution over sets of possibilities is regular just in case it assigns probability 0 only to the null set, and therefore probability 1 only to the set of all possibilities. (shrink)

Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur. If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur. And so on for other (...) kinds of probability, such as evidential probability. The formal analogue of this picture is the regularity constraint: a probability distribution over sets of possibilities is regular just in case it assigns probability 0 only to the null set, and therefore probability 1 only to the set of all possibilities. (shrink)

Fallibilism is an attractive epistemological position, avoiding the Scylla of rationalism, and the Charybdis of scepticism. Acknowledging, on the one hand, human imperfection, yet claiming that science and rational inquiry are possible. Fallibilism is a thesis, but equally importantly – an epistemological recommendation. that we should never be absolutely sure of anything. My aim in this paper is to drive a wedge between the thesis and the recommendation. The (eminently plausible) doctrine, I shall argue, cannot be used to ground the (...) epistemological prescription for caution. (shrink)

The aim of the paper is to draw a connection between a semantical theory of conditional statements and the theory of conditional probability. First, the probability calculus is interpreted as a semantics for truth functional logic. Absolute probabilities are treated as degrees of rational belief. Conditional probabilities are explicitly defined in terms of absolute probabilities in the familiar way. Second, the probability calculus is extended in order to provide an interpretation for counterfactual probabilities--conditional probabilities where the condition has zero probability. (...) Third, conditional propositions are introduced as propositions whose absolute probability is equal to the conditional probability of the consequent on the antecedent. An axiom system for this conditional connective is recovered from the probabilistic definition. Finally, the primary semantics for this axiom system, presented elsewhere, is related to the probabilistic interpretation. (shrink)

Newcomb's problem and similar cases show the need to incorporate causal distinctions into the theory of rational decision; the usual noncausal decision theory, though simpler, does not always give the right answers. I give my own version of causal decision theory, compare it with versions offered by several other authors, and suggest that the versions have more in common than meets the eye.

Then, in 1960, Carnap drew up a plan of articles for Studies in Inductive Logic and Probability — a surrogate for Volume II of the ...

Bayesians have a seemingly attractive account of rational credal states in terms of coherence. An agent's set of credences are synchronically coherent just in case they conform to the probability calculus. Some Bayesians impose a further putative coherence constraint called regularity: roughly, if X is possible, then it is assigned positive probability. I look at two versions of regularity – logical and metaphysical – and I canvass various defences of it as a rationality norm. Combining regularity with synchronic coherence, we (...) have a set of constraints known as strict coherence.I argue that strict coherence is untenable. In particular, I attack regularity as a rationality norm. First, I rebut each of the various defences of regularity. Then I argue directly against regularity: it conflicts with the Bayesian decision‐theoretic treatment of rational action. Thus, seemingly plausible theoretical and pragmatic norms turn out to be inconsistent.[Barbossa is about to kill Will,but Jack Sparrow shows up:]Barbossa: It's not possible!Jack: Not probable.To be uncertain is to be uncomfortable,but to be certain is to be ridiculous. (shrink)

‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.’ This paper is an attempt to follow Russell’s advice by using a puzzle about the contingent a priori to test and explore certain theories of reference and modality. No one could claim that (...) the puzzle is of any great philosophical importance by itself, but to understand it, one has to get clear about certain aspects of the theory of reference; and to solve it, one has to think a little more deeply than one is perhaps accustomed about what it means to say that a statement is contingent or necessary. (shrink)

‘A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science.’ This paper is an attempt to follow Russell’s advice by using a puzzle about the contingent a priori to test and explore certain theories of reference and modality. No one could claim that (...) the puzzle is of any great philosophical importance by itself, but to understand it, one has to get clear about certain aspects of the theory of reference; and to solve it, one has to think a little more deeply than one is perhaps accustomed about what it means to say that a statement is contingent or necessary. (shrink)

What is consciousness? How does the subjective character of consciousness fit into an objective world? How can there be a science of consciousness? In this sequel to his groundbreaking and controversial The Conscious Mind, David Chalmers develops a unified framework that addresses these questions and many others. Starting with a statement of the "hard problem" of consciousness, Chalmers builds a positive framework for the science of consciousness and a nonreductive vision of the metaphysics of consciousness. He replies to many critics (...) of The Conscious Mind, and then develops a positive theory in new directions. The book includes original accounts of how we think and know about consciousness, of the unity of consciousness, and of how consciousness relates to the external world. Along the way, Chalmers develops many provocative ideas: the " consciousness meter", the Garden of Eden as a model of perceptual experience, and The Matrix as a guide to the deepest philosophical problems about consciousness and the external world. This book will be required reading for anyone interested in the problems of mind, brain, consciousness, and reality. (shrink)

Van Fraassen has maintained that acceptance of a scientific theory does not involve the belief that the theory is true. Blackburn, Mitchell and Horwich have claimed that acceptance, as understood by van Fraassen, is the same as belief; in which case, van Fraassen's position is incoherent. Van Fraassen identifies belief with subjective probability, so the question at issue is really whether acceptance of a theory involves a high subjective probability for the theory. Van Fraassen is not committed to this, and (...) hence the charge of incoherence is misplaced. Indeed, van Fraassen is correct on this point. However, he is wrong to think that acceptance requires a high subjective probability that the theory is empirically adequate; and his reason for thinking that science aims at empirical adequacy rather than truth rests on an overly crude theory of rational choice. (shrink)