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)

A defense of material implication as implication.

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...) class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains. (shrink)

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

Practical deliberation often involves conditional judgements about what will happen if certain alternatives are pursued. It is widely assumed that the conditionals useful in deliberation are counterfactual or subjunctive conditionals. Against this, I argue that the conditionals of deliberation are indicatives. Key to the argument is an account of the relation between ‘straightforward’ future-directed conditionals like ‘If the house is not painted, it will soon look quite shabby’ and ‘ “were”ed-up’ FDCs like ‘If the house were not to be painted, (...) it would soon look quite shabby’: an account on which both of these types of FDCs are grouped with the indicatives for semantic treatment and on which, while conditionals of both types are properly used in means/ends deliberations, those of the ‘were’ed-up variety are especially well suited for that purpose. (shrink)

Practical deliberation often involves conditional judgements about what will (likely) happen if certain alternatives are pursued. It is widely assumed that the conditionals useful in deliberation are counterfactual or subjunctive conditionals. Against this, I argue that the conditionals of deliberation are indicatives. Key to the argument is an account of the relation between 'straightforward' future-directed conditionals like ' If the house is not painted, it will soon look quite shabby' and * "w e r e ' ' e d F (...) D C s like ' If the house were not to be painted, it would soon look quite shabby': an account on which both of these types of FDCs are grouped with the indicatives for semantic treatment and on which, while conditionals of both types are properly used in means/ends deliberations, those of the ' were'ed-up variety are especially well suited for that purpose. (shrink)

This book develops in detail the simple idea that assertion is the expression of belief. In it the author puts forward a version of 'probabilistic semantics' which acknowledges that we are not perfectly rational, and which offers a significant advance in generality on theories of meaning couched in terms of truth conditions. It promises to challenge a number of entrenched and widespread views about the relations of language and mind. Part I presents a functionalist account of belief, worked through a (...) modified form of decision theory. In Part II the author generates a theory of meaning in terms of 'assertibility conditions', whereby to know the meaning of an assertion is to know the belief it expresses. (shrink)

THE INDICATIVE CONDITIONAL. A PROBABILISTIC CRITERION OF SOUNDNESS FOR DEDUCTIVE INFERENCES Our objective in this section is to establish a prima facie case ...

The standard use of the propositional calculus ('P.C.?) in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be ?safely? used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions, that P. C. may be safely used, except in inferences whose conclusions are conditionals whose antecedents are incompatible with the premises in (...) the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

This book is meant to be a primer, that is, an introduction, to probability logic, a subject that appears to be in its infancy. Probability logic is a subject envisioned by Hans Reichenbach and largely created by Adams. It treats conditionals as bearers of conditional probabilities and discusses an appropriate sense of validity for arguments such conditionals, as well as ordinary statements as premisses. This is a clear well-written text on the subject of probability logic, suitable for advanced undergraduates or (...) graduates, but also of interest to professional philosophers. There are well-thought-out exercises, and a number of advanced topics treated in appendices, while some are brought up in exercises and some are alluded to only in footnotes. By this means, it is hoped that the reader will at least be made aware of most of the important ramifications of the subject and its tie-ins with current research, and will have some indications concerning recent and relevant literature. (shrink)

This book is meant to be a primer, that is, an introduction, to probability logic, a subject that appears to be in its infancy. Probability logic is a subject envisioned by Hans Reichenbach and largely created by Adams. It treats conditionals as bearers of conditional probabilities and discusses an appropriate sense of validity for arguments such conditionals, as well as ordinary statements as premisses. This is a clear well-written text on the subject of probability logic, suitable for advanced undergraduates or (...) graduates, but also of interest to professional philosophers. There are well-thought-out exercises, and a number of advanced topics treated in appendices, while some are brought up in exercises and some are alluded to only in footnotes. By this means, it is hoped that the reader will at least be made aware of most of the important ramifications of the subject and its tie-ins with current research, and will have some indications concerning recent and relevant literature. (shrink)

First Published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.

An assertion is a speech act in which something is claimed to hold, e.g. that there are infinitely many prime numbers, or, with respect to some time t, that there is a traffic congestion on Brooklyn Bridge at t, or, of some person x with respect to some time t, that x has a tooth ache at t. The concept of assertion has often occupied a central place in the philosophy of language, since it is often thought that making assertions (...) is the use of language most crucial to linguistic meaning, and since assertions are the natural expressions of cognitive attitudes, and hence of importance for theories of knowledge and belief. (shrink)

The dissertation gives an account of the principles guiding the rational revision of belief. I develop a non-probabilistic account of belief revision. My central thesis is the claim that there are two quite different kinds of rational belief change; two methods suited to two different sorts of situation. I call these methods updating and supposing. This claim, presented in Chapter Two, is argued on the basis of results proved in Chapter One. Chapters Three and Four are applications of the distinction (...) between updating and supposing to two areas of current philosophical debate: the semantics of conditionals; and the theory of deliberation dynamics. The discussion of conditionals appeals to the temporal asymmetry in knowledge. Why is it that we know more about the past than about the future? Chapter Five offers a new answer to that old question, based on an account of recording devices as physical systems stable under perturbation. ;I hope to have shown that many of these philosophical questions--questions about belief revision, decision theory, and conditionals, that have traditionally been framed in probabilistic terms--can be most fruitfully discussed without ever mentioning probability. (shrink)