The purpose of this paper is to solve a serious problem for the projection postulate involving the time-energy uncertainty relation. The problem was recently raised by Teller, who believes that the problem is insoluble and, consequently, that the projection postulate should no longer be regarded as a serious focus for interpretive investigation.

Richard Jeffrey and Michael Goldstein have both introduced systematic approaches to the structure of opinion changes. For both approaches there are theorems which indicate great generality and width of scope. The main questions addressed here will be to what extent the basic forms of representation are intertranslatable, and how we can conceive of such programs in general.

We show there is only one consistent way to update a probability assignment, that given by Bayes's rule. The price of inconsistent updating is a loss of efficiency. The implications of this for the problem of induction are discussed.

Using three intuitive notions about causes, including Redhead's robustness condition, I formulate necessary conditions on partial causes. I then demonstrate that we cannot explain the EPR correlations in terms of partial causes unless we abandon the quantum mechanical framework and adopt a nonlocal hidden-variable theory. The argument, unlike its predecessors, does not appeal to relativity theory.

The paper is inspired by the arguments raised recently by Grünbaum criticizing the current approaches of many cosmologists to the problem of spacetime singularity, matter creation and the origin of the universe. While agreeing with him that the currently favored cosmological ideas do not indicate the biblical notion of divine creation ex nihilo, I present my viewpoint on the same issues, which differs considerably from Grünbaum's. First I show that the symmetry principle which leads to the conservation law of energy is violated when the time axis is terminated at t = 0. Next I discuss why this epoch (t = 0) is more a mathematical artifact whose supposed significance may disappear when one goes beyond the classical relativistic cosmology. This is illustrated by the example of quantum cosmology.

Much contemporary epistemology is informed by a kind of confirmational holism, and a consequent rejection of the assumption that all confirmation rests on experiential certainties. Another prominent theme is that belief comes in degrees, and that rationality requires apportioning one's degrees of belief reasonably. Bayesian confirmation models based on Jeffrey Conditionalization attempt to bring together these two appealing strands. I argue, however, that these models cannot account for a certain aspect of confirmation that would be accounted for in any adequate holistic confirmation theory. I then survey the prospects for constructing a formal epistemology that better accommodates holistic insights.

Gödel began to seriously study Husserl's phenomenology in 1959, and the Gödel Nachlass is known to contain many notes on Husserl. In this paper I describe what is presently known about Gödel's interest in phenomenology. Among other things, it appears that the 1963 supplement to “What is Cantor's Continuum Hypothesis?”, which contains Gödel's famous views on mathematical intuition, may have been influenced by Husserl. I then show how Gödel's views on mathematical intuition and objectivity can be readily interpreted in a phenomenological theory of intuition and mathematical knowledge.

Philip Kitcher has proposed a theory of explanation based on the notion of unification. Despite the genuine interest and power of the theory, I argue here that the theory suffers from a fatal deficiency: It is intrinsically unable to account for the asymmetric structure of explanation, and thus ultimately falls prey to a problem similar to the one which beset Hempel's D-N model. I conclude that Kitcher is wrong to claim that one can settle the issue of an argument's explanatory force merely on the basis of considerations about the unifying power of the argument pattern the argument instantiates.

This paper studies the extent to which probability functions are recursively definable. It proves, in particular, that the (absolute) probability of a statement A is recursively definable from a certain point on, to wit: from the (absolute) probabilities of certain atomic components and conjunctions of atomic components of A on, but to no further extent. And it proves that, generally, the probability of a statement A relative to a statement B is recursively definable from a certain point on, to wit: from the probabilities relative to that very B of certain atomic components and conjunctions of atomic components of A, but again to no further extent. These and other results are extended to the less studied case where A and B are compounded from atomic statements by means of “∀” as well as “~” and “&”. The absolute probability functions considered are those of Kolmogorov and Carnap, and the relative ones are those of Kolmogorov, Carnap, Rényi, and Popper.

The violation of the Bell inequality means that measurement-results in the two wings of the experiment cannot be screened off from one another, in the sense of Reichenbach. But does this mean that there is causation between the results? I argue that it does, according to Lewis's counterfactual analysis of causation and his associated views. The reason lies in his doctrine that chances evolve by conditionalization on intervening history. This doctrine collapses the distinction between the conditional probabilities that are used to state screening off, and the counterfactuals with chance consequents that are used to state lack of causation. I briefly discuss ways to evade my argument.

This paper examines Wesley Salmon's “process” theory of causality, arguing in particular that there are four areas of inadequacy. These are that the theory is circular, that it is too vague at a crucial point, that statistical forks do not serve their intended purpose, and that Salmon has not adequately demonstrated that the theory avoids Hume's strictures about “hidden powers”. A new theory is suggested, based on “conserved quantities”, which fulfills Salmon's broad objectives, and which avoids the problems discussed.

Popper's paradox of ideal evidence has long been viewed as a telling criticism of Keynes's logical theory of probability and its associated concept of the weight of argument. This paper shows that a simple addition to Keynes's definitions of irrelevance enables his theory to elude the paradox with ease. The modified definition draws on ideas already present in Keynes's Treatise on Probability (1973). As a consequence, relevant evidence and the weight of argument may increase, even when new evidence leaves the probability unaltered.

Davidson's principle of the anomalousness of the mental was instrumental in discrediting once-popular versions of mind-brain reductionism. In this essay I argue that a novel account of intertheoretic reduction, which does not require the sort of cross-theoretic bridge laws that Davidson's principle rules out, allows a version of mind-brain reductionism which is immune from Davidson's challenge. In the final section, I address a second worry about reductionism, also based on Davidson's principle, that survives this response. I argue that new reductionists should revise some significant details of the program, particularly the conception of theories, to circumvent this more potent Davidson-inspired worry.

In a number of publications, John Earman has advocated a tertium quid to the usual dichotomy between substantivalism and relationism concerning the nature of spacetime. The idea is that the structure common to the members of an equivalence class of substantival models is captured by a Leibniz algebra which can then be taken to directly characterize the intrinsic reality only indirectly represented by the substantival models. An alleged virtue of this is that, while a substantival interpretation of spacetime theories falls prey to radical local indeterminism, the Leibniz algebras do not.

I argue that the program of Leibniz algebras is subject to radical local indeterminism to the same extent as substantivalism. In fact, for the category of topological spaces of interest in spacetime physics, the program is equivalent to the original spacetime approach. Moreover, the motivation for the program—that isomorphic substantival models should be regarded as representing the same physical situation—is misguided.

Von Mises defined a “physical” probability as a strict limit of the relative frequency of occurrence of an event in repeated trials. As a result of a number of criticisms of von Mises's approach, the more favored approach became the “propensity” interpretation. It is argued here that this interpretation is not compelling and that the only problem in von Mises's approach is the assumption that the relative frequency converges in a strict sense. This problem is then remedied by deducing the axioms of probability theory from the assumption that the relative frequency converges only in the sense of the weak law of large numbers.

This paper describes a theory of accuracy or approximate truth and applies it to problems in the realist interpretation of scientific theories. It argues not only that realism requires approximate truth, but that an adequate theory of approximation also presupposes some elements of a realist interpretation of theories.

The paper distinguishes approximate truth from vagueness, probability and verisimilitude, and applies it to problems of confirmation and deduction from inaccurate premises. Basic results are cited, but details appear elsewhere. Objections are surveyed, including arguments by Miller, Laymon, and Laudan. Comparison is made with Niiniluoto's theory of verisimilitude, and the utility of his theory for realism assessed.

In trying to characterize the relationship between psychology and neuroscience, the trend has been to argue that reductionism does not work without suggesting a suitable substitute. I offer explanatory extension as a good model for elucidating the complex relationship among disciplines which are obviously connected but which do not share pragmatic explanatory features. Explanatory extension rests on the idea that one field can “illuminate” issues that were incompletely treated in another. In this paper, I explain how this “illumination” would work between psychology and neuroscience.

Standard philosophical discussions of theory-ladeness assume that observational evidence consists of perceptual outputs (or reports of such outputs) that are sentential or propositional in structure. Theory-ladeness is conceptualized as having to do with logical or semantical relationships between such outputs or reports and background theories held by observers. Using the recent debate between Fodor and Churchland as a point of departure, we propose an alternative picture in which much of what serves as evidence in science is not perceptual outputs or reports of such outputs and is not sentential in structure.

Scientific realists contend that theory-conjunction presents a problem for empiricist conceptions of scientific knowledge and practice. Van Fraassen (1980) has offered a competing account of theory-conjunction which I argue fails to capture the mercenary character of epistemic dependence in science. Representative cases of theory-conjunction developed in the present paper show that mercenary reliance implies a “principle of epistemic symmetry” which only a realist can consistently accommodate. Finally, because the practice in question involves the conjunction of theories, a version of realism more robust than the “entity realism” of Cartwright (1983, 1989) and Hacking (1983) is required to explain the success of theory-conjunction.