The use of negative probabilities is discussed for certain problems in which a stochastic process approach is indicated. An extension of probability theory to include signed (negative and positive) probabilities is outlined and both philosophical and axiomatic examinations of negative probabilities are presented. Finally, a class of applications illustrates the use and implications of signed probability theory.

I examine to what extent accounts of mechanisms based on formal interventionist theories of causality can adequately represent biological mechanisms with complex dynamics. Using a differential equation model for a circadian clock mechanism as an example, I first show that there exists an iterative solution that can be interpreted as a structural causal model. Thus, in principle, it is possible to integrate causal difference-making information with dynamical information. However, the differential equation model itself lacks the right modularity properties for a full integration. A formal mechanistic model will therefore have to leave out either noncausal or causal explanatory relations.

A number of models of general relativity seem to contain “holes” that are thought to be “physically unreasonable.” One seeks a condition to rule out these models. We examine a number of possibilities already in use. We then introduce a new condition: epistemic hole-freeness. Epistemic hole-freeness is not just a new condition—it is new in kind. In particular, it does not presuppose a distinction between space-times that are “physically reasonable” and those that are not.

Today we are in the midst of a far-reaching shift in scientific thought involving the recasting of many of our long-cherished ideas and preconceptions. To some this appears but the orderly evolution of scientific thought, while to others it portends a revolution in both the ideas and the methods of scientific inquiry.

Modernism in the philosophy of science demands a unified story about what makes an inquiry scientific (or a successful science). Fine's “natural ontological attitude” (NOA) is “postmodern” in joining trust in local scientific practice with suspicion toward any global interpretation of science to legitimate or undercut that trust. I consider four readings of this combination of trust and suspicion and their consequences for the autonomy and cultural credibility of the sciences. Three readings take respectively Fine's trusting attitude, his emphasis upon local practice, and his antiessentialism about science as most fundamental to NOA. A fourth, more adequate reading, prompted by recent feminist interpretations of science, offers less restrictive readings of both Fine's trust and his suspicion toward approaching science with “ready-made philosophical engines” (Fine 1986b, 177).

There are two opposing traditions in contemporary quantum field theory (QFT). Mainstream Lagrangian QFT led to and supports the standard model of particle interactions. Algebraic QFT seeks to provide a rigorous consistent mathematical foundation for field theory, but cannot accommodate the local gauge interactions of the standard model. Interested philosophers face a choice. They can accept algebraic QFT on the grounds of mathematical consistency and general accord with the semantic conception of theory interpretation. This suggests a rejection of particle ontology. Or they can accept the standard model on the grounds of its established success. This alternative, which I defend, suggests revising philosophical accounts of scientific theory and finding some way of accommodating particles.

Kin selection is a core aspect of social evolution theory, but a small number of critics have recently challenged it. Here I address these criticisms and show that kin selection remains an important explanation for much (though not all) social evolution. I show how many of the criticisms rest on historical idiosyncrasies of the way the field happened to develop, rather than on the real logic and evidence.

We offer a new account of the role of values in theory choice that captures a temporal dimension to the values themselves. We argue that nonepistemic values sometimes serve as “inquiry tickets,” justifying scientists’ pursuit of certain questions in the short run, while the answers to those questions mitigate transient underdetermination in the long run. Our account of inquiry tickets shows that the role of nonepistemic values need not be restricted to belief or acceptance in order to be relevant to hypothesis choice: the relevance of nonepistemic values to a particular cognitive attitude with respect to h varies over time.

Structural realism first emerged as an epistemological thesis aimed to avoid the so-called pessimistic metainduction on the history of science. Some authors, however, have suggested that the preservation of structure across theory change is best explained by endorsing the metaphysical thesis that structure is all there is. Although the possibility of this latter, ‘ontic’ form of structural realism has been extensively debated, not much has been said concerning its justification. In this article, I distinguish between two arguments in favor of ontic structural realism that can be reconstructed from the literature and find both of them wanting.

Sober has reconstructed the biological design argument in the framework of likelihoodism, purporting to demonstrate that it is defective for intrinsic reasons. We argue that Sober’s restriction on the introduction of auxiliary hypotheses is too restrictive, as it commits him to rejecting types of everyday reasoning that are clearly valid. Our account shows that the design argument fails, not because it is intrinsically untestable but because it clashes with the empirical evidence and fails to satisfy certain theoretical desiderata (in particular, unification). Likewise, Sober’s critique of the arguments from imperfections and from evil against design is off the mark.

The foundation of the mathematical theory of probabilities is still a controversial subject. There are schools of insufficient reasoning and of cogent reasoning, of a priori determination and of frequency determination, of subjective and of objective probability. Two main difficulties exist. The first is the definition of equally like events. The second difficulty is the relation between the laws of causal natural science (mechanics, electrodynamics, etc.) and the laws of statistical regularity. Is it really necessary to add to the laws of mechanics one or more independent “laws of large numbers” to explain the regularities in dice throwing? In all these cases different answers exist, and the existence of a mathematical theory of probabilities remains a kind of miracle, as esoteric to the further domain of natural science as the resurrection of the dead.

Professor Buck has given an illuminating account of the logical status of reflexive predictions in the social sciences. He tells us that the classification of a prediction as reflexive is predicated on a tacit distinction between the “normal” and the “abnormal” or perturbed conditions under which it is made. This seems to me to be a perceptive and sound circumscription of the class of reflexive predictions as encountered in the social sciences. He goes on to show helpfully how the social scientist can cope with the pitfalls of spurious disconfirmation and spurious confirmation which are created by “self-frustrating” and “self-fulfilling” predictions respectively. And Professor Buck then offers some searching doubts concerning the adequacy of regarding self-fulfilling predictions as the pattern of racial discrimination against minority groups. Finally, he presents objections to my critique ([1], pp. 239–240) of Robert Merton's claim that self-defeating and self-fulfilling predictions are endemic to the domain of human affairs and are “not found among predictions about the world of nature.” ([2], p. 181).

Do masses, electrons, atoms, magnetic field strengths, etc., exist? Nothing is more surprising indeed than the fact that in these days of minute quantitative analysis, of relativistic thought, most of us still expect an answer to this question in terms of yes or no. The physicist frowns upon questions of the sort: is this object green?; or what time is it on a distant star? For he knows that there are many different shades of green, and that the time depends on the state of motion of the star. Almost every term that has come under scientific scrutiny has lost its initially absolute significance and acquired a range of meaning of which even the boundaries are often variable. Apparently the word to be has escaped this process.

The commensurability of two theories can be defined (relative to a given set of questions) as the ratio of the total information of their shared answers to the total information of the answers yielded by the two theories combined. Answers should be understood here as model consequences (in the sense of the author's earlier papers), not deductive consequences. This definition is relative to a given model of the joint language of the theories, but can be generalized to sets of models. It turns out to capture also the idea of incommensurability as conceptual alienation. Incommensurability so defined does not imply incomparability.

The Bayesian theory is outlined and its status as a logic defended. In this it is contrasted with the development and extension of Neyman-Pearson methodology by Mayo in her recently published book (1996). It is shown by means of a simple counterexample that the rule of inference advocated by Mayo is actually unsound. An explanation of why error-probablities lead us to believe that they supply a sound rule is offered, followed by a discussion of two apparently powerful objections to the Bayesian theory, one concerning old evidence and the other optional stopping.

1. Ramsey Sentences and the Function of Theoretical Concepts. In his famous paper “Theories,” Frank Ramsey (1931, 212–236; 1978, Ch. 4) introduced a technique of examining a scientific theory by means of certain propositions, dubbed later “Ramsey Sentences.” They are the results of what is often called Ramsey elimination. This prima facie elimination is often presented as a method of dispensing with theoretical concepts in scientific theorizing. The idea is this: Assume that we are given a finitely axiomatized scientific theory

where O1, O2, … are the primitive observation terms (individual constants, predicate constants, function constants, etc.) of (1) and H1, H2, … its primitive theoretical terms. For simplicity, it will be assumed that (1) is a first-order theory. Since it is finitely axiomatizable, we may think of it as having the form of a single complex proposition, i.e., the conjunction of all the axioms. What can then be done is to generalize existentially with respect to (1). The result is a sentence of the form

In (2), the theoretical terms H1, H2, … do not occur any longer. They have been replaced by the variables X1, X2, … bound to initial existential quantifiers. In this sense at least, Ramsey sentences do effect on elimination. Unlike (1), (2) is not a first-order sentence but a second-order one.

Doubts concerning the validity of logic are as old as the empirical criticism of science. In the last two decades the idea that truth is relative to given sets of basic assumptions has been prominent; and the controversy about the principle of excluded middle has focussed renewed attention upon the nature of logic and its fundamental principles.

Recent investigations in formal logic have contributed greatly to the understanding of the principles of logic. It is simply a misunderstanding to conclude from them that the logical principles have been suspended, despite the various formal structures which are called “logics.” The purely formal treatment of problems concerning the foundations of logic, while necessarily undertaken as far as it can go, has essential limitations.

Rational actions reflect beliefs and preferences in certain orderly ways. The problem of theory is to explain which beliefs and preferences are relevant to the rationality of particular actions, and exactly how they are relevant. One distinction of interest here is between an agent's beliefs and preferences just before an action's time, and his beliefs and preferences at its time. Theorists do not agree about the times of beliefs and desires that are relevant to the rationality of action. Another distinction is between actions that would, in one sense or another, maximize expected utilities given relevant beliefs and desires, and actions, decisions for which would, in one sense or another, be stable. There is disagreement about the relevance of these things to the rationality of actions. Here, in the first part below, several possible positions on these issues are explained and compared. In the second part, I contrast perspectives on these issues, and comment on arguments that might be brought against the position I favor. In the third part, I restate and elaborate on this position.