While pragmatic arguments for numerical probability axioms have received much attention, justifications for axioms of qualitative probability have been less discussed. We offer an argument for the requirement that an agent’s qualitative (comparative) judgments be probabilistically representable, inspired by, but importantly different from, the Money Pump argument for transitivity of preference and Dutch book arguments for quantitative coherence. The argument is supported by a theorem, to the effect that a subject is systematically susceptible to dominance given her preferred acts, if and only if the subject’s comparative judgments preclude representation by a standard probability measure (or set of such measures).

In this article, I examine the relationship between physical quantities and physical states in quantum theories. I argue against the claim made by Arageorgis that the approach to interpreting quantum theories known as Algebraic Imperialism allows for “too many states.” I prove a result establishing that the Algebraic Imperialist has very general resources that she can employ to change her abstract algebra of quantities in order to rule out unphysical states.

What is the role of bridge laws in intertheoretic relations? An assumption shared by many views about these relations is that bridge laws enable reductions. In this article, I acknowledge the naturalness of this assumption, but I question it by presenting a context within thermal physics (involving phase transitions) in which the bridge laws, puzzlingly, seem to contribute to blocking the reduction.

Kuhn made two attempts at providing an evolutionary analogy for scientific change. The first attempt, in The Structure of Scientific Revolutions, is very brief and unstructured; in this article I discuss some of its weaknesses. Alexander Bird takes this attempt more seriously and provides a criticism based on oversimplified evolutionary assumptions. These assumptions prove to be inadequate for the second, more articulate, evolutionary analogy suggested by Kuhn in “The Road since Structure.” I argue, however, that this second Kuhnian attempt is undermined by his inadequate view of biological progress and by his misunderstanding of the concept of ecological niche.

Under what conditions does machine learning (ML) model opacity inhibit the possibility of explaining and understanding phenomena? In this article, I argue that nonepistemic values give shape to the ML opacity problem even if we keep researcher interests fixed. Treating ML models as an instance of doing model-based science to explain and understand phenomena reveals that there is (i) an external opacity problem, where the presence of inductive risk imposes higher standards on externally validating models, and (ii) an internal opacity problem, where greater inductive risk demands a higher level of transparency regarding the inferences the model makes.

While philosophers have focused on epistemological and ethical challenges of using artificial intelligence (AI) in science, scientists have focused largely on opportunities. I argue that this disconnect between philosophical pessimism and scientific optimism is driven by failures to critically examine the practice of AI-infused science. To appreciate the epistemic justification for AI-powered breakthroughs, philosophers must analyze the role of AI as part of a wider process of discovery. I demonstrate the importance of this with two cases from the scientific literature, and show that epistemic opacity need not diminish AI’s capacity to lead scientists to significant and justifiable breakthroughs.

According to a standard view of the second law of thermodynamics, our belief in the second law can be justified by pointing out that low-entropy macrostates are less probable than high-entropy macrostates, and then noting that a system in an improbable state will tend to evolve toward a more probable state. I would like to argue that this justification of the second law is unhelpful at best and wrong at worst, and will argue that certain puzzles sometimes associated with the second law are merely artifacts of this questionable justification.

In The Logic of Decision Richard Jeffrey defends a version of expected utility theory that advises agents to choose acts with an eye to securing evidence for thinking that desirable results will ensue. Proponents of “causal” decision theory have argued that Jeffrey's account is inadequate because it fails to properly discriminate the causal features of acts from their merely evidential properties. Jeffrey's approach has also been criticized on the grounds that it makes it impossible to extract a unique probability/utility representation from a sufficiently rich system of preferences (given a zero and unit for measuring utility). The existence of these problems should not blind us to the fact that Jeffrey's system has advantages that no other decision theory can match: it can be underwritten by a particularly compelling representation theorem proved by Ethan Bolker; and it has a property called partition invariance that every reasonable theory of rational choice must possess. I shall argue that the non-uniqueness problem can be finessed, and that it is impossible to adequately formulate causal decision theory, or any other, without using Jeffrey's theory as one's basic analysis of rational desire.

Conditions are stated under which the “argument by analogy” is consistent with the principle of inverse probability. It is contended that the argument by analogy, in conjunction with a crucial test, has a legitimate place in scientific logic. As an example the astrophysical problem of solar granulation is discussed in detail and other examples are mentioned more briefly.

The formal time symmetry of the quantum measurement process is extensively discussed. Then, the origin of the alleged association between a fixed temporal direction and quantum measurements is investigated. It is shown that some features of such an association might arise from epistemological rather than purely physical assumptions. In particular, it is brought out that a sequence of statements bearing on quantum measurements may display intrinsic asymmetric properties, irrespective of the location of corresponding measurements in time t of the Schrödinger equation. The situation of an observer performing two measurements in two opposite directions of t is eventually investigated. Essential differences are found between two descriptions of this situation: the internal one (taking only into account what is recorded in the observer's memory) and the external one (whereby the observer is considered as a quantum system ruled by the Schrödinger equation). Finally, a method allowing several observers to establish a correspondence between their memory sizes is analyzed. The most important facts that usually lead to the associating of a preferential temporal direction with quantum measurements may be inferred from this correspondence.

In this essay I present a statement of Quine's indeterminacy thesis in its general form. It is shown that the thesis is not about difficulties peculiar to so-called “radical translation.” It is a general thesis about meaning and reference with important consequences for any theory of our theories and beliefs. It is claimed that the thesis is inconsistent with Quine's realism, his doctrine of the relativity of reference, and that the argument for the thesis has the consequence that the concept of stimulus meaning is empty.

The sense in which linguistic science, as a branch of behavioral science, is “part of physics” is discussed. An alternative to Quine's view of the nature and content of linguistic science is proposed. It is shown to be consistent with Quine's assumptions concerning the legitimate scope of behavioral science and not to involve the notions of analyticity, synonymy and “prevalent attitudes toward meaning, idea and proposition” rejected by Quine.

This paper discusses the controversy between philosophers of science (e.g. Grünbaum) and historians of science (e.g. Holton) regarding Einstein's discovery of STR. Although Holton is surely correct on the historical point that experimental results (especially the Michelson–Morley experiment) had little influence on Einstein's development of STR, this fact is not sufficient to establish his (and Polanyi's) claim that major scientific discoveries are primarily matters of private, nonspecifiable insights into physical reality. It is possible that Einstein's work was based primarily on non-empirical but nonetheless publicly discussable, objective considerations. And a more comprehensive survey of the discovery of STR shows that this was indeed the case and thus excludes STR as a supporting instance of Holton's and Polanyi's assertions of the primacy of “private science.”

I discuss two case studies from classical electrodynamics challenging the distinction between laws that delineate physically possible words and initial conditions. First, for many reasonable initial conditions there exist no global solutions to the Maxwell-Lorentz equations for continuous charge distributions. Second, in deriving an equation of motion for a charged point particle one needs to invoke an asymptotic condition that seems to express a physically contingent fact even though it is mathematically necessary for the derivation.

Conventional wisdom currently has it that chaotic behavior is either strongly suppressed or absent in quantum models. Indeed, some researchers have concluded that these considerations serve to undermine the correspondence principle, thereby raising serious doubts about the adequacy of quantum mechanics as a fundamental physical theory. Thus, the quantum chaos question is a prime subject for philosophical analysis. The most significant reasons given for the absence or suppression of chaotic behavior in quantum models are the linearity of Schrödinger's equation and the unitarity of the time-evolution described by that equation. Both are shown in this essay to be irrelevant by demonstrating that the crucial feature for chaos is the nonseparability of the Hamiltonian. That demonstration indicates that quantum chaos is likely to be exhibited in models of open quantum systems. A measure for probing such models for chaotic behavior is developed, and then used to show that quantum mechanics has chaotic models for systems having a continuous energy spectrum. The prospects of this result for vindicating the essence of the correspondence principle are then briefly examined.

I wish, for the sake of the vivacity of any discussion which might ensue, that I could find myself more in disagreement with Dr. Brodbeck than I do. As a matter of fact, however, I find myself in substantial agreement with her on practically all of the points upon which she takes issue with Hayek. There are, to be sure a few questions of relatively minor import that I should like to ask Dr. Brodbeck, but in the main I have confined my own discussion to an elaboration and supplementation of some of the points considered in her paper, and some related considerations raised in Hayek's book but which Dr. Brodbeck did not have the time, perhaps, to treat.

This paper digests technical commonplaces of quantum field theory to present an informal interpretation of the theory by emphasizing its connections with the harmonic oscillator. The resulting “harmonic oscillator interpretation” enables newcomers to the subject to get some intuitive feel for the theory. The interpretation clarifies how the theory relates to observation and to quantum mechanical problems connected with observation. Finally the interpretation moves some way towards helping us see what the theory comes to physically.

The paper also argues that, in important respects, interpretive problems of quantum field theory are problems we know well from conventional quantum mechanics. An important exception concerns extending the puzzles surrounding the superposition of properties in conventional quantum mechanics to an exactly parallel notion of superposition of particles. Conventional quantum mechanics seems incompatible with a classical notion of property on which all quantities always have definite values. Quantum field theory presents an exactly analogous problem with saying that the number of “particles” is always definite.

The rapid development of physics, the result of observations made and ideas introduced within the last few decades, has brought about a change in the whole system of physical concepts. This fact is common knowledge, and has already attracted the attention of philosophers. It is less well known that geometry too has had its crises, and undergone a reconstruction. For centuries, so-called “geometrical intuition” was used as a method of proof. In geometrical demonstrations, certain steps were allowed because they were “self-evident,” because the correctness of the conclusion was “shown by the adjoined diagram,” etc. A crisis occurred in geometry because such intuition proved to be untrustworthy. Many of the propositions regarded as self-evident or based upon the consideration of diagrams turned out to be false. And so Euclidean geometry was reconstructed by methods free from all intuitive elements and strictly logical in nature. Moreover, for more than a century, various other geometries have been devised purely as logical constructions. Since they start with assumptions different from those of Euclid, and lead to conclusions partly in contradiction with his theorems, they are called “non-Euclidean.” Nevertheless, each one of these geometries is a closed system of propositions exempt from contradiction. Recently, some of them have even found application in physics.

Concepts originating in the philosophy of science generally are used only ritualistically and in careful isolation from research practice in political science. But philosophical considerations are fundamental to political research, and critically influence its decisions. The question is whether ideas offered by philosophers of science have practical (that is to say, theoretical) significance for political researchers. This essay argues that philosophy of science has extremely relevant ideas to offer. The argument proceeds through an initial presentation of some elementary notions drawn from reconstructions of the nature of concept formation-theory construction. These are then utilized in a critique of the research of quantitative political scientists. Three rather central concerns of this, still very young, discipline are discussed: measurement problems, the use of recursive and structural systems in causal modeling, and the primary logical function of multivariate analysis in political studies. The discussion is viewed as supporting the general point that applied philosophy of science ought to be, not an adjunct, but one of the key critical contributors to political research.

This essay comments on the theory of social norms developed by Cristina Bicchieri in The Grammar of Society (2006). It applauds her theory of norms but argues that it cannot account for the experimental results concerning ultimatum games. A theory of fairness is also needed. It develops a number of specific criticisms of her way of incorporating the influence of norms into preferences.

I critically discuss a recent innovation in the debate surrounding the plausibility of rational choice theory (RCT): the appeal to evolutionary theory. Specifically, I assess Gigerenzer and colleagues’ claim that considerations based on natural selection show that, instead of making decisions in a RCT-like way, we rely on ‘simple heuristics’. As I try to make clearer here, though, Gigerenzer and colleagues’ arguments are unconvincing: we lack the needed information about our past to determine whether the premises on which they are built are true—and, hence, we cannot tell whether they, in fact, speak against RCT.