Garber (1983) and Jeffrey (1991, 1995) have both proposed solutions to the old evidence problem. Jeffrey's solution, based on a new probability revision method called reparation, has been generalized to the case of uncertain old evidence and probabilistic new explanation in Wagner 1997, 1999. The present paper reformulates some of the latter work, highlighting the central role of Bayes factors and their associated uniformity principle, and extending the analysis to the case in which an hypothesis bears on a countable family of evidentiary propositions. This extension shows that no Garber-type approach is capable of reproducing the results of generalized reparation.

I argue against Matthew Slater’s rejection of what he calls the grounding claim in his stable property cluster (SPC) account of natural kinds. This claim states that the epistemic value of natural kinds depends on the existence of some ground to bind together a kind’s properties. Using two test cases from academic medicine, I show that grounds are genuinely explanatory of scientific epistemic practices and that the SPC account should not do without them in its philosophical analysis of natural kinds.

The creation-of-matter hypothesis of the Bondi-Gold-Hoyle steady-state cosmology requires that in an infinite time to which the first transfinite number may be assigned the number of atoms of matter produced would be equal to the cardinal number of the set of mathematical points in the continuum. The existence of a set of finite atoms with that cardinal number is physically unacceptable. The argument for the production of a non-denumerable set of atoms, in infinite time, is given in terms of a model which is shown to be isomorphic with the original Cantor “diagonal” proof for the existence of a non-denumerable infinity. An alternative model which meets the requirements of the steady-state theory is presented; in this model, the number of atoms is explicitly no greater than countably infinite, and remains countably infinite as long as the past time of the universe is restricted to the unlimited set of finite unit-time intervals. If the origin of the steady-state universe is taken as being within that infinite set, expressed by the negative natural numbers, the contradiction of an atom at every mathematical point does not arise. The contradiction does arise if the origin is not within the set of finite numbers, and accordingly there is a restriction as to which concept of infinite past may properly be maintained in the steady-state theory.

The Fitzgerald–Lorentz contraction hypothesis, proposed as an explanation of the Michelson–Morley result, fails to account for the Kennedy–Thorndike result. Hence, Grünbaum argues, the hypothesis has been falsified.

However, the contraction hypothesis as formulated by Lorentz is false for the very fundamental reason that it entails a contradiction, namely, the consequence that light waves must have a variable velocity along what by definition is taken to be a rest length. Furthermore, the attempt to resolve this contradiction by coupling the Fitzgerald–Lorentz contraction with the hypothesis that clock rates are a function of velocity, is open to a sound, methodological objection. The Michelson–Morley result is fully satisfied, provided only that the lengths of the interferometer arms, in the longitudinal and transverse positions, are thought to be related to one another in a certain ratio, and this ratio may be interpreted as a contraction in both arms. Since this twofold contraction hypothesis suffices to explain both the Michelson–Morley and the Kennedy–Thorndike results, and since it entails no contradiction, there is no need to correct both the length of rods and the rate of clocks. Therefore, the combined clock-rod hypothesis, and with it the Fitzgerald–Lorentz contraction hypothesis, must be rejected.

Examination of attempts at theory reduction (S to T) shows that a process of cognitive emergence is involved in which concepts of S, Cs, emerge from T. This permits the ‘bridge laws’ to be stated. These are not in conflict with incommensurability of the Cs with the CT. Cognitive emergence may occur asymptotically or because of similarities of mathematical expressions; it is not necessarily holistic. Mereologically and nonmereologically related theory pairs are considered. Examples are chosen from physics. An important distinction is made between ‘theory reduction’ and ‘reductive explanation’.

Much of the criticism of Stevens's criterion for permissible statistics as applied to measurement data results from a lack of clarity in Stevens's position. In this paper set-theoretical notions have been used to clarify that position. We define a sig-function as a function defined on numerical assignments. If u and ℜ are empirical and numerical relational systems, respectively, then a sig-function F is constant on u with respect to ℜ if, and only if, the value of F is the same for all numerical assignments for u with respect to ℜ. Using these notions we prove rigorously certain generalizations of Stevens's results.

Professor Massey's exposition and analysis [5] of Professor Grünbaum's writings on metric aspects of space seem to me both very helpful in understanding those writings and to contain a considerable original contribution to the subject. Nevertheless I would like to argue that there is an alternative to Massey's explication which seems to me more faithful to Grünbaum's remarks; it seems at least to have the virtue of not forcing Grünbaum to reject the usual mathematical definitions of the notions used.

It is claimed that unacceptable constraints on initial data are imposed by certain responses to paradoxes that threaten time travel, closed timelike curves (CTCs) and other backwards causation hypotheses. In this paper I argue against the following claims: to say “contradictions are impossible so something must prevent the paradox” commits in general to constraints on initial data, that for fixed point dynamics so-called grey state solutions explain why contradictions do not arise, and the latter have been proved to avoid constraints on initial data.

Philosophers sometimes claim that economics, and the idealizing strategies it employs, is ultimately unable to provide genuine laws of nature. Therefore, unlike physics, it does not qualify as an actual science. Careful consideration of thermodynamics, a well-developed physical theory, reveals substantial parallels with economic methodology. The corrective account of scientific understanding I offer appreciates these parallels: understanding in terms of efficient performance.

Much philosophical attention has been devoted to whether economic models explain and more generally to how scientific models represent. Yet there is an issue more practically important to economics than either of these, which I label the efficiency question: regardless of how exactly models represent, or of whether their role is explanatory or something else, is current modeling practice an efficient way to achieve these goals or should research efforts be redirected? In addition to showing how the efficiency question has been relatively neglected, I give two examples of the kind of analysis it requires.

In a recent paper, Pettigrew (2022) reports a generalization of the celebrated accuracy-dominance theorem due to Predd et al. (2009), but Pettigrew’s proof is incorrect. I will explain the mistakes and provide a correct proof.

It has been argued repeatedly that the modern study of social and cultural evolution took its inspiration and form from Charles Darwin's Origin of Species and Descent of Man. In 1920, Robert H. Lowie (27; pp. 55–56) observed that it was after evolutionary principles had been accepted in biology that they were applied to social phenomena, and that Lewis Henry Morgan was among the first to make the application. Sir James George Frazer (16; p. 581), at about the same time, dated the birth of anthropology from the promulgation of the evolution theory of Darwin and Wallace in 1859 and maintained that “this conception of evolution … supplies a basis for the modern science of anthropology.” Harry Elmer Barnes (1; pp. 25–26) similarly traced the development of anthropology from the theory of organic evolution and advised the student that he “need not concern himself with the history of method in sociology before the entry of Darwinian concepts.”

It is shown that the logical theory of belief statements must be prepared to take into account relationships among statements which are subtler and more delicate than is requisite in other contexts. It is necessary here to draw distinctions (of a modal and semantical character) which the standard assertory logic can ignore with impunity. This is due to the fact that it is entirely possible to be in ignorance of various logical relationships (eg., entailment, equivalence, etc.) that in fact obtain among believed statements, and so, for example to believe the premisses of a valid deductive argument, and yet disbelieve the conclusion which follows from them. The implications of such difficulties for the logic of belief statements are examined.

The use of null hypothesis significance testing (NHST) in psychology has been under sustained attack, despite its reliable use in the notably successful, so-called “hard” areas of psychology, such as perception and cognition. I argue that, in contrast to merely methodological analyses of hypothesis testing (in terms of “test severity,” or other confirmation-theoretic notions), only a patently metaphysical position can adequately capture the uneven but undeniable successes of theories in “hard psychology.” I contend that Measured Realism satisfies this description, and characterizes the role of NHST in hard psychology.

Subjunctive conditionals are fundamental to rational decision both in single agent and multiple agent decision problems. They need explicit analysis only when they cause problems, as they do in recent discussions of rationality in extensive form games. This paper examines subjunctive conditionals in the theory of games using a strict revealed preference interpretation of utility. Two very different models of games are investigated, the classical model and the limits of reality model. In the classical model the logic of backward induction is valid, but it does not use subjunctive conditionals; the relevant subjunctive conditionals do not even make sense. In the limits of reality model the subjunctive conditionals do make sense but backward induction is valid only under special assumptions.

I examine recent arguments based on functionalism that claim to show that Bohm's theory fails to solve the measurement problem, or if it does so, it is only because it reduces to a form of the many-worlds theory. While these arguments reveal some interesting features of Bohm's theory, I contend that they do not undermine the distinctive Bohmian solution to the measurement problem.

Most patterns of an organism develop reproducibly and predictably. Thus, most biological patterns are largely predetermined by the nature of the zygote and by the nature of the surrounding world. Some ontogenetic patterns can also be considered to be preformed. Eighteenth and nineteenth century definitions of ‘preformation’ suggested that all aspects of a precursor pattern—its elements and its configuration—are preserved during development. Today, the idea of preformed configurations has been lost. To revive this lost idea, we offer the following biologically contemporary definition for preformed ontogenetic patterns: preformed patterns are those patterns with topologies that have been conserved during their ontogenies. This definition is presented in precise mathematical language, and its application is demonstrated in a system of developing, abstract patterns.

Much of the current thought concerning mathematical ontology and epistemology follows Quine and Putnam in looking to the indispensable application of mathematics in science. A standard assumption of the indispensability approach is some version of confirmational holism, i.e., that only “sufficiently large” sets of beliefs “face the tribunal of experience.” In this paper I develop and defend a distinction between a pure mathematical theory and a mathematized scientific theory in which it is applied. This distinction allows for the possibility that pure mathematical theories are systematically insulated from such confirmation in virtue of their being distinct from the “sufficiently large” blocks of scientific theory that are empirically confirmed.

Reference models of the earth’s interior play an important role in the acquisition of knowledge about the earth’s interior and the earth as a whole. Such models are used as a sort of standard reference against which data are compared. I argue that the use of reference models merits more attention than it has gotten so far in the literature on models, for it is an example of a method of doing science that has a long and significant history, and a study of reference models could increase our understanding of this methodology.