Various senses in which laws of nature are supposed to be “universal” are distinguished. Conditions designed to capture the content of the more important of these senses are proposed and the relations among these conditions are examined. The status of universality requirements is briefly discussed.

Question: What is a (or the) scientific theory V based on a set B of syntactical L -formulas, interpreted according to the intended interpretations of the language L? What probably corresponds to the traditional candidate for V is found to be inadequate for use in deductively explaining experimental facts of a certain form. A second candidate for V, called a strong scientific theory (SST), does not suffer such an inadequacy because it is existentially strong, i.e., it has considerable existential import. It even satisfies the particle physicist's dictum: WHAT IS NOT FORBIDDEN WILL HAPPEN.

It has been the dominant view that probabilistic explanations of particular facts must be inductive in character. I argue here that this view is mistaken, and that the aim of probabilistic explanation is not to demonstrate that the explanandum fact was nomically expectable, but to give an account of the chance mechanism(s) responsible for it. To this end, a deductive-nomological model of probabilistic explanation is developed and defended. Such a model has application only when the probabilities occurring in covering laws can be interpreted as measures of objective chance, expressing the strength of physical propensities. Unlike inductive models of probabilistic explanation, this deductive model stands in no need of troublesome requirements of maximal specificity or epistemic relativization.

I invoke the conceptual machinery of contemporary possible-world semantics to provide an account of the metaphysical status of “bridge laws” in intertheoretic reductions. I argue that although bridge laws are not definitions, and although they do not necessarily reflect attribute-identities, they are supervenient. I.e., they are true in all possible worlds in which the reducing theory is true.

In this paper a model is presented for the growth of knowledge in a dynamic scientific system. A system which is in some respects an idealization of a Lakatosian research program. The kinematics of the system is described in terms of two probabilistic variables, one of which is related to the evolution of its theoretical component and the other—to the growth of the empirical component. It is shown that when the empirical growth is faster than the theoretical growth the posterior probability of the theoretical component increases. Thus, empirical progressiveness of a research program, as explicated in this model, is accompanied by an increase in the degree of confirmation. In such a case the system grows in a Popperian-like spirit, while learning from experience in a Bayesian manner.

Theoretical simplicity is difficult to characterize, and evidently can depend upon a number of distinct factors. One such desirable characteristic is that the laws of a theory have relatively few “counterinstances” whose accommodation requires the invocation of a ceteris paribus condition and ancillary explanation. It is argued that, when one theory is reduced to another, such that the laws of the second govern the behavior of the parts of the entities in the domain of the first, there is a characteristic gain in simplicity of the sort mentioned: while I see no way of quantitatively measuring the “amount” of defeasibility of the laws of a theory, microreduction can be shown to decrease that “amount.”

The Relevance Criterion of confirmation gained prominence as the underlying principle of the class-size approach (CSA) to Hempel's paradoxes of confirmation. The CSA, however, yields counter-intuitive results for (c) instances, and this failing cast serious doubt on the acceptability of the Relevance Criterion. In this paper an attempt is made to rescue the Relevance Criterion from this embarrassment. This is done by incorporating that criterion into a new resolution of the paradoxes, a resolution based on a theory of selective confirmation and a distinction between mere confirmation in principle and evaluative confirmation (E-confirmation).

Extensive measurement is called weak if the axioms allow two objects to have the same scale value without being indifferent with respect to the order. Necessary and/or sufficient conditions for such representations are given. The Archimedean and the non-Archimedean case are dealt with separately.

Beauregard ([1], p. 488) claims that Bowman and I were mistaken in saying that “… if the empirical predictions of the Special Theory regarding clock transport are correct, [then] a slow transport definition of simultaneity can be constructed that is logically independent of any signal definition, but is in fact equivalent to the standard signal definition” ([2], p. 131) His objection is not to the empirical concordance of the two criteria, but to the claim that the two are logically independent. His argument is that we fail to take account of Winnie's Passage Time Principle ([4], p. 228), and that if due account is taken of this principle, then “the concordance between the two criteria is logically guaranteed by the synchrony-free factual core of the STR” ([1], p. 488). However, one cannot show that A is not logically independent of B by showing that it is not independent of B and C. Hence, Beauregard's argument fails against the quoted passage.

In [2] I have presented a sketch of a principle which I suggested was powerful enough to enable us with its aid to solve a number of well known problems in the philosophy of science. James Moor in [1] expresses the opinion that my principle is too strong so as to be destructive and proposes instead a considerably watered down alternative which may be used for constructive purposes only. I shall deal here with his two major objections only and show that on a careful enough analysis it becomes evident that he has not raised any difficulties for my principle.