The aim of this paper is to present and discuss a probabilistic framework that is adequate for the formulation of quantum theory and faithful to its applications. Contrary to claims, which are examined and rebutted, that quantum theory employs a nonclassical probability theory based on a nonclassical “logic,” the probabilistic framework set out here is entirely classical and the “logic” used is Boolean. The framework consists of a set of states and a set of quantities that are interrelated in a specified manner. Each state induces a classical probability space on the values of each quantity. The quantities, so considered, become statistical variables (not random variables). Such variables need not have a “joint distribution.” For the quantum theoretic application, there is a uniform procedure that defines and determines the existence of such “joint distributions” for statistical variables. A general rule is provided and it is shown to lead to the usual compatibility-commutivity requirements of quantum theory. The paper concludes with a brief discussion of interference and the misunderstandings that are involved in the false move from interference to nonclassical probability.

Discussions of the interpretation of quantum theory are at present obstructed by (1) the increasing axiomania in physics and philosophy which replaces fundamental problems by problems of formulation within a certain preconceived calculus, and (2) the decreasing (since 1927) philosophical interest and sophistication both of professional physicists and of professional philosophers which results in the replacement of subtle positions by crude ones and of dialectical arguments by dogmatic ones. More especially, such discussions are obstructed by the ignorance of both opponents, and also defenders of the Copenhagen point of view, as regards the arguments which once were used in its defence. The publication of Bunge's Quantum Theory and Reality and especially of Popper's contribution to it are taken as an occasion for the restatement of Bohr's position and for the refutation of some quite popular, but surprisingly naive and uninformed objections against it. Bohr's position is distinguished both from the position of Heisenberg and from the vulgarized versions which have become part of the so-called “Copenhagen Interpretation” and whose inarticulateness has been a boon for all those critics who prefer easy victories to a rational debate. Einstein's main counterargument is discussed, and Bohr's refutation restated. The philosophical background and earlier forms of Bohr's views are stated also. Considering that these views are more detailed, better adapted to the facts of the microdomain than any existing alternative it follows that fundamental discussion must first return to them. Their uniqueness is not asserted, however. Here the author still maintains that a hundred shabby flowers are preferable to a single blossom, however exquisite. But a hundred shabby flowers plus an exquisite blossom are more desirable still.

The overall purpose of this paper is to clarify the physical meaning and epistemological status of the term ‘measurement’ as used in quantum theory. After a review of the essential logical structure of quantum physics. Part I presents interpretive discussions contrasting the quantal concepts observable and ensemble with their classical ancestors along the lines of Margenau's latency theory. Against this background various popular ideas concerning the nature of quantum measurement are critically surveyed. The analysis reveals that, in addition to internal mathematical difficulties, all the so-called quantum theories of measurement are grounded in unjustifiable, classical presuppositions.

After precisely specifying the thesis of the causal theory of time, Grünbaum's program developed to support this thesis is examined. Four objections to his definition of temporal order in terms of a more primitive causal relation are put and held to be conclusive. Finally, the philosophical arguments that Grünbaum has proposed supporting the desirability of establishing a causal theory of time are shown to be either invalid or inconclusive.

It is now commonly accepted that N. Goodman's predicate “grue” presents the theory of confirmation of C. G. Hempel (and other such theories) with grave difficulties. The precise nature and status of these “difficulties” has, however, never been made clear. In this paper it is argued that it is very unlikely that “grue” raises any formal difficulties for Hempel and appearances to the contrary are examined, rejected and an explanation of their intuitive appeal offered. However “grue” is shown to raise an informal, “over-arching” difficulty of great magnitude for all theories of confirmation, including Hempel's theory.

To what extent is the scientist's endeavor qua scientist influenced by his philosophic image of himself? A preliminary and partial answer to this question is suggested by a study of eight physiological thinkers of the second half of the eighteenth century, a period during which biology was much influenced by the scientific and philosophical ideas of Isaac Newton. At this time, physiologists invoked certain “principles,” “properties,” and “powers” which were deemed useful as explanatory devices, even though they could not themselves be explained. The use of these devices in physiology was often defended in terms of their supposed similarity to devices used in mathematics and Newtonian physics. The results of this practice are considered critically, partly in the light of current studies of scientific explanation.

The article is a reappraisal of the requirement of maximal specificity (RMS) proposed by the author as a means of avoiding “ambiguity” in probabilistic explanation. The author argues that RMS is not, as he had held in one earlier publication, a rough substitute for the requirement of total evidence, but is independent of it and has quite a different rationale. A group of recent objections to RMS is answered by stressing that the statistical generalizations invoked in probabilistic explanations must be lawlike, and by arguing that predicates fit for occurrence in lawlike statistical probability statements must meet two conditions, at least one of which is violated in each of the counterexamples adduced in the objections. These considerations suggest the conception that probabilistic-statistical laws concern the long-run frequency of some characteristic within a reference class as characterized by some particular “description” or predicate expression, and that replacement of such a description by a coextensive one may turn a statement that is lawlike into another that is not. Finally, to repair a defect noted by Grandy, the author's earlier formulation of RMS is replaced by a modified version.

It is generally agreed that the method of explication consists in replacing a vague, presystematic notion (the explicandum) with a precise notion (the explicatum) formulated in a systematic context. However, Carnap and others who have used this and related terms appear to hold inconsistent views as to what constitutes an adequate explication. The central feature of the present explication of ‘explication’ is the correspondence condition: permitting the explicandum to deviate from some established “ordinary-language” conventions but, at the same time, requiring that the explicatum correspond (via an effective translation) to the chosen “definitive intension” of the explicandum. (In effect, the first stages of an explication provide an informal characterization of a vague and possibly inconsistent language convention.) The present account of explication contrasts sharply with that sketched by Quine in Word and Object (although Quine accepts a correspondence condition of a sort). The terms ‘explication1’ and ‘explication2’ are used to indicate these quite different senses of the term. In Kaplan's terminology, explication1 is intended to remedy “external vagueness” while explication2 is intended to remedy “internal vagueness.”

In this paper I attempt to elucidate the nature of that sense of ‘methodology’ which is concerned with the strategics, techniques, and procedures of scientific experimentation. It is claimed that methodology in this sense is at bottom a set of logical relations between sentences expressing pervasive facts of the subject matter and sentences describing experimental behavior. In particular a successful methodology is one in which the set of these sentences is logically consistent. I then turn to the problems involved in teaching and learning an explicit methodology. Finally, I argue that this analysis throws fresh light on the distinction between knowing a fact and possessing a skill or competence.

An objective and relational theory of local time is expounded and its philosophical implications are discussed in Sect. 2. In Sect. 3 certain physical and metaphysical questions concerning time are taken up in the light of that theory.

Some materialists argue that we can eliminate mental entities such as sensations because, like electrons, they are theoretical entities postulated as parts of scientific explanations, but, unlike electrons, they are unnecessary for such explanations. As Quine says, any explanatory role of mental entities can be played by “correlative physiological states and events instead.” But sensations are not postulated theoretical entities. This is shown by proposing definitions of the related terms, ‘observation term,’ and ‘theoretical term,’ and then classifying the term ‘sensation.’ The result is that although ‘sensation’ is a theoretical term, it is also a reporting term because it is used to refer to phenomena we are aware of. Consequently sensations are not postulated and cannot be eliminated merely because they are unnecessary for explanation.

This portion of the essay concludes a two-part paper, Part I of which appeared in an earlier issue of this Journal. Part II begins with a careful study of the quantum description of real experiments in order to motivate a proposal that two distinct quantum theoretical measurement constructs should be recognized, both of which must be distinguished from the concept of preparation. The different epistemological roles of these concepts are compared and explained. It is then concluded that the only possible type of “quantum measurement theory” is one of little metaphysical interest and that quantum measurement seems problematical only when viewed from an overly narrow classical perspective.

Controversy over the adequacy of the regularity or covering law theory of explanation when applied to historical actions continues to rage. A detailed analysis is here made of Professor A. Donagan's recent attack on this theory, as representative of many others. His alternative model of deductive non-law explanation, based on Popper's notion of the “logic of the situation,” is then shown to be invalid and generally defective. Finally, four sources of the difficulty are elicited which, when resolved, provide support for the regularity theory in its probabilistic version. We suggest that this theory, despite recent criticism, can be fruitfully extended to historical explanation by uncovering and codifying a major difference between history and science, the rational actions of historical agents, without distorting it.

When Hempel's “paradox of confirmation” is developed within the confines of conditional probability theory, it becomes apparent that two seemingly equivalent generalities (“laws”) can have exactly the same class of observational refuters even when their respective classes of confirming observations are importantly distinct. Generalities which have the inductive supports we commonsensically construe them to have, however, must incorporate quasi-logical operators or connectives which cannot be defined truth-functionally. The origins and applications of these “modalic” concepts appear to be intimately linked with a number of basic conundrums in the philosophy of science, such as causation and the nature of explanation.

The metamathematical theorems of Gödel and Church are frequently applied to the philosophy of mind, typically as rational evidence against mechanism. Using methods of Post and Smullyan, these results are presented as purely mathematical theorems and various such applications are discussed critically. In particular, J. Lucas's use of Gödel's theorem to distinguish between conscious and unconscious beings is refuted, while more generally, attempts to extract philosophy from metamathematics are shown to involve only dramatizations of the constructivity problem in foundations. More specifically, philosophical extrapolations from metamathematics are shown to involve premature extensions of Church's thesis.

1. Introduction. Professor Nagel's account of the “cognitive status” of scientific theories has been attacked by P. K. Feyerabend [5] and M. B. Hesse [8] in terms of his alledgedly misguided distinction between experimental laws and theories. The difficulty lies, these critics agree, in Nagel's attempt to find a stable basis for scientific theories in an observational basis of experimental laws. Both Feyerabend and Hesse note the vacillation in Nagel's account of the stability of the meaning of experimental terms and in his discussion of the status of observational as opposed to theoretical terms. They find Nagel too “positivistic” and see as a first step toward a more adequate account of scientific theories the abandonment of the theoretical-observational dichotomy as having more than a pragmatic significance. Nagel's discussion of the theoretical-observational dichotomy is, I agree, inadequate in certain respects. I shall, however, suggest a quite different remedy from those of Feyerabend and Hesse, one that depends neither on a phenomenalistic reduction of theoretical entities nor on a blurring of the theoretical-observational dichotomy.

In his article [5], Brian Skyrms adduces (on p. 233) some generalizations which, he claims, receive no confirmatory support from their positive instances even though all the predicates they contain are well entrenched in Goodman's sense. Invoking the principle that “a generalization is lawlike if it is capable of receiving confirmatory support from its positive instances” (p. 232; actually, the converse is needed and, I will assume, intended by him), he claims that his examples “provide striking demonstration of the fact that the lawlikeness of a hypothesis is not a simple function of the projectibility of its constituent predicates.” I think the claim is of great interest; but I will try to show that Skyrms's argument fails to establish it because it presupposes an unwarranted assumption which raises a problem of general importance for confirmation theory.

Professor Bergmann is an original thinker who has for many years wrestled with some of the most important and difficult problems of philosophy. Although at first mainly interested in epistemology, he has gradually come to the conclusion that the fundamental questions of philosophy are ontological and that even epistemology is in the last analysis “the ontology of the knowing process.” He holds that by neglecting the explicit formulation of his ontology, a philosopher courts intellectual disaster because the inadequacies of the ontological foundation are likely to affect all philosophical superstructures built on it. In his last book [1], Bergmann explains some of the main features of his ontology in systematic form and criticizes competing systems, especially those of Brentano and Meinong, by comparing them with his own. In the critical parts of his work he tries to show that the competing ontologies are not adequate to the tasks for which they are intended and why this is so. The constructive and the critical parts supplement each other very well, since Brentano's and Meinong's questions and emphases are similar to Bergmann's. Broadly speaking, he regards his own ontology as a phase in a development of ontological insight which consists, at least negatively, in the gradual elimination of three major errors: nominalism, reism, and representationalism.