A notation for the language of physics is given, and a system of axioms constructed. It is argued that from the standpoint of a ‘realistic’ ontology our method is preferable to Carnap's ‘coordinate languages.’ The primitive ideas are the part-whole relation μ and the set ℜ of coordinate systems. Only such statements are intended in the axioms as are non-controversial; i.e. no open cosmological questions are prejudged.

Although there is a complete consensus among working physicists with respect to the practical and operational meanings of quantum states, and also a rather loosely formulated general philosophic view called the Copenhagen interpretation, a great deal of confusion and divergence of opinions exist as to the details of the measurement process and its effects upon quantum states. This paper reviews the current expositions of the measurement problem, limiting itself for lack of space primarily to the writings of physicists; it calls attention to inconsistencies and proposes resolutions. Except for a summary of the properties of statistical matrices which are needed in Part II, the first part is non-mathematical and deals largely with two kinds of probability, reducible and irreducible probabilities, which need to be distinguished for a proper understanding of the measurement act.

Confirmation theorists seek to define a function that will take into account the various factors relevant in determining the degree to which an hypothesis is confirmed by its evidence. Among confirmation theorists, only Rudolf Carnap has constructed a system which purports to consider factors in addition to the number of instances, viz. the variety manifested by the instances and the amount of analogy between the instances. It is the purpose of this paper to examine the problem which these additional factors raise for confirmation theory, and to prove that, despite Carnap's claim, no confirmation function satisfying the requirements he has specified can take account of variety and analogy. This result is first proved for a special case, and then, in a subsequent section, is generalized through the introduction of a theorem (the proof of which is given in Appendix I). In the final section of the paper it is shown that, contrary to a claim which Carnap has made, not even the concept of the “logical width” of a predicate will enable confirmation functions satisfying his requirements to take adequate account of analogies between instances.

The conceptual excitement of science often seems geared only to work in contemporary physics. Thus, philosophers regularly discuss current cosmology, relativity, or the foundations of microphysics. In these areas one's philosophy is stretched and strained far beyond what our ancestors might have anticipated. Historians of science have also focused attention on past events by remarking their analogies and similarities with perplexities in physics today.

But there are statements, hypotheses and theories of the past which are rewarding in themselves, without having to be referred to the agonies which now confound quantum theory and cosmology. Specifically, the First Law of Motion—the “Law of Inertia”—this has everything a logician of science could look for. Understanding the complexities and perplexities of this fundamental mechanical statement is in itself to gain insight into what theoretical physics in general really is. With this in view a study of the law is undertaken.

This paper examines problems of order and periodicity which arise when the attempt is made to define a confirmation function for a language containing elementary number theory as applied to a universe in which the individuals are considered to be arranged in some fixed order. Certain plausible conditions of adequacy are stated for such a confirmation function. By the construction of certain types of predicates, it is proved, however, that these conditions of adequacy are violated by any confirmation function defined for the type of language in question.

Various possible solutions to these difficulties are explored and found tobe inadequate. In particular, a proposal which stems from the suggestion to restrict a fundamental principle of confirmation to hypotheses containing only non-positional predicates is cited. This proposal, however, is shown to prevent confirmation functions from taking periodicities into account, and so is deemed unsatisfactory. A general theorem is proved to the effect that if non-positional predicates are taken to satisfy the conditions of adequacy which have been formulated, then no periodicity predicates whatsoever (i.e., predicates used in formulating hypotheses which foretell periodicities) can be subject to these conditions, on pain of contradiction. Yet it seems that periodicity predicates must be subject to these conditions of adequacy if a confirmation function is to recognize periodic occurrences. Thus, an impasse seems to be reached.

In the final sections we consider the beginnings of one possible solution to these difficulties. Our proposal involves treating sets of individuals, rather than individuals themselves, as instances, of an hypothesis which predicts a periodicity. On this basis we formulate new conditions of adequacy which are free from the previous difficulties and which will permit a confirmation function that satisfies them to take periodicities into account.

Peter Achinstein gives in his papers [1] and [2] interesting analyses of some problems of inductive logic and of some approaches I have proposed. I shall discuss here some of these problems in order to clarify my present position. My comments will mainly concern the variety of instances, and only briefly the analogy influence, and the inductive methods for a coordinate language.

In this paper we attempt to formulate logical foundations for a theory of actions or performance. Human beings act in various ways, and their actions are intimately interrelated with their use of language. But precisely how actions and the use of language are interrelated is not very clear. One of the reasons is perhaps that we have no precise vocabulary in terms of which such interrelations may be handled. There is need for developing a systematic theory in which different kinds of actions may be discussed, contrasted, and compared. Then the various interrelations between actions and linguistic usage may perhaps be discussed rather more carefully and thoroughly than heretofore.

Although much important preliminary work has been done in the analysis of actions, no one it seems has attempted to develop a strict logical theory for such analysis. A few tentative and programmatic steps were taken in the author's Toward a Systematic Pragmatics.1 Let us attempt here to improve those and take a few more. Any first attempts of this kind are of course fraught with difficulties. There inevitably will be some oversimplification or some overelaboration here or there. Ultimately of course we are interested in interrelating performance with various notions from syntax, semantics, and quantitative pragmatics.2 But this is not easy and only a few tentative suggestions toward such a development can be given here.

In § 1 the distinction between action-kinds and action-events is drawn, and the character of the primitive or primitives needed for the theory of performance is discussed. In § 2 some further notions are then defined. Certain Rules of Performance are suggested in § 3. In § 4 there is discussion of the somewhat tenuous notion of acceptance as a basis for action. In § 5 the fundamental notions required for Parsons and Shils’ theory of social action is discussed briefly. In § 6 we attempt to define the two basic notions required in Leonard's recent papers concerning authorship and purpose. Finally, in § 7, the theory of performance is interrelated with von Wright's deontic logic, in which such notions as permission and obligation are considered.

This paper is intended to explore Jeffrey's proposal for the measurement of the simplicity of scientific laws. The first part is a sketch of Jeffreys’ development of a view on simplicity, which will be followed by a discussion of what seem to be some rather crucial defects in the proposal as it stands. It will be suggested here that no plausible way of countering these defects seems available.

In this paper, some qualitative scientific laws are treated in a way that is analogous to the method by which Karl Menger has clarified the nature of quantitative laws such as Boyle's law about ideal gases. The qualitative analogue of the number-valued fluents, such as temperature, are fluents whose domains consist of physical objects while their values are T and F (true and false).

This paper examines the current variant of the view that meaningful human actions are not amenable to causal, scientific explanation. Rather, the view examined holds that, understanding the language, we understand the meaning of other people's overt acts by analyzing the concepts appropriately applied to the situation, tracing their logical connections with other mentalistic concepts. A matter of conceptual analysis, our understanding of man is held to be a priori and necessary rather than, as with the natural sciences, a posteriori and contingent.

Various uses of ‘concept’, ‘meaning’, and ‘understanding’ are here distinguished. It is then shown, first, how the objectivist can in principle account for intentionality and for “rule-governed” behavior, that is, for the presence and efficacy of mind in the world. Secondly, current criticisms of the objectivist program are examined. An uncritical use of ‘concept’ and of ‘rule’, as well as a fusion of various uses of ‘meaning’ and ‘understanding’, gives those criticisms a specious plausibility that does not withstand close analysis. It is concluded that the objectivist program has not been shown to be untenable.

This is the second, mathematically more detailed part of a paper consisting of two articles, the first having appeared in the immediately preceding issue of this Journal∗. It shows that a measurement converts a pure case into a mixture with reducible probabilities. The measurement as such permits no inference whatever as to the state of the physical system subjected to measurement after the measurement has been performed. But because the probabilities after the act are classical and therefore reducible, it is often possible to adjust them so that Von Neumann's projection postulate is true.

Among the more specific features dealt with in Part II is the occurrence of negative joint probabilities for the measurement of non-commuting operators in certain (not all!) quantum states. The general conclusions reached are stated at the end of the article.

A theory of true observation is developed as a generalization of the method of inter-observer agreement that scientists use to determine the objectivity and reliability of observations. A true observation is defined as a statement included in a set of statements in which there is statistical dependence and perfect agreement between the statements made by a universe of experimentally independent persons. Meaningfulness—the existence of an objective referent—for each form of statement included in the set is inferred from statistical dependence, correct meaning within the universe of observers from the absence of disagreement. In this theory truth is inferred from a spatio-temporal pattern of statements as behavior rather than from the traditional correspondence between observation and object or logical relationships among statements.

The relations between simplicity and economy, and between simplicity and complexity, are briefly discussed, and it is suggested that an appearance of simplicity may arise out of the matching of two complexities, e.g. in the perception of a simple color. Following out this idea, it is shown that scientific activity may be regarded as a matching of theoretical complexity against the complexity of nature, which leads to an expectation of an optimum theoretical complexity for successful scientific work. Some senses of “success” in this context are discussed, and the role of computing machines in helping to achieve it assessed.

Recent discussions in the philosophy of science have devoted considerable attention to the analysis of conceptual issues relating to the methodology of explanation and prediction in the sciences. Part of this literature has been devoted to clarifying the very ideas of explanation and prediction. But the discussion has also ranged over various related topics, including the status of laws to be used for explanatory and predictive purposes, the logical interrelationships between explanatory and predictive reasonings, the differences in the strategy of explanatory argumentation in different branches of science, the nature and possibility of teleological explanation, etc. The aim of the present article is to examine the issues involved in such questions from the specialized perspective afforded by one particular kind of physical systems—namely, systems, here to be characterized as discrete state systems, whose behavior has been studied extensively in the scientific literature under the general heading of Markov chains. These systems have been chosen as our focus because their behavior over time can be analyzed at once with great ease and with extraordinary precision.

This article is concerned to argue that the social sciences and notably social anthropology, must necessarily be concerned with the physical environment of the societies investigated (which includes the biological nature of its members), and not only with the social reality which is at the centre of their concern. This is argued with special reference to fields such as kinship and politics, and to social relationships such as paternity or feuding. The article is concerned to refute arguments put forward in support of the logical autonomy of social studies, particularly in the sphere of kinship, in earlier articles by Barnes and Needham.

A mathematical theory is proposed and exemplified, which covers an extended class of black boxes. Every kind of stimulus and response is pictured by a channel connecting the box with its environment. The input-output relation is given by a postulate schema according to which the response is, in general, a nonlinear functional of the input. Several examples are worked out: the perfectly transmitting box, the damping box, and the amplifying box. The theory is shown to be (a) an extension of the S-matrix theory and the accompanying channel picture as developed in microphysics; (b) abstract and applicable to any problem involving the transactions of a system (physical, biological, social, etc.) with its milieu; (c) superficial, because unconcerned with either the structure of the box or the nature of the stimuli and responses. The motive for building the theory was to show the capabilities and limitations of the phenomenological approach.

This paper deals with the problem of vindicating a particular type of inductive rule, a rule to govern inferences from observed frequencies to limits of relative frequencies. Reichenbach's rule of induction is defended. By application of two conditions, normalizing conditions and a criterion of linguistic invariance, it is argued that alternative rules lead to contradiction. It is then argued that the rule of induction does not lead to contradiction when suitable restrictions are placed upon the predicates admitted. Goodman's grue-bleen paradox is considered, and an attempt to resolve it is offered. Finally, Reichenbach's pragmatic argument, hinging on convergence properties, is applied.

Tarski's equivalence, as he allows, applies only roughly to assertions in ordinary language. Some of the relevant exceptions are of merely grammatical importance but others leave scope for interesting metaphysical pronouncements on science, mathematics and other fields of assertion. To understand these latter exceptions is to gain insight into Baylis’ and Lukasiewicz’ views on the question “Are some Propositions neither True nor False?” (this journal, 1936). From different standpoints each is right and each is wrong. This comment also applies to some later contributions to their controversy.