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.

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.

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).

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.

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.