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.

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 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.

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.