Lately, an increased interest in formal devices has led to an attempt on the part of some mathematicians to do without those aspects of mathematics which require intuition. One consequence of this movement has been a new conception of pure mathematics as a science of axiomatic systems. According to this conception, there is no reality beyond an axiomatic system which the statements of mathematics are about; the fact that a statement is a theorem in the system is all that is of interest. This is a sort of nominalist position, since the contrary position seems to be committed to a belief in the existence of a domain of mathematical entities, which are just as suspect as the universale commonly discussed in metaphysical treatises. More often it is called formalism.

The period between 1945 and 1952 marked the development of Professor Ryle's conception of the principles of inference as performance rules. This development has paralleled that of his now well-known distinction between knowing-how and knowing-that. Indeed, the former is a corollary to the latter. Beginning with the inaugural address to the Aristotelian Society in 1945 (2) and reaching full fruition in The Concept of Mind in 1949 (4), it finds its most detailed and illuminating expression in “‘If’, ‘So’, and ‘Because’,” which appeared in 1950 (5). The present essay will attempt to explore this conception of rules in some detail, in the hope of clarifying the nature of Professor Ryle's views on classical logic and on certain problems within the philosophy of logic. Professor Ryle belongs, if his views may be so labeled, to the school of informal language analysts. On the other hand, we incline more toward formalism. We tend to agree with those philosophers who consider certain schemata indispensable tools for the solution of philosophical problems. Logic and the philosophy of logic are, as everyone knows, the areas in which the formalists’ technique originated. In these areas it is accepted by virtually everybody. The only recent exception is a group of English writers, many of whom take their inspiration from Ryle. One may hope, then, that the present criticism of Ryle's view from the other standpoint will throw some light on both positions. What follows falls naturally into two parts. The first deals mainly with Ryle's objections to current logical theory, the second with his own philosophy of logic.

Current preoccupation with learning-theory has led psychologists, and other social scientists, to expect more from it than can presently be delivered. The subsequent reflections are submitted in order to suggest that at least some formulations of the relation between learning-theory and the “culture-concept” are somewhat defective. More specifically, I shall examine two recent contributions by O. K. Moore (one of which appeared in this journal (1)), whose attempts at definition are distiguished by the employment of the formidable weapons of symbolic logic. Without denying the advantages to be gained, by the sciences in general and the social sciences in particular, from the introduction of this new logic, I would justify my critical concern with Moore's definition of “culture” in terms of “learning-theory,” because it may become representative of other contributions whose partial inadequacies are easily obscured by the technicality of a symbolic language into which the actual empirical complexity of an issue could be falsely thought to have been properly translated.

1. Introduction. The germ of the clock paradox was contained in Einstein's fundamental paper on the special theory of relativity, where he declares that the retardation of a moving clock “still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.” This remark soon gave rise to a criticism which was to play a prominent role in the discussions of the consistency of the theory of relativity. It was charged that this theory allows the paradoxical conclusion that at the instant of the return of a moving clock U1 to its point of departure A, the time shown by Ul is both earlier and later than the corresponding reading of a clock U2 which has remained stationary at A during U1's journey. Critics based this contention on the following assumptions, for which they claimed the sanction of relativity: (i) The relative motion of U1 and U2 is such that the kinematic process seen by an observer on one of these clocks is of the same character as that seen by an observer on the other, and this symmetry allows each of these two clocks to be used as a reference frame from which to describe the motion of the other, and (ii) there is reciprocity between these two reference frames such that in each of them, the moving clock must be slow upon returning to the stationary one.

There has been much discussion in recent years of the possibilities for and nature of “value science.” The present paper is intended to be a contribution to this discussion. One encouraging feature of the bulk of current discussion of value science is that its protagonists have a definite end in view, namely, “human betterment,” taking that phrase in the common sense as covering, at least, a process of creating and maintaining such conditions of life as enable human beings successfully to engage in satisfying activities.

When, in recent years, philosophers of science attend to the physical sciences, their activity centers on the analysis and clarification of the methods and theories of these sciences. Thus philosophers have made remarkable contributions to our understanding of mechanics, the relativity theory, the quantum theory, probability, and geometry, as well as to the foundations of mathematics. More general discussions about theory construction, explanation, and concept formation always are illustrated and illuminated by reference to specific theories within science. In our generation, most philosophers of science have taken for granted that physical science is descriptive, empirical, functional, and—leaving aside controversial interpretations of quanta—deterministic.

The purpose of this note is to present a set of rules for the syllogism which not only is equivalent with the set ordinarily used, but also is the dual of the latter. It must be emphasized, however, that the discussion of both of these sets presupposes the hypothetical interpretation of universal propositions, and would not hold true of the existential interpretation of such propositions. A universal proposition is interpreted hypothetically, rather than existentially, when it is not assumed that the class denoted by its subject must have members. Thus the hypothetical interpretation of “All unicorns are mammals” would be just “If anything is a unicorn, then it is a mammal—but it is not necessarily true that unicorns exist.” One important consequence of the distinction between these two modes of interpretation is that rule 3, below, is true for the hypothetical interpretation, but not for the existential.

It has been shown by several authors that in operations involving information a quantity appears which is the negative of the quantity usually defined as entropy in similar situations. This quantity ℜ = − KI has been termed “negentropy” and it has been shown that the negentropy of information and the physical entropy S are mirrorlike representations of the same train of events. In physical terminology the energy is degraded by an increase in entropy due to an increased randomness in the positions or velocities of components, wave functions, complexions in phase space; in informational terminology some information about the same components has been lost or the negentropy has been decreased. In equilibrium the system has for a given energy content maximum randomness (or minimum information is required). One consequence of this dual aspect was the idea to apply the methods of statistical mechanics to problems of communication and Brillouin showed that Fermi-Dirac statistics or generalized Fermi statistics are applicable for example to a transmission of signals such as telegrams.

Philosophizing about the social sciences involves an initial problem of denotation. Although the natural sciences are the scene of intramural disputes like those between proponents of quantum mechanics and relativity theory, no one doubts either what the natural sciences are or that they are sciences; and all of them may be said to use, broadly speaking, the same scientific method. But the case of the social sciences is different. It resembles somewhat the situation in mathematics where the intuitionists deny that non-constructible concepts or problems belong to mathematics; and even more the situation in philosophy where groups like the analysts and the existentialists not only do not speak the same language but do not even recognize one another's right to be called “philosophy.” Similarly, the disciplines which comprise the social sciences today differ from one another in basic ways, involving long-standing disputes over which ones have a right to the names of the several social sciences and what their proper methods are. Familiar examples of these disputes are the controversies between the classicists and institutionalists in economics, and between the analytical and sociological schools in jurispurdence. Consequently, it is impossible for philosophers, or social scientists philosophizing about their general field, to proceed to discuss “the” subject-matter or “the” method of “the” social sciences as if the phrases containing these definite articles were definite descriptions on whose objects there was general agreement.

When the terms ‘control’ and ‘experiment’ are used in reference to the methodological procedures of the social sciences, frequently the question is raised as to whether or not the investigator uses the terms in the same sense as the natural scientist. The purpose of this paper is to show that the social scientist has good reason to use them in the same sense and that in fact this usage is consistent with a long tradition of social research. This will be shown by an investigation of some common assumptions in the social sciences, such as, (a) the claim that the social sciences are younger than the natural sciences and that the former have depended upon the latter for methodological cues, (b) that human behavior is ultimately inexplicable and unpredictable, and (c) that the social scientist is unable to observe human behavior under controlled, experimental conditions except in trivial instances. Of course, not all social scientists make these assumptions but they occur in the literature and their significance is considerable when the scientific status of the social sciences is being discussed.

I wish, for the sake of the vivacity of any discussion which might ensue, that I could find myself more in disagreement with Dr. Brodbeck than I do. As a matter of fact, however, I find myself in substantial agreement with her on practically all of the points upon which she takes issue with Hayek. There are, to be sure a few questions of relatively minor import that I should like to ask Dr. Brodbeck, but in the main I have confined my own discussion to an elaboration and supplementation of some of the points considered in her paper, and some related considerations raised in Hayek's book but which Dr. Brodbeck did not have the time, perhaps, to treat.

In his reexamination of the relationship between quality and quantity, Professor Plochmann has avoided the method of linguistic analysis in favor of a more traditional method of philosophizing. Since I agree with him that in general quality and quantity are irreducible one to the other, but may both be reducible to some category more fundamental than either, my comments are to be considered supplementary to his. In particular, I should like to see what clarifications, if any, arise if one considers qualities and quantities from the purely linguistic point of view.