We now proceed to define certain terms which we shall apply to sets of axioms and derive a few properties. A great deal of what follows in this section is still based on a two-valued logic, while our criticism of the usual independence and consistency proofs is based on an n-valued logic. The necessary alterations are now being worked out by the author.

This paper is a tentative step toward formalizing in symbolic logic some of the central assumptions of Clark L. Hull's theory of behavior. There will be noticeable deviations from Hull's own terminology and form of statement, but this will be largely in the interest of greater logical simplicity. The notation of symbolic logic will not be used, but the behavioral axioms will be so stated as to admit of easy translation into such notation. Such easy translatability seems to be a prerequisite if theorems are to be derivable with genuine deductive rigor.

This essay explores the metaphorical use of the area of nonlinear dynamics popularly known as “chaos theory,” surveying its use in one particular field: legal theory. After sketching some of the mistakes encountered in these efforts, I outline the possibility of the fruitful use of nonlinear dynamics for thinking about our legal system. I then offer some general lessons to be drawn from these examples—both cautionary maxims and a limited defense of cross-disciplinary borrowing. I conclude with some reflections on the nature of arguments that seek to establish intellectual authority or epistemic merit by analogical reasoning.

This paper states two sets of axioms sufficient for extensive measurement. The first set, like previously published axioms, requires that each of the objects measured must be classifiable as either greater than, or less than, or indifferent to each other object. The second set, however, requires only that any two objects be classifiable as either indifferent or different, and does not need any information about which object is greater. Each set of axioms produces an extensive scale with the usual properties of additivity and uniqueness except for unit. Moreover, the axioms imply Weber's Law: whether two objects are indifferent depends only upon the ratio of their scale values.

This study is an attempt partially to describe the sociological foundations of modern science. When the question is put, under what social circumstances did the idea of science develop, one sees that there is here an inadequately explored sociological area. Perhaps a definition and a contrast will make this clearer. By the idea of science is meant simply the proposition that the valid source of human knowledge is to be found in the analysis of experience. But knowledge in this sense was not a problem in the medieval period. In the first place, it was then taken for granted that the universe was intelligible to man on the basis of divinely revealed principles. Secondly, man constituted the center of the universe, which in its entirety was thought to be subordinate to man's destiny. Thirdly, not only was the universe which existed for man then known by him, but it was endowed with human qualities. The categories of interpretation were substance, essence, form, matter, quality, and purpose. The reason why rain fell upon the earth was to grow crops; the purpose of the moon and the stars was to light the earth at night, and to act as guideposts for him on his travels. Bodies tended to their proper places, light ones upward, heavy ones earthward. Quantitative differences were inferred from these qualitative ones. It is well-known, for example, how tenaciously was the knowledge held, that heavier objects fall more quickly than lighter ones. And finally, the universe was religious. If the world existed for the benefit of man, man existed for the glory of God. Human sojourn upon the earth was merely preparation for permanent residence in eternity.

The widespread publicity and the consequent furor created by Dr. J. B. Rhine's experiments on telepathy and clairvoyance, have been interpreted in some quarters as a call for a thorough-going revision of the entire field of psychological thought. This revision, it is held, must be in the direction of philosophic idealism, and away from previously accepted materialistic doctrines. The present paper points out the non-verifiable nature of the entities postulated by the believers in “supernormal” phenomena. Furthermore, the interpretations of contemporary science held by such individuals are not in themselves on a scientific plane. Specific errors in reasoning made by workers in the field of psychical research, are presented. In short, “psychical research … cannot turn the universe into a non-material, non-objective one, on either the basis of misinterpretations of current physical thought or on the basis of its own work.”

To illustrate one way in which philosophy may be helpful rather than merely critical in the present state of psychoanalytic theorizing, an attempt is made to disentangle issues in controversies about the unconscious. Eleven questions are distinguished and discussed. Logical, linguistic, methodological, metaphysical, empirical, and pragmatic components are set apart. It is found that there are no logical barriers to a construct of the unconscious, that it is linguistically feasible, need violate no methodological concepts, nor foreclose a metaphysical issue, nor have deleterious pragmatic effect. Feasibility and desirability of the construct in all these respects will depend on the character and extent of the scientific findings. Some issues are also raised concerning desirable types of models in the explanation of conduct, and concerning the relevance of recent studies of consciousness.

In this paper, I elucidate the main points involved in the question of the non-triviality of the conventionality of simultaneity within the kinematics of special relativity. I argue that there is an important distinction to be made between the inherited component and the sui generis component of the conventionality of simultaneity. The factual core of the kinematics of special relativity is explored, and it is shown that the Round-Trip Clock Retardation effect obtains if, and only if Winnie's Passage Time Principle holds. Some consequences of this fundamental fact are then explored. In particular, Grünbaum's view that the epistemological conventionality of simultaneity is logically prior to the physical inter-frame relativity of simultaneity is found to be based largely on what I call the inherited component of the former. Finally, a question is raised as to the very self-consistency of the claim, made by Ellis and Bowman, that standard signal synchrony and slow-transport synchrony are logically independent. In some concluding remarks, the author's general agreement with Grünbaum's conception of bridled conventionalism is indicated.

Abner Shimony called it coherence; John Kemeny called it strict fairness; today many people speak of strict coherence. According to Shimony's definition, a set of betting rates on a series of propositions hi and ei is strictly incoherent, when “there exists a choice of stakes Si such that, if X accepts the series of bets at these stakes, then no matter what the actual truth values of hi, and ei may be, X can at best lose nothing, and in at least one possible eventuality he will suffer a positive loss” ([3], p. 9).

Carl G. Hempel has often stated that inductive-statistical explanations, as he conceives them, are inductive arguments. This discussion note raises the question of whether such arguments are to be understood as (1) arguments of the traditional sort, containing premises and conclusions, governed by some sort of inductive “acceptance rules,” or (2) something more closely akin to Carnap's degree of confirmation statements which occur in an inductive logic which entirely eschews inductive “acceptance rules.” Hempel's writings do not seem unequivocal on this issue. It is suggested that adoption of construal (2) would remove the need for Hempel's high probability requirement on I-S explanations.

Ludwig Wittgenstein and certain of his friends and followers have offered an interesting answer to the question of the relation “one fact (such as a sentence) [must] have to another in order to be capable of being a symbol for that other”. The answer in brief, as Russell puts it, is that, “in order that a certain sentence should assert a certain fact there must … be something in common between the structure of the sentence and the structure of the fact”. Wittgenstein himself in the Tractatus usually denominates this common element as logical structure. The sentence is said to picture its fact; it reflects, mirrors, shows or exhibits by means of its own structure the structure of the fact it is about. Critics and interpreters generally agree with Russell's broad characterization of the theory but disagree greatly as to the exact nature of this postulated common structure. Consequently, the evaluation of the theory which this paper proposes to make must include an examination of its several alternative interpretations.

In this study we shall analyze the postulate set into its various elements. In order to carry out our analysis, it is advisable to have before us a typical set.

We take the set of five postulates for Boolean Algebras given by H. M. Sheffer in Trans. Am. Math Soc. 14, p. 482 ff.

The basic issues which this paper will be concerned with are: how has history been defined, what has been asked about history, and what sort of answers have been found. These questions may also be stated as: what is the nature of historical theory (since “theory” here will mean any set of definitions, assumptions, and operating hypotheses) and how do different theories affect what may “be done” with history.