Professor Everett W. Hall's new book, Modern Science and Human Values, one of the most important to have appeared in the field of Value Theory in the last ten years, shares in rich measure the common characteristic of so many other “prolegomena” to the future discipline of values: it is almost maddeningly frustrating. It sees with crystal clearness the essence of the scientific method and describes it in brilliant detail, from Galileo to Einstein; but it fails to draw a positive moral for value theory. On the contrary, its thesis is thoroughly negative: although value must be known as thoroughly as fact if the world is to survive, the scientific method that has brought us knowledge of fact can never bring us knowledge of value. For fact and value are fundamentally different, fact is known by science in a way that excludes value, and hence, whatever may be the way by which value is to be known, it cannot be science. It is true, science has given the most powerful and incisive formulation to fact while value theory has done nothing of the sort for value. Value theory, therefore, must be brought up to the level of science, otherwise there is danger that we may perish under the impact of science. But how to bring this about, how to construct a value theory as powerful and as representative of value as science is of fact, that is the question which the book can only ask but not answer.

In 1954 Hempel wrote “Once the idea of a partial specification of meaning is granted, it appears unnecessarily restrictive, however, to limit the sentences effecting such partial interpretation to reduction sentences in Carnap's sense. … Generally, then, a set of one or more theoretical terms, t1, t2 ⃛, tn, might be introduced by any set M of sentences such that (i) M contains no extralogical terms other than t1, t2 ⃛, tn, and observation terms, (ii) M is logically consistent, and (iii) M is not equivalent to a truth of formal logic. The last two of these conditions serve merely to exclude trivial extreme cases. A set M of this kind will be referred to briefly as an interpretative system, its elements as interpretative sentences.” This is the last move in a process in which the idea of definition has been widened beyond the explicit or equivalence definition which was the basis of earlier thought on the subject of introducing new words into a language. It would seem that the scheme proposed by Hempel must represent the final move, for it would seem difficult to conceive any more liberal description of a purely direct and verbal scheme (that is, one excluding watching, and processes of suggestion). Among the predecessors of Hempel in this liberalising movement I will mention Ramsey and Braithwaite whose views stem ultimately from Campbell, and are based on the idea that the “interpretative system” is essentially a scientific theory, and Carnap who introduced the particular notion of a “reduction sentence” (mentioned in the quotation above), and who was more directly the source of Hempel's own ideas.

By dialectical fundamentalism I mean the view that maintains the inerrancy of the orthodox classical scriptures of dialectical materialism; by flexible scientific naturalism I mean the view recognizing the past heuristic value of dialectical materialism, but also the realization for the need to develop and change it along lines suggested by complementary philosophies relevant to the scientific outlook.

The Reformation, it has been said, changed the course of history. Most people would agree. At the very least, agree or not, they would hold the proposition to be one worth considering. They would be unlikely to reject it out of hand as incapable of being either true or false because it had no meaning. For, of course, “everybody knows” what the Reformation was and, elaborating a little, we can make clear what we meant by changing the course of history. Yet it is just statements of this sort that cause much methodological wrangling. Their controversial nature is due, in large part, to controversy over the status of such terms as “the Reformation” and, generally, group or macroscopic concepts. Since not only history, but sociology, political science, social psychology, and economics also widely use concepts referring to groups and their properties, rather than to individuals, the controversy has wide ramifications. And because there are, as it were, so many vested interests involved, the dispute also tends to acquire an ideological tone not altogether consonant with dispassionate inquiry. Bad temper and mutual recrimination in scientific discussion are generally a sign that ideological defenses are being shored up. Just possibly, a philosopher whose substantive concern in any empirical field is minimal may hope to be considered above the battle, as one who, having no private axe to grind, can be concerned only with clarifying the logical issues involved. In this hope, I wish to explore as systematically as possible the tangled web of issues woven about the status of group concepts and their relationship to those referring to individuals. Intertwined in this controversy are two different issues. One has to do with the nature of the terms or concepts of social science; the other with the nature of its laws and theories and their relationship in turn to those in other areas. The first issue is one of meaning, the second of reduction. Success in unsnarling the various strands of this web may alone help abate the fury of the controversy.

Radical ethical relativism as presented in Ruth Benedict's Patterns of Culture not only denies absolute values, its thesis of the incommensurability of cultural configurations precludes possibility of any agreement on values by individuals of different cultures. This fact provides the proper perspective from which to judge the current controversy between radical and “modified” ethical relativists. A double error is committed, therefore, by those who contend that there has been no reduction of the “area of indeterminacy” existing between the ethical principles of different cultures since, despite the newer developments in the social sciences, there are still no absolutely valid ethical values. Not only is the term “validity” vague and in need of reinterpretation, but, in assuming the denial of absolute values to be the distinguishing characteristic of radical relativism, they actually identify this theory with modified relativism. This brief paper attempts to prove the untenability of the denial of cross cultural agreement on ends and means by treating the question first, from the point of view of C. L. Stevenson's Dewey-inspired notion of the derivation of ends from means, and, second, from that of Stevenson's more original idea, complex ethical agreement.

Moral philosophers have often felt the need of a concept which would cover all those cases where we are prevented from achieving our ends through no fault of our own: a criterion for saying when failure is not blameworthy. The deontologists thought we were not to blame for actions done in genuine ignorance of the facts. Kant declared in a famous passage that we were not morally responsible for failures due to the “niggardliness of stepmother nature.” In this article I want to introduce into moral philosophy a new concept for clarifying the failures for which we are not to blame: the notion of scarcity, taken from economic theory.

The trouble with the idea of measurement is its seeming clarity, its obviousness, its implicit claim to finality in any inquisotory discourse. Its status in philosophy of science is taken to be utterly primitive; hence the difficulties it embodies, if any, tend to escape detection and scrutiny. Yet it cannot be primitive in the sense of being exempt from analysis; for if it were every measurement would require to be simply accepted as a protocol of truth, and one should never ask which of two conflicting measurements is correct, or preferable. Such questions are continually being asked, and their propriety in science indicates that even measurement, with its implication of simplicity and adroitness, points beyond itself to other matters of importance on which it relies for validation.

When a body is turned through 180°, reversal occurs in two dimensions. If it is turned about the vertical axis, then left and right sides change places, and also front and back. If it is turned about the horizontal axis which runs from side to side, then top and bottom change places, and also front and back. If, finally, it is turned about the horizontal axis which runs from front to back, then left and right change places as well as top and bottom. All this appears to follow from the properties of three-dimensional space and of rigid bodies. If XOX' is the axis of rotation of a three-dimensional structure, then there are two axes YOY' and ZOZ' at right angles to XOX', and if one of these moves round 180°, then so must the other. It follows that a body is always reversed in two dimensions whenever it is turned about an axis in the third. It follows also that there are always two ways of turning a body in space so as to reverse it in a given dimension: namely by turning it about either of two axes perpendicular to the given dimension.

Despite the rapid strides made in observational and theoretical astronomy, particularly in our century, there are two fundamental questions respecting the universe that defy solution. One pertains to the age of the universe, that is, did the universe have a beginning and therefore have a finite time-scale or has the universe existed without beginning. The other question deals with the dimensions of the universe, that is, is the universe infinite or not. For the time being no satisfactory proof or disproof has been offered either on purely logical grounds or through empirical evidence revealing whether the universe is boundless and eternal or not. It is for this reason that cosmologists must resort to a variety of unverifiable philosophic postulates in the hope of constructing a cosmological model that correlates the known laws of the physical world with the observed facts of nature and simultaneously presents a consistent picture of the universe as it changes in time.

The problem of the “proper” relation of philosophy and science has been the source of many disputes in our intellectual history. Recently some philosophers and scientists have insisted that technical philosophy is neglecting the results of the social sciences to the detriment of philosophy. The purpose of this paper is to consider the attempts made by contemporary philosophers to utilize material from the behavioral sciences (for a few recent examples, see 2, 15, 19, 20, 23, 24, 29, 38, 41, 50), to review certain of the arguments in favor of the utilization of such material, and to consider the criticisms of that approach.

The problem in the philosophy of science which interests me beyond all others is that of constructing an abstract deductive system isomorphic with the theory of the natural sciences. Clearly, this task must be the work of many years and many minds. Some portions of it have already been accomplished; but a great deal remains to be done, and the difficulties of the problems yet unsolved impress me as formidable. I believe, however, that it would be hard to overestimate the benefits which might follow from the construction of such an abstract theory, always provided that that theory met certain conditions. Not only must the system in question measure up to the standards of rigor and precision set by the logicians, but it must also be cast in such form that a working scientist could learn to understand at least that part of it applicable to his own specialty without being forced to drop his professional work and devote the labor of years to mastering the subject.

We will be dealing with “sequential circuits” in the sense of E. F. Moore and G. H. Mealy. Each such circuit is assumed to have a finite number of input wires (possibly none) and a finite number of output wires (but at least one). Each element of such a circuit will be assumed to be an and-circuit, an or-circuit, a not-circuit, or a delay circuit, for some specified temporal delay. Each element has one output wire which, however, may branch in order to serve several purposes simultaneously. (Similarly the inputs of the total circuit may be allowed to branch.) The and-circuits and or-circuits have two input wires each, while the not-circuits and the delay circuits have one input wire each.

Most philosophical systems of ethics are based upon the reciprocity principle as expressed by the Golden Rule: “Do unto others as you would have them do unto you!” The same idea underlies Kant's categorical imperative: “Act always on such a maxim as thou canst at the same time will to be a universal law!” Here, the individual act is generalized into, and considered as the specific application of the general law of ethics.

The question, what a given statement is “about,” often occurs in philosophic discussion. I shall use this question in the hope of illustrating how a relatively simple application of symbolic logic can clarify a problem which might otherwise turn into a maze of complications.

Can history be objective? Is history a science or humanistic discipline? What is its subject-matter? These three questions are variations on a single theme—the objectivity of history—which I want to explore. Faced with the welter of claims and counter-claims regarding objectivity in history, there is need to be explicit about one's approach to these claims. My prime endeavor in this paper is to reformulate these questions from my scheme of reference. I want to consider the objectivity of historical knowledge from a framework that does justice both to philosophic and methological issues and to historical knowledge-claims themselves. How this philosophic framework be labeled is immaterial. What is alone important is that it does distinguish philosophy proper from both science and its methodological analysis. Confusion between the three, I believe, frequently generates problems out of whole cloth. The result is that obfuscation of issues present in much recent literature concerning history.

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.

If we were to name the two greatest mathematicians of antiquity, we would probably choose Archimedes and Euclid. The first excelled in research, the second in synthesis or system. The synthesis or system is closely associated with the theory or philosophy of that subject; and Euclid's Elements, which has been characterized as “one of the noblest monuments of antiquity”, is the best concrete instance of the theory of mathematics according to the ancient Greeks. Now Aristotle had a theory of mathematics, although he was not a practicing mathematician. It is the purpose of this article to show that the mathematical method according to Aristotle is superior to and more modern than that according to Euclid. For references to Aristotle's works we shall use pages and lines according to the standard Bekker's edition (Berlin, 1831). By “a number” we shall mean a positive integer or a whole number. We proceed to a brief outline of Euclid's Elements.

Dmitri Mendeleev, while not creatively a philosopher of science, nor a student of systematic philosophy, was eminently a philosophical scientist. Concern about the nature and foundations of his science is evident throughout the text and footnotes of the Principles of Chemistry. One has to presume that his conclusions provided him with some direction for “the study of his great generalizations” in chemistry, especially for the greatest fruit of his efforts, the Periodic System of the Elements. At least it is apparent that somehow he acquired a much greater confidence in the feasibility of systemizing extant chemical knowledge than almost any of his contemporaries.

The year 1897 saw the publication of the first of the modern logical paradoxes. It was published by Cesare Burali-Forti, the Italian mathematician whose name it has come to bear. Burali-Forti's own formulation of the paradox was not altogether satisfactory, as he had confused well-ordered sets as defined by Cantor with what he himself called “perfectly ordered sets” (“Classe parfettamente ordinata”). However, he soon realized his mistake, and published a note admitting the error and making the correction. He concluded the note with the observation that his result could be established on the basis of the correct definition of well-ordered set as easily as for the “perfectly ordered sets” for which it had first been obtained. We shall reproduce his results in their corrected form.