Every month some one pronounces that science must be rejected if we are to preserve a belief in human freedom, or that only by a faith in freedom that flies in the face of logic and the principle of causality can democracy be justified. Equally often other authors insist that the increase of knowledge in the science of human behavior makes plain the irrelevance and sentimentality of pious talk about free and rational choice. What is the source of this dispute? Why is no resolution of it arrived at?

In accepting the invitation of your society to discuss some aspects of the philosophy of science, particularly as they might bear on the problems of an experimental psychologist, I should like from the start to make it very clear that I do not consider myself a philosopher, not even an amateur one. Like most empirical scientists, particularly of the laboratory variety, I usually take it for granted that my world is real and that the things I perceive as existing in it can be investigated by my empirical methods. I seem to get along quite well with this unpremeditated, common-sense realism, and, for the most part, I go along minding my own experimental business. As the psychologists among you may know, however, every once in a while I seem to have to abandon this happy, naive state and let myself get involved in questions about my science, the kinds of questions that are more properly the business of the philosopher of science.

Since the time, about a century ago, when DeMorgan (8), Boole (1) and Jevons (12), inaugurated the study of the logic of numerically definite reasoning, no one has been concerned to establish the validity rules for a very general type of numerically definite inference which is a strong analogue of the classical syllogism. The reader will readily agree that the traditional rules of syllogistic inference cannot even begin to decide whether the following proportionally quantified syllogism is a valid argument: at most 4/7 p are at most 2/3 not-m and at least 3/5 s are precisely 7/8 m, hence, at most 1/3 s are p. Likely reasons, of broad methodological interest, why this readily definable type of formal inference has been neglected will presently be proposed. Among the masters of twentieth century logic, Hilbert and Bernays (11) have, to be sure, meticulously shown how such numerically definite propositions as “at least 7 individuals have the property p” can be expressed in the predicate calculus with the use of the identity relation. They do not, since their concern with such propositions is indirect, proceed to establish a systematic calculus of classes whose “size” or extent is numerically definite. As we shall always notice, traditional logic and even ordinary Boolean algebra prefer to generalize about the laws governing the interrelationship of classes in inference systems without making any hypotheses concerning class “size” or extent except by the classical quantifier “some”, which quantifier admits the measure or extent of a class only in terms of the proposition that a given class contains or does not contain at least one member. Such a restricted admission of the relevance for inference of class size is among the fundamental reasons for the neglect of proportional quantifiers, i.e., quantifiers where numerical value is any rational number r such that 0/100 ≤ r ≤ 100/100. It can, of course, also be pointed out that the traditional syllogism and ordinary Boolean algebra do not i.e. measure, numerically define, the degree of inclusion of one class in another. Inclusion is taken either as total or partial, with no discrimination of the degree of partial inclusion.

This paper is the forerunner of an extensive logical analysis of the relativity idea, in which an axiomatic structure based upon the principles of topology is developed. It is meant to expose the manner in which relativity stretches from the pole of pure conception to that of factual observation, from the a priori to the a posteriori. We take pains to show, in connection with special relativity, precisely which elements are postulational and which are verifiable empirically. Our attempt can be somewhat naively characterized as an effort to show how misguided it is to “derive” relativity from such experimental facts as the Michelson-Morley experiment—as so many textbooks profess to do.

It is by now a commonplace that the classification of sciences into nomological and ideographical, which originated with Windelband, is neither exhaustive nor exclusive. Rather, there are sciences in which nomothetical (law establishing) activities are prevalent and there are sciences in which ideographical (describing peculiarities) efforts dominate. A third kind of enterprise is widespread throughout most, if not all, sciences: typological undertakings. In some sciences these are the most important and dominant projects. Linguistics tries to establish types of expressions: phonemes, morphemes, syntactical categories. History of art endeavors to set up various styles, i. e., types of art. General history attempts at well founding of such notions as revolution, reaction, buonapartism, findesieclism. When a historian declares that a revolution starts when a housewife cannot buy a chicken on the market, he divides the stream of events into periods according to a criterion that seems to him important, establishes similarities between different periods, and classifies them into types. Such typological activities are common not only in social sciences and humanities but also in physics which speaks about explosions, collisions, changes from a positive to a negative acceleration. A mathematician often enters into a typological venture, e.g., when he analyzes a function as increasing in an interval or describes it as concave upward in another interval. Typology may be conceived as containing the theory of classification. But there are typological problems that are not included in the theory of classification. A classification is performed on a class when its subclasses are defined. Typology, as suggested by the examples, may take a single object and try to conceive it as a summation of its fragments. To find a segmentation suitable from some point of view is not a classification. Rather, classification presupposes segmentation.

Until the theory of evolution was developed in recent times, two theories of change were more or less in competition with each other. The first held that ends, purposes, goals, (teleos), are both the cause of change and constitute that toward which change is directed, as when the form of man directs the growth of a child and is the aim of growth. Hence, from this point of view, change is both accounted for and understood through what were called “final causes.”

Bertrand Russell in “New Hopes for a Changing World” (1) writes the following passage:

We are all acquainted with persons who seem to have a talent for making things over-complex, persons who invent exceedingly devious explanations for what can be simply explained. Such individuals strike us as hardened violators of Occam's Razor: Entities are not to be multiplied unnecessarily. We shall say briefly that such persons goropise.

The repudiation of propositions as “obscure entities” which is prevalent among logicians and philosophers of “nominalistic” persuasion, is frequently justified by pointing out that no agreement seems ever to have been reached about the identity-condition of propositions. And if we cannot specify, so they argue, under what conditions two sentences express the same proposition, then we use the word “proposition” without any clear meaning. Quine, for example, feels far less uneasy about quantification over class-variables than about quantification over attribute-variables and propositional variables, because there is a clear criterion for deciding whether we are dealing with two classes or with only one class referred to by different predicates: two classes are identical if they have the same membership. And such a criterion of identity is alleged to be lacking for intensions.

As a preliminary to the modern theory of measurement with which this paper is chiefly concerned, it is desirable to review a few of the characteristics and implications of classical physics to illustrate the far reaching changes that have taken place in our conception of nature as the result of the development of quantum mechanics.

1. Argument. Questions that have arisen about the “existence” of elementary particles and other entities of physics have often been dismissed as unprofitable, with the tacit assumption that the categories suitable for the discussion of everyday knowledge are not suitable for the discussion of physical knowledge, which requires mathematical treatment. But for the layman who stumbles at the discontinuity between his world and that of mathematical physics, and for the physicist who wishes his knowledge of the world to have some kind of unity, a scheme which will embrace both kinds of knowledge is essential. Such a scheme is developed from a consideration of the dependence on mind, and conceptual modes of thought, common to science and all other intellectual approaches to the world, which is seen clearly in the growth of science from more primitive concepts. It begins with the concept as the most elementary category of the organization of experience, and moves to the construct, a distinctly scientific category arising out of the concept, and the isolate, corresponding to elements of reality not directly perceived. An escape from certain paradoxes generated by the incomplete nature of perceptual experience is thus provided.

The present article is a continuation of an earlier paper, entitled “Dialectical Materialism: A Friendly Interpretation” (hereafter quoted as “Friendly Interpretation”), which appeared in this journal. In the “Friendly Interpretation”, the emphasis was on formal and systematic exposition. Here, familiarity with the basic tenets of dialectical materialism is presumed, and some peripheral topics, which were deleted from the “Friendly Interpretation” lest they interrupt its continuity, are treated in five essay-type sections. First, an interpretation of dialectical materialism proposed by Rosenfeld, according to which the usual acausal interpretation of quantum mechanics is consistent with, and even an instructive illustration of dialectical materialism, is criticized. In the second section, the connection between positivism and Orwell's “doublethink” is pointed out. This is done in order to exhibit certain difficulties to which consistent positivism leads, but which are avoided by both materialism and objective idealism; in particular, the language of positivism, lacking the concept of “existence”, is inadequate to distinguish by any absolute criterion between reality and a dream world. In the last three sections, two acausal philosophies are compared and contrasted to dialectical materialism. First, in the third section, Landé‘s argument, showing the incompatibility of the principles of complete causality and of continuity of cause and effect, is summarized. It is shown that Landé‘s choice, in favor of continuity of cause and effect, is not the only consistent one, and that if one accepts the outlook of dialectical materialism, the opposite choice can and should be made. In the fourth section, Margenau's interpretation of quantum mechanics is criticized, both in terms of the criteria proposed by Margenau, and from the point of view of the doctrine of rationalism, which, in the “Friendly Interpretation”, was included as part of dialectical materialism. The interpretation of Bohm, de Broglie, and Takabayasi is preferred to that of Margenau, which is akin to the usual Bohr-Heisenberg interpretation of quantum mechanics. Margenau's sharp distinction between concepts applicable to the microcosm, and those useful in macroscopic considerations, is criticized. In the fifth (and last) section, Margenau's use of the term “historical reality” in connection with the microcosm is criticized. It is argued that the reality of historical concepts is not intrinsically different from the reality of physical concepts. This leads to a further discussion of “free will”.

The sense-datum theory of perception has been under heavy attack in the last two decades. Recently, by way of counterattack, some of its defenders have accused what they take to be its chief rival, the “theory of appearing”, of various deficiencies. In particular, they have claimed that there are some perceptual, or pseudo-perceptual, situations, such as hallucinations and dreams, of which the theory of appearing can give no adequate account. For in these cases, they argue, the question, “What is it that is appearing?”, can be given no satisfactory answer. The conclusion is then drawn that only a language containing sense-datum terms is generally adequate to our perceptual experience. Moreover this line of argument has been taken seriously by at least one partisan of the theory of appearing, Professor Virgil C. Aldrich, who has been driven to the expedient of suggesting that in these cases it is an image which appears.

Historians, philosophers, and men of affairs frequently raise questions about the “meaning” of history, or of selected segments of history, and frequently disagree about the relative merits of competing interpretations of specific historical periods or of the historical process as a whole. Such discussions are anything but idle. They affect what historians and others say about the past, and, in doing so, they influence the construction of social policies in the present. Indeed, they affect the very quality of a culture. For the view that a group of people hold towards their past is one of the controlling factors in their morals, religion, art, and intellectual pursuits, to say nothing of the sights, sounds, and actual feel of their daily experience.

In this paper I wish to reformulate in my own way some parts of Whitehead's theory of prehensions. This reformulation will deviate in various respects from Whitehead's own detailed views and terminology, but the main inspiration is from Whitehead (1).

This paper is inter-disciplinary. Its disadvantage is that the author is not sufficiently conversant with the disciplines it is inter. He may however, like Lord Wavell, claim that at least the thread that binds them is his own.

The paper is of philosophic interest in that it is inspired by, and hopes to shed some light on, the notion of an ideal language. It is of interest to social anthropology in that its main subject is kinship structure. It may be of interest to mathematicians in setting a task.

To-day economics is considered the most highly developed discipline among the social sciences. Yet, its explanatory and predictive powers are admitted by all hands to be weak compared to those possessed by the physical sciences. This weakness is still frequently explained by apologetic references to the relatively tender age of economic science. This apparently implies that in the normal course of time economics will grow up and achieve the stature and powers of say, physics. The trouble with this argument is that economics is certainly as old as physics. If it lags behind other disciplines in predictive and explanatory powers, lack of time cannot be the cause.

In a contribution to a symposium on “Causality in the Social Sciences,” Lewis Feuer remarks in passing that “Functionalism, in the form which Malinowski gave it, affirms that culture is an ‘organic unity’; it is the principle that in every culture, each custom, belief, and behavioral form ‘represents an indespensible part within a working whole.’” That culture is an integrated and organic unity is a view found quite often in the writings of Malinowski, though he does not maintain it with full consistency. Sometimes he seems to say that a culture is made up of a number of grand institutions, each of which is an integrated unity, though the totality need not be. But whether affirmed or denied this thesis is not the doctrine, characteristic of almost every attempt made by Malinowski to explain cultural phenomena during the last quarter century of his life, which may be properly called “Malinowskian functionalism.” And that the doctrine cited by Feurer is sometimes formulated in such a way that the term “functional” or some variant is used, as in “culture is a functionally integrated organic unity,” makes no difference to my claim. I am not at all certain that the addition of the word “functionally” does anything for the view in question; it surely makes no difference to its scientific sterility. But that apart, the point I wish to make here is that a good many scholars who make references to Malinowski's functionalism have never bothered to discover just what in the world this is. They have been all too ready to cite the vague programmatic pronouncements in which Malinowski's writings abound, while seemingly oblivious to the fact that with rare exception every major attempt by Malinowski to account systematically for some kind of sociocultural phenomena reveals one and the same pattern of explanation. And it is this pattern alone which may be spoken of as Malinowski's method of functional analysis.

One example which Peirce chose to illustrate his pragmatic maxim as thus stated was the familiar theological distinction between transubstantiation and consubstantiation. Now (Peirce says) since these two doctrines agree in all of the effects which they conceive the sacrament to possess and which may have practical bearings, here and hereafter, it is absurd to say that there is any real distinction between the two doctrines. Peirce declares in the same passage that, having used the question as a logical example only, he does not care to pause to anticipate the theologian's reply.

The semantic confusion in Europe about the term “anthropology” has of late been considerable. On the one hand there is meant by it, and quite justifiably, human biology and medical anthropology. On the other hand, the work of some contemporary thinkers, under the name of “philosophical anthropology,” has recently gone beyond the narrower compass. This has been noticeable at both the German and the international European philosophical conventions since the last war. In addition to this, there appeared the term “Kulturanthropologie,”—for the first time probably as the title of E. Rothacker's contribution to Systematische Philosophie, a collection of essays edited by Nicolai Hartmann and published in 1942. But “Kulturanthropologie,” in Rothacker's sense, is not a translation of “cultural anthropology,” which has in recent years grown to such eminence among scholarly fields in England and America. In the United States, (1) “anthropology” designates a group of scholarly fields ranging on the one hand from biological anthropology to archaeology and the study of the beginnings of history on the other, often including history, linguistics, and other realms of research; (2) it is neither one of the natural sciences nor of the humanities but one of the social sciences; and (3) the actually new results of this young discipline, especially at Harvard, Yale, and the University of Chicago, are arrived at by means of team work by anthropologists, psychologists, and sociologists, which in Germany has not been the case so far.