For thirty years at least, I have designated myself as a zoologist interested in the “philosophical aspects of biology”. But I have now to admit that not until within the last two or three years have I recognized that logic, particularly in its inductive aspect, is involved in such interest.

For me as a zoologist with a predilection for natural history, observation has had a place of wide application and of implicit confidence. Until recently, I had rested in the supposition that after all of the devices practiced by naturalists to insure certainty of their observations, nothing further was needed so far as the information and understanding they gained was concerned. I had gone ahead with my reasoning, my logic, with no more qualms about the trustworthiness of the “inductive” than of the “deductive” side of it. I had not taken seriously the assertion, made years ago in my hearing by an eminent philosopher, that no one can be a philosopher without being skeptical and critical of the use of his senses in getting knowledge. Latterly, however, I have come to see that traditional philosophers take themselves very seriously in such assertions. This realization has been due to the discovery that the recent advances in physics and mathematics have led most of the leaders in these fields to believe that observation and the inductive side of logic may be left where they were a hundred years ago. These scientists seem to be about where John Stuart Mill was in his effort to improve Lord Bacon's effort for a better understanding of both observation and induction.

It is strange to note so little discussion of the exclusion principle in the philosophical literature. Philosophers, largely engrossed in their perennial problems, are hardly aware of the fact that, during the last two decades, there has been introduced into physical methodology a principle of utmost philosophical importance, easily rivaling that of relativity and, in some respects, indeed that of causality. Discovered by Pauli in 1925, it immediately elucidated a whole realm of physical facts and was accepted by physicists with wide acclaim. Called the exclusion principle—or Pauli principle, or principle of anti-symmetry—it was embodied in the axiomatics of quantum mechanics; its peculiar methodological significance passed out of view.

One of the initial obstacles to the study of the theory of value is the fact that practically every author whom the student consults on the subject characterizes value and valuation differently, and seems to trace them ultimately to a different source. For example, one writer will formulate a theory of value in terms of pain and pleasure (1); another, in terms of feeling (16, p.22); another, in terms of desires or wants (3, p.1); still others, in terms of “requiredness” (8, p.63), of interest (11, p.115), of striving (4, pp.1–29); and so on.

This study purports to demonstrate the possibility of applying logical analysis in the field of jurisprudence, and the usefulness of this method for exhibiting some essential features of the law.

logical analysis applies to language systems. To carry out the logical analysis of a language, is to construct a simplified model language “in close connection with” the given language, and to study the conditions of validity of the sentences of this model language. The given language is subjected to a kind of purifying chemical process. To deal with this simplified language seems to be a detour; it is, however, the most direct way to an ultimate insight into the logical structure of the given language.

In a recent paper I criticized the pragmatist theory of truth from the frame of reference of modern logical positivism (scientific empiricism). By showing the similarity between Karl Mannheim's claims of epistemological relevance for sociology of knowledge and certain pragmatist notions concerning truth I made criticism of the latter with the former. The aim of this present paper is to extend and elaborate upon those critical remarks regarding pragmatism both in order to answer objections raised since and to clarify what was said there. Moreover, the evaluation of the pragmatist theory of truth may have been surprising to some since so much lately has been made of the points of agreement between pragmatism and modern positivism. It is thus also my intent to delimit agreements and disagreements and compare the respective emphases in pragmatist and positivist thought concerning the nature of truth.

In a recent article P. Henle gave an analysis of the notion of emergence. His inquiry deals with what he calls, quite appropriately, the emergence of characteristics. Such emergence, that is, the emergence of qualities and relations is undoubtedly the primary connotation of the term, and I feel that Henle has been very successful in clarifying it. The purpose of the present paper is to discuss in some detail one special aspect of Henle's analysis. This is done because the precise formulation of this particular aspect sheds light on the notion of elementarism. And the opposite of this notion, holism or organicism, belongs undoubtedly to the variety of fused and confused meanings the idea of emergence has come to cover.

Only one philosopher has succeeded in building his reputation on silence—Cratylus. It is said that under no circumstance would he say anything, but would merely crook his finger. Nor is it known whether he achieved this unique glory by a persistence that lasted from toothless youth to toothless old age, or whether he merely petered out into withering speechlessness before the follies of man and the grandeur of God. More likely it was something like the latter, for otherwise we would be confronted by the delicate riddle: why was he called a philosopher?

Nevertheless, a tenable explanation is that Cratylus' reputation was arrived at by an experiment. Arranging philosophers on a scale of self .control in speech, one might derive the plausible law: the less one says the more he is of a philosopher. Ergo, say nothing and be declared the worthiest of philosophers. The difficulties in such an extrapolation, however, are very great. It is hard to see what harm just one word can do, and even two or three, or several, if they but fall short of being a sentence. Why absolute silence? Then, again, what harm is there in repeating even a multitude of words, the entire dictionary if you please, plus whatever sounds you can think of, provided you say nothing? And since we have progressed so far with the argument, what harm can there be even in connected speech, grammatical, fluent and mellifluous, provided you still say nothing? Cratylus, apparently, was playing a safe bet with a vengeance. He must have feared being understood (or misunderstood) by accident!

The most direct manner of formulating the objective of this paper is to consider some passages in which Whitehead states the conception of the “subject” espoused by the organic philosophy.

“The subjectivist principle is that the whole universe consists of elements disclosed in the analysis of the experiences of subjects.” “The reformed subjectivist principle adopted by the philosophy of organism ...” is “... that apart from the experiences of subjects there is nothing, nothing, nothing, bare nothingness.”

The first thing to realize about grading as a psychological process is that it precedes measurement and counting. Judgments of the type “A is larger than B” or “This can contains less milk than that” are made long before it is possible to say, e.g., “A is twice as large as B” or “A has a volume of 25 cubic feet, B a volume of 20 cubic feet, therefore A is larger than B by 5 cubic feet,” or “This can contains a quart of milk, that one 3 quarts of milk, therefore the former has less milk in it.” In other words, judgments of quantity in terms of units of measure or in terms of number always presuppose, explicitly or implicitly, preliminary judgments of grading. The term four means something only when it is known to refer to a number which is “less than” certain others, say five, six, seven, arranged in an ordered series of relative mores and lesses, and “more than” certain others, say one, two, three, arranged in an ordered series of relative mores and lesses. Similarly, a foot as a unit of linear measure has no meaning whatever unless it is known to be more than some other stretch, say an inch, and less than a third stretch, say a yard.

Some recent discussions of A. N. Whitehead's treatment of the problem of value have stressed the point that his work in this field is open to serious objection. For example, Professor John Goheen claims that Whitehead's attempt to indicate distinguishing characteristics of experience of “the Good”, is too general to be adequate. He also suggests that this generality of approach makes it impossible for Whitehead to differentiate between different species of value. Further, according to Goheen, Whitehead involves himself in confusion when he claims that satisfaction (value) is achieved when experience is characterized by order (unity); and yet he also suggests that in some cases, the presence of disorder makes possible a higher type of satisfaction. Professor P. A. Schilpp agrees with Goheen in feeling that Whitehead's explanation of the good life in terms of “pattern” is too vague. In Schilpp's opinion, Whitehead does not answer the basic question: “What kind of pattern?” There is a further objection to Whitehead's “theory of the close connection between morality and beauty,” because at times it looks like an actual identification. Schilpp also objects to what appears to be Whitehead's identification of “good” with “interest”. Finally, it is claimed by Schilpp that Whitehead subordinates goodness to beauty. This interpretation is apparently supported by Prof. George Morgan who states: “Truth and moral values are instrumental except in so far as they enhance beauty.” Professor B. Morris objects to Whitehead's attempt to apply the mathematical method to aesthetic experience. He suggests that the method of symbolic logic is too abstract to deal adequately with concrete aesthetic data. Professor J. W. Blyth, as the result of his examination of Whitehead's theory of truth, reaches the conclusion that “the various elements involved in Whitehead's theory of truth cannot be brought together in one coherent and consistent system.

If we may rely for our evidence on simple observation, it would appear that the tendency of random or unguided activity in external nature is opposed to the development of complex organization and favorable to structural simplicity—in the sense of uniformity in the distribution of elements. This anti-organizing trend of purely physical processes is illustrated in ordinary large-scale mixing and stirring operations, as well as in the automatic increase of entropy with time in systems subject to the laws of thermodynamics (material or molecular systems in general). It is common experience that complex systems which are the seat of physical activity tend to become simpler when left to themselves, i.e., they lose organization. Recently Eddington has given the whole matter an admirably clear expression: “Entropy may most conveniently be described as the measure of disorganization of a system. ... We can see chance creeping in where formerly it was excluded.” Unless counteracted by directive action the casual or random element in nature tends to increase. If things are left to chance, not only does organization of any high degree of complexity fail to develop, but what organization there is tends to lapse or disappear. Hence in those cases, such as living organisms, where the existence and activity of the system depend on a special and complex organization, it appears necessary to assume the continued operation of a stable directive influence or factor which pervades the whole system and excludes or compensates casual factors as far as possible. The presence of this factor is what makes possible the development and maintenance of the organization required for vital activity.

Only those whose work and interests have led them to notice it, will have realised, in all probability, the remarkable extent to which the term organization has gained currency, or acquired new and special emphasis, throughout the entire range of scientific and sociological literature during the last ten or twenty years.

In biology and bio-chemistry organization has been discussed or used as a technical term, mostly since 1930 by at least thirty well-known authors; amongst the more prominent are Huxley, Wilson, Woodger, Cannon, Waddington, McDougall, Needham, Block, Hopkins and Sherrington. Under this magic term some authors refer to the physico-chemical nature of the cell or cytoplasm, and usually with special reference to selective or directive catalysis; others to the general constitution or structure of the organism and almost indistinguishable from general morphology and physiology; others to embryological development as such (i.e. progressive differentiation under specific chemical stimuli); others more especially to “relations” between cells, organs and structural parts, often in an abstract sense; others refer more particularly to a hypothetical integrating and/or co-ordinating factor (“entelechy', ”field“, ”formative force“, ”telepathic hierarchial monads“, ”diffused Maxwell's Demon“, and so forth): a few refer to re-constitution from dissociated cells (so-called ”re-organization“) as observed in experiments with Sponges and Hydroids.

The existing literature treats of several investigations with a certain bearing on the question which is roughly indicated by the title “Imperatives and Logic.” Some of those investigations, however, are entirely outside the scope of the present work.

Mally sets himself the task of developing a “Logik des Willens” constituting a parallel to the usual logic, the “Logik des Denkens". In order to emphasize its independence, the author also calls this “Logik des Willens” “Deontik”, and he conceives it as being based on the “Wesensgesetze” of will in the same way as the usual logic is conceived as being based on the “Wesensgesetze” of thought. The author develops a formalistic deductive system on the basis of 5 axioms of demands (Grundsatze des Bollen), including the axiom that there is at least one fact which is unconditionally demanded, and through a lengthy series of theorems he arrives at the sentence that what is unconditionally demanded is identical with what is actually the case: “was sein soll, ist Tatsache”. Similarly, the author develops a system of axioms for “right” volition, including the axiom that right volition is non-contradictory.

Operationism may tentatively be defined as that scientific method which defines its concepts in terms of observable or communicable operations, however carried out. With few exceptions, it has been put forward as representing positivism in contemporary sociology. Sellars refers to it as a new and virulent form of positivism—logical positivism. In philosophy, logical positivism is the culmination of the sensationalism of Berkeley and Hume, the positivism of Mach and Avenarius and Comte, and the logistic of Russell and Wittgenstein. In sociology, the philosophic assumptions of this school have been stated in a naive form, in addition to presenting Kantian idealism contradicted by an assumption of philosophic realism.

The complexity and the technical obscurity of the scientific method have rendered science ever likely to be misunderstood both by scientists themselves and by the general public. Difficulties which remain unrecognized constitute the most formidable obstacles to success in any field. There are such difficulties lurking in the treatment which the scientific method accords its subject-matter. In this essay, I propose to point to one such pitfall in the path of the progress of science. By exposing it, something will already be accomplished toward its avoidance and elimination, and the vast public of uninstructed persons will be able to skirt one more confusion in the effort to understand what the scientists are trying to do.

My discussion will concern itself with mathematics, medicine and the possible relations between the two. It will be an exercise in logical analysis, a review of some sad, sad facts, and in some sense a promise of glad tidings. In short, it will be an effort to bring the immortal inhabitants of the mathematical heaven into harmonious relations with the mortal ills of man's vale of tears.

As to the curious role of mathematics with respect to the natural sciences, several preliminary observations insist on prompt consideration. It is a matter of common knowledge, for example, that mathematics is being constantly applied to physics. With great success, Galileo wedded the two in his study of motion down an inclined plane. The mathematics he used to describe the physical phenomenon involved the equation of a parabola. His daring genius thus got far beyond the conventional circles that were permitted to motion by theology. His courageous use of the then “higher mathematics” was followed by centuries of application of still higher and higher mathematics, till now a small army of mathematicians is busy almost exclusively with the problem of inventing or discovering new varieties of mathematics which could serve physics better and better. The mathematical physicist of to-day is a specialist, nine-tenths mathematician, one-tenth physicist, with the nine-tenths serving the one-tenth.

When all sorts of material entities from atoms to people and from bacilli to stars are plotted on a scale of time and a scale of mass some very interesting alignments and symmetries emerge. It is observed that the data of the physical, biological, psychological, and social sciences form a neat isosceles triangle as shown in Figure 1 below. The facts are simple as graphed in Figure 1 on logarithmic scales; their explanation or interpretation is not apparent. Is Figure 1 merely an interesting diagram useful in teaching the masses and evolutionary ages of the phenomena of various classes of science, or has it some more fundamental scientific significance? The graph will be first described and then its uncertainties and possible implications will be discussed.

The purpose of this paper may be found in the following quotation. “Whenever an argument can be made to lead to a descending infinitude of natural numbers the hypothesis upon which the argument rests becomes untenable. This method of proof is called the method of infinite descent; .... It would be interesting and valuable to compare this method with the method of mathematical induction.”