It is proposed to examine the consequences which ensue if philosophy is deliberately oriented around the methods and results of science. That such reorientation has been more or less unconsciously taking place for centuries is evident; the problem demands particular discussion at this time only because the reorientation has gone so far and with such success as to challenge seriously certain past conceptions of philosophy and to demand of philosophers what, if anything, is left for them to do. For present purposes the revolution indicated will be regarded as a fait accompli, and the sole concern will be with what alternatives remain open. The conclusions differ from those of certain others who accept the same fait accompli only in believing that more alternatives do in fact remain open than they envisage.

In the course of modern philosophy, there have been several attempts to demonstrate the existence of ultimately simple objects by purely logical methods. One of the most recent of such attempts forms part of the foundation of Wittgenstein's logical doctrine. As Wittgenstein has, until quite recently, been considered the authoritative source of Logical Positivism, an examination of his supposed demonstration of logical simples is propaedeutic to an evaluation of the method of the school.

I. The present state of philosophy contrasted with that of the sciences. Both philosophy and science seek not mere opinion but knowledge. The sciences, however, have by now won a vast body of knowledge, and daily make positive additions to it notwithstanding their theoretical controversies. In philosophy, on the contrary, the same great problems are discussed by generation after generation with rather meager results other than a multiplication of theories and schools of opinion. One is therefore moved to wonder whether philosophy is forever doomed to inconclusiveness, or whether on the contrary knowledge and definite progress are possible in its field in the same sense as in the sciences.

The purpose of this paper is to examine briefly what is meant by the term “philosophy” as it occurs in such expressions as “philosophy of physics,” “philosophy of mathematics,” “philosophy of science” and the like. The discussion will be divided into three parts: the first will consider several distinct meanings of the term “philosophy;” the second will discuss one of these in some detail, namely, philosophy as analysis; the third will seek to answer an important question concerning the results of philosophic analysis.

“A millennium has gone by since the idea of the relationship of all things, the chain of causes was born. A comparison of the meaning of what we call causes throughout the history of human thinking could give us, no doubt, a conclusive epistemology.” (Lenin, V. I., Unpublished Notes to Lasalle's Heraclite.)

In the following, limiting ourselves to two objects—the processes X and Y—we will compare three kinds of regularities in their specific manifestation in physics: (1) interaction; (2) causality; and (3) functional dependence. In considering as objective all the regularities which are inherent in things and material processes themselves, and in considering causality and functional dependence merely as one-sided abstractions of interaction, which in its turn is an abstraction from the universal interconnection of things, we avoid such an arbitrary definition of causality as, for instance, the possibility of exact prognosis which leads to the negation of causality. We also avoid placing functional dependence above causality.

What is metaphysics? There is real danger of taking the meaning of this term too much for granted, and of leaning too heavily upon an undefined word in the very act of dismissing metaphysics as word jugglery. Metaphysics is not, as I conceive it, the study of the wholly transcendent or supersensible. It may sometimes have been so conceived, and this is, indeed, one reason why some of its alleged results are so unsatisfactory—or, as positivists would say, meaningless. Such a meaningless “metaphysical” idea is the mediaeval doctrine of God as a power acting upon the world but not reacted upon by it, as purposive but non-temporal, loving but “impassive,” etc. Such is the windowless monad of Leibniz, connected with other monads only by pre-established harmony. Such is the Aristotelian idea of substance as that in which other things inhere but which itself is in nothing (apparently not even in the world or nature). The history of metaphysics is, indeed, strewn with failures to achieve meaning. But does this mean that metaphysics has scored no successes? Surely we must remember that human success is invariably of the fumble-and-correction type. Ideas such as those mentioned may be meaningless as they stand, and yet have potential meaning in that some modification of them might render them significant conceptions. We must also remember that mankind now possesses new instruments of logical analysis, and that these instruments may prove useful in metaphysics—not, as logical positivism holds, with the result of banishing all metaphysical ideas, but of correcting their erroneous aspects.

It is by no means impossible that the discussion of epistemological problems, at the present stage of our understanding of the issues involved, may be futile. But so long as anyone desires to “know” anything at all, just so long it will be impossible for thoughtful men to leave the questions of epistemology alone. So, futile or not, this paper is concerned with an analysis of one of the most fundamental of epistemological problems, namely that of the ‘given.’ It is true, the ‘given’ has recently received an unusual amount of attention from philosophers. What with two of the American Philosophical Association's presidential addresses last year having much to say on the subject, and what with the logical positivists making the ‘given’ the cap-stone of their radical empiricism? All of which, it will be claimed, proves the contention that any attack upon the problems of epistemology, from the standpoint of our present knowledge and understanding of the total situation involved, is condemned to hopeless futility. Why, then, add one more hopelessly futile attempt to those of all the rest? If, despite such initial misgivings, I shall proceed to my own analysis of the ‘given,’ I shall do so, first of all, in recognition of the indisputable fact that everyone of us, even though we should be blind, deaf and dumb, do, as a matter fact, find ourselves confronted with something ‘given’; and, secondly, because it appears to me that, as philosophers, it is still our task seriously to concern ourselves with unsolved problems, even though they may not yet be capable of being so stated that a unanimously acceptable solution for them may be—at present—possible. Even the logical positivists, who, of course, are most critical of what philosophy is or ought to be, insist that “the object of philosophy is the logical clarification of thoughts.” Since the ‘given’ is a concept (thought) most widely used not only by so-called ‘pseudo-philosophers’ but even by the logical positivists themselves, it certainly cannot be denied that the clarification of the concept of the ‘given’ is decidedly a philosophical task. More than that: it is a necessary philosophical task just so long as there is such wide difference of opinion concerning the ‘given’ among philosophers.

The keynote of our investigation is suggested by a remark made by Enriques, “the young student of mathematics would indeed look in vain to the classical logic into which he was initiated for an adequate conception of the structure of a deductive science like Geometry let alone for an explanation of the value and meaning of the principles of such a discipline. What are axioms, postulates, definitions? What place do they occupy in the edifice of the theory? What criteria determine their choice and how can we establish whether they are acceptable or not?” These are in general the questions we shall seek to answer in part and then we shall make a special analysis of two of the criteria determining the choice of the axioms.

The general concept of a causal system has been basic in scientific thought. It may be formulated as follows. The system in question possesses certain measurable attributes such as those of dimensions, temperature, and so forth. In the case of a causal system, it is affirmed that the subsequent development of the system from a known initial condition—that is, a condition in which the measurable variables have known values—is uniquely determined by these values. More definitely, the value of these same variables after any interval of time depends only on the initial values of the variables and the time interval which has elapsed.

In our previous writings we have outlined a mathematical theory of biological phenomena. In our systematic construction of “mathematical biology,” similar in its aims to mathematical physics, we have started with the fundamental unit,—the living cell. After having established a physico-mathematical theory of the fundamental properties of the cell, we have studied the interaction of several cells. This led us into two different fields. On the one hand we studied such interactions of cells, which determine the form of cellular aggregates, constituting multicellular organisms. On the other hand we studied different types of functional interactions, which determine the reactions of the aggregate as a whole to different environmental changes. While the first field leads us eventually to the theory of organic form, the second brings us to the physico-mathematical theory of behavior.

Introduction. Topology (sometimes called analysis situs) is the most general and most fundamental branch of geometry. Logically its study should precede that of other kinds of geometry. But mathematical knowledge, whether regarded as part of our cultural heritage or as the possession of an individual, does not come into being like a building, from a completed foundation to a limited superstructure, but rather grows like a tree with ever-deepening roots as well as ever-spreading branches. So, historically, systematic studies in topology lagged behind Euclid's elements some 2000 years and were unknown a century ago. There has, however, been considerable activity in this field by the present generation, and a number of modern treatments are available for the specialist. In spite of its fundamental nature, the subject is difficult, and many of its problems remain unsolved even today. This difficulty makes it pedagogically advisable to avoid questions of topology germane to other branches of mathematics and there is a distinct scarcity of material available even to the mathematician, whose main interest lies outside this field.

Do masses, electrons, atoms, magnetic field strengths, etc., exist? Nothing is more surprising indeed than the fact that in these days of minute quantitative analysis, of relativistic thought, most of us still expect an answer to this question in terms of yes or no. The physicist frowns upon questions of the sort: is this object green?; or what time is it on a distant star? For he knows that there are many different shades of green, and that the time depends on the state of motion of the star. Almost every term that has come under scientific scrutiny has lost its initially absolute significance and acquired a range of meaning of which even the boundaries are often variable. Apparently the word to be has escaped this process.

We pause in the process of exposition to note what continuity we may in the progress of the theories of discontinuity we have been discussing. The following trends are rather distinct: (1) the development of more and more general mathematical approaches, (2) a marked broadening of the field of experimental issues, and (3) an increasing attention to analysis of fundamental concepts, the philosophy of physics.

Methodology might be understood to mean a description of various individual procedures which have led to the successful solution of specific problems. In studying the subject of physics from this point of view, i.e. with special emphasis on method, one would naturally turn his attention to the traditional divisions of experimental and theoretical physics, the former with its measuring devices and the latter with its mathematical technique. In no other sense than this does the term methodology make any direct appeal to the working physicist, and if you would ask him to define his methods he would probably answer with a description of experimental technique or the methods of setting up and solving differential equations. His answer would tell you how he solves his problems, but hardly how he finds them and why he solves them.

The necessity for a clear understanding of the dual character of scientific method (verified observation on the one hand and theoretical analysis on the other) and of its applicability in social study as in the physical and biological sciences, can hardly receive too much emphasis at the present stage of development. Such an understanding, however, merely provides the proper beginning or orientation in the organization of any scientific discipline. That which is a common element in all scientific procedure can hardly serve to differentiate one science from another.

It is the contemporary belief, in American legal circles at all events, that law or jurisprudence, whatever it may have been in the past, has now the status of a social science. This is an assumption easier to make than to substantiate, and in view of the increasing insistence upon this point, it is now appropriate to inquire whether or not it possesses a tangible foundation. This requires a consideration of the distinctive characteristics of social science, the determination whether or not jurisprudence exhibits these characteristics, and, if not, if it is possible for it to assume them. It will be convenient to begin, briefly and concisely, with an examination of the characteristics of modern legal thought.

In studying various possible physico-chemical interpretations of biological phenomena we arrived by a systematical development of what we have called “Mathematical Biophysics” at the interpretation of even such complex phenomena, as those involved in learning, Gestalt-discrimination and Gestalt-transposition. Yet, in spite of the apparent progress made along this newly trodden road, a sophisticated mind may feel that we are advancing into a peculiar “cul-de-sac.” Indeed we are discussing possible physico-chemical mechanisms underlying the discrimination, recognition and constancy-properties of various spatial forms. Yet we have not touched at all the much more fundamental question, which logically precedes all the above, namely, what can be the physicochemical interpretation of the general and primordial fact that we perceive those forms as spatial? Can we conceive any physicochemical model at all, which would illustrate how and why we experience everything as being in space?

Since the seventeenth century, when Descartes divided the universe into two realms, the distinctive character of one of which being its spatiality or extendedness, philosophers have been increasingly concerned with the analysis of the category of Space. Scientists, too, have been interested in the concepts of Space and Time, especially since the promulgation of the theory of relativity.

The species concept is one of the oldest and most fundamental in biology. And yet it is almost universally conceded that no satisfactory definition of what constitutes a species has ever been proposed. The present article is devoted to an attempt to review the status of the problem from a methodological point of view. Since the species is one of the many taxonomic categories, the question of the nature of these categories in general needs to be entered into.