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 (Lenin, V. I., Unpublished Notes to Lasalle's Heraclite.)

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.

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.

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?

In the survey and criticism of science and philosophy we are considering systems of knowledge and thought rationally developed from coherent human experience. These rational systems are in a definite sense intellectually organized. Where intellectual and social problems are real and urgent the relevant knowledge and thought should be organized socially and purposively to achieve tentative, if not adequate or definitive solutions.