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.

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.

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.

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.

Today we are in the midst of a far-reaching shift in scientific thought involving the recasting of many of our long-cherished ideas and preconceptions. To some this appears but the orderly evolution of scientific thought, while to others it portends a revolution in both the ideas and the methods of scientific inquiry.

It is the traditional view of psychology that the attributes of sensation show a one-to-one correspondence to the dimensions of the stimulus. Some such view is also implicit in the naïve epistemology of the physicist. He often thinks of pitch as if it were the perception of the frequency of a tone, but that view soon runs into difficulties. Within psychology it was Wundt who originally equipped sensation with two attributes, quality and intensity, thus making sensations mirror the more obvious aspects of stimuli which differ as to kind and in degree. Later it became clear to Külpe that extension must be an attribute of visual and tactual sensations because the retina and the skin are areal organs and because extent enters into perception quite as ‘immediately’ as does intensity. A loud sound is not a congeries of faint sounds, nor is a perceived line a row of sensations. In a similar reaction against Wundtian atomism Külpe also added duration (protension) to the list, for a tone that lasts 0.8 sec. yields a different perception from one that lasts 0.6 sec. and yet there is no sense to saying that the first represents a greater number of seried sensations than the second. Thus the four classical attributes of sensation are quality, intensity, extensity and protensity. The conventional view has been that they are respectively correlated with four aspects of the stimulus, and this paper is written with the intention of refuting this view.

At the present time there is a tremendous discussion of the scientific method. But there is almost no discussion of the scientific aim. This is a paradoxical state of affairs. Is it possible to discuss method intelligently unless the question of aim is first given thorough and serious consideration? Is not a method, by virtue of the very fact that it is a method, something which is subordinate to an aim and determined by that aim ? Is not a method something which is to be understood, evaluated, attacked and defended only in relation to the particular aim which it serves? Surely to deal with method in any other way is to mishandle the situation. Yet at the present day we witness this tremendous volume of discussion of method, with almost no discussion of aim.