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cepts, and considers them correct in their relation to the direct experience of the organs of sense—what we see, hear, touch. That is, positive philosophy recognizes the subjectivity of our receptivity, and recognizes everything that we perceive in objects as imposed upon them by ourselves but this in relation to the direct experience of the senses only.

When it concerns itself with "scientific experience" however, in which precise instruments and calculations are used, positive philosophy evidently considers Kant's view in relation to that invalid, assuming that "scientific experience" makes known to us the very substance of things, the true causes of our sensations—or if it does not do so now, it brings us closer to the truth of things, and can inform us later.

Contrary to Kant, the positivists are sure that "more clear knowledge of phenomena makes them acquainted with things in themselves." They think that in looking upon physical phenomena as the motions of the ether, or as electrical or magnetic phenomena, and calculating their motions, they begin to know the very substance of things, i. e., the causes of phenomena; in other words, they believe exactly in the possibility of what Kant denied the comprehension of the true substance of things by means of the investigation of phenomena. Moreover many physicists do not consider it necessary even to know Kant; and they could not themselves exactly define in what relation they stand toward him. Of course it is possible not to know Kant, but it is impossible to controvert him. Every description of physical phenomena, by its every word, is related to the problems set forth by Kant—remains in this or that relation to them.

In general, the position of "science" in regard to this question of "subjectively imposed" or "objectively cognized" is more than tottering, and in order to form its conclusions "science" is forced to accept many purely hypothetical suppositions as things known —as indubitable data, not demanding proof.

Moreover, physicists forget one very significant fact: in his book, Analysis of Sensations, Mach says:

In the investigation of purely physical processes we generally employ concepts of so abstract a character that as a rule we think only cursorily, or not at all, of the sensations (elements) that lie at their base. . .

MACH'S ANALYSIS

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The foundation of all purely physical operations is based upon an almost unending series of sensations, particularly if we take into consideration the adjustment of the apparatus which must precede the actual experiment. Now it can easily happen to the physicist who does not study the psychology of his operations, that he does not (to reverse a well-known saying) see the trees for the wood, that he overlooks the sensory element at the foundation of his work... Psychological analysis has taught us that this is not surprising, since the physicist is always operating with sensations.*

Mach here calls attention to a very important thing. Physicists do not consider it necessary to know psychology and to deal with it in their conclusions.

But when they are more or less acquainted with psychology, with that part of it which treats of the forms of receptivity, and take it into consideration, then they hold the most fantastic duality of opinion, as in the case of the man of orthodox belief who tries to reconcile the dogmas of faith with the arguments of reason, and who is obliged to believe simultaneously in the creation of the world in seven days, seven thousand years ago, and in geological periods hundreds of thousands of years long, and in the evolutionary theory. He is thus forced to resort to sophisms, and demonstrate that by seven days is meant seven periods. But why seven, exactly, he is unable to explain. For physicists the role of the "creation of the world" is played by the atomic theory and the ether, with its wave-like vibrations, and further by the electrons, and the energetic, or electromagnetic theory of the world.

Or sometimes it is even worse, for the physicist in the depth of his soul feels the falsity of all old and new scientific theories but fears to hang in the air, as it were; to take refuge in mere negation. He has no system in place of that whose falsity he already feels; he is afraid to make a plunge into mere emptiness. Lacking sufficient courage to declare that he believes in nothing at all, he accoutres himself in all contradictory theories, as in an official uniform, only because with this uniform are bound up certain rights and privileges, outer as well as inner, consisting of a certain confidence in himself and in his surroundings, to forego which he has no strength and determination. The unbelieving positivist—this is the tragic figure of our times, analogous to the atheist or unbelieving priest of the times of Voltaire.

* Open Court Publishing Co.'s edition of Mach's work. 1914, pages 41, 42, and 43.

Out of this abhorrence of a vacuum come all dualistic theories which recognize "spirit" and "matter" existing simultaneously and independently of one another.

In general, to a disinterested observer, the state of our contemporary science should be of great psychological interest. In all branches of scientific knowledge we are absorbing an enormous number of facts destructive of the harmony of existing systems. And these systems can maintain themselves only by reason of the heroic attempts of scientific men who are trying to close their eyes to a long series of new facts which threatens to submerge everything in an irresistible stream. If in reality we were to collect these system-destroying facts they would be so numerous in every department of knowledge as to exceed those upon which existing systems are founded. The systematization of that which we do not know may yield us more for the true understanding of the world and the self than the systematization of that which in the opinion of "exact science" we do know.

CHAPTER II

A new view of the Kantian problem. The books of Hinton. The "spacesense" and its evolution. A system for the development of a sense of the fourth dimension by exercises with colored cubes. The geometrical conception of space. Three perpendiculars—why three? Can everything existing be measured by three perpendiculars? The indices of existence. Reality of ideas. Insufficient evidence of the existence of matter and motion. Matter and motion are only logical concepts, like "good" and "evil."

A

S already stated, Kant propounded the problem, but gave no solution of it, nor did he point the way to a solution. And not one of the known commentators, interpreters, followers or adversaries of Kant has found a solution, or the way to it.

I find the first flashes of a right understanding of the Kantian problem, and the first suggestions in regard to a possible way toward its solution, in the attempts at a new treatment of the problem of space and time, involving the concept of the "fourth dimension" and higher dimensions in general. An interesting synopsis of many things developed in this direction is that of C. H. Hinton, author of the books, A New Era of Thought, and The Fourth Dimension.

Hinton notes, among other things, that in commenting upon Kantian ideas, only their negative side is usually insisted upon, namely, the fact that we can cognize things in a sensuous way, in terms of space and time only, is regarded as an obstacle, hindering us from seeing what things in themselves really are, preventing the possibility of cognizing them as they are, imposing upon them that which is not inherent in them, shutting them off from us.

But (says Hinton) if we take Kant's statement simply as it is not seeing in the spatial conception a hindrance to right receptivity—that we apprehend things by means of space—then it is equally allowable to consider our space sense not as a negative condition, hindering our perception of the world, but as a positive means by which the mind grasps its experiences, i. e., by which we cognize the world.

There is, in so many books in which the subject is treated, a certain air of despondency—as if this space apprehension were a kind of veil which shut us off from nature. But there is no need to adopt this feeling. The first postulate of this book is a full recognition of the fact that it is by means of space that we apprehend what is.

Space is the instrument of the mind.

Very often a statement which seems to be most deep and abstruse and hard to grasp, is simply the form into which deep thinkers have thrown a very simple and practical observation. And for the present let us look on Kant's great doctrine of space from a practical point of view, and it comes to this it is important to develop the space sense, for it is the means by which we think about real things.

Now according to Kant [Hinton goes on to say] the space sense, or the intuition of space, is the most fundamental power of the mind. But I do not find anywhere a systematic and thorough-going education of the space sense. It is left to be organized by accident. Yet the special development of the space sense makes us acquainted with a whole series of new conceptions.

Fichte, Schelling, Hegel, have developed certain tendencies and have written remarkable books, but the true successors of Kant are Gauss and Lobachevsky.

For if our intuition of space is the means whereby we apprehend, then it follows that there may be different kinds of intuitions of space. Who can tell what the absolute space intuition is? This intuition of space must be colored, so to speak, by the conditions (of psychical activity) of the being which uses it.

By a remarkable analysis the great geometers above mentioned have shown that space is not limited as ordinary experience would seem to inform us, but that we are quite capable of conceiving different kinds of (A New Era of Thought.)

space.

Hinton invented a complicated system for the education and development of the space sense by means of exercises with groups the cubes of different colors. The books above mentioned are devoted to the exposition of this system. In my opinion Hinton's exercises are interesting from a theoretical standpoint, but they are practically valuable only for such as have the same turn of mind as Hinton's own.

Exercises of the mind according to his system must first of all lead to the development of the ability to imagine objects, not as the eye sees them, i. e., in perspective, but as they are geometrically—to learn to imagine the cube, for example, simultaneously from all sides. Moreover such a development of the imagination

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