SPACE, that phase of the world which we express in terms of right and left, forward and backward, up and down, etc.; the actual experienced system which we are accustomed to handle by means of geometry. Many theories have been held concerning its nature. The an cient views are not at all clear, but unfil Aristotle, at any rate, the existence of empty space is not recognized and there is a general tendency to subordinate space to matter. The modern theory of space begins with Descartes, who makes extension the distinguishing 'mark of matter. Spinzoa, though he finds in matter an attribute of God rather than an independent substance, follows Descartes in this respect. Leibnitz does not attribute to space an inde pendent existence, but makes it merely an un clear recognition of the logical relations of the monads. Newton on the other hand, claims an independent existence for space and maintains that position is absolute, not relative. Kant solves the dispute between Leibnitz and Newton by finding in space and time, respec tively, that a priori form of the external and internal senses, so that geometry is independent of experience, yet spatial entities do not exist apart from sense. Among the present views on the subject is the curious one of Bergson, who regards the spatial description of the uni verse as a scientific, intellectual perversion of the temporal flux is directly presented to intui tion.
The old dispute as to whether the idea of space is innate or acquired belongs to a past stage of philosophical discussion and one may take it as an established fact that the empirical status of extension is quite analogous to that of any of the sensory qualities. Just as my experience of this red blotter before me is preconditioned by the fact that I am so con stituted — unlike some color-blind persons — as to be able to perceive red, so my experience of space depends on my having a nature fitted to perceive spatial entities. it seems that as far as the mere nature of the experience is concerned, there is no reason for dividing qualities into the primary, such as those of space and time and the secondary, of color, sound, etc. The distinguishing characteristics of space
reside in its organization rather than in its quality. This organization forms the subject matter of geometry, it is probably dependent in part on the intrinsic nature of the things which are in space and go to make up our spatial experience, but it is unquestionably also in a large measure dependent on the arrange ment which we more or less consciously make of these sense-data, and by the arrangement of the entities of any system a system may be obtained whose formal properties are just about what you choose. Space thus becomes as Poincare has shown, a more or less pliable tool for scientific description, so that the ques tion, °What is the structure of space?" may almost be translated into °What spatial struc ture is the simplest and most manageable for purposes of scientific description?" As a con sequence, as the formula of science do not seem to be markedly simplified by the postula tion of a non-Euclidean space (see GEOMETRY, NON-EUCLIDEAN) or of any other spatial struc ture other than that which is familiar to us in our elementary geometry and as this elementary geometry is simpler in its formula than non Euclidean geometry or other similar systems, we choose — albeit unconsciously — the struc ture of our space in such a way that it shall be Euclidean. The three-dimensional character of space is likewise due to the fact that a three dimensional system forms the simplest and most appropriate background to the observed facts of physics and is not, as Kant supposed, an a priori truth. If we should suddenly find masses varying in such a manner as to be susceptible of an easy and direct explanation by a motion perpendicular to our space, the very next work on physics would speak just as confidently of a space of four dimensions as we now speak of a space of three. A change of a similar nature has taken place in the last few years. (See RELATIVITY, THE PRINCIPLE OF).