Now, Plato’s view of a soul leads us to the hypothesis that that which we designate as an act of apprehension may be a very complex event, both physically and personally. He does not seek to explain what an intuition is; he makes it a basis from whence he sets out on a voyage of discovery. Knowledge means knowledge; he puts conscious being to account for conscious being. He makes an hypothesis of the kind that is so fertile in physical science—an hypothesis making no claim to finality, which marks out a vista of possible determination behind determination, like the hypothesis of space itself, the type of serviceable hypotheses. And, above all, Plato’s hypothesis is conducive to experiment. He gives the perspective in which real objects can be determined; and, in our present enquiry, we are making the simplest of all possible experiments—we are enquiring what it is natural to the soul to think of matter as extended. Aristotle says we always use a “phantasm” in thinking, a phantasm of our corporeal senses a visualisation or a tactualisation. But we can so modify that visualisation or tactualisation that it represents something not known by the senses. Do we by that representation wake up an intuition of the soul? Can we by the presentation of these hypothetical forms, that are the subject of our present discussion, wake ourselves up to higher intuitions? And can we explain the world around by a motion that we only know by our souls? Apart from all speculation, however, it seems to me that the interest of these four-dimensional shapes and motions is sufficient reason for studying them, and that they are the way by which we can grow into a fuller apprehension of the world as a concrete whole. SPACE NAMES. If the words written in the squares drawn in fig. 1 are used as the names of the squares in the positions in which they are placed, it is evident that a combination of these names will denote a figure composed of the designated squares. It is found to be most convenient to take as the initial square that marked with an asterisk, so that the directions of progression are towards the observer and to his right. The directions of progression, however, are arbitrary, and can be chosen at will. [Illustration: Fig. 1.] Thus _et_, _at_, _it_, _an_, _al_ will denote a figure in the form of a cross composed of five squares. Here, by means of the double sequence, _e_, _a_, _i_ and _n_, _t_, _l_, it is possible to name a limited collection of space elements. The system can obviously be extended by using letter sequences of more members. But, without introducing such a complexity, the principles of a space language can be exhibited, and a nomenclature obtained adequate to all the considerations of the preceding pages. 1. _Extension._