VII. PRIVATE SPACE AND THE SPACE OF

PERSPECTIVES
We have now to explain the ambiguity in the word " place," and how it comes that two places of different sorts are associated with every sense-datum, namely the place at which it is and the place from which it is per- ceived. The theory to be advocated is closely analogous to Leibniz's monadology, from which it differs chiefly in being less smooth and tidy.
The first fact to notice is that, so far as can be dis- covered, no sensibile is ever a datum to two people at
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once. The things seen by two different people are often closely similar, so similar that the same words can be used to denote them, without which communication with others concerning sensible objects would be impossible. But, in spite of this similarity, it would seem that some difference always arises from difference in the point of view. Thus each person, so far as his sense-data are con- cerned, lives in a private world. This private world contains its own space, or rather spaces, for it would seem that only experience teaches us to correlate the space of sight with the space of touch and with the various other spaces of other senses. This multiplicity of private spaces, however, though interesting to the psychologist, is of no great importance in regard to our present problem, since a merely solipsistic experience enables us to correlate them into the one private space which embraces all our own sense-data. The place at which a sense-datum is, is a place in private space. This place therefore is different from any place in the private space of another percipient. For if we assume, as logical economy demands, that all position is relative, a place is only definable by the things in or around it, and therefore the same place cannot occur in two private worlds which have no common constituent. The question, therefore, of combining what we call different appearances of the same thing in the same place does not arise, and the fact that a given object appears to different spectators to have different shapes and colours affords no argument against the physical reality of all these shapes and colours.
In addition to the private spaces belonging to the private worlds of different percipients, there is, however, another space, in which one whole private world counts as a point, or at least as a spatial unit. This might be
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described as the space of points of view, since each private world may be regarded as the appearance which the universe presents from a certain point of view. I prefer, however, to speak of it as the space of Perspectives, in order to obviate the suggestion that a private world is only real when someone views it. And for the same reason, when I wish to speak of a private world without assuming a percipient, I shall call it a " perspective."
We have now to explain how the different perspectives are ordered in one space. This is effected by means of the correlated " sensibilia " which are regarded as the appear- ances, in different perspectives, of one and the same thing. By moving, and by testimony, we discover that two different perspectives, though they cannot both contain the same ' sensibilia," may nevertheless contain very similar ones ; and the spatial order of a certain group of
' sensibilia ' in a private space of one perspective is found to be identical with, or very similar to, the spatial order of the correlated " sensibilia " in the private space of another perspective. In this way one " sensibile " in one perspective is correlated with one " sensibile ' in another. Such correlated ' sensibilia ' will be called
1 appearances of one thing." In Leibniz's monadology, since each monad mirrored the whole universe, there was in each perspective a " sensibile " which was an appear- ance of each thing. In our system of perspectives, we make no such assumption of completeness. A given thing will have appearances in some perspectives, but presumably not in certain others. The " thing ' being defined as the class of its appearances, if K is the class of perspectives in which a certain thing 6 appears, then 0 is a member of the multiplicative class of A: , K being a class oi mutually exclusive classes of " sensibilia." And
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similarly a perspective is a member of the multiplicative class of the things which appear in it.
The arrangement of perspectives in a space is effected by means of the differences between the appearances of a given thing in the various perspectives. Suppose, say, that a certain penny appears in a number of different perspectives ; in some it looks larger and in some smaller, in some it looks circular, in others it presents the appear- ance of an ellipse of varying eccentricity. We may collect together all those perspectives in which the appearance oi the penny is circular. These we will place on one straight line, ordering them in a series by the variations in the apparent size of the penny. Those perspectives in which the penny appears as a straight line of a certain thickness will similarly be placed upon a plane (though in this case there will be many different perspectives in which the penny is of the same size ; when one arrangement is com- pleted these will form a circle concentric with the penny), and ordered as before by the apparent size of the penny. By such means, all those perspectives in which the penny presents a visual appearance can be arranged in a three- dimensional spatial order. Experience shows that the same spatial order of perspectives would have resulted if, instead of the penny, we had chosen any other thing which appeared in all the perspectives in question, or any other method of utilising the differences between the appearances of the same things in different perspectives. It is this empirical fact which has made it possible to construct the one all-embracing space of physics.
The space whose construction has just been explained, and whose elements are whole perspectives, will be called " perspective-space."
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