The second possibility also, Lotze thinks, is not that of Metageometry, but in truth it comes nearer to it than any of the other possibilities discussed. If a non-Euclidean were at the same time a believer in the subjectivity of space, he would have to be an adherent of this view. Let us see more precisely what the view is. In Book II., Chapter I., Lotze has accepted the argument of the Transcendental Aesthetic, but rejected that of the mathematical antinomies: he has decided that space is, as Kant believed, subjective, but possesses nevertheless, what Kant denied it, an objective counterpart. The relation of presented space to its objective counterpart, as conceived by Lotze, is rather hard to understand. It seems scarcely to resemble the relation of sensation to its object--_e.g._ of light to ether-vibrations--for if it did, space would not be in any peculiar sense subjective. It seems rather to resemble the relation of a perceived bodily motion to the state of mind of the person willing the motion. However this may be, the objective counterpart of space is supposed to consist of certain immediate interactions of monads, who experience the interactions as modifications of their internal states. Such interactions, it is plain, do not form the subject-matter of Geometry, which deals only with our resulting perceptions of spatial figures. Now if Lotze's construction of space be correct, there seems certainly no reason why these resulting perceptions should not, for one and the same interaction between monads, be very different in beings differently constituted from ourselves. But if they were different, says Lotze, they would have to be utterly different--as different, for example, as the interval between two notes is from a straight line. The possibility is, therefore, in his opinion, one about which we can know nothing, and one which must remain always a mere empty idea. This seems to me to go too far: for whatever the objective counterpart may be, any argument which gives us information about it must, when reversed, give us information about any possible form of intuition in which this counterpart is presented. The argument which Lotze has used in his former chapter, for example, deducing, from the relativity of position, the merely relational nature of the objective counterpart, allows us, conversely, to infer, from this relational nature, the complete relativity of position in any possible space-intuition--unless, indeed, it bore a wholly deceitful relation to those interactions of monads which form its objective counterpart. But the complete relativity of position, as I shall endeavour to establish in Chapter III., suffices to prove that our Geometry must be Euclidean, elliptic, spherical or pseudo-spherical. We have, therefore, it would seem, very considerable knowledge, on Lotze's theory of space, of the manner in which what appears to us as space _must_ appear to any beings with our laws of thought.