Note 133 — Introductory material

The above argument, it may be urged, has overlooked a possibility. It has used a transcendental argument, so an opponent may contend, without sufficiently proving that knowledge about externality must be possible without reference to the matters external to each other. The definition of a position may be impossible, so long as we neglect the matter which fills the form, but may become possible when this matter is taken into account. Such an objection can, I think, be successfully met, by a reference to the passivity and homogeneity of our form. For any dependence of the definition of a position on the particular matter filling that position, would involve some kind of interaction between the matter and its position, some effect of the diverse content on the homogeneous form. But since the form is totally destitute of thinghood, perfectly impassive, and perfectly void of differences between its parts, any such effect is inconceivable. An effect on a position would have to alter it in some way, but how could it be altered? It has no qualities except those which make it the position it is, as opposed to other positions; it cannot change, therefore, without becoming a different position. But such a change contradicts the law of identity. Hence it is not the position which has changed, but the content which has moved in the form. Thus it must be possible, if knowledge of our form can be obtained at all, to obtain this knowledge in logical independence of the particular matter which fills it. The above argument, therefore, granted the possibility of knowledge in the department in question, shows the necessity of a finite integral number of dimensions.