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In return, the theory of knowledge becomes an infinitely difficult enterprise, and which passes the powers of the intellect alone. It is not enough to determine, by careful analysis, the categories of thought; we must engender them. As regards space, we must, by an effort of mind sui generis, follow the progression or rather the regression of the extra-spatial degrading itself into spatiality.
Abstract unity and abstract multiplicity are determinations of space or categories of the understanding, whichever we will, spatiality and intellectuality being molded on each other. But what is of psychical nature cannot entirely correspond with space, nor enter perfectly into the categories of the understanding. Is my own person, at a given moment, one or manifold?
Our perception, whose rôle it is to hold up a light to our actions, works a dividing up of matter that is always too sharply defined, always subordinated to practical needs, consequently always requiring revision. Our science, which aspires to the mathematical form, over-accentuates the spatiality of matter; its formulae are, in general, too precise, and ever need remaking.
We may go further: the other half of knowledge is no longer so radically, so definitely relative as certain philosophers say, if we can establish that it bears on a reality of inverse order, a reality which we always express in mathematical laws, that is to say in relations that imply comparisons, but which lends itself to this work only because it is weighted with spatiality and consequently with geometry.
In this last respect sculpture should be credited with having first revealed the inner and spiritual essence in its eternal repose and essential self-possession. To such repose and unity with itself corresponds only that external element which itself persists in unity and repose. Such an element is the form taken in its abstract spatiality.
We have treated of the first point elsewhere. As to the second, we will limit ourselves to pointing out that perfect spatiality would consist in a perfect externality of parts in their relation to one another, that is to say, in a complete reciprocal independence. Now, there is no material point that does not act on every other material point.
If on one side matter lends itself to a division into active and passive bodies, or more simply into coexistent and distinct fragments, it is from this side that intelligence will regard it; and the more it busies itself with dividing, the more it will spread out in space, in the form of extension adjoining extension, a matter that undoubtedly itself has a tendency to spatiality, but whose parts are yet in a state of reciprocal implication and interpenetration.
It understands only what is discontinuous, inert, and fixed, that which has neither change nor duration; it bathes in an atmosphere of spatiality; it uses mathematics continually; it feels at home only among "things," and everything is reduced by it to solid atoms; it is naturally "materialist," owing to the very fact that it naturally grasps "forms" only.
And when we examine this exact fitting, shall we not be led, in one point at least, to suppose a pre-established harmony between things and our mind an idle hypothesis, which Kant was right in wishing to avoid? At bottom, it is for not having distinguished degrees in spatiality that he has had to take space ready-made as given whence the question how the "sensuous manifold" is adapted to it.
Thus, the space of our geometry and the spatiality of things are mutually engendered by the reciprocal action and reaction of two terms which are essentially the same, but which move each in the direction inverse of the other. Neither is space so foreign to our nature as we imagine, nor is matter as completely extended in space as our senses and intellect represent it.
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