a sphere is what determines the correctness of the subsumption. The older logicians, such as Lambert and Ploucquet, have been at the pains of inventing a notation by means of which the relation in inference may be reduced to that of identity, that is, to the abstract mathematical relation of equality, so that inference is shown to be the mechanism of a kind of calculation. As regards, however, the further nature of knowledge in such an external connection of objects, which in their very nature are external in themselves, we shall have to speak of it presently under the name of mediate knowledge, and to consider the opposition in its more definite form.
As regards these forms which are called species, laws, forces, and so on, knowledge does not stand to them in an external relation; they are rather its products. But the knowledge which produces them, as has been shown, produces them only by abstraction from what is objective; they have their root in this, but are essentially separated from what is actual; they are more concrete than mathematical figures, but their content differs essentially from that from which the start was made, and which must constitute their only foundation of proof.
The defective element in this mode of knowledge has thus attention drawn to it in a different form from that shown in the way of looking at it, which declares the products of knowledge to be mere phenomena, because knowledge itself is only a subjective activity. But the general result, however, is the same, and we have now to see what has been set over against this result. What is determined as insufficient for the aim of the Spirit, which is the absorption into its very nature of what is infinite, eternal, divine, is the activity of the Spirit which in thinking proceeds by means of abstraction, inference, and proof. This view, itself the product of the mode of thought characteristic of the period, has jumped straight over to the other extreme in giving out a proofless,
