Lectures on the Proof of the Existence of God #3 by georg Friedrich Hegel
0The knowledge which we have here before us can only attain its greatest perfection in this field, because that field contains only simple and definite qualities, and the dependence of these upon each other, the insight into the nature of which is proof, is thus stable, and ensures for proof the logical progress of necessity. This kind of knowledge is capable of exhausting the nature of its objects. The logical nature of the process of proof is not, however, confined to mathematical content, but enters into all departments of natural and spiritual material; but we may sum up what is logical in knowledge in connection with proof by saying that it depends on the rules of inference; the proofs of the existence of God are therefore essentially inferences. The express investigation of these forms belongs, however, partly to logic, and for the rest the nature of the fundamental defect must be ascertained in the course of the examination of these proofs which is about to be taken in hand. For the present it is enough to remark further, in connection with what has been said, that the rules of inference have a kind of foundation which is of the nature of mathematical calculation. The connection of propositions which are requisite to constitute a syllogistic conclusion depends on the relations of the sphere which each of them occupies as regards the other, and which is quite properly regarded as greater or smaller. The definite extent of such 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.