PROP. III.————
in the opposites of the axioms. Hence this study merely shows us that there can be no knowledge of these opposites; it does not open our eyes to the fact that there can be no ignorance of them. It is obvious, however, that it is just as impossible for us to be ignorant of them as it is impossible for us to know them. No man can know that two and two make five,—but just as little can any man be ignorant of this; for suppose him ignorant of it,—in that case his ignorance could be removed only by teaching him that two and two do make five; but such instruction, instead of removing his ignorance, would remove his knowledge, and instead of giving him knowledge, would give him ignorance, or rather absurdity. The cure in this case would be itself the disease.
There can be no ignorance of the contradictory.5. An attention to the fact, that it is impossible for us (or for any intelligence) to be ignorant of the contradictory, that is, of the opposites of the necessary truths of reason, or, in other words, of that which cannot be known on any terms by any intelligence, though of no importance in mathematics, is of the utmost importance in metaphysics. Speculation can obtain a footing in ontology only by attending carefully to this circumstance, and by working it out through all its consequences. This truth is the key to the whole philosophy of ignorance. When we consider it well, we discover that