PROP. I.————
must either know or be ignorant of whatever is non-contradictory, because whatever is non-contradictory is knowable, and, therefore, if we do not know it, we must be ignorant of it: there can be no doubt about that. But the case is very different in regard to the contradictory or absolutely unknowable: of this there can be no knowledge and no ignorance. Can any man be cognisant of two and two making five, or of two straight lines enclosing a space? No. Can any man be ignorant of these absurdities? Just as little. Speaking ironically, or in jest, a person might, indeed, say that he was ignorant of two and two making five, or of the inequality of the radii of a circle, but he could not say this seriously without talking irrationally. These instances are adduced merely as illustrations. But it is obvious that every contradictory, or whatever is absolutely unknowable, is that of which there can neither be any knowledge nor any ignorance. The law, therefore, of excluded middle must be accepted with this qualification, that it is valid and true only in reference to the non-contradictory.
Origin of the mistake in regard to this law. 9. The prevalent mistake on this subject has its origin in the cause alluded to in the Introduction, § 69, where it was stated that philosophers have generally confounded together under a common category the simply unknowable and inconceivable by us, and the absolutely unknowable and inconceivable in itself. The simply unknowable by