PROP. I.————
In what respect it is wrong.6. The error which the counter-proposition presents is contained in the statement that there is no middle between knowledge and ignorance, and that whatever we do not know we must be ignorant of. As this doctrine—the law of excluded middle, as it is called—is nowhere very clearly explained, and seems to be insufficiently understood by philosophers in general, a few remarks may here be made in elucidation of it.
The law of the excluded middle stated.7. There is no medium, it is said, between knowing and being ignorant of a thing—we must either know it, or not know it. This is one of the forms of the law of contradiction (see Introduction, § 28), and under this expression it is called the law of excluded middle, which means that we have no alternative except either to know or to be ignorant of a thing; in other words, that it is impossible for us neither to know nor to be ignorant of it. If we do not know it, we must be ignorant of it; and conversely, if we are not ignorant of it, we must know it. Such is the law of excluded middle, considered in reference to knowledge and ignorance; and it is laid down by logicians as subject to no restriction or qualification.
How this law must be qualified.8. It is obvious, however, that this law is subject to a very considerable restriction or qualification. It applies only to non-contradictory things. We
