# Philosophical Works of the Late James Frederick Ferrier/Institutes of Metaphysic (1875)/Section 2/Proposition 3

The Institutes of Metaphysic, Philosophical Works of the Late James Frederick Ferrier (1875 ed., Vol. 1). (E. L. Lushington, & A. Grant, Eds.) Edinburgh: William Blackwood and Sons. pp. 412-416.
PROPOSITION III.
THE LAW OF ALL IGNORANCE.
DEMONSTRATION.
If we could be ignorant of what could not possibly be known by any intelligence, all ignorance would not be possibly remediable. The knowledge in which we were deficient could not be possessed by any intelligence. But all ignorance is possibly remediable (by Prop. II.) Therefore, we can be ignorant only of what can possibly be known; in other words, there can be an ignorance only of that of which there can be a knowledge.
OBSERVATIONS AND EXPLANATIONS.
1. This is the most important proposition in the agnoiology: indeed, with the exception of the first ​1. This is the most important proposition in the agnoiology: indeed, with the exception of the first
Importance of this position.of the epistemology, it is the most fruitful and penetrating proposition in the whole system. It announces—for the first time, it is believed—the primary law of all ignorance, just as the first of the epistemology expresses the primary law of all knowledge. It is mainly by the aid of these two propositions that this system of Institutes is worked out. All the other propositions have an essential part to play in contributing to the final result; but these two are the most efficient performers in the work. If the reader has got well in hand these two truths—first, that there can be a knowledge of things only with the addition of a self or subject; and, secondly, that there can be an ignorance only of that of which there can be a knowledge—he will find himself in possession of a lever powerful enough to break open the innermost secresies of nature. These two instruments cut deep and far—they lay open the universe from stem to stern.
Symbols illustrative of the law of ignorance.2. The law of all ignorance may be illustrated by the same symbols which were used in Proposition IV. of the epistemology, Obs. 11, to illustrate the law of all knowledge. Just as there can be a knowledge of X only when there is a knowledge of Y, so there can be an ignorance of X only when there is an ignorance of Y. Because if there could be an ignorance of X without Y, but not a knowledge of X without Y, something would be ignored ​which could not be known—a supposition which is contradictory and absurd.
Distinction between ignorance and nescience of the opposites of necessary truth.3. Ignorance, properly so called—that is, the ignorance which is a defect—must not be confounded with a nescience of the opposites of the necessary truths of reason; in other words, with a nescience of that which it would contradict the nature of all intelligence to know. Such nescience is no defect or imperfection—it is, on the contrary, the very strength or perfection of reason; and therefore such nescience is not to be regarded as ignorance. This simple but very important distinction must be explained and illustrated, for it is one which is very apt to be lost sight of; or confounded; indeed, it has been altogether overlooked until now.
There can be no ignorance of the opposite of the geometrical axioms.4. When boys at school are taught Euclid, they learn that "the enclosure of space by two straight lines" is what cannot be known,—that "if equals be added to equals the wholes are unequal" is what cannot be known,—that "a part is greater than the whole" is what cannot be known, and so forth; but they do not learn that they are equally incapable of being ignorant of such matters. It is not necessary to apprise them of this in order to carry them forward in the study of mathematics. Nothing in geometry depends on the circumstance that we cannot be ignorant of what is deponed to ​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 ​the supposition that we can be ignorant of that which is absolutely and necessarily unknowable to all intelligence, is as extreme a violation of the law of contradiction as it is possible to conceive. We perceive that a nescience of the contradictory is not ignorance, but is the very essence of intelligence; and that there can be an ignorance only of that which can be known, or, otherwise expressed, of that which is non-contradictory. With this discovery, light breaks into every cranny and recess of our science: the "holy jungle" of metaphysic is laid open to the searching day, and now no obstacle can stop the onward course of speculation.
Third counter-proposition6. It may be doubtful whether and how far, this proposition has ever been denied. But as it is not improbable that an obscure impression popularly prevails that we are most ignorant of that which cannot be known, the following counter-proposition is appended. Third Counter-proposition: "We can be ignorant of what cannot possibly be known—indeed, that of which there can be no knowledge, is precisely that of which there must be the profoundest ignorance." If any such doctrine as this is, or ever was, entertained, it is conceived that it cannot hold its ground before the present proposition and its demonstration.