# Philosophical Works of the Late James Frederick Ferrier/Institutes of Metaphysic (1875)/Section 3/Proposition 1

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. 451-460.
SECTION III.
THE ONTOLOGY, OR THEORY OF BEING
PROPOSITION I.
THE THREE ALTERNATIVES AS TO ABSOLUTE EXISTENCE.
DEMONSTRATION.
If a thing is not this, it may be that; but if it is not this, and not that, it must be neither this nor that. (This is one of the strongest forms in which the law of contradiction, the criterion of all necessary truth, can be expressed.) Hence if absolute existence is not that which we know, it may be that which we are ignorant of; but if it is not that which we know, and not that which we are ​ignorant of, it must be that which we neither know nor are ignorant of. Therefore absolute existence is either, first, That which we know; or, secondly, That which we are ignorant of; or, thirdly, That which we neither know nor are ignorant of; and no other alternative is possible.
OBSERVATIONS AND EXPLANATIONS.
The problem of ontology stated. 1. The problem of ontology, as announced in the Introduction, § 54, is, What is? in the proper and emphatic sense of the word IS. What absolutely and independently exists? What, and what alone, possesses a clear, detached, emancipated, substantial, genuine, or unparasitical Being? What can that which possesses this be declared to be? What is its character? What predicate can be attached to it? This is the problem which ontology is called upon to resolve; and it will be seen as we advance, that without the whole of the preceding demonstrations, this question is insoluble, but with them its reasoned settlement may be reached.
2. This proposition opens the way. It exhibits the alternatives, any of which, so far as we see at present, Absolute Existence may be, and one or other of which it must be; for the three alternatives are exhaustive, as must be obvious to any one who considers the proposition even without the ​demonstration. Absolute existence may possibly be that which we are cognisant of, or it may possibly be that which we are ignorant of; but if it is not that which we are cognisant of, and not that which we are ignorant of, it must be that which we are neither cognisant of nor ignorant of; and no other alternative is possible. This conclusion seems sufficiently obvious. To those, however, who may desire a more concrete example of the kind of syllogism here employed, the following illustration will be of service: If it is not summer, it may be winter; but if it is not summer, and not winter, it must be neither summer nor winter. Therefore it is either summer or winter, or neither; and no other alternative as to time and season is possible. For suppose it to be spring; but spring is neither summer nor winter, and therefore the conclusion of the syllogism is unshaken. Such, mutatis mutandis, is the present reasoning in regard to Absolute Existence.
The third alternative has to be eliminated.3. All the alternatives which Absolute Existence is capable of being, having been exhibited in this proposition, the next step which the system takes is to reduce these alternatives from three to two. This elimination is accomplished in Propositions II. III. IV. Meanwhile the counter-proposition is subjoined.
​First counter-proposition.4. First Counter-proposition.—"There are only two alternatives in regard to Absolute Existence. If Absolute Existence is not what we know, it must be what we are ignorant of; for there is no middle between knowledge and ignorance. Whatever we do not know, we must be ignorant of; in other word; it is impossible neither to know nor to be ignorant of a thing."
In what respect this counter-proposition is right.5. There is nothing wrong in this counter-proposition, in so far as it maintains that there are only two alternatives in regard to absolute existence. This is the very conclusion which the ontology is proceeding to establish in the subsequent propositions; but it must be established in an orderly manner, and not taken for granted at the outset. At first sight the alternatives of Absolute Existence are apparently three, and accordingly they have been set forth as three in the opening proposition, in order that the Theory of Being may be cleared from the very commencement, may proceed by deliberate and legitimate steps, and may leave in arrear or unremoved no difficulty or objection to which it may seem to be exposed. Its labours would have been considerably abridged had it held itself entitled to start from the affirmation that the alternatives of Absolute Existence are only two; but such a starting-point would have been not strictly legitimate.
​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 ​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 ​us is excluded from our knowledge, but it is not excluded from our ignorance. In regard to this (the simply unknowable), there is no middle—a third alternative is excluded. We do not know it, and therefore we must be ignorant of it. Here the law applies; but the absolutely unknowable is excluded from our knowledge; and it is excluded equally from our ignorance. In regard to this, there is nothing but a third or middle alternative. We can neither know it, nor be ignorant of it. Here the law does not apply. Hence there is a middle between knowledge and ignorance; a middle which is excluded alike from our knowledge and from our ignorance, and this middle is the contradictory, or that which the laws of all reason prevent from being known on any terms by any intelligence. The counter-proposition, therefore, which lays down the law of excluded middle without any qualification, and denies that it is subject to any limitation, is erroneous.
The want of a clear doctrine of the contradictory has been the cause of much error in philosophy.10. One of the principal retarding causes of philosophy has been the want of a clear and developed doctrine of the contradictory. This desideratum could not be supplied so long as philosophers refused, as they have hitherto done, to found speculative science upon reason, and to carry it out from beginning to end, as a concatenated system of necessary truths. To this cause the error which we have just been considering, and many ​other errors, are to be attributed. Throughout these Institutes a correct doctrine of the contradictory, showing distinctly what it is (namely, that it is either of the factors of cognition taken by itself or apart from its co-factor), has been developed. Philosophers have hitherto supposed that propositions alone could be contradictory: in this work their attention is directed more particularly to the consideration of contradictory terms; for these, no less than propositions, may express that which is contradictory.
Distinction between the singly and doubly contradictory.11. In further explanation of this doctrine, a distinction may here be pointed out between the singly contradictory and the doubly contradictory. The two co-factors of cognition (subject and object), when considered singulatim, or apart from each other, are only the singly contradictory,—a centreless circle, or a stick with only one end, is the doubly contradictory. To redeem any object (a stick, or a circle, or whatever it may be) from contradiction—in other words, to render it apprehensible—the subject must know itself along with it. Here only one supplementation is required—the me must be known along with the thing. But to redeem from contradiction a centreless circle or a stick with only one end, two supplementations are required: first, the centre must be supplied to the circle; and secondly, the me must, moreover, be taken into account.