Fundamental Philosophy. Jaime Luciano Balmes
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Let us now see what happens in the purely ideal order, where the word being is taken copulatively. Propositions of the purely ideal order are of two classes; in the first, the subject is a generic idea, which, by the union of the specific difference, becomes a determinate species; in the second, the subject is this determinate species, or the generic idea joined with the difference. The word angle expresses the generic idea comprehending all angles, which, united with the corresponding difference, constitutes the species of acute, obtuse, or right angle. At every step we modify the generic idea in various ways, and as a succession, in which are represented to us distinct conceptions, all having for their basis the generic idea, necessarily enters into it, it follows that we consider this idea as a being which is successively transformed. To express this succession, which is purely intellectual, we employ the idea of time; and here is one of the reasons which justify the use of this condition even in the purely ideal order. Thus we say, an angle cannot at the same time be both a right angle and a not-right angle; for the idea of angle may be successively determined by the difference which constitutes it a right angle, and a not-right angle; but these determinations cannot co-exist even in our conception, for which reason we do not assert the union of the difference with the genus to be absolutely impossible, but limit the impossibility to the condition of simultaneousness.
In this proposition, a right angle cannot be obtuse; the subject is not the generic idea alone, but is united with the difference expressed by the word right. In the conception formed of these two ideas, right and angle, we see the impossibility of uniting the idea obtuse with them. This is without any condition of time, and here there is none expressed. We frequently say, an angle cannot be at the same time right and obtuse; but we never say, a right angle can never at the same time be obtuse, but, absolutely, a right angle cannot be obtuse.
200. Kant observes that the equivocation proceeds from commencing by separating the predicate of a thing from the conception of this thing, and afterwards joining to this same predicate its opposite, which never makes a contradiction to the subject, but to the predicate, which is synthetically united with it; a contradiction which happens only when the first and second predicates are supposed at the same time. This observation of Kant is at bottom very true, but it has its defects: first, it pretends to be original, when it only says things already well known; and secondly, it is used to combat an equivocation existing only in the mind of the philosopher who wants to free others from it. The two propositions analyzed in the last paragraph confirm what we have just said. An angle cannot be both right and not right. Here the condition of time is necessary, because the opposition is not between the predicate and the subject, but between the two predicates. The angle may be right or not right, only at different times. A right angle cannot be obtuse; here the condition of time must not be expressed, because the idea right entering into the conception of the subject, entirely excludes the idea obtuse.
201. If the principle of contradiction were to serve only for analytic judgments, that is, for those in which the predicate is contained in the idea of the subject, the condition of time should never be expressed; but as this principle is to guide us in all other judgments, it follows that, in the general formula, we cannot abstract a condition absolutely indispensable in most cases. In the present state of our understanding, while we are in this life, non-abstraction of time is the rule, abstraction the exception; and would you have a general formula conform to the exception and neglect the rule?
202. We cannot conceive what reason Kant had to illustrate this subject with the examples above cited. Nothing can be more common and inopportune than what he adds in illustration of this matter by examples. "If I say a man who is unlearned is not learned, the condition at the same time must be understood; for he who is unlearned at one time, may very well be learned at another." This is not only very common and inopportune, but it is exceedingly inexact. If the proposition were: a man cannot be ignorant and instructed; then the condition at the same time should be added, because not giving preference to either predicate over the other indicates the manner of the opposition, which is of predicate to predicate, and not of predicate to subject. But in the example adduced by Kant, "the man that is ignorant is not instructed." The subject is not man alone, but an ignorant man; the predicate instructed devolves on man modified by the predicate ignorant, and, consequently, the expression of time is not necessary, nor is it used in ordinary language.
There is a great difference between these two propositions: a man that is ignorant is not instructed; and a man that is ignorant cannot be instructed. The condition of time must not be expressed in the former, for the reason already given; it must be in the latter, because speaking of the impossibility in an absolute manner, we should deny the ignorant man even the power to be instructed.
203. Kant's other example is the following: "But if I say no unlearned man is learned, the proposition is analytical, since the sign of unlearnedness now constitutes the conception of the subject, and then the negative proposition is immediately evident from the principle of contradiction, without it being necessary for the condition at the same time to be added." We cannot see why Kant makes so great difference between these two propositions: a man who is unlearned is not learned, and no unlearned man is learned; in both, the predicate relates not only to man, but to an unlearned man; and it is the same to say, a man that is unlearned, as, an unlearned man. If, then, the expression of time is not necessary in the one, neither is it in the other.
If the idea of unlearned affects the subject, the predicate is necessarily excluded, because the ideas, learned and unlearned, are contradictory; and we encounter the rule of logic, that in necessary matters, an indefinite is equivalent to a universal proposition.
The principle of contradiction must, therefore, be preserved as it is; the condition of time must not be suppressed, for this would render the formula, in many cases, inapplicable.(20)
CHAPTER XXI.
DOES THE PRINCIPLE OF CONTRADICTION MERIT THE TITLE OF FUNDAMENTAL; AND IF SO, IN WHAT SENSE?
204. Having cleared up the true sense of the principle of contradiction, let us now see whether it merits to be called fundamental, whether it possesses all the characteristics requisite to such a dignity. These characteristics are three in number: first, that it depend on no other principle; secondly, that its fall involve the ruin of all others; thirdly, that it may, while it remains firm, be conclusively urged against all who deny the others, and be of avail to bring them back to the truth by a demonstration at least indirect.
205. In order completely to solve all questions depending on the principle of contradiction, we shall state a few propositions, and accompany them with their proper demonstrations:
FIRST PROPOSITION.
If the principle of contradiction be denied, all certainty, all truth, and all knowledge are at an end.
Demonstration.—If a thing may be and not be at the same time, we may be certain and not certain, know and not know, exist and not exist; affirmation may be joined with negation, contradictory things united, distinct things identified, and identical things distinguished: the intellect is a chaos to the full extent of the word; reason is overturned; language is absurd; subject and object clash in the midst of frightful darkness, and all intellectual light is for ever extinguished. All principles are involved in the universal wreck, and consciousness itself would totter, were it not, when this absurd supposition is made, upheld by the invincible hand of nature. Consciousness, indeed, in this absurd hypothesis, does not perish, for this is impossible, but it sees itself carried away by this violent whirlwind, which precipitates it and every thing else into chaotic darkness. In vain does it strive to save its ideas; they all vanish before the force of contradiction: in vain does it generate new ideas to be substituted for those it loses; these also disappear: in vain does it seek new objects, for they, too, disappear in like manner, and it endures only to feel the radical impossibility of all thought, and see contradiction lording it over the intellect, and destroying, with irresistible might, whatever would germinate there.