Читать книгу Fundamental Philosophy - Jaime Luciano Balmes - Страница 33

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278. The great importance attributed by the German philosopher to his imaginary discovery, requires us to examine it at length. This importance may be estimated from what he himself says: "If any of the ancients had only had the idea of proposing the present question, it would have been a mighty barrier against all the systems of pure reason down to our days, and would have saved many vain attempts which were blindly made without knowing what was treated of."[23] This passage is quite modest and naturally excites our curiosity to know what is the problem which needed only to be proposed in order to avoid all the aberrations of pure reason.

Here are his words: "All empirical judgments, as such, are synthetic. For it would be absurd to ground an analytic judgment on experience, since I am not obliged to go out of the conception itself in order to form the judgment, and therefore can have no need of the testimony of experience. That a body is extended, is a proposition which stands firm a priori. It is no empirical judgment; for, prior to experience, I have all the conditions of forming it in the conception of body, from which I deduce the predicate, extension, according to the principle of contradiction, by which I at once become conscious of its necessity, which I could not learn from experience. But, on the other hand, I do not include, in the primitive conception of body in general, the predicate, heaviness; yet this conception of body in general indicates, through experience of a part of it, an object of experience, to which I may add from experience other parts also belonging to it. I can attain to the conception of body beforehand, analytically, through its characteristics extension, impenetrability, form, etc., all of which are included in the primary conception of body. But I now extend my cognition, and, as I recur to experience, from which I have obtained the conception of body in general, I find along with these characteristics the conception of heaviness. I therefore add this, as a predicate, to the conception of body. The possibility of this synthesis therefore rests on experience; for both conceptions, although one does not contain the other, yet belong as parts to a whole, that is to say, to experience, which is itself a union of synthetic, though contingent intuitions. But in the case of synthetic judgments a priori we have not this assistance. Here we have not the advantage of returning and supporting ourselves on experience. If I must go out of the conception A in order to find another conception B, which is to be joined to it, on what am I to rely? and by what means does the synthesis become possible?"[24]

279. The reason of this synthesis is found in the faculty of our mind of forming total conceptions, in which the relation of the partial conceptions composing it is discovered; and the legitimacy of the same synthesis is founded on the principles on which the criterion of evidence is based.

The synthesis of the schoolmen consists in the union of conceptions, and does not refuse to admit as analytical the total conceptions, from the decomposition of which results the knowledge of the relations of the partial conceptions.

If Kant had stopped with the judgments of experience, there would be no objection to his doctrine. But extended to the purely intellectual order, it is either inadmissible, or at least expressed without much exactness.

260. Kant says all mathematical judgments are analytic, and that this truth which in his opinion "is certainly incontestible and important on account of its consequences, seems to have hitherto escaped the sagacity of the analysts of human reason, causing very contrary opinions." We think it is the sagacity of his Aristarchus, and not that of the analysts, that is at fault.

"One would certainly think at first sight that the proposition, 7 + 5 = 12, is a purely analytic proposition, which follows from the conception of a sum of seven and five, according to the principle of contradiction. But if we examine it more closely, we find that the conception of the sum of seven and five contains nothing farther than the union of both numbers in one, from which it cannot by any means be inferred what this other number is which contains them both."[25]

Were we to say that whoever hears seven plus five, does not always think of twelve, because he does not see clearly enough that one conception is the same as the other, although it is under a different form, it would be true. But from this it does not follow that the conception is not purely analytic. The mere explanation of both suffices to show their identity.

That this may be better understood, we will invert the equation thus: 12 = 7 + 5. It is evident that if any one does not know that 7 + 5 = 12, he will not know that 12 = 7 + 5. Now, in examining the conception 12, we certainly see 7 + 5 contained in it. Therefore, the conception of 12 is identical with the conception of 7 + 5; and just as, because he who hears 12, does not always think of 7 + 5, we cannot thence infer that 12 does not contain 7 + 5; so, also, we cannot, because he who hears 7 + 5, does not always think of 12, thence infer that the first conception does not contain the second.

The cause of the equivocation is, that the two identical conceptions are presented to the intellect under different forms; and until we have the form, and look to what is under it, we shall not discover the identity. This is not, strictly speaking, reasoning but explanation.

What Kant adds concerning the necessity of recurring, in this case, to an intuition, with respect to one of the numbers, adding five to seven on the fingers, is exceedingly futile. First, in whatever way he adds the five, there will never be anything but the five that is added, and it will neither give more nor less than 7 + 5. Secondly, the successive addition on the fingers is equivalent to saying 1 + 1 + 1 + 1 + 1 = 5. This transforms the expression, 7 + 5 = 12, into this other, 7 + 1 + 1 + 1 + 1 + 1 = 12; but the conception, 1 + 1 + 1 + 1 + 1, has the same relation to 5, as 7 + 5 to 12; therefore, if 7 + 5 are not contained in 12, neither are 7 + 1 + 1 + 1 + 1 + 1 contained in it. It may be replied that Kant does not speak of identity, but of intuitions. This intuition, however, is not the sensation, but the idea; and if the idea, it is only the conception explained. Thirdly, we know this method of intuition not to be even necessary for children. Fourthly, this method is impossible in the case of large numbers.

281. Kant adds that this proposition, "a right line is the shortest distance between two points," is not purely analytic, because the idea of shortest distance is not contained in the idea of right line. Waiving the demonstrations which some authors give, or pretend to give, of this proposition, we shall confine ourselves to Kant's reasons. He forgets that here the right line is not taken alone, but compared with other lines. The idea of right line alone neither does nor can contain the ideas of more or less; for these ideas suppose a comparison. But from the moment the right line and the curve are compared, with respect to length, the relation of superiority of the curve over the right line is seen. The proposition is then the result of the comparison of two purely analytic conceptions with a third, which is length.

282. If Kant's reasoning were good, even this judgment, "the whole is greater than its part," would not be analytic; for the idea of greater enters not into the conception of the whole until the whole is compared with its part. Thus, the judgment, four is greater than three, would not be analytic, because the idea of four until compared with three does not include the conception of greater.

The axiom: "things which are equal to the same thing are equal to each other," would not be analytic, because the conception, equal to each other, does not enter into the conception of things which are equal to the same thing, until we reflect that the equality of the middle term implies the equality of the extremes.

The x, of which Kant speaks, would be found in almost all judgments, if we could not form total conceptions involving comparison of partial conceptions: in this case we should have no analytic judgments except such as are wholly identical, or directly contained in this formula, A is A.

283. The comparison of two conceptions with a third, does not take from the result the character of analytic judgment, as a predicate cannot be seen in the idea of the subject, without the aid of this comparison. This comparison is often necessary, because we only confusedly think of what is contained in the conception which we already have; and sometimes it even happens that we do not think at all of it. One often says a thing and then contradicts himself, not observing that what he adds is opposed to what he had already said. We often ask, in conversation, do you not see that you suppose the contrary of what you just said; that the conditions you have just established imply the contrary of what you now assert?

284. A conception includes not only all that is expressly thought in it, but all that can be thought. If, on decomposing it, we find in it other things, it cannot be said that we add them, but that we find them. It is not a synthesis, but an analysis. Otherwise we must admit no analytic conceptions, or only such as are purely identical. Except in this last case, of which the general formula is, A is A, there is always in the predicate something not thought in the subject, if not in substance at least in form. The circle is a curve; this undoubtedly is one of the simplest analytical propositions imaginable; still the predicate expresses the general conception of curve, which may be contained in the subject, in a confused manner, with relation to a particular species of curve. Following a gradation in geometrical propositions, we may observe that there is nothing in one proposition not in the preceding, except the greater or less difficulty of decomposing the conception, so as to see in it what before we had not seen.

If we say, the circle is a conic section, evidently any one ignorant of the terms, or who has not reflected on their true sense, will not think of the attribute in the subject. No addition is made to the conception of the circle; only a property not before known is discovered, and this discovery results from comparison with the cone. Is there any synthesis here? No. There is only an analysis of the two conceptions, the circle and the cone, compared. As this error destroys the foundation of Kant's doctrine on this point, we will develop it and place it on a more solid foundation.

285. Synthesis, properly so called, requires something to be added to the conception, which in nowise belongs to it, as the example brought by Kant shows. The conception, extension, is contained in the conception, body; but heaviness is an entirely foreign idea, which we can unite to the conception, body, only because experience authorizes it. Only with this addition is there properly synthesis. The union of ideas which results from the conception of the thing, although comparison may be necessary in order to fecundate them, does not make a synthesis. The conceptions are not wholly absolute, they contain relations, and the discovery of these relations does not give a synthesis, but a more complete analysis. If it be said that in this case there is something more than the primitive conception, we answer that the same thing happens in all not purely identical. We may also add that by the comparison a new total conception is formed resulting from the primitive conceptions; and the properties of the relations are then seen, not by synthesis, but by the analysis of the total conception.

According to Kant, true synthesis requires the union of things so different from one another, that the bond uniting them is a sort of mystery, an x, whose determination is a great philosophical problem. If this x is found in the essential relation of the partial conceptions constituting the total conception, the problem is resolved by a simple analysis, or, to speak more exactly, it is shown that the problem did not exist, because the x was a known quantity.

We know of no judgment more analytical than that in which we see the parts in the whole, since the whole is only the parts united. If we say, one and one are two, or, two is equal to one plus one; it cannot be denied that we have a total conception, two, in the decomposition of which, we find one plus one. If this be not an analytic conception, that is to say, if the predicate be not here contained in the idea of the subject, it will be hard to tell what is. But even here there are different conceptions, one plus one; unite them, and they form the total conception. The relation, although most simple, exists; and whether it be more or less, simple or complicated, and, consequently, seen with more or less facility, does not alter the character of the judgments, or from synthetic convert them into analytic.

286. We will complete this explanation with an example from elementary geometry. "The surface of a rhomboid is equal to the surface of a rectangle having the same base and altitude." First: in the idea of the rhomboid, we do not see the idea of its equality with the rectangle; and this we cannot see, because the relation does not exist when there is no other term to which it may relate. The idea of the parallelogram does not contain that of the rectangle, and consequently not that of equality. Second: the relation results from the comparison of the rhomboid with the rectangle; and, consequently, it must be found in a total conception containing them both. It cannot, therefore, be said that we add any thing to the conception of the parallelogram which does not belong to it. On the contrary, we see this equality flow from the conception of the rhomboid and that of the rectangle, as partial conceptions of the total conception, formed by the combination of them both. The analysis of this total conception opens to us the relation we are now in quest of; for it must be observed that when the simple union of the conceptions compared does not suffice, we make use of another including them, and also something more; and from the new conception, duly analyzed, we deduce the relation of the parts compared.

287. In the geometrical construction, that serves for the demonstration of the above theorem, which we have used as an example, may be seen what we have just explained with regard to total conceptions containing other conceptions besides those compared. If we place the rectangle and the rhomboid upon the same base, we at once see that there is something common to both, namely, the triangle formed by the base, a part of one side of the rhomboid, and a part of one side of the rectangle. Neither synthesis nor analysis is here required, because there is perfect coincidence, and this in geometry is equivalent to perfect equality. The difficulty is in the two remaining parts, that is, in the trapezoids to which the parallelograms are reduced by the subtraction of the common triangle. The mere sight of the figures teaches nothing concerning the equivalence of the two surfaces; we see only that the two sides of the rhomboidal surface go on extending, but including a less distance in proportion as the angle becomes more oblique, under these two conditions: length of sides, and diminution of distances between two limits, of which one is infinity, and the other the rectangle. The relation of the equivalence of the surfaces may be demonstrated by prolonging the parallel opposite the base, and thus forming a quadrilateral of which the trapezoids are parts; to discover the equality of these trapezoids, it is only necessary to decompose the quadrilateral, attending to the equality of two triangles, each respectively formed by one of the trapezoids and a common triangle. Is any thing here added to the conception of each trapezoid? No. We only compare them. They could not be compared directly, and therefore we included them in a total conception, the mere analysis of which enabled us to discover the relation sought for. The conception does not give this relation; it only shows it; for if the conception of the two figures compared were more perfect, so that we might intuitively behold the relation existing between the increment of the sides and the decrement of their distance from each other, we should see that there is here a constant law, which supplies on one side what is lost on the other; and consequently we should discover, in the very conception of the rhomboid, the fundamental reason of the equality, that is, the permanent value of the surface, notwithstanding the greater or less obliquity of the angles; thus obtaining what we deduced from the above comparison, and generalize with reference to two constant lineal values, base and altitude. The same would happen with respect to the equivalence of all variable quantities differently expressed, could we reduce their conceptions to such clear and simple formulas as those of apparent functions; for example, nx/mx, from which, whatever the value of the variable, there always results the same value of the expression, which is constant, to wit, n/m.

288. Let not these investigations be imagined useless. In this, as in many other questions, it happens that most important truths are the result of a philosophical problem which, in appearance, is merely speculative. Thus, in the present case, we observe Kant explaining the principle of causality, in an inexact, and, as we understand him, in an altogether false sense; but, perhaps, the origin of his equivocation lies in his considering the principle of causality as synthetic, although a priori, whereas it must be regarded as analytic, as we shall show when treating of the idea of cause.

In consideration of the great importance of clear and distinct ideas on the present subject, we will in a few words, sum up the doctrine we have explained concerning mediate and immediate evidence.

There is immediate evidence when, in the conception of the subject, we see its agreement or disagreement with the predicate, without requiring any other means than mere reflection on the meaning of the terms. Judgments of this class are with propriety called analytic, because we have only to analyze the conception of the subject to find therein its agreement or disagreement with the predicate.

There is mediate evidence when, in the conception of the subject, we do not immediately see its agreement or disagreement with the predicate, and therefore have to call in a middle term to make it manifest.

290. Here arises the question whether judgments of mediate evidence are analytic. It is clear that if we mean by analytic only those in which we have solely to understand the meaning of the terms in order to see the agreement or disagreement of the predicate, the judgments of mediate evidence cannot be called analytic; but if by analytic judgment we mean a judgment in which it is only necessary to decompose the conception of the subject in order to find therein its agreement or disagreement with the predicate, we must say that the judgments of mediate evidence are analytic, and the means employed is only the formation of a total conception containing the partial conceptions, the relation of which we seek to discover. In the union of these partial conceptions there is a synthesis, it is true; but there is none in the discovery of their relation, for this is done by analysis.

A judgment is not the less analytic because formed by the union of different conceptions; for then no judgment would be analytic. When we say, man is rational, the two conceptions of animal and rational enter into the conception of man, but do not take from it its analytical character; for this, as its very name imports, consists in the analysis of a conception, being sufficient to show certain predicates in it, without reference to the manner of this conception's formation, whether two or more conceptions are united in it, or not.

291. This clearly shows in what mediate evidence consists. The predicate is indeed contained in the idea of the subject; but, owing to the limitation of our intellect, either these ideas are incomplete, or we do not see them in all their extension, or else we do not well distinguish what we in a confused manner perceive in them; and hence, to know the meaning of the terms does not enable us immediately to see that the predicate is contained in the idea of the subject. Moreover, the objects, even such as are purely ideal, are presented to us separately; and hence, not knowing the sum of them all, we pass successively from one to another, discovering their mutual relations in proportion as we approach them.

292. It may, from what we have said, be inferred that all judgments in the purely ideal order are analytic, since every cognition of this order is obtained by the intuition of whatever is more or less complicated in the conception, and there is no more synthesis than is necessary to bring the objects together, by uniting their conceptions in one total conception, which serves for the discovery of the relation of the partial conceptions.

293. The x, therefore, of which Kant speaks, and the removal of which is one of the most important problems of philosophy, is nothing more than the faculty possessed by the soul to unite the conceptions of different things in one total conception, and to discover in it their mutual relations. This faculty is no new discovery, for the schools have all recognized it under one name or another. No one ever denied to the intellect the faculty of comparing; and comparison is the act whereby the intellect places two or more objects before its sight so as to perceive their mutual relations. In this act the intellect forms a total conception, of which the conceptions compared are a part. Thus we have seen that in geometry to verify the mutual relation of certain figures, we construct a new figure which includes them all, and is a sort of field whereon the comparison is made.

This exposition of analytic and synthetic judgments will suffice for the present; as we proposed to treat of them here only in general, and as related to certainty; consequently we will not descend to their particular application to various ideas, the analysis of which belongs to other parts of this work.