Kitabı oku: «Fundamental Philosophy, Vol. 2 (of 2)», sayfa 11

CHAPTER VI.
IN WHAT SENSE THE IDEA OF BEING IS THE FORM OF THE UNDERSTANDING

40. When it is asserted that the object of the understanding is being, there is room to doubt whether it is meant that the idea of being is the general form of all conceptions, or only that all the understanding conceives is being; or, in other words, whether the quality of object is attributed to being, as being, in such a way that under this form alone objects are conceivable, or only that the quality of being belongs to all that the understanding conceives.

In the first case the proposition might be taken in a reduplicative sense, and would then be equivalent to this: "The understanding conceives nothing save inasmuch as it is being;" in the second it might be taken formally, and be equivalent to this: "whatever the understanding conceives is being."

41. We are of opinion that it cannot be said that the object of the understanding is being only inasmuch as being; in such a way as to make the idea of being the only form of the understanding's conceiving; but that this form is an essential condition to all perception.

42. If we remark that the idea of being, in itself considered, neither includes any determination or variety, nor expresses any thing more than being, in its greatest abstractness, we shall not fail clearly to perceive that this idea of being is not the only form conceived by the understanding; if, therefore, the understanding do not perceive any thing besides this idea in its objects, it cannot know their differences; nor can its perception go beyond that which is common to all, being.

43. If it be said that the differences perceived are modes of being, modifications of that which is represented in the general idea, it is at once agreed that being in itself is not the only form perceived; since both modification and mode of being add something to the idea of being. The rectangular triangle is a kind of triangle: its idea is a modification of the general idea, and no one will pretend that the idea of rectangular adds nothing to that of triangle, or that they are both the same thing. The same is verified in the idea of being and its modifications.

44. We have already seen²¹ that indeterminate ideas by themselves alone do not lead to positive cognitions; and certainly no idea better merits the name of indeterminate than that of being. Were our understanding limited to it, perception would be nothing but a vague conception, incapable of any combination.

45. Negation itself, as we shall hereafter see, is known to us, but this it could not be were we to admit that the understanding knows nothing save inasmuch as it is being; in which case the indispensable condition of all cognition, the principle of contradiction, would deceive us.

46. These reasons suffice to place beyond all doubt what we have proposed to show, but as this point is intimately connected with what is most transcendental in logic and metaphysics, we will endeavor to explain it more at large in the following chapter.

CHAPTER VII.
ALL SCIENCE IS FOUNDED IN THE POSTULATE OF EXISTENCE

47. We have said that the idea of being is not the sole form perceived, but that it is a form necessary to all perception. We do not mean by this to say that we cannot perceive without the actually existing; but that existence enters in some degree as a condition of every thing perceived. We will explain ourselves. When we simply perceive an object, and affirm nothing of it, it is always offered to us as a reality. Our idea certainly expresses something, but it has nothing excepting reality. Even the perception of the essential relations of things involves the condition that they exist. Thus, when we say that in the same circle or in equal circles equal arcs are subtended by equal chords, we suppose impliedly this condition, "if a circle exists."

48. Since this manner of explaining the cognition of the essential relations of things may seem far-fetched, we will endeavor to present it under the clearest possible point of view. When we affirm or deny an essential relation of two things, do we affirm or deny it of our own ideas or of the things? Clearly of the things, not of our ideas. If we say, "the ellipse is a curve," we do not say this of our idea, but of the object of our idea. We are well aware that our ideas are not ellipses, that there are none in our head, and that when we reflect, for example, upon the orbit of the earth, that this orbit is not within us. Of what, then, do we speak? Not of the idea, but of its object; not of what is in us, but of what is without us.

49. Nor do we mean that we see it thus, but that it is thus; when we say the circumference is greater than the diameter, we do not mean that we see it thus, but that it is thus. So far are we from speaking of our idea, that we should assert it to be true although we did not see it, and even although it were not to exist. We speak of our idea only when we doubt of its correspondence with the object; then we do not speak of reality, but of appearance, and in such cases our language is admirably exact, for we do not say, it is, but, it seems to us.

50. Our affirmations and negations, therefore, refer to their objects. Now, we argue thus: what does not exist is pure nothing, and nothing can either be affirmed or denied of nothing, since it has no property or relation of any kind, but is a pure negation of every thing; therefore, nothing can be affirmed or denied; there can be no combination, no comparison, no perception, except on condition of existence.

We say on condition, because we know the properties and relations of many things which do not exist; but in all that we do know of them, this condition always enters: if they exist.

51. Hence it follows that our science rests always on a postulate; and we purposely use this mathematical expression in order to show that those sciences which are called exact by antonomasy do not disdain this condition which we exact from all science. The greater part of them commence with this postulate: "Let a line be drawn, &c.," "Suppose B to be a right angle, &c.," "Take a quantity A greater than B, &c." This is the way the mathematician, with all his rigor, always supposes the condition of existence.

52. It is necessary to suppose this existence, otherwise nothing could be explained. Common sense teaches us what has escaped some metaphysicians. To prove it, let us see how a mathematician, who never dipped into metaphysics, would talk. We will suppose the interlocutor to set out to demonstrate to us that in a rectangular triangle the square of the hypothenuse is equal to the sum of the squares of the base and perpendicular; and that we, in order to exercise his intelligence, or rather to make him show us, without himself being aware of it, what is passing in his own mind with respect to the perception of its object, put various questions to him, in reality searching, although apparently asked out of ignorance. We will adopt the form of a dialogue for the sake of greater clearness, and will suppose the demonstration to be given from memory, without the aid of figures.

Demonstration. Drop a perpendicular from the right angle to the hypothenuse.

Where?

Why, in the triangle of which we speak, of course.

But, sir, if there be no such triangle —

Why then, what are we talking of?

We are talking of a rectangular triangle, and the case supposed is that there is none.

Is not, but can be. Take paper, a pencil, and ruler, and we will have one right away.

That is to say, you speak of the triangle we may make?

Yes, sir.

Ah, I understand; but then we should have it; now, we have not got it.

All in good time. But if we had drawn it, could we not drop the perpendicular?

Certainly.

That is all I meant to say.

But you were saying drop —

No doubt we cannot drop a perpendicular in a triangle unless the triangle exists, since then there is neither vertex of a right angle, hypothenuse, nor any thing else; but when I say, drop a perpendicular, I always suppose a triangle; and as it is evident that the triangle may exist, I do not express the supposition, but understand it.

I comprehend this; but then we should drop the perpendicular only in this triangle, but you spoke as if we might drop it in all triangles.

I only took this triangle for an example; we can clearly do with all others what we can do with this one.

With all?

Certainly. Can you not see how, in every rectangular triangle, a perpendicular may be drawn from the right angle to the hypothenuse?

Yes, in your figure; but since what is in my head is not a triangle, for I imagine some with sides a thousand miles long, and there is not in my head room enough —

There is no question of what is in your head, but of triangles themselves —

But these triangles do not exist; therefore, we can say nothing of them.

Yes; but may they not exist?

Who doubts it?

Well then, if they do exist, be they large or small, in one position or another, here or there, is it not true that a perpendicular may be drawn from the vertex of the right angle to the hypothenuse?

Evidently.

I have then only to say that, in every rectangular triangle, this perpendicular may be drawn.

Then you do not speak of those which do not exist? Is it not so?

I speak of all, whether they do or do not exist.

But a perpendicular cannot be drawn in a triangle which does not exist. What does not exist is nothing.

But perhaps that which does not exist may exist; and I see with perfect clearness how every thing said would be verified, supposing it to exist. Thus we can and do speak of all existences and non-existences without any exception.

We leave it to the reader to judge if we have not, while thus rudely troubling our good mathematician with our importunate questions, made him reply as would have replied every one not at all acquainted with metaphysics. It is evident that these replies ought to be accepted as reasonable, as satisfactory, and as the only ones in this case that all the mathematicians in the world could give.

This being so, all that we have advanced is found in these replies and explications. All science is founded on the postulate of existence; every argument, to demonstrate even the most essential properties and relations of things, must start with the supposition of their existence.

CHAPTER VIII.
THE FOUNDATION OF PURE POSSIBILITY, AND THE CONDITION OF ITS EXISTENCE

53. We have said that the foundation of the pure possibility of things, and of their properties and relations, is founded in the essence of God, wherein is the reason of every thing.²² And it may at first sight seem that science needs only this foundation, and does not require to rest upon the condition of the existence of things; because, if essences are represented in God, the object of science is found in the Divine essence; and consequently, the argument founded upon the impossibility of asserting any thing of nothing, is not conclusive. Supposing there to be such a representation, science is not occupied with a pure nothing, but with a real thing; and it has consequently in view a positive object, even when it abstracts the reality of the thing considered.

Let us see how we can solve this difficulty.

54. The necessary relations of things, independently of their existence, must have a sufficient reason; and this can only be in necessary being. The condition, therefore, of existence, presupposes the representation of the essence of the contingent being in necessary being; the condition, therefore, "if it exist," cannot be brought in unless it presupposes the foundation of possibility.

55. This remark shows that there are two questions: – 1st: What is the foundation of the intrinsic possibility of things? 2d: Supposing possibility, what condition is involved in so much as it is affirmed or denied of the possible object? The foundation of the possibility is God; and the condition is the existence of the objects considered.

Both are requisite to science; if the foundation of intrinsic possibility be wanting, the condition of existence cannot come in; and if, admitting the possibility, we omit the condition, science has no object.

56. We would remark, for the better understanding of this whole subject, that we do not, in affirming or denying the relations of beings represented in God, treat of what these beings are in God, but of what they would be in themselves were they to exist. In God, all are the same God; for all that is in God, is identical with God. If, then, we consider things only as they are in him, we shall have God, not the things, for object. Certain it is, that in God is the foundation, or the sufficient reason, of geometrical truths: but geometry does not consider them such as they are in God, but such as they are or may be realized. In God, there are neither lines nor dimensions of any kind; he, therefore, is not the object of geometry properly so called. Geometrical truths have in him an objective value or representative value, but not subjective; we should otherwise be obliged to say that God is extensive.

57. Here, then, is seen that what we said above in the place cited, does not conflict with what we have here established; and that to make God the foundation of all possibility, does not exclude the scientific necessity of the condition of existence.

58. We will, in order to place this beyond all doubt, present the question under another aspect, by showing that when God knows finite truths, he sees in them this condition likewise: "If they exist." God knows the truth of this proposition: "Triangles of equal base and altitude are of equal superfices: " this is true as well in the eyes of infinite intelligence, as in ours; were it not thus the proposition would not be true in itself, and we should be in error. This being so, there are in God, who is most simple being, no true figures, although he has the intellectual perception of them. The cognition, then, of God, in what relates to finite things, refers to their possible existence, and consequently involves the condition that they exist.

The cognition of God does not refer to their purely ideal representation, but to their actual or possible reality; when God knows a truth of finite beings, he does not know it from the sole representation of those truths which he has in himself, but from that which they would be were they to exist.

59. Every object may be considered either in the real or in the ideal order. The ideal is their representation in an understanding, which has a value only inasmuch as it refers to possible or actual reality. In this manner alone can the idea have objectiveness, since otherwise it could only be a purely subjective fact, of which, excepting the purely subjective, nothing could be either affirmed or denied. The idea which we have of the triangle aids us, in so far as it has a real or possible object, to know and combine: we refer what we affirm or deny of it to its object: if this disappear, the idea is converted into a purely subjective fact, to which we cannot apply the properties of a triangular figure without an open contradiction.

CHAPTER IX.
IDEA OF NEGATION

60. It is said that the understanding does not conceive nothing: this is true in the sense that we do not conceive nothing as something, which would be a contradiction; but it does not therefore follow, that we do not in any mode conceive nothing. Not-being is nothing, and yet we conceive not-being. This perception is necessary to us; without it we could not perceive contradiction; for which reason the principle of contradiction: "It is impossible for a thing to exist and not to exist at the same time: " fundamental as it is in our cognitions, would fail us.

61. It may be said that to conceive nothing, not-being, is not to conceive, but to not-conceive: this, however, is false, for it is not the same thing to conceive that a thing is not, and not to conceive it. The former involves a negative judgment, and may be expressed by a negative proposition; and the latter is the simple absence of the act of perception; the former is objective, the latter subjective. We do not when asleep perceive things; but this non-perception is by no means equivalent to perceiving that they are not. It may be said of a stone that it does not perceive another stone; but not that it perceives the non-being of the other stone.

62. The perception of not-being is a positive act; and it would be a contradiction to say that it is the very perception of being; for it would follow, that whenever we perceive being, we perceive its negation, not-being, and vice versa, which is an absurdity.

63. When we perceive not-being, we do, it is true, perceive it in relation to being; and it is equally true, an understanding perceiving absolute not-being, without any idea of being, is altogether inconceivable; but this does not prove the two ideas not to be distinct and contradictory.

64. It is remarkable that the idea of negation, besides entering into the fundamental principles of our understanding: "It is impossible for a thing to be and not to be at the same time: " "Every thing either is or is not: " is also necessary to almost all of our perceptions. We do not conceive distinct beings without conceiving that one is not the other, and we cannot form a negative judgment into which negation does not enter. Hence it results that just as the idea of being is absolute and relative, also is the idea of not-being: thus, we say, "The sun is;" "All the diameters of a circle are equal;" and we also say, "The phœnix is not:" "The diameters of an ellipse are not equal."

65. We may ask those who hold that every idea is the image of the object, what sort of an image the idea of not-being would form? This confirms what we have already advanced, that it is a mistake to imagine all ideas as a kind of types, similar to things, and that we cannot oftentimes explain any of those inward phenomena, called ideas, notwithstanding we know and explain their objects by them.

66. It is also said that the object of the understanding is being; but this is inexplicable in the sense that the understanding does not perceive not-being; and can be understood only in the sense that we perceive not-being as coordinated to being, and that not-being of itself alone, cannot be the origin of any cognition.

Remark here an important difference. By the idea of being every thing may be understood; and the more of being there is in the idea, the more do we understand; and if an idea be supposed to represent a being without any limitation, or, which is the same thing, without any negation, we should have a cognition of an infinite being. On the contrary, the perception of not-being teaches us nothing, save inasmuch as it shows us the limitation of determinate beings and their relations; and if we suppose the idea of not-being to be gradually extended, we shall see that in proportion as it approaches its limits, that is, pure not-being, absolute nothing, the understanding loses its object; the points of comparison and the elements of combination fail; all light goes out, and intelligence dies.

67. We know universal, absolute nothing, only as a momentary condition which we imagine, but do not admit. In it we see that it is impossible that something should not exist; for, could any one instant be designated in which nothing existed, nothing could now exist. In this imaginary nothing, we discover no point of departure for the understanding; all combinations become impossible and absurdities; the mind sees itself perishing in the vacuum it has itself created.

68. If the idea of negation be not combined with that of being, it is perfectly sterile; but thus combined, it has a kind of fecundity peculiar to itself. The ideas of distinction, of limitation, and of determination, involve a relative negation, for we do not conceive distinct beings without conceiving that one is not another; nor limited beings, without conceiving that they are wanting, that is, that in some sense they are not; nor determinate beings, without conceiving something which makes them what they are and not others.