Fundamental Philosophy, Vol. 2 (of 2)

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.

CHAPTER X.

IDENTITY; DISTINCTION; UNITY; MULTIPLICITY

69. Let us examine how we may draw from the idea of not-being the explication of the ideas of identity and distinction, unity and multiplicity.

Let us conceive a being, and fix our attention solely on it, and compare it with nothing which is not it, nor permit any idea of not-being to come in; we shall then, with respect to it, have the ideas of identity and unity; or, to speak more exactly, these ideas of identity and unity will be nothing else than ideas of this same being. Ideas of unity and identity are for this reason inexplicable by themselves alone; they are simple, or are confounded with a simple idea in which can be no comparison, and into which if negation enter, it is not noted, nor can be made the object of reflection. Thus, for instance, the idea of not-being enters in some manner into the perception of every limited being; but we can abstract this negation, and consider what the object is, not what it is not.

70. If we perceive a being, and afterwards another being, the perception that one is not the other gives the idea of distinction, and consequently that also of multiplicity. There is, then, no distinction or number without perception of relative not-being combined with being; but this perception is all that is requisite to distinction and number.

71. The ideas of identity and unity are simple, those of distinction and number composite; the former involve no negation, the latter imply a negative judgment; "this is not that." It is impossible for A to be presented to us as distinct from B, if we do not perceive that B is not A; and on the other hand, we need only to know that B is not A, in order to enable us to say they are distinct. These expressions, "A is not B," or, "A and B are distinct," are perfectly identical.

72. From this we infer that the primary combination of our intelligence consists in the perception of being and not-being. By it we perceive identity and distinction, unity and number; by it we compare, affirm, or deny; without it we cannot even think. Without the perception of negation, we can have only the perception of being, that is, an intuition fixed upon an identical object, one and immutable, such as we conceive the Divine Intelligence to be, contemplating the infinity of being in the infinite essence.

73. Does God know negations? Certainly; for when a being ceases to exist, God knows this truth, in which there is a negation. He knows the truth of all negative propositions, whether it expresses substantive or relative being; therefore, he knows negation. But this is no imperfection, since it cannot be an imperfection to know truth; the imperfection is in the objects, which, by the very fact of being finite, include negation, being combined with not-being. Were God not to know negation, it would be because negation is in itself impossible; which would be equivalent to the impossibility of the existence of the finite, and would lead to the absolute and exclusive necessity of one sole infinite being.

CHAPTER XI.

ORIGIN OF THE IDEA OF BEING

74. If it be impossible to think without the idea of being, it exists prior to any reflex act, and it cannot have sprung from reflection. The idea of being must therefore be innate. Let us investigate this question.

75. We have shown in the preceding chapter that we cannot think without the idea of being; let whoever doubts this consult his own experience, and make, if he can, a reflex act into which the idea of being will not enter. We have already seen that we cannot exclude it in the conception of first principles, and beyond these it is certain no one will go.

76. Can this idea have come to us from sensation? Sensation in itself offers us only determinate objects, whereas the idea of being is an indeterminate thing: sensation offers us only particular things, whereas the idea of being is the most general it is possible to have: sensation teaches us nothing, tells us nothing, except what it is, a simple affection of our soul, whereas the idea of being is a vast idea, extending to all, and, fecundating our mind in an admirable manner, is the element of all reflection and alone sufficient to found a science: sensation never leaves itself, nor extends to another sensation; the sense of touch has nothing to do with that of hearing; all belong to an instant of time, and only exist during it, whereas the idea of being guides the mind through every class of beings, the corporeal and the incorporeal, the real and the possible, the temporal and the eternal, the finite and the infinite.

If we discover any thing by sensations, if they produce any intellectual fruit, it is because we reflect upon them; but reflection is impossible without the idea of being.

77. Neither does it seem that the idea of being can be formed by abstraction. To abstract is of necessity to reflect; and reflection is impossible without this idea; therefore, it is necessary to abstraction, and consequently cannot have abstraction for its cause.

78. On the other hand, an exceedingly simple explication of the method in which abstraction is made, may be opposed to this argument apparently so conclusive. We see the paper upon which we write; this sensation involves two things, whiteness and extension. Were we limited to simple sensation, here we should stop, and receive only the impression, extension and whiteness. But having within ourselves a faculty distinct from that of feeling, which makes us capable of reflecting upon the very sensation we experience, we can consider that this sensation has some similarity to others which we recollect to have experienced. We can then consider extension and whiteness in themselves, abstracting the actual affection which they produce in us. Afterwards we can reflect upon the fact that these sensations have something in common with others, inasmuch as they all affect us in a certain manner, and then we have the idea of sensation in general. If, then, we consider that these sensations all have something in common with all that is in us, in so far as they modify us in a certain manner, we shall form an idea of a modification of the me, making abstraction, however, of its being a sensation, a thought, or an act of the will; and if, finally, we abstract from these things being in us, their being substances or modifications, and attend only to the fact that they are something, we shall have attained the idea of being. This idea may, therefore, be formed by abstraction. This explication, seductive as it is by reason of its simplicity, is open to grave objections.

79. From the very beginning of this process we make use, without adverting to it, of the idea of being; we therefore deceive ourselves when we imagine that we form it. We cannot reflect upon extension and whiteness without remarking that they exist, that they are something similar to other sensations. When we think upon what affects us, we know that we are, that that which affects us is, and we speak of its being or not being, of its having or not having something common; and finally, when we abstract the modifications of our mind as being this or that, and regard them only as thing, as something, as a being, we evidently cannot so consider them if there does not exist in us the idea of something in general, that is, of being. Thus being is a predicate which we apply to things; we do, therefore, know this predicate. We only collect in one general and indeterminate idea, particular and determinate things, already existing in our understanding. The successive operations made by means of abstraction are only a decomposition of the object, a classification of it in various general ideas so as to attain to the superior idea of being.

80. It is difficult in view of these reasons, which are all strong, to decide without danger of erring for either of the opinions advanced. Nevertheless, we shall give our own in accordance with the principles we have laid down in different parts of this work. We hold that the idea of being is not innate, in the sense that it pre-exists in our understanding as a type anterior to all sensation and to all intellectual acts;23 but we see no impropriety in calling it innate, if nothing more be meant than the innate faculty of our understanding to perceive objects under the general reason of being or existence, so often as it reflects upon them. Thus the idea does not flow from sensations; it is recognized as a primary element of pure understanding; but it is not formed by abstraction, which separates it from others, and purifies it, so to speak, itself contributing to this purification. In this sense it may exist before reflection, and yet be the fruit of reflection, according to the various stages in which we consider it. Inasmuch as it is mixed and confused with other ideas, it exists before reflection; but inasmuch as it has been separated and purified, it is the fruit of the same reflection.

81. We must, in order to give a complete solution of the difficulties proposed, give our ideas precision and exactness.

The idea of being is not only general but also indeterminate; it offers to the mind nothing real or even possible, since we do not conceive that a being, which is only being, does or can exist, if no property besides that of being can be affirmed of it. In God is the plenitude of being; he is his own being; with reason does he call himself, I am, who am; but we also affirm of him, with all truth, that he is intelligent, that he is free, and that he possesses other perfections not expressed in the pure and general idea of being.

From this we infer that we ought not to regard the idea of being as a type representing to us something determinate, even something in general.

82. The act by which we perceive being, existence, reality, is necessary to our understanding, but it is confounded with all other intellectual acts, as a condition sine qua non of them all, until reflection comes to separate it from them, purifying it, and making it the object of our perception.

Since, when we perceive, we perceive something, it is evident that the reason of being is always involved in all our perceptions; by the simple fact of knowing we know being, that is, we know a thing. But as we do not always, when we fix our perception upon an object, distinguish the various reasons into which it may be decomposed, although the idea of being is contained in every object perceived, it is not directly perceived by our understanding until reflection separates it from all else.

83. If we reflect upon an azure object, evidently the idea of color enters into that of azure; but without reflection we shall not distinguish the genus, color, and the difference, azure. These two things are not really distinguished in the object perceived; for it would be ridiculous to pretend that in a particular azure-colored object, color is one thing and azure another. Nevertheless we can, when we reflect upon the object, very easily distinguish between the two ideas of color and azure, and we can discuss one without paying attention to the other. Must we say we have the idea of color in general, prior to the sensible representation? Most certainly not: it is only necessary to recognize an innate force of the mind to generalize what is presented to it in particular, and to decompose a simple object into various ideas or aspects.

84. Our understanding is endowed with an intellectual force, by virtue of which it can conceive unity under the idea of multiplicity, and multiplicity under the idea of unity. We discover an example of the latter when we unite what is really multiple in a single conception. Our understanding may be compared to a prism which decomposes a ray of light into many colors; hence different conceptions relating to one simple object. When multiplicity is to be reduced to unity, the intellectual force operates in an altogether contrary manner; instead of dispersing, it unites; the variety of colors disappears, and the ray of light is restored in all its purity and simplicity.

85. Our mind, from the fact that it is limited to know many things by conceptions only, and not by intuitions, requires the faculty of composing and decomposing, of seeing a simple thing under distinct aspects, and of joining different things under a common reason.

We must not fail to observe that the power of generalizing and of dividing, given to our understanding, is a great help to it, indicating, however, its weakness in the intellectual order, and continually warning it to proceed with due circumspection, when it has to decide upon the intimate nature of things.

86. According to this doctrine, general, and more particularly indeterminate ideas result from the exercise of reflection upon our own perceptive acts; and there is in the general idea nothing more than is seen in the particular perception, excepting its own generality produced by the elimination of all individuating conditions. This is especially verified in the idea of being, which, as we have seen, enters as a necessary condition into all our perceptions, and is, moreover, requisite to all operations as well of composition as of decomposition.