16. This system, by reason of its philosophical meagerness, is fatal to all moral ideas. What becomes of morality if there are no ideas, except sensations? What becomes of duty if every thing is reduced to sensible necessity, to pleasure or pain? And what becomes of God, and of all man's relations to God?
CHAPTER III.
DIFFERENCE BETWEEN GEOMETRICAL IDEAS AND THE SENSIBLE REPRESENTATIONS WHICH ACCOMPANY THEM
17. Sensible representations always accompany our intellectual ideas. This is why in reflecting upon the latter we are apt to confound them with the former. We say, in reflecting upon them, not in making use of them. We none of us, have any trouble in making use of ideas according to circumstances; the error lies in the reflex, not in the direct act. It will be well to bear this last observation in mind.
18. It is next to impossible for the geometrician to meditate upon the triangle without revolving in his imagination, the image of a triangle as he has seen it drawn a thousand times; and he will, for this reason, be disposed to believe that the idea of the triangle is nothing else than this sensible representation. Were it thus, Condillac's assertion that the idea is only the recollection of the sensation would be verified in the idea of the triangle. In fact, this representation is the sensation repeated: the only difference between the two affections of the mind is that the actual sensation is caused by the actual presence of its object, wherefore it is more fixed and vivid. To prove that the difference is not essential, but consists only in degree, it is sufficient to observe, that if the imaginary representation attain a high degree of vividness we cannot distinguish it from sensation, as it happens to the visionary, and as we have all experienced in our dreams.
19. By noticing the following facts, we shall readily perceive how different the idea of the triangle is from its imaginary representation.
I. The idea of the triangle is one, and is common to all triangles of every size and kind; the representation of it is multiple, and varies in size and form.
II. When we reason upon the properties of the triangle, we proceed from a fixed and necessary idea; the representation changes at every instant, not so, however, the unity of the idea.
III. The idea of a triangle of any kind in particular is clear and evident; we see its properties in the clearest manner; the representation on the contrary is vague and confused, thus it is difficult to distinguish a right-angled from an acute-angled triangle, or even a slightly inclined obtuse-angled triangle. The idea corrects these errors or rather abstracts them; it makes use of the imaginary figure only as an auxiliary, in the same manner as we give our demonstrations when we draw figures upon paper, abstracting their exactness or inexactness, often when we know that they are not exact, which they cannot always be.
IV. The idea of the triangle is the same to the man born blind and to him who has sight; and the proof of this is that both, in their arguments and geometrical uses, develop it in precisely the same manner. The representation is different, for us it is a picture, which it cannot be for the blind man. When he meditates upon the triangle he neither has, nor can have, in his imagination, the same sensible representation as we, since he wants all that can relate to the sensation of sight. If the blind man experiences any accompanying representation of the idea, he can have received it only from the sense of touch; and in the case of large triangles, the three sides of which cannot be touched at the same time, the representation must be a successive series of sensations of touch, just as the recollection of a piece of music is essentially a successive representation. With us the representation of the triangle is almost always simultaneous, excepting the case of exceedingly large triangles, much larger than we usually see, in which case, especially when we are unaccustomed to consider such, it seems necessary to go on extending the lines successively.
20. What has been said of the triangle, the simplest of all figures, may with still greater reason be said of all others, many of which cannot be distinctly represented by the imagination, as we see in many-sided figures; and even the circle, which for facility of representation rivals the triangle, we cannot so perfectly imagine as to distinguish it from an ellipse whose foci are only at a trifling distance from each other.
CHAPTER IV.
THE IDEA AND THE INTELLECTUAL ACT
21. Having shown that geometrical ideas are not sensible representations, we can safely conclude that no kind of ideas are. Could there be a difficulty concerning any, it would be concerning geometrical ideas, for the objects of the latter can be sensibly represented. When objects have no figure, they cannot be perceived by any of the senses; to speak in such a case of sensible representations is to fall into a contradiction.
22. These considerations draw a dividing line between the intellect and the imagination; a line which all the scholastics drew, which Descartes and Malebranche respected and made still more prominent, but which Locke began to efface, and Condillac entirely obliterated. All the scholastics recognized this line; but they, like many others, used a language which, unless well understood, was of a character to obscure it. They called every idea an image of the object, and explained the act of the understanding as if there were a kind of form in the understanding which expressed the object, just as a picture presented to the eyes offers them the image of the thing pictured. This language arose from the continual comparison which is very naturally made between seeing and understanding. When objects are not present we make use of their pictures, and thus, since objects themselves cannot be present to our understanding, we conceive an interior form which performs the part of a picture. On the other hand, sensible things are the only ones which are strictly susceptible of representation; we never discover within ourselves the form in which the objects are portrayed, except in the case of imaginary representations; and therefore it was rash to call this an idea, and every idea an imaginary representation, in which the whole system of Condillac consists.
23. St. Thomas calls the representations of the imagination phantasmata, and says that so long as the soul is united to the body we cannot understand except per conversionem ad phantasmata; that is, unless the representation of the imagination, which serves as material for the formation of the idea, and assists in clearing it up, and heightening its colors, precedes and accompanies the intellectual act. Experience teaches that whenever we understand, certain sensible forms relative to the object which occupies us, exist in our imagination. Now, they are the images of the figure and color of the object, if it have any; now, the images of those with which they are compared, or the words which denote them in the language we habitually speak. Thus, even when thinking of God, the very act by which we affirm that he is most pure spirit, offers a kind of representation to the imagination under a sensible form. When we speak of eternity, we see the Ancient of days, as we have often seen him represented in our churches; when we speak of the infinite intelligence, we imagine perhaps a sea of light; infinite mercy, we picture to ourselves as a pitying likeness; justice, with angry countenance. To force ourselves to form some conception of the creation, we fancy a spring whence light and life both flow, and thus also we endeavor to render immensity sensible by imagining unlimited extension.
The imagination always accompanies the idea, but is not itself the idea; and we perceive the evident and unimpeachable proof of the distinction between the two, if we ask ourselves, while in the very act of imagining a sea of light, an old man, an angry or placid countenance, a fountain or extension, if God is any one of these, or any thing resembling them; for, we very promptly answer, no, that this would be impossible. All this demonstrates the existence of an idea which has no connection with these representations, but essentially excludes what is contained in them.
24. What we have said of the idea of God, may be said of many other ideas. Rarely do we understand any thing into which the idea of relation does not enter as an indispensable element. How then is relation represented? In the imagination, in a thousand different manners; as the point of contact of two objects; as the link which unites them. But is relation any one of these? No! When we inquire in what it does consist, is there the slightest shadow of doubt that it is no one of these? Certainly not.
25. It is an error to call every idea an image, if you mean to consider ideas as something distinct from the intellectual act, which places itself before the understanding when it is in the exercise of its functions. An image is that which represents, as a likeness: and how, I ask, do we know that this representation or likeness exists? And how do we know that in order to reason we need an internal form, which is, as it were, a picture of the object? What is a picture beyond the sensible order? There are, it is true, similarities in the intellectual order, but not in the sense in which we perceive them in the material order. I think; so does my neighbor: here is a similarity, since the same thing is found in both one and the other, identical in species, but not in number. But this similarity is of a different order from that of sensible similarities.
26. When we understand, we know that which is in the object understood; but whether this be understood by a simple act of the intellect, or a medium be required to represent the similarity, we do not know. We understand the thing, not the idea; and it is as difficult to say how the intellect perceives without the idea, as it is to say how the supposed representation refers to its object. How does our idea refer to an object? If by itself, then by itself alone, since it is purely internal, it refers to the external, and requires no intermediary to place the subject in relation with external objects. What it does, the intellectual act of itself alone can also do. If we perceive the relation of the idea with the object by means of another idea, this intermediate idea presents the same difficulty as the preceding idea; and so at last we must come to a case in which there is a transition from the intellect to the object without any intermediary.
If we see an object which is the image of another not known, we shall see the object in itself, but we shall not know that it has the relation of image, unless informed that it has: we shall know its reality, but not its representation. The same will happen in ideas which are images; these, therefore, do not at all explain how the transition from the internal act to the object is made; for this would require them to do for the understanding that which we find them unable to do for themselves.
27. There is something mysterious in the intellectual act, which men seek to explain in a thousand different ways, by rendering sensible what they inwardly experience. Hence so many metaphorical expressions, useful only so long as they serve merely to call and fix the attention, and give an account of the phenomenon, but hurtful to science if they go beyond these limits, if it be forgotten that they are metaphors, and are never to be confounded with the reality.
By intelligence we see what there is in things, we experience the act of perception; but when we reflect upon it we grope in the dark, as if there were a dense cloud about the very source of light, preventing us from seeing it with clearness. Thus the firmament is at times flooded with the light of the sun, although the sun is encircled with clouds and hidden from our view, so that we cannot even determine its position upon the horizon.
28. One cause of obscurity in this matter is the very effort to clear it up. The act of the understanding is, in its objective part, exceedingly luminous, since by it we see what there is in objects; but in its subjective nature, or in itself, it is an internal fact, simple indeed, but incapable of being explained by words. This is not a peculiarity of the intellectual act, it is common to all internal phenomena. What is it to see, to taste, to hear? What is a sensation, or feeling of any kind whatsoever? It is an inward phenomenon, of which we are conscious, but which we cannot decompose into parts; nor can we explain with words the combination of these parts. A word is enough to indicate the phenomenon, but this word has no meaning for him who does not now experience this phenomenon, or has not oat some former time experienced it. No possible explanations would ever enable a man born blind to understand color, or a deaf man sound.
The act of understanding belongs to this class; it is a simple fact which we can point out, but not explain. An explanation supposes various notions, the combination of which may be expressed by language; in the intellectual act there are none of these. When we have said, I think, or, I understand, we have said all. This simplicity is not destroyed by objective multiplicity; the act by which we compare two or more objects is just as simple as the act by which we perceive a single object. If one act be not enough, more will follow; and finally one act will unite or sum them all up; but it will not be a composite act.
CHAPTER V.
COMPARISON OF GEOMETRICAL WITH NON-GEOMETRICAL IDEAS
29. The idea is a very different thing from the sensible representation, but it has certain necessary relations with it which it will be well to examine. When we say necessary, we speak only of the manner in which our mind, in its actual state, understands, abstracting the intelligence of other spirits, and even that of the human mind when subject to other conditions than those imposed by its present union with the body. So soon as we quit the sphere in which our experience operates, we must be very cautious how we lay down general propositions, and take care not to extend to all intelligences qualities which are possibly peculiar to our own, and which, even with respect to it, will perhaps be entirely changed in another life. Having made these previous observations, which will be found of great utility to mark the limits of things there is danger of confounding, we now proceed to examine the relations of our ideas with sensible representations.
30. A classification of our ideas into geometrical and non-geometrical naturally occurs when we fix our attention upon the difference of objects to which our ideas may refer. The former embrace the whole sensible world so far as it can be perceived in the representation of space; the latter include every kind of being, whether sensible or not, and suppose a primitive element which is the representation of extension. In their divisions and subdivisions the latter present simply the idea of extension, limited and combined in different ways; but they offer nothing in relation to the representation of space, and even when they refer to it, they only consider it inasmuch as numbered by the various parts into which it may be divided. Hence the line which in mathematics separates geometry from universal arithmetic; the former is founded upon the idea of extension, whereas the latter considers only numbers, whether determinate, as in arithmetic properly so called, or indeterminate, as in algebra.