Читать книгу Fundamental Philosophy, Vol. 2 (of 2) - Balmes Jaime Luciano - Страница 3

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.