CHAPTER II.
IMPORTANCE AND ANOMALY OF THE QUESTIONS ON THE IDEA OF THE INFINITE.
12. The examination of the idea of the infinite is of the highest importance, not only because we meet it in various sciences, the exact sciences among others, but because it is one of the principal characteristics by which we distinguish God from creatures. A finite God would be no God; an infinite creature would not be a creature.
In the scale of finite beings we discover a gradation, by which they are interlinked; the less perfect, as they are perfected, go on approaching the perfect; and there are, preserving the limits of each one's nature, points of comparison by which we may measure their respective distances. Between the finite and the infinite there is no comparison; all measures are inadequate and as nothing. We pass from an imperceptible drop to an immense ocean; from the atom which escapes observation to the abundance of matter diffused through all space; and much as these transitions express, they are as nothing to the transition from the finite to the infinite; these oceans, compared with the infinite truth, become in their turn imperceptible drops, and thus an interminable scale baffles the efforts of the mind in search of something to correspond to its idea. The examination of the idea of the infinite ought to occupy an important place in the study of philosophy, although it served for no other purpose than the contemplation of infinite greatness.
13. The disputes on the idea of the infinite, not only in relation to its nature, but also to its existence, present a strange anomaly. If it exists in our mind it ought to fill it entirely, so that it must be impossible to cease to perceive it. Yet it is well known that philosophers dispute even on the existence of this idea; although it is an infinite treasure, those who possess it doubt its reality—just as the heroes in romance, when they find themselves in a castle richly and splendidly adorned, imagine it the effect of enchantment.
14. The mere dispute as to whether the idea of the infinite be positive or negative, is equivalent to the question of its existence. If it is negative, it expresses an absence of being; if positive, the plenitude of being. What question can be more vital to an idea than the dispute whether it represents the absence or the plenitude of being?
15. Here again we meet the fact which we have observed in the preceding discussions. Reason, after digging at its own foundations, is threatened with death under the ruins of its loftiest edifices.