Fundamental Philosophy, Vol. 2 (of 2)

by Jaime Luciano Balmes

51. Since we find a limit in both internal and external experience, it is evident that we can form the general idea of limit, that is, of a negation applied to an object.

52. The same experience teaches that what is the limit of some things is not the limit of others, and that the limit applied to one object must be denied of another. When we compare different beings together, we frequently find ourselves denying certain limits. As our understanding has the faculty of generalizing, it is evident that we may conceive in general the negation of certain limits, and form an indeterminate conception, including the two ideas of negation and limit.

53. I do not see what objection can be made either to the possibility or to the existence of this conception; but as this fact is necessary for the explanation of the idea of infinity, I shall make some further observations for the purpose of confirming it.

We have an idea of negation in general; this is a primitive fact of our mind: without it no negative judgments would be possible, nor could we even know the principle of contradiction. It is impossible for any thing to be and not be at the same time; when we say not be we express a negation, we therefore have the conception of negation. This conception is general, because it involves no determination; we speak of not-being without applying it to any particular object, nor even to any determinate species or genus. Therefore the conception of negation is general and absolutely undetermined.

54. We have the idea of limit; for, as we have seen, it is a negation applied to a being. We have also the idea of the negation of limit; for just as we conceive the limit as applied or applicable, we may and do conceive it as not applied or not applicable. At every moment we deny certain limits; this idea generalized becomes the negation in general of limit in general.

55. After these remarks we may establish what is contained in the idea of the infinite. This idea is a general conception involving the conception of being in general, and the negation of limit in general. The union of these two conceptions constitutes the abstract idea of the infinite.

56. The general conception of the negation of limit gives us an idea of infinity in the abstract, but not any infinite thing. Without the intuitive cognition of an infinite object, and with only a very imperfect idea of it, we may speak of infinity without falling into contradiction, and determine the cases in which it may be applied to a being or to an order of beings, whether real or possible. Man has many ideas of this vague kind, which nevertheless answer his necessities. We shall make this palpable by examples.

57. Suppose we take an uneducated person and point out to him a number of learned men, telling him that one of them knows more than all the rest. The uneducated person has no idea of what the man knows who knows the most, nor the man who knows the least; he has no idea of the degrees of science, nor of what science itself is; but he possesses the general ideas of degree, of more and less, and also of knowledge, and this enables him to speak, without contradiction or confusion, of the greater science of the one and the less science of the others, and even to solve with certainty the questions concerning the science of those individuals, in so far as these questions are contained in the general idea that the science of one is greater than that of all the others.

A servant in an establishment where the most beautiful products of art are collected, may speak of them all without contradiction or confusion, although he may be incapable of knowing their merit, and entirely ignorant of the circumstances which constitute the beauty of the objects. It is sufficient for him to have the idea of perfection or beauty in general, and to arrange by certain arbitrary signs the degrees of perfection or beauty of the objects, in order to be able to point them out to visitors, and talk of the greater skill of one artist, the poorer success of another; the greater effect and value of the works of the former, and the inferiority of those of the second, and to make other remarks of a similar nature, which at first might make us suppose him a consummate artist, or, at the least, an amateur of a great intellect and exquisite taste.