18. Infinite and indefinite express very different meanings. The infinite implies the absence of limits; the indefinite implies that these limits retire continually from us; it abstracts their existence, and only says that they cannot be assigned. 19. Whatever exists is finite or infinite; for it either has limits or it has not: in the first case, it is finite; in the second, infinite: there is no medium between yes and no. 20. Hence, properly speaking, there is in reality nothing indefinite; this word only expresses a mode of conceiving things, or rather a vagueness in the conception, or indecision in the judgment. When we do not know the limits of any thing, and, on the other hand, do not dare to affirm its infinity, we call it indefinite. Thus, space is called indefinite by those who see no way of assigning a limit to it, and yet are unwilling to say that it is infinite. Even in ordinary language we call a thing indefinite which has no limits assigned to it; thus, we say "a concession has been made for an indefinite time," although it is limited to some time which has not been determined. 21. The idea of the infinite does not consist in conceiving that another quantity may always be added to a given quantity, or that a perfection may be made more intense; this expresses only the possibility of a series of conceptions by which we endeavor to approach the absolute idea of the infinite. It is easy to see that the absolute idea is something distinct from those conceptions, because we regard it as a type to which the series of connections is referred, but which it can never equal, no matter how greatly prolonged. 22. Let us consider the words in which we naturally express what passes within us when we think of the infinite. What is an infinite line? A line which has no limits. Is it a million, or a billion miles in length? There is no number to express its length; it will always be greater than the number. But do we not approach the infinite in proportion as we prolong a finite line? Certainly, in so far as _approaching_ means only placing quantities which are found in what we approach; but not in so far as it means that this difference can be assigned. There is no comparison between the finite and the infinite; and therefore it is not possible to assign the difference between them. Would an infinite line be formed by the addition of all finite lines? No; for we can conceive the multiplication of each of the terms of the addition, and therefore an increase in the infinite, which would be absurd. Would the infinity of the line consist in our not knowing its limits, or not thinking of them? No; but in its not having them.