23. Thus, we see, that the idea of the infinite, is in the reach of the most common intellects, and expresses only what any person of ordinary understanding would say, even though he had never occupied himself with philosophical studies; that the idea of the infinite is in our understanding, as a constant type, to which all finite representations are unable to arrive. We know the conditions which must be fulfilled, but at the same time, we see the impossibility of fulfilling them. When any one tries to persuade us of the contrary, we reflect on the idea of the infinite, and say: "No; it is a contradiction of infinity; it is not infinite, but finite." We distinguish perfectly well between the absence of the perception of the limit and its non-existence. If any one tries to make us confound these two ideas, we answer, "No; they must not be confounded; there is a great difference between our not perceiving an object and the non-existence of that object, and we are not now examining whether we conceive the limit, but whether it exists." Though the limit retire and hide itself, so to speak, from our eyes, we are not deceived: it exists, or does not exist. If it exists, the condition involved in the conception of infinity is not fulfilled, and the object is not infinite, but finite; if it does not exist, there is true infinity,--the condition is complied with. 24. When the idea of the infinite is considered in general, it can never be confounded with the idea of the finite. There is a line which divides them, and which prevents all error; for it is the principle of contradiction itself; it is the distinction between _yes_ and _no_. When we say _finite_, we affirm the limit; when we say _infinite_, we deny it. No ideas can be clearer or more exact. CHAPTER IV. THE LIMIT. 25. The word _infinite_ is equivalent to _not finite_, and seems to express a negation. But negations are not always truly such, although the terms imply it; for if that which is denied, be a negation, the denial of it is an affirmation. This is the reason why two negatives are said to be equivalent to an affirmative. If I say, it has not varied, and you deny it, you deny my negation; for it is the same thing to deny that it has not varied, as to affirm that it has varied. In order, therefore, to determine whether the word _infinite_ expresses a true negative, we must know what is meant by the word _finite_. 26. The finite is that which has a limit. A limit is the term beyond which there is nothing of the object limited. The limits of a line, are the points beyond which the line does not extend; the limit of a number, is the extreme where the number stops; the limit of human knowledge, is the point to which we may arrive, but which we cannot go beyond. A limit being a negation, to deny a limit, is to deny a negation, and is consequently an affirmation.