In the order in which Locke takes up his topics (and in which Leibniz follows him) we have omitted one subject, which, however, may find its natural place in the present connection,--the subject of infinity. In Locke's conception, the infinite is only a ceaseless extension or multiplication of the finite. He considers the topic immediately after the discussions of space, time, and number, and with good logic from his standpoint; for "finite and infinite," he says, are "looked upon by the mind as the modes of _quantity_, and are attributed, in their first designation, only to those things which have parts and are capable of increase and diminution." This is true even of the application of the term "infinite" to God, so far as concerns the attributes of duration and ubiquity; and as applied to his other attributes the term is figurative, signifying that they are incomprehensible and inexhaustible. Such being the idea of the infinite, it is attained as follows: There is no difficulty, says Locke, as to the way in which we come by the idea of the finite. Every obvious portion of extension and period of succession which affects us is bounded. If we take one of these periods or portions, we find that we can double it, or "otherwise multiply it," as often as we wish, and that there is no reason to stop, nor are we one jot nearer the end at any point of the multiplication than when we set out. "By repeating as often as we will any idea of space, we get the idea of infinity; by being able to repeat the idea of any length of duration, we come by the idea of eternity." There is a difference, then, between the ideas of the infinity of space, time, and number, and of an infinite space, time, and number. The former idea we have; it is the idea that we can continue without end the process of multiplication or progression. The latter we have not; it would be the idea of having completed the infinite multiplication, it would be the result of the never-ending progression. And this is evidently a contradiction in terms. To sum the matter up, the term "infinite" always relates to the notion of quantity. Quantity is that which is essentially capable of increase or decrease. There is then an infinity of quantity; there is no quantity which is the absolute limit to quantity. Such a quantity would be incapable of increase, and hence contradictory to quantity. But an actual infinite quantity (whether of space, time, or number) would be one than which there could be no greater; and hence the impossibility of our having a positive idea of an actual or completed infinite.