But not only is the earth an indefinitely multiple object, but so is the rock; nay, even the smallest grain of sand. Suppose the rock to be a rod in diameter; microscope magnifying two and a half millions of diameters would make its apparent magnitude as large as the earth. It is thus only a question of relative distance from the person conceiving, and this reduces it to the mere sensuous image of the retina. Remove the earth to the distance of the moon, and our conception of it would, upon these principles, become quite adequate. But if our conception of the moon be held inadequate, then must that of the rock or the grain of sand be equally inadequate. Whatever occupies space is continuous and discrete; i. e., may be divided into parts. It is hence a question of relativity whether the image or picture of it correspond to it. The legitimate conclusion is that all our conceptions are symbolic, and if that property invalidates their reliability, it follows that we have no reliable knowledge of things perceived, whether great or small. Mathematical knowledge is conversant with pure lines, points, and surfaces; hence it must rest on inconceivables. But Mr. Spencer would by no means concede that we do not know the shape of the earth, its size, and many other inconceivable things about it. Conception is thus no criterion of knowledge, and all built upon this doctrine (i. e. depending upon the conceivability of a somewhat) falls to the ground. But he applies it to the questions of the divisibility of matter (page 50): “If we say that matter is infinitely divisible, we commit ourselves to a supposition not realizable in thought. We can bisect and rebisect a body, and continually repeating the act until we reduce its parts to a size no longer physically divisible, may then mentally continue the process without limit.” Setting aside conceivability as indifferent to our knowledge or thinking, we have the following solution of this point: I. That which is extended may be bisected (i. e. has two halves). II. Thus two extensions arise, which, in turn, have the same property of divisibility that the first one had. III. Since, then, bisection is a process entirely indifferent to the nature of extension (i. e. does not change an extension into two non-extendeds), it follows that body is infinitely divisible. We do not have to test this in imagination to verify it; and this very truth must be evident to him who says that the progress must be “continued without limit.” For if we examine the general conditions under which any such “infinite progress” is possible, we find them to rest upon the presupposition of a real infinite, thus: Infinite Progress.