Mr. Spencer compares our apprehension of space-relations to our inherited habit to grasp with our hands and to walk with our feet. This comparison is misleading and inappropriate. That we grasp with our hands and walk with our feet is incidental. There are animals who have developed other limbs for the same purposes. There are monkeys who grasp with their tails and the elephant grasps with his nose. There is no necessity and no universality in our predisposition of grasping with our hands. Yet there resides necessity and universality in the laws of formal thought so that wherever animals develop rational thought we are sure that to them twice two will always equal four just as much as it does to us. However they may be different in other respects: they may be winged creatures or may be somewhat like our ants, they may have developed other bodily structures than we can dream of, nevertheless their arithmetic, their logic, and their mathematics will in all essentials be exactly the same as ours. There are animals whose thought-forms are not as highly developed as in man, but there are no animals in whom they are developed differently. We must consider it as impossible even that on other stars rational creatures can be found whose reason differs from ours. To them also twice two will be four. II. THE PROBLEM OF APRIORITY. Kant did not call the formal laws _a priori_ in order to characterise them as innate ideas, but simply to denote that their validity is necessary and universal. If I have to walk twice a distance of two miles, I know “beforehand” (i. e. _a priori_) that I shall have to walk four miles—even before I have made the actual experience. And this wonderful quality of giving information beforehand is characteristic of all the laws of formal thought. It is certain that our ability of applying the laws of formal thought has been acquired by experience in the race as well as in the individual. But their necessity has to do with experience in so far only as its recognition is the indispensable condition of all methodical experience—i. e. of science. The laws of formal thought and our recognition of their necessity and universality (alias, “apriority”) are the organ of any and all scientific cognition. The methods of the sciences are exact measuring and counting based upon the faith that the laws of measuring and counting are unalterable and unfailingly reliable. We know beforehand that they will hold good for all possible cases.