Mr. Mill was mistaken when he thought Kant meant _a priori_ cognitions were innate ideas which came to man from spheres unknown. The very first sentence of Kant’s “Critique of Pure Reason” proves that Kant knew of no other knowledge than that which begins with experience. Kant says, “That all our knowledge begins with experience there can be no doubt.” But our knowledge consists of two elements, viz. the empirical and the formal. The former bears always the character of the special and incidental, the latter of the universal and necessary. The former is sensory, being furnished by the senses, the latter is properly mental originating in and with the action of the mind in dealing with sense-materials, in arranging them and bringing them into certain relations. Formal knowledge is different in kind from empirical knowledge. The rule “twice two is four” will hold good for all possible cases, but the statement “A swan is white” does not hold good for all possible cases. European swans as a rule are white, but Australian swans are black, and for all we know, we might find swans that are blue, or red, or yellow. Empirical knowledge is full of exceptions, formal knowledge is rigid, there is no exception to any rule of formal knowledge. All formal knowledge has developed by degrees. The history of the sciences, of mathematics, logic, arithmetic, and also of the natural sciences furnishes sufficient evidence. The formal part of the natural sciences, by Kant called _reine Naturwissenschaft_, consists of such cognitions as the law of cause and effect and the law of the conservation of matter and energy. The formulation of these laws has been accomplished after much and careful empirical investigation. And it could not be otherwise. The latter law was elaborated in its full clearness long after Kant. The law of causality and the law of the conservation of matter and energy are purely formal, they are not sense-impressions and do not contain any sensory elements. They are general rules of universal applicability which being rigidly universal and without exceptions are necessary under all conditions. Before we make any experiment we can know that they will hold good in the experiment. Indeed all our experimenting is based upon the supposition that the law of causation holds good and that there can be neither an increase nor a decrease of matter and energy. The mistake made by the so-called transcendentalists is this, that they consider formal thought as having an independent existence, being ready at hand before cognition is possible, while in fact it is a part of cognition which at least in its germ is present in every actual experience.