It will be easier to understand Kant’s arguments if we invert the order of the _Critique_ and begin with examining the nature of the principles of the understanding or of one of them. The categories which are of importance in Kant’s argument are quantity, quality, substance, causation, and reciprocity, and necessity, possibility, and actuality. The last three are less important than the others, and we shall not deal with them. To the first five of these categories correspond the following principles: (1) Quantity. "All phenomena are, with reference to their perception, extensive quantities." (2) Quality. "In all phenomena the real, which is the object of a sensation, has intensive quantity, that is, a degree." The last three are classed under a general heading of _Analogies of Experience_, whose principle is: "Experience is possible only through the representation of a necessary connection of perceptions." They are (3) _The principle of the permanence of substance_. "In all changes of phenomena the substance is permanent, and its quantum is neither increased nor diminished in nature." (4) _Principle of the succession of time, according to the Law of Causality_. "All changes take place according to the law of connection between cause and effect." (5) _Principle of co-existence, according to the law of reciprocity or community_. "All substances, so far as they can be perceived as co-existent in space, are always affecting each other reciprocally." These principles, Kant points out, are assumed in the sciences of applied mathematics. The application of geometry to the world we experience assumes that all phenomena are extensive quantities; physics assumes that quantitative expression can be given to the qualities of objects other than their size, their weight, _e.g._, and all scientific determination of change assumes the three principles which Kant calls analogies of experience: the permanence or conservation of amount in changes, the necessary connection of things in time, and the reciprocal interdependence of things which exist at the same time. These principles are not proved by science; their validity is assumed in all scientific investigation. On what, then, does it rest?