The criticism of Positivism has taught us that there is no knowledge possible without _à priori_ elements--that is to say, without laws inherent in thought, which impose themselves upon phenomena, so as to constitute veritable knowledge. This is the system of Kant, and thus that system avoids not only empiricism, but scepticism as well, though commonly confounded with it. For without necessary laws phenomena only form an arbitrary succession, entirely dependent upon the organization of the individual; we have no longer anything but individual sensations. In the Kantian philosophy, however, the individual is subjected to laws that are superior to himself; these are the laws of human thought, and even, perhaps, of all thought whatever. These laws impose themselves on each one of us in a necessary and universal manner, and by so doing communicate to phenomena an objective reality in this sense at least, that they are for individuals veritable objects; and thus it is that mathematical truths are objects to the intellect, even supposing they should be nowhere realized in any existence independent of thought. But are these laws of thought anything else than laws of thought? Do they really attain to objective reality--to _things in themselves_. Kant has denied that they do, and our author, in following in his steps, agrees, or seems to agree, with the "Kritik" of Kant. Let us then resolve the fundamental laws of the human intellect into five principal concepts: these are, space and time, forms of sensibility, substance and cause, laws of external experience, and, lastly, the Absolute, the final and supreme condition of all knowledge. Now, according to Kant and our author, these notions, at least the four first, are at the same time necessary as subjective conditions of thought, and contradictory so soon as we seek to realize them outside of thought. For example, that space and time are found by implication in every internal or external representation, that they are not the result of abstraction and generalization, this has been firmly established by Kant; for the elements from which some have sought to derive them already imply them. But, at the same time, they are only internal conditions, of which the objects are unrealizable outside of ourselves, and the reason of this is given by M. Liard, as follows:--Space and time have three essential characteristics, they are homogeneous, continuous, and unlimited. Now, if we seek to make of space and time _things in themselves_ we may doubtless conceive them as homogeneous and continuous, but not as unlimited, for no actual magnitude is unlimited; all magnitude is expressed in numbers, and numbers are necessarily finite, an infinite number involving a contradiction.