The philosophy of Science consists of two principal parts; the methods of investigation, and the requisites of proof. The one points out the roads by which the human intellect arrives at conclusions, the other the mode of testing their evidence. The former if complete would be an Organon of Discovery, the latter of Proof. It is to the first of these that M. Comte principally confines himself, and he treats it with a degree of perfection hitherto unrivalled. Nowhere is there anything comparable, in its kind, to his survey of the resources which the mind has at its disposal for investigating the laws of phaenomena; the circumstances which render each of the fundamental modes of exploration suitable or unsuitable to each class of phaenomena; the extensions and transformations which the process of investigation has to undergo in adapting itself to each new province of the field of study; and the especial gifts with which every one of the fundamental sciences enriches the method of positive inquiry, each science in its turn being the best fitted to bring to perfection one process or another. These, and many cognate subjects, such as the theory of Classification, and the proper use of scientific Hypotheses, M. Comte has treated with a completeness of insight which leaves little to be desired. Not less admirable is his survey of the most comprehensive truths that had been arrived at by each science, considered as to their relation to the general sum of human knowledge, and their logical value as aids to its further progress. But after all this, there remains a further and distinct question. We are taught the right way of searching for results, but when a result has been reached, how shall we know that it is true? How assure ourselves that the process has been performed correctly, and that our premises, whether consisting of generalities or of particular facts, really prove the conclusion we have grounded on them? On this question M. Comte throws no light. He supplies no test of proof. As regards deduction, he neither recognises the syllogistic system of Aristotle and his successors (the insufficiency of which is as evident as its utility is real) nor proposes any other in lieu of it: and of induction he has no canons whatever. He does not seem to admit the possibility of any general criterion by which to decide whether a given inductive inference is correct or not. Yet he does not, with Dr Whewell, regard an inductive theory as proved if it accounts for the facts: on the contrary, he sets himself in the strongest opposition to those scientific hypotheses which, like the luminiferous ether, are not susceptible of direct proof, and are accepted on the sole evidence of their aptitude for explaining phenomena. He maintains that no hypothesis is legitimate unless it is susceptible of verification, and that none ought to be accepted as true unless it can be shown not only that it accords with the facts, but that