The Principle which Comte adopted to guide him in his Classification was the following: 'All observable phenomena may be included within a very few natural categories, so arranged as that the study of each category may be grounded on the principal laws of the preceding, and serve as the basis of the next ensuing. This order is determined by the degree of simplicity, or, what comes to the same thing, of generality of their phenomena. Hence results their successive dependence, and the greater or lesser facility for being studied.' In accordance with this Principle, Comte establishes what he denominates the _Hierarchy of the Sciences_. Mathematics stands at the base of this, as being that Science whose Phenomena are the most general, the most simple, and the most abstract of all. Astronomy comes next, wherein the Static and Dynamic properties of the heavenly bodies complicate the nature of the investigation; in Physics, Phenomena must be considered in the midst of the still greater complications of Weight, Light, Heat, Sound, etc.; Chemistry has additional characteristics to trace in its subjects; Biology adds the intricacies of vital Phenomena to all below it; and Sociology, the sixth and last of Comte's Hierarchy--all other departments of thought other than those previously excluded from his survey, being regarded as out of the bounds of human cognition--deals with the still more complicated problem of the relations of men to each other in society. This Classification is admirable for the purpose of showing the mutual interdependence of the branches of Knowledge included in it; but aside from its covering only a small part of our intellectual domain, it is also defective in not distinguishing with sufficient clearness that which is properly Science, from that which is merely Theory or Plausible Conjecture. Biology and Sociology are classed with Mathematics as _Positive_ Sciences, as if the Laws or Principles which correlated the Phenomena of the former were established as certainly and definitely as those of the latter; while there is no prominence given to the different nature of _proof_ in Mathematics and that in every other department of investigation--except in so far as Mathematical Phenomena and Processes enter into the latter--if, indeed, the founder of Positivism has even anywhere distinctly stated it. Chemistry, Biology, and Sociology, leaving Astronomy and Physics aside for the present, are not yet _Positive_ Sciences, in any such sense as Mathematics. The lack of _exact_ analysis is apparent in all of Comte's generalizations, otherwise magnificent and masterly as they undoubtedly are. In respect to the matter under consideration, it renders his Classification unavailing for determining with sufficient precision and exactitude the character of any intellectual domain. History, while it is the source whence the proof of his fundamental positions is drawn, finds no place in his Scientific schedule.