fication and cannot be devoted to the purpose for which Comte employed it. Spencer's is a formal or logical classification, Comte's a genetic or serial one. The former shows the relations of coexistence among the sciences, the latter those of sequence and natural subordination. Spencer's is essentially a statical presentation of the facts, Comte's a dynamic one. The most important thing to determine was the natural order in which the sciences stand—not how they can be made to stand, but how they must stand, irrespective of the wishes of any one. What is true cannot be made truer. The world may question it and attack it and "hawk at it and tear it" but it will survive. It makes no difference either how humble the source from which the truth may emanate. It is not a question of authority. If it is truth it may come from a carpenter of Nazareth or from an attic in the Latin Quarter; sooner or later all the world will accept it. One of the most convincing proofs of the truth of Comte's system is found in the fact that Spencer himself, notwithstanding all his efforts to overthrow it, actually adopted it in the arrangement of the sciences in his synthetic philosophy and has never suggested that they should be otherwise arranged.
But any such sweeping classification of the sciences must recognize the necessity of the broadest generalization, and must not attempt to work into the general plan any of the sciences of the lower orders. The generalization must go on until all the strictly coordinate groups of the highest order are found, and then these must be arranged in their true and only natural order. This Comte accomplished by taking as the criterion of the position of each the degree of what he called "positivity," which is simply the degree to which the phenomena can be exactly determined. This, as may be readily seen, is also a measure of their relative complexity, since the exactness of a science is in inverse proportion to its complexity. The degree of exactness or positivity is, moreover, that to which it can be subjected to mathematical demonstration, and therefore mathematics, which is not itself a concrete science, is the general gauge by which the position of every science is to be determined. Generalizing thus
