We must therefore not take too much notice of Comte’s urging and bitterness, when he criticises the narrowness of mind and the “imphilosophisme” of geometers.[92] Undoubtedly he never tires of safeguarding the higher sciences against the encroachments of mathematics, and of showing the impossibility of a philosophy founded exclusively upon their principles. But he none the less recognises that this science possesses the double privilege of having furnished historically, the first model of the positive method, and of presenting still to-day its finest and purest examples. However, Comte, even more than Descartes, takes care not to transform the mathematical method into a universal method by a simple generalisation. Nothing would be more contrary to the positive spirit. For the development of this spirit the study of mathematics is a necessary introduction. It is, however, but an introduction. The use which mathematics can make of deduction, on account of the extreme simplicity of their subject produces a very false idea of the power of our understanding, and disposes us to reason more than to observe. Far from preparing us for the method which must be followed for the study of the other orders of natural phenomena, the exclusive habit of mathematics tends rather to draw us from it. In a word it is a dangerous error to take this “initial degree of sound logical education for the final degree.”[93] In order to grasp the positive method in its entirety, we must not consider only mathematics, but the whole series of the fundamental sciences. This method, always fundamentally identical, takes particular determinations in adapting itself to each new order of phenomena. Each of these orders introduces, so to speak, the use of some of the principal processes of which the method is composed, and “it is always at their source that these notions of universal logic must be examined. Thus the mathematical science is the one which gives the best knowledge of the elementary conditions of positive science. In it all the artifices of the art of reasoning, from the most spontaneous to the most sublime are continually practised with far more variety and fecundity than anywhere else. Astronomy then teaches us, in its initial purity, the art of observation accompanied by that of forming hypotheses. It shows in what the rational provision of phenomena consists, and that science always ends in assimilation or in combination. Physics initiate us to the theory of experimenting, chemistry to the general art of nomenclatures, the science of organic bodies to the theory of classifications. Biology specially makes use of the comparative method, and finally with sociology appears the “transcendant” process which Comte calls the historical method.[94]