All natural laws, must be conceived as rigorously invariable, whether it be a question of mathematical or of sociological laws. If we could conceive, in any case, that under the influence of conditions exactly similar the phenomena should not remain perfectly identical, not only in kind, but also in degree, all scientific theory would at once become impossible.[72] This principle is the very condition of the possibility of prevision, and consequently of positive science. Claude Bernard will call it “the absolute determinism of phenomena.” Comte admits no absolute: but he considers nevertheless that the invariability of natural laws does not permit of exception. In the case of certain laws their invariability can be directly verified, since they come before us in a mathematical form. Such are, for instance, the mechanical, astronomical and physical laws. Others, on the contrary, such as the biological laws, refuse to be dealt with by numbers and cannot be reduced to equations. But this evidently comes from their complexity: “If it were possible rigorously to isolate each one of the simple causes which concur in producing the same physiological phenomenon, everything tends to show that under well determined circumstances, it would appear to be possessed of a kind of influence and of a quantity of action, as exactly fixed as we see it to be in universal gravitation.”[73] Every elementary phenomenon has its curve. If then in all cases we could go back to the elementary phenomena, we could undoubtedly also formulate their mathematical law. In this sense, mathematical analysis would apply to all the phenomena of the world without exception. But, nearly always, the decomposition of given phenomena into elementary phenomena is impossible to us. At any rate the work of synthesis or of re-composition taken in the reverse order is far beyond our mathematical powers. The only phenomena to which we apply the analysis without too much trouble are the most simple of all, the geometrical and mechanical phenomena. The difficulty grows very rapidly with the complication of astronomical, physical, and especially chemical phenomena. When we reach the realm of living nature, the elementary phenomena escape us altogether. They are given to us in a state of almost infinite complexity, and, in virtue of the biological _consensus_, closely bound up with others of no less complex a character. These phenomena are in themselves syntheses depending upon other syntheses all in a state of mutual influence and of constant instability. Then, although, in principle, it remains true that identical antecedents can only have identical consequents, in fact, because of the very great number of elementary actions which concur in the production of each phenomenon, there have perhaps never been, there perhaps never will be, two cases rigorously similar.