IV.

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.

It follows that we must not confuse “the subordination of any events whatever to invariable laws with their irresistible necessary accomplishment.”[74] Relatively single phenomena appear indeed to us to be produced with an irresistible necessity: for instance, the facts of gravitation. But complex phenomena, in virtue of the more and more varied combinations which their several necessary conditions admit of no longer present this character. They are more “modifiable” and less “irresistible.” In other words, as one considers more elevated, more complex, more “noble” categories of facts, the laws become removed from the type of mathematical necessity, and admit more of an ever increasing element of “contingency”?

The order of the world can then be conceived as a “modifiable fatality.”[75] In the eyes of the greater number of present thinkers, says Comte, this formula will seem contradictory. This comes from old habits of mind which are not easily broken with. In the same way, as we have had a great deal of trouble in representing truth to ourselves otherwise than as immutable, so we are unwilling to conceive order otherwise than as necessary. During a long time the science of mathematics has been the only positive science. The idea of law formed itself in this science, that is to say according to the necessary relations which are demonstrated in it. It came to be afterwards transferred, just as it was, into the other orders of phenomena, as the positive spirit progressed. But orders of phenomena differ qualitatively from one another. All laws ought not to be conceived according to the single type of geometrical and algebraical laws. In order to obtain a complete idea of a natural law, we must not confine ourselves to the mathematical order, which is an “exception” in this respect. All the orders of phenomena must be considered. We then see that law must be defined “constancy in variety.”

In fact, “the normal type is never suited to any but a medium state, more ideal than real, around which effective existence ceaselessly oscillates, so long as the deviation does not go beyond the limits which are compatible with the duration of the system. Order, even isolated, is no more eternal than it is absolute.”[76] In this passage, Comte is speaking of astronomical order, but the same consideration applies to all the systems or groups of phenomena. Every law is necessarily something abstract. Being indispensable to the intelligibility of the real, every law allows prevision and science to exist. But it is not an adequate expression of this reality, which never remains identical with itself.

Comte goes so far as to say that our requirement of precision in the study of natural laws must not be pushed too far. For the laws which it has been possible to establish within certain degrees of approximation vanish if this approximation is pushed further. Not that the phenomena cease to be subject to laws; but these laws becoming too complex, escape us. For instance, it has been possible to establish with our thermometers the laws of the variation of temperature of a body under certain conditions. With very much more sensitive thermometers the variations becomes incessant and very complicated. The known laws disappear without our being in a condition to establish others.[77]

The order which positive science shows us in nature is then very far from being absolute. It is, to speak truly, the outcome of the combined

## activity of our mind and of things. We cannot separate what belongs

to each of these two factors, but it appears from what has just been said that the mind plays a great part, that the external relations are far more contingent than suits our blind instinct of universal connection.”[78] Nevertheless the phenomena are not irreducible to order, since science and prevision remain possible. But this order, entirely relative in respect to our understanding is only established within certain limits. More powerful minds than ours would probably construct richer and more complex orders for themselves. For us, beyond a certain point of complexity our vision becomes confused and our logical requirements are no longer satisfied. Limits would thus seem to be placed upon scientific investigation, and these in the interest of science itself.

Finally we reach the last consequence of this theory founded upon experience, the principle of laws and the principle of the conditions of existence only insure a provisional order. Comte readily admits that it might not exist. “This order might become so irregular that it might even escape brains superior to ours. There is nothing to prevent us from imagining words outside our solar system, always given over to an inorganic and entirely disordered agitation, which would not even allow of a general law of gravitation.”[79] This is the very hypothesis formulated by John Stuart Mill, in almost similar terms, and in which a kind of _reductio ad absurdum_ of his own theory was thought to be found. It is, however, compatible with the existence of a science which does not claim to possess an absolute value. Moreover Comte at once adds, “Still, even if order should be found to be particular to our world, in fact, it would be in no way accidental in it, since it is the first condition for human existence.” In virtue of the principle of the conditions of existence, the presence of a being such as man implies the whole of the laws which govern our world.