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.
V.
The laws which for us constitute the order of the world are of two kinds. Some are established by the positive method in each order of phenomena separately considered; the astronomical laws, physical laws, chemical laws, etc. They belong to the domain of science properly so-called. The others are apprehended when the mind leaves the special point of view of science, and places itself at the universal point of view of philosophy. They are found again in the different orders of phenomena, whose relations they express without compromising their respective independence. They represent them severally connected, or, according to Comte’s expression, as convergent. Comte calls these last encyclopædic laws. They tend to realise the unity which the mind claims, not in pursuing the chimerical reduction of all laws to a supreme law, but in showing that the systems of irreducible laws are nevertheless harmonious among themselves.
Generally speaking, these laws have been known for a long time, but only as special laws of such and such an order of phenomena. It belongs to positive philosophy to give them their encyclopædic character, that is to say, to make them universal. For instance, d’Alembert’s principle is known in mechanics as a law which connects questions of movement with questions of equilibrium. Philosophy finds a similar law in biology: (physiological questions are correlated to anatomical questions); and also in sociology (“progress is the development of order”). It then formulates the encyclopædic law which generalises these three laws, that is, the principle of the conditions of existence.
Similarly the three great laws of mechanics, known under the name of the laws of Kepler, of Galileo and of Newton, must be universalised and become encyclopædic for they are applicable to all the orders of phenomena.[80] The law of Kepler, in the first place, expresses the spontaneous tendency of all natural phenomena to persevere indefinitely in their state, if no disturbing influence supervenes; a tendency whence are derived inertia in mechanics, habit in living bodies, and the conservative instinct in societies. The law of Galileo which reconciles every common movement with the various particular movements, applies to all the organic and inorganic phenomena. For, in any system, we can always ascertain the independence of the several active or passive mutual relations with regard to any action which is exactly common to the various parts, whatever may be their kind and degree. Finally the universal character of Newton’s law (reaction is equal to action), is evident at first sight. It is accidentally, not essentially, that these laws have at first been mechanical laws. They could have been equally attained by the study of biological or social phenomena. If the science of mechanics was the first to formulate them it is because it has for its object the less complicated phenomena.
A complete and rational system of encyclopædic laws would realise the “philosophia prima” which Bacon dimly foresaw. In the actual condition of the sciences this would probably be a rash undertaking. Comte attempted it in the fourth volume of the Politique positive.[81] One can hardly say that the trial was a decisive one. It is true that at that moment Comte was already entirely taken up with religious preoccupations.
However, the encyclopædic laws are destined to play a part in the positive philosophy of nature, which may be compared, in some respects, with that of the categories in Aristotle’s philosophy. They are the most general forms under which the phenomena given in experience become objects of scientific thought for us. As in each class of phenomena we determine laws, principles of order and of harmony, so the encyclopædic laws make the order and the harmony of the different classes among themselves. They are, so to speak, the laws of laws. Through them the human mind which has already reached unity of method, may some day reach a certain unity of knowledge. But this unity will always differ by two essential characteristics from that which metaphysicians have pursued up to the present time: it will respect the irreducibleness of the various fundamental sciences, and it will remain relative, both by the conditions of the object and by those of the subject, upon which it equally depends.
Our conception of universal order “results from a necessary concurrence between that which is without us, and that which is within. The laws, that is to say the general facts, are never anything but hypotheses confirmed by observation. If harmony in no way existed outside us our mind would be entirely incapable of conceiving it, but in no case is it verified so much as we suppose it to be.”[82] We neither make order nor perceive it entirely. By long and arduous labour the human intellect gradually disengages the concept of order out of the facts that come crowding within its reach. It is an imperfect, contingent, perishable order, in a word, an order, relative like the mind itself. It is order nevertheless, and a necessary condition for ethics as well as for science.
[CHAPTER VI]
SCIENCE (CONTINUED)—POSITIVE LOGIC
Logic, says Comte, almost in the terms of Descartes, is the sole portion of ancient philosophy which is capable of still presenting some appearance of utility.[83] And does even this appearance correspond to a very solid reality?
If we distinguish, according to custom, formal logic from applied logic, Comte in his system will find no place for the former, which establishes a priori the principles and the mechanism of reasoning. As to the principles, which are the laws of the understanding, positive philosophy has shown that the only way to discover them is to study the products of the human intellect, that is to say, the development of the sciences. And it is again from these sciences that, through observation, the theory of reasoning must be drawn. Formal logic, as metaphysicians have constructed it, especially develops the dialectical faculty, that is to say, an aptitude more harmful than useful, for proving without finding.[84] Descartes said the same, in speaking of the syllogism, that it serves more for explaining to others the things which we know, than to discover those which we ignore.
All the utility which we can attribute to the study of logic properly so-called is found again more extended, more varied, more complete, more luminous, in mathematical studies. The mechanism of reasoning is everywhere the same. Whatever may be the phenomena which are the objects of a science the nature of deduction and induction never changes in them. Thus in practising these forms of reasoning in the most simple and the most general phenomena, those whose science is most advanced, we learn to know them with the most entire evidence, and in all the generality of which they are capable. Nowhere is reasoning so exact, so rigorous as in mathematics. They accustom the mind not to feed upon false reasons, and it is in that school that men ought to learn the theory and the practice of reasoning.
But, if the old pure logic is thus replaced by mathematics, must we not at least preserve the general study of the processes used in the various sciences, which is called methodology? Has not Comte himself insisted upon the irreducibleness of the several orders of laws to one another, and in particular to the mathematical laws? Is not the legitimate object of logic to define the processes of investigation and of proof particular to each of the fundamental sciences?
Comte does not think so. This applied logic does not appear to him to be more indispensable than formal logic. In the first place, the former, in fact, supposes the latter. It proceeds from the same philosophical conception. In order to determine a priori, in a general way, the rules of the application of the mind to its various scientific objects, we should first have to possess a knowledge of the laws of the mind. But, according to Comte, this knowledge can only be obtained by the observation of the methods which the mind has indeed followed. Moreover, no art is taught abstractedly, not even the art of reasoning well, nor that of experimenting, of finding hypotheses, etc. It has never been sufficient to know the rules of versification in order to write true poetry. A deep knowledge of the rules of method will not lead to scientific discoveries.[85] Whatever we learn of an art, it is practice that has taught us. Nothing here can replace time, natural disposition, and experience.
Methods then cannot be studied apart from the positive researches in which men of learning make use of them. Even supposing that in the far future, when the sciences are advanced, the methods and their applications could be taught by themselves, the study would run a great risk of yielding poor results.[86] Up to the present time all that has been said of the method, considered in the abstract, reduces itself to vague generalities. When, in logic, we have thoroughly established that all our science of nature must be founded upon observation, that we must proceed sometimes from facts to principles, sometimes from principles to facts, and a few other similar aphorisms, we know far less of the method than the man who has studied a single one of the positive sciences somewhat deeply, even without any philosophical purpose. It is thus that Eclectic philosophers have imagined to make their psychology into a science, thinking they could understand and practice the positive method because they had read the Novum Organum and the Discours de la Méthode. But did not Bacon, Pascal, Descartes, and the other great scientific leaders insist on the uselessness of abstract considerations about method? They never separated the rules they formulated from their application to positive research.
Comte himself, their successor and their heir, uses no other language. In his long study of the fundamental sciences he never fails to distinguish the contents of the science from its method, what he calls “the scientific point of view and the logical point of view.” But, while distinguishing them, he considers that they are correlated and closely allied among themselves. He no more conceives method as separated from the science which he studies, than science as separated from its method. Both constitute one intellectual reality seen under two aspects closely allied to one another.[87] To conclude, traditional logic is fast disappearing. In its theoretical parts it is superannuated like the metaphysical philosophy whence it proceeds. In its applied parts it is barren if separated from the practice of the sciences.