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. Whatever104 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 is105 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 separated106 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. II.   There is however a positive logic, and in it we can also distinguish a theoretical and a practical part.   The theoretical part deals with logical laws. These laws which, finally, govern the intellectual world, are invariable, and common not only to all time and places, but also to all subjects whatever without any distinction even between those which Comte calls real and chimerical. They are observed, fundamentally, even in dreams.88 But this universality of logical laws is not understood by him in the sense in which the rationalist philosophers understand it. Comte is only concerned with a permanence and continuity purely historical in character. The mind of man, like the rest of his nature remains identical with itself, through the diversity of epochs and situations. It evolves without changing fundamentally “without other differences than those of gradually developed maturity and experience.”   Ancient philosophy claimed to discover the intellectual laws by reflection, as if the mind could think and at the same time see itself thinking, reason and observe its reasoning Comte rejects this introspective method, which yields no scientific results. If we apply the method of positive investigation to the intellectual phenomena as to all the others, two ways only are open. We can look at it from the static point of view, that is to say, study the conditions upon which107 these phenomena depend, and refer the phenomena to them as we refer generally the function to its organ. In this sense the study of the intellectual phenomena belongs to biology. Or else, from the dynamic point of view, we can consider these phenomena in their evolution, by observing the successive phases through which they pass. And since the life of the individual is too short for this “progress” to be appreciable, it must be studied in the life of the species. So understood, the science of the intellectual laws comes within the sphere of sociology.   Now, higher biology which deals with moral and intellectual phenomena, has only just been founded by Cabanis and Gall. Comte discovered that it could not be constituted as a science without the help of sociology. It is then to this newly born study that the search after intellectual laws in every way belongs.   Positive logic abstains, as we see, from speculating upon the leading principles of knowledge, principles of identity, of contradiction of causality, etc. These kinds of principles are not objects of examination or of discussion. Comte upon this point is in full accord with the Scottish school. No positive science questions its own principles, for how can we submit the very principles of all reasoning to criticism? Nothing is less in accordance with the positive spirit than an attempt of this kind. It is simply metaphysical and has no chance of success.   The intellectual laws of which the research is positive are such as the law of the three states (which is the most general of all), or such, for instance, as these: the human mind always makes an effort to place its conceptions in accordance with its observations; in every case the human mind forms the simplest hypothesis, etc. These laws, which are derived from the nature of the human mind, and whose action has always been felt, could only be discovered and formulated108 quite recently. For biology and sociology, to which they are related, could not be constituted before the more simple fundamental sciences were sufficiently advanced. To reach a scientific knowledge of the intellectual laws, to found a “positive logic,” nothing less was needed than the long evolution whose term is marked by Comte’s philosophy.   Applied logic, or theory of method, also finds a new meaning in the positive doctrine. Comte does not fall into the mistake which he has criticised. He does not propose to teach an art ex professo, and he will not formulate the rules which positive research must follow in order to be productive. Here again Comte will found his doctrine upon the intellectual evolution of humanity.   In the first place, like the sciences, the positive methods are collective works, “the work of the species gradually developed in the long sequence of centuries.” Comte considers as impertinent the pretensions of some modern scientists, who pride themselves upon having invented the comparative method in biology. As if Aristotle had not already practised it! And Aristotle had not been the first to do so. The processes of the positive methods do not reveal themselves all at once, under a perfect and final form. They gradually come to light during a long period of groping. The human mind notices the processes which have succeeded in simple cases. It endeavours to generalize them, and tests them in new and slightly more complex cases. It seeks for the reason why in certain cases the end is reached, in others it is missed. Method is thus insensibly formed by a kind of practical induction. Its essential processes are, like the leading ideas in the sciences, “inspirations from universal wisdom.” The office of great men—and this is sufficient for them to earn our gratitude—is to recognise the value and the fecundity of these inspirations, to set them at work, and especially to endow them with an often indefinite extension by separating109 them from the concrete conditions in which they were at first manifested.   Thus positive philosophy, less ambitious than its predecessors, does not take upon itself to legislate upon method. But neither does it confine itself to the mere duty of making statements, that is to say to simply register the processes made use of in the sciences. Is not its proper function to represent in human knowledge the “universalizing mind” which in Comte’s language is synonymous with government? He himself calls the fifty-eighth lesson of the Cours de philosophie positive his Discours de la Méthode.89 He rises above the necessarily peculiar position which belongs to specialists, and places himself at the central and universal point of view which is proper to the philosopher. Thence he embraces under one point of view, the entire hierarchy of the fundamental sciences. Out of this well-ordered whole, he watches as they arise, first the essence of the positive method, and then the relations of the various elements in this method to one another.   In its essence, the positive method is one, as science is one. For it ever tends towards the same end: the establishment of the invariable relations which constitute the effective laws of all observable events, “thus capable of being rationally foreseen from one another.” The positive method proceeds to this by means of a threefold abstraction. It first separates the practical requirements from theoretical knowledge, to be only concerned with the latter, it seeks for the laws of phenomena without troubling itself, at least provisionally, with any possible applications. It also puts aside ?sthetic considerations, which ought not to intervene in scientific investigation. Finally—and here is the condition for the very existence of science—the positive method always carefully distinguishes between the abstract and the concrete point of view. It studies not beings, but pheno110mena. Even in the simplest cases, in astronomy for instance, no general law can be established so long as bodies are considered in their concrete existence. The principal phenomenon has had to be detached, so to speak, so as to submit it alone to an abstract study, afterwards allowing us to return successfully to the consideration of more complex realities. This is what the ancients had known how to do in geometry; and this is what Comte himself has done in the most complex of all sciences, in sociology. Instead of stopping at the concrete reality of history, he determined, by a bold abstraction, the law of the essential movement in human society “leaving to subsequent labours the care of bringing apparent anomalies into line with it.”90   In the main, these general characteristics of the positive method bring it singularly near to the Cartesian method. Comte’s “Threefold gradual abstraction” seems indeed to have for its end, like Descartes’ analysis, to go back to what is simplest and easiest to know, and then to come down, by a synthetic and progressive advance, towards the reality which is given to us in experience. The one and the other of these methods witness, here, to an effort towards generalising the spirit of the mathematical method. Let us never forget, writes Comte, that the general spirit of positive philosophy was first formed by the culture of mathematics, and that we must necessarily go back so far, in order to know this spirit in its elementary purity. The mathematical processes and formul? are rarely capable of being applied to the effective study of natural phenomena, when we wish to go beyond the most extreme simplicity in the real conditions of the problems. But “the true mathematical spirit, so distinct from the algebraical spirit, with which it is too often confounded, is on the contrary, constantly of value.”91   We must therefore not take too much notice of Comt111e’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 which112 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   Positive logic extends to all the fundamental sciences the use of the processes at first peculiar to each one of them. Each great logical artifice, once studied in the portion of natural philosophy which shows its most spontaneous and most complete development, can afterwards be applied, with the necessary modifications, to the perfecting of the other sciences. For instance, the comparative method belongs in the first place to biology. But, when brought back to its principle and generalised, it becomes a precious instrument for sociology, for physics, and even for mathematics. In every science, the method is completed by the auxiliary use of the processes whose power and whose sphere of action have been made known by the other sciences. By these mutual loans, in each one of them, the positive method reaches its maximum of production.   To be cultivated in the most rational manner possible, the sciences must then be subject to the direction of a general system of positive philosophy, “the common basis and the uniform combining element of all truly scientific labours.”95113 The scientific man must at the same time be a philosopher, since philosophy alone puts him in possession of all the resources of positive method. For instance, this philosophy will show the geometer that he must at least have a general knowledge of biology and of sociology. Biology will teach him the comparative method, of which he can make use when occasion offers, and sociology by showing him the history of his science in the general development of the human mind, will help him better to understand it. If the geometers had a more philosophical mind, their science would be better taught. The great conceptions of Descartes, of Leibnitz, of Lagrange, would be more intelligently explained and brought to light.   If it is useful for the geometer to have studied the other fundamental sciences, it is not less indispensable for other learned men to have gone through the study of mathematics. As an “initial” discipline, this science can be neglected by no one. It is the common school of positivity for all minds. It is therefore to be regretted that the scientific education of future physiologists should be mainly made up of literary studies and of a few notions of physics and chemistry. The more complex the phenomena whose laws they will have to seek, the more necessary will it be for them to have become familiarised in mathematics and in astronomy, with the precise idea of scientific truth. And, as a matter of fact, until this century, the study of the exact sciences had always been regarded as a preliminary condition for that of the natural sciences. Buffon and Lamarck in their day had still received this discipline. If it has been so difficult to constitute social science, it comes, among other reasons, from the lack of scientific education among those who, up to the present time, have wished to study social phenomena. Where, for instance, could economists have found the scientific idea of what constitutes natural laws, ignoring as most of them did not only114 biology which was being formed beside them, but even the sciences which had already reached a positive state?   The exclusive cultivation of a single science is always a danger for the intellect. Nevertheless, so long as the chief task of the positive spirit was to disorganise the system of beliefs which constituted theological and metaphysical philosophy, the speciality of the works and of the methods was an inconvenience of secondary importance. It mattered little that the discoveries of the astronomers, the physicians, the biologists should be more or less co-ordinated and directed by a universal positive method, so long as they did their work and prepared the future. But, when the positive spirit had to become organic instead of critical, when it had to substitute a new philosophy to the one which it had overthrown, then it was obliged to subordinate the special processes which it had made use of until then to a single universal method. Should the “scientific anarchy” have lasted, the progress of the positive spirit would undoubtedly have led to the discrediting of the metaphysical régime, but without replacing it, and consequently without having done with it. By rejecting any new general discipline, modern scientific men would unknowingly tend to re-establish the system which they seemed to have shattered for ever.   In a word, the triumph of the positive method, to be final, presupposes the acceptance of the positive philosophy by all men of learning. The old logic was bound by the narrowest ties to the metaphysical doctrines which were then dominant. In the same way positive logic is bound up with positive philosophy. Speaking more precisely, it is an expression of this very philosophy.   115 III.   Is the general method of positive philosophy objective, or subjective, or both at once? As we know, this question has raised passionate discussion among positivists.96 Outside the school it has been solved by some historians as if Auguste Comte, at the end of his life, had gone back to a doctrine very different from the one set forth by him in the Cours de philosophie positive. It suffices, however, to distinguish, with him, two successive points of view, to see how the two methods, antagonistic in a certain sense, can, in another one, be very well reconciled.   If we only consider the process followed by our mind in the explanation of natural phenomena, that is to say the object of positive philosophy taken in the strict sense of the word, it is true that two opposite methods are found face to face. The subjective method goes from the consideration of man to that of the world, the objective method goes from the knowledge of the world to that of man. The first gives rise to theological and metaphysical philosophy, the latter to positive philosophy. The incompatibility of the two philosophies proceeds from that of the methods, which is irreducible. It allows us to say: “This will kill that.”97 In this sense, the final establishment of the objective method, which is completed by the foundation of sociology, implies the exclusion, also final, of the subjective method.   But “having reached its full maturity, true philosophy should inevitably tend to reconcile these two antagonistic methods,” wrote Comte in 1838, in the third volume of the Cours de philosophie positive, that is to say, long before the time of what has been wrongly called his second philosophy.98 This reconciliation will be accomplished by means of the116 distinction between the special point of view of the sciences, and the universal point of view of philosophy. The scientific investigation of the laws of natural phenomena can only be made by means of the objective method: Comte never varies in his thought on this point. But these sciences are but the parts in a greater whole, for which the subjective method alone is suitable.   Two arguments especially prove this, one belonging to the logical, the other to the moral and the religious order.   The supreme requirement of our intellect is unity. Shall we ever reach this unity by using the objective method in the sciences? Evidently not. Even in each order of phenomena separately considered we do not see how to reduce the laws which we know to a single law of a more general character. And what are the laws known to us compared with those which elude our search, and which perhaps may do so for ever? Considered in its object, each one of our sciences reaches, so to speak, to infinity, far beyond our limited horizon. If then, in order to satisfy us, a single conception of the world is necessary, we shall never obtain such a conception from the objective point of view. But if we change our point of view, if we refer the whole of the sciences to man, or better, to humanity, as a centre, we shall then be able to realise the unity which we seek. This is precisely what is made possible by sociology, by subordinating the hierarchy of the positive sciences to the final science of humanity.   To consider the other fundamental sciences as “indispensable preliminaries,”99 to represent the evolution which has brought them forth in turn as the very history of human progress; to verify the law of the three states in all our beliefs, and in all our knowledge; finally, to control all scientific research from the sociological point of view: this is what Comte understands by the conciliation of the two methods.   117   The whole development of positive science from mathematics to sociology, lies between the new use which is made of subjective method and that which was spontaneously made of it by theological philosophy. When theological philosophy considered the knowledge of man and that of the world as interdependent, the instinct which animated it was a just one. But it was imagining instead of observing. It represented the world as filled with “causes” analogous to the will of man and equally capricious. The new subjective method rests, on the contrary, upon the very results of the positive sciences, brought to a synthesis in sociology. It takes as established that the intellectual and moral phenomena depend upon the biological laws, and that the biological laws themselves are subordinate to the laws of the inorganic milieu. But, since the “final systematisation of all these laws”100 must always remain impossible from the objective point of view, the new subjective method undertakes it from the point of view of humanity as a centre.   We can thus distinguish two great periods in the intellectual advance of humanity. During the first, the positive spirit successively applies the scientific, that is to say objective, method, to higher and higher orders of phenomena. The foundation of sociology marks the term of this progress. Then the second period begins. The positive spirit from special has become universal, from analytical synthetical. It reacts upon the particular sciences, and henceforth makes use of the “regenerated” subjective method, to govern the whole of them.   From the moral and religious point of view, once sociology has been constituted, and positive philosophy has been established, the functions proper to religion appear. The intellect recognises that its end does not lie within itself, and that it is incapable of determining its own rule and aim.118 It submits to a directing authority, which will guide its efforts and fix their object. To act from affection, and to think in order to act. But if the mind understands that it is destined to be used in the service of humanity, it sees at the same time that in the complete positive doctrine, which contains religion, the objective method gives precedence to the subjective, or rather that they mutually support each other. If we were pure intellects we should probably always go from the world to man. But in us the intellect is only a means. Love is the principle, action is the end; and it is to man, finally, that our study of the world must be referred.   Towards the end of his life, Comte replaced the logic of the mind, “especially guided by artificial signs,” by the logic of the heart “founded upon the direct connection of the feelings.”101 We shall not here insist upon a conception which is closely allied to his religious system. We will only conclude that, from the philosophical point of view the two methods objective and subjective, in Comte’s thought, are easily reconciled, provided that both have been “systematically regenerated.” Now, the regeneration is obtained as soon as sociology is founded. On the one hand, as a matter of fact, it furnishes the sciences formed by the objective method with a principle of unity, since henceforth they are all subordinated to the single science of Humanity. And, on the other hand, the subjective method acquires the positivity which it lacked, for sociology has substituted to the arbitrary “individual subject,” the “universal subject,” that is to say again, Humanity.