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 which 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 formulated 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 separating 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 æsthetic 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 phenomena. 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 formulæ 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 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]
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.”[95] 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 only 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.