Truth is then at each period “the perfect logical coherence,” or the correspondence between our conceptions and our observations. The history of human thought is composed of a progressive series of alternating periods. At a certain moment the mind has placed what it conceives in accordance with what it knows. But, by degrees, new facts are observed, known facts are better interpreted, discoveries burst forth. The harmony between the conceptions and the observations then becomes precarious. Minds find a greater and greater difficulty in fitting all the acquired knowledge into the traditional frame. At last the frame gives way. Then the harmony is re-established in a more comprehensive form, which in its turn is destined to become insufficient. Here positive philosophy recognises a sociological law. It gives up the vain dream of immutable truth. It no longer regards the truth of to-day as absolutely true, nor the truth of yesterday as absolutely false. It ceases to be critical in regard to the past.”
To conclude, the theory of science can therefore only be accomplished from the sociological point of view. It remains imperfect so long as “we” has not been substituted to “I,” the universal subject which is humanity to the individual subject, and a philosophical history of the sciences to mere reflective analysis. To the logical conditions of science, to define it completely, its biological and social conditions must be joined. Then, but then only, it will be understood, that, at each period, science is at the same time true and relative, without its relativity placing its truth in danger.
[CHAPTER V]
SCIENCE (CONTINUED)
PHENOMENA AND LAWS
The perfection of the positive system, towards which it unceasingly tends, although very probably it may never reach it, would be to represent all observable phenomena as particular cases of a single general fact, such as, for example, that of gravitation. The fundamental identity of phenomena, the reduction of particular laws to a supreme law; this is an ideal which we are free to entertain. Comte, after d’Alembert and Saint-Simon, has formulated it himself at the beginning of the Cours de philosophie positive.[46]
Unfortunately this ideal is not realisable. We apply a very weak intellect to a very complicated world.[47] The unity which, scorning experience, we might establish, would naturally be valueless. For the several categories of phenomena proposed to us seem irreducible. If this[48] be the case, the pursuit after scientific unity is “irrational.” Comte ended by treating it as an “absurd utopia.”[49]
However, this utopia is forever reappearing; for the human mind is secretly attached to it. It is because, on the one hand, unity pleases it above all things, and on the other hand because there is here an illusion produced and maintained by a philosophy born of mathematical inspiration. Descartes’ discovery which allowed questions of geometry to be dealt with by algebra has been the occasion of a grave error. It gave rise to the thought that differences of quality could be reduced to differences of quantity. Hence the idea of “reducing” the various categories of phenomena to one another. But this was a wrong interpretation of the principle of analytical geometry. Even there, we have a translation, not reduction, “The geometrical ideas of form and of situation,” says Comte—and Mr. Renouvier will repeat it after him—“are not naturally more like numerical notions than the other real conceptions. Every phenomenon, even social, would certainly have its equation, as a figure or a motion if its law were known to us with sufficient precision.
Analysis is therefore but an instrument of incomparable power for the study of phenomena. But, from the fact that we can make use of it, it does not in the least follow that the phenomena may be all brought back to an identical type. Quality is in no way by this means reduced to quantity, which is something entirely abstract, and this no more takes place in the case of geometrical quality than in the case of any other. Neither can the geometrical quality be reduced to pure analysis, nor the physical to the geometrical, nor the living to the inorganic, nor the social to the biological. At every stage something qualitatively new appears. Whether or no we can formulate the relations of phenomena in the form of an equation, their heterogeneity subsists always irreducible.
What is true of phenomena is also true of their laws. Each order of phenomena has its special laws over and above those which result from its relations with the less complicated and more general orders. The idea of a supreme law from which all the others would be deduced must therefore be forsaken. Even within the range of each fundamental science, it is doubtful how far the unity dreamt of could ever be attained. The number of irreducible laws is far more considerable than is imagined by a false appreciation of our mental powers and of scientific difficulties. For instance, in physics, how can optics and acoustics be reduced to one another? Physiological considerations, in default of other reasons, would be opposed to such a confusion of ideas.[50] Likewise in biology, how can the laws of animal life be reduced to those of lower organic life? and in sociology, the laws of human society, implying a course of history, to those of animal societies which do not do so?
Instead, therefore, of conceiving a priori, the phenomena and the laws as capable of a “reduction” which is, in fact, impossible, the positive method requires the determination of the general characters of these phenomena and of these laws by observations. It first establishes the following: