The Philosophy of Auguste Comte

by Lucien Lévy-Bruhl

To the use of the experimental method, physics can often join that of mathematical analysis. But in the employment of the latter it must be extremely cautious, and we must only have recourse to this application of mathematics after having “carefully considered the reality of the starting point,” which alone can guarantee the solidity of the deductions. In a word, the spirit proper to physical investigation, must constantly direct the use of this powerful instrument. Now, this condition has not always been fulfilled. Too often the preponderance of mathematical analysis has been the cause of the neglect of experimental studies. Not only has mathematical analysis in this way retarded the progress of physics but it has even tended to vitiate the conception of that science, and to bring it back to a state of obscurity and uncertainty which, says Comte, notwithstanding the apparent severity of the forms differs little, at bottom, from its old metaphysical state.[136]

For this reason, the application of analysis to physics must not be left to geometers who are chiefly concerned with the instrument. It must belong to the physicists who before all things consider the use to be made of it. Mathematicians have often encumbered physics with a quantity of analytical labour founded upon very doubtful hypothesis; they must give way to physicists trained in experimental studies, and, nevertheless, with sufficient knowledge of mathematics to make use of the analysis whenever it is possible. Within these limits mathematical analysis will render the greatest service to the science of physics. Would optics, acoustics, the theories of heat and of electricity have reached the point where we see them to-day without the powerful help of analysis? Yet even here, physical researches are almost always so complex that, in order to assume a mathematical form, they demand the setting aside of a more or less essential portion of the conditions of the problem. Indeed we are here in presence of the general problem of the translation of the concrete into the abstract. This problem, which is admirably solved in mathematics, and sufficiently in astronomy, is only imperfectly solved in physics. The art of closely combining experience and analysis, says Comte, is still almost unknown. It constitutes the final progress of the method proper to the deeper study of physics.[137] We may add, and this is in Comte’s mind, that conversely the progress made by this art would be useful to analysis itself.

II.

Astronomy has reached a perfect state of “positivity.” All trace of the metaphysical spirit has disappeared from it. Can we say as much of physics? It would not seem so, when we see the hypotheses which play so great a part in this science, and of which a few are keenly contested by Comte.

How can we distinguish the valuable hypotheses from the useless ones, those which are useful to physics from those which are merely an encumbrance and should be rejected? This is not a question which can be solved by referring to abstract rules. In order to answer it, we must study the use of hypotheses where it is perfect, and decide according to this example. To my mind, says Comte, the deeper study of the art of hypotheses in astronomy can alone establish the rules which are suitable to direct the use of this precious artifice in physics, and more so still in the remainder of natural philosophy.[138] Now of what use is it to astronomers? To anticipate the results of deduction or of induction, “by making a provisional supposition concerning some of the very notions which constitute the final object of the research.” It is a process of which the methods of approximation used by geometers originally suggested the general idea. They “supposed” that the circumference was the limit of the perimeters of inscribed and circumscribed polygons the number of whose sides went on increasing. In the same way, hypotheses provisionally fill up the “lacunæ” of our knowledge.

An hypothesis should always be open to a positive verification, “whose degree of precision is in harmony with that of the corresponding phenomena.” For it only expresses beforehand what experience and reasoning might have made known immediately, if the circumstances of the problem had been more favourable. If, therefore, an hypothesis claimed to attain that which in its nature is inaccessible to observation and to reasoning, it would immediately become illegitimate and harmful. In a word, it must bear exclusively upon laws, and never upon causes or the modes of production of phenomena.

In the physics of his own time Comte finds the two kinds of hypotheses, but he also finds more bad hypotheses than good ones. He especially protests against the ethers and the fluids to which the phenomena of heat, light, electricity and magnetism were attributed. These hypotheses, according to him, are destined to disappear from science. It is true that the physicists deny that they attribute an objective reality to their ethers and their fluids. They claim to need them absolutely in order to facilitate the conception and the combination of phenomena. However, in spite of themselves, they are drawn into speaking of their ethers as if they really existed. Moreover, do they not see that astronomy gets on very well without similar hypotheses? In order to conceive the phenomena it is enough to observe and analyse them attentively. And, as to combining them, that depends upon the knowledge which has been obtained of their positive relations.

The corpuscular theory is, on the contrary, an example of a good hypothesis in physics, where it plays a part analogous to that of the inertia of bodies in mechanics.[139] The innermost structure of bodies is unknown to us. But we have a right to introduce all the hypotheses which can help us in our research, and in particular the hypothesis of atoms, so long as we do not understand it as something representing a reality.

The ethers and the fluids tend to “explain” the physical phenomena by the nature of the agent which produces them. It is here that these hypotheses bear the mark of the metaphysical spirit. To understand the appearance and especially the persistence of these hypotheses, it is not enough to consider them in themselves. We must get back to the history of physics, and compare it with that of the other fundamental sciences. Was it possible for physics to pass suddenly from the period in which phenomena are referred to causes and essences, to the positive period where they are conceived as simply subject to laws? A period of transition was necessary. The scholastic entities, before disappearing, became semi-materialised. They were transformed into fluids. What is heat conceived as existing apart from a hot body, light independent of a luminous body, electricity separated from an electric body? They are the old entities in a new garment, more easily grasped, in spite of their “equivocal corporeity.” They gradually lead to the more and more exclusive consideration of phenomena and of laws, until, in their turn, they disappear.

Astronomy went through the same phases before Physics. In it we have also seen hypotheses which cannot be verified come to facilitate the transition from the theological to the positive state. Such was the conception of Descartes who explained the celestial motions by the system of vortices. Those famous vortices introduced the idea of a mechanism where Kepler himself had only dared to conceive the incomprehensible action of souls and genii. Then Newton came, who preserved the idea of mechanism, while giving up the vortices. In vain did the Cartesians fight against his entirely positive conception. Their arguments in favour of fluids and ethers were as plausible as those of the physicists of our own time. But we have ceased to listen to them. Having become entirely positive, astronomy no longer seeks anything but the laws at work in the phenomena observed. Every accessory hypothesis aiming at anything else has no further interest for us.