The Positive Philosophy of Auguste Comte

"In an empirical way, this has hitherto been the custom,—a custom which arose from the great antiquity of mathematical science. We now see why it must be renewed on a rational foundation."

"We have now considered, in the form of a philosophical problem, the rational plan of the study of the Positive Philosophy. The order that results is this; an order which of all possible arrangements is the only one that accords with the natural manifestation of all phenomena. Mathematics, Astronomy, Physics, Chemistry, Physiology, Social Physics."

"If there is difficulty about the measurement of lines, the embarrassment is much greater when we have to deal with surfaces, volumes, velocities, times, forces, etc., and in general with all other magnitudes susceptible of estimate, and, by their nature, difficult of direct measurement."

"[F]inding direct measurement so often impossible, we are compelled to devise means of doing it indirectly. Hence arose Mathematics."

"It is by such labours that Man has learned to know, not only the distances of the planets from the earth and from each other, but their actual magnitude,—their true form, even to the inequalities on their surface, and... their respective masses, their mean densities ...etc."

"Through the power of mathematical theories, all this and very much more has been obtained by means of a very small number of straight lines, properly chosen, and a larger number of angles."

"[T]he spirit of Mathematics consists in regarding as mutually connected all the quantities which can be presented by any phenomenon whatsoever, in order to deduce all from each other."

"[T]here is evidently no phenomenon which may not be regarded as affording such considerations. Hence results the naturally indefinite extent, and the rigorous logical universality of Mathematical science. As for its actual practical extent, we shall see... hereafter."

"It might even be said that Mathematics might enable us to dispense with all direct observation, by empowering us to deduce from the smallest possible number of immediate data the largest possible amount of results. Is not this the real use, both in speculation and in action, of the laws which we discover among natural phenomena?"

"If so, Mathematics merely urges to the ultimate degree, in its own way, researches which every real science pursues, in various inferior degrees, in its own sphere."

"Every mathematical solution spontaneously separates into two parts. The inquiry being... the determination of unknown magnitudes, through their relation to the known..."

"[T]he student must... first... ascertain what these relations are... This... is the Concrete part of the inquiry. When it is accomplished, what remains is... the determination of unknown numbers, when we know by what relation they are connected with known numbers. This second operation is the Abstract part of the inquiry."

"Therefore... physiological study should begin with inorganic phenomena..."

"We have not to investigate the nature of either; for the positive philosophy does not inquire into natures."

"Each of these great halves of natural philosophy has subdivisions. Inorganic physics must... be divided into two sections—of celestial and terrestrial phenomena. Thus we have Astronomy, geometrical and mechanical, and Terrestrial Physics."

"Astronomical phenomena are the most general, simple, and abstract of all; and therefore the study of natural philosophy must... begin with them. ...[T]he laws to which they are subject influence all others whatsoever."

"The most difficult astronomical question involves less intricacy than the simple movement of even a solid body, when the determining circumstances are to be computed."

"[W]e find a natural division of Terrestrial Physics into two, according as we regard bodies in their mechanical or their chemical character. Hence we have Physics... and Chemistry. Again, the second class must be studied through the first."

"An analogous division arises in the other half of Natural Philosophy—the science of organized bodies."

"Here we find ourselves presented with two orders of phenomena; those which relate to the individual, and those which relate to the species, especially when it is gregarious. With regard to Man, especially, this distinction is fundamental."

"As social conditions modify the operation of physiological laws, Social Physics must have a set of observations of its own."

"It would be easy to make the divisions of the Organic... by dividing physiology into vegetable and animal, according to popular custom. But this distinction... hardly extends into those Abstract Physics... Vegetables and animals come alike... when our object is to learn the general laws of life— ...[i.e.,]to study physiology. ...[T]he distinction grows ever fainter and more dubious with new discoveries, it bears no relation to our plan of research..."

"The first considers the most general, simple, abstract, and remote phenomena known to us, and those which affect all others without being affected by them. The last considers the most particular, compound, concrete phenomena, and those which are the most interesting to Man."

"Between these two, the degrees of speciality, of complexity, and individuality are in regular proportion to the place of the respective sciences in the scale exhibited."

"There is no refusing a principle which distributes the interior of each science after the same method with the aggregate sciences."

"This gradation is in essential conformity with the order which has spontaneously taken place among the branches of natural philosophy, when pursued separately, and without any purpose of establishing such order."

"If no leading science can be effectually pursued otherwise than through those which precede it in the scale, it is evident that no vast development of any science could take place prior to the great astronomical discoveries to which we owe the impulse given to the whole. The progression may since have been simultaneous; but it has taken place in the order we have recognized."

"This consideration is so important that it is difficult to understand without it the history of the human mind. The general law which governs this history... cannot be verified, unless we combine it with the scientific gradation just laid down: for it is according to this gradation that the different human theories have attained in succession the theological state, the metaphysical, and finally the positive."

"This fact is completely accounted for by the gradation we have laid down; and we shall see... that the possibility of applying mathematical analysis to the study of phenomena is exactly in proportion to the rank which they hold in the scale of the whole."

"We must beware of confounding the degree of precision which we are able to attain in regard to any science, with the certainty of the science itself."

"A very absurd proposition may be very precise; as if we should say, for instance, that the sum of the angles of a triangle is equal to three right angles; and a very certain proposition may be wanting in precision in our statement of it; as, for instance, when we assert that every man will die."

"If the different sciences offer to us a varying degree of precision, it is from no want of certainty in themselves, but of our mastery of their phenomena."

"Physical philosophers cannot understand Physics without at least a general knowledge of Astronomy; nor Chemists, without Physics and Astronomy; nor Physiologists, without Chemistry, Physics, and Astronomy; nor, above all, the students of , without a general knowledge of all the anterior sciences."

"As such conditions are, as yet, rarely fulfilled, and as no organization exists for their fulfilment, there is amongst us, in fact, no rational scientific education."

"If the fact is so in regard to scientific education, it is no less striking in regard to general education."

"Our intellectual system cannot be renovated till the natural sciences are studied in their proper order."

"Thus the Dogmatic Method is for ever superseding the Historical, as we advance to a higher position in science."

"If every mind had to pass through all the stages that every predecessor in the study had gone through... however easy it is to learn rather than invent, it would be impossible to effect the purpose of education,—to place the student on the vantage-ground gained by the labours of all the men who have gone before. By the dogmatic method this is done, even though the living student may have only an ordinary intellect, and the dead may have been men of lofty genius."

"By the dogmatic method, therefore, must every advanced science be attained, with so much of the historical combined with it as is rendered necessary..."

"The only objection to the preference of the Dogmatic method is that it does not show how the science was attained; but... this is the case also with the Historical method."

"To pursue a science historically is quite a different thing from learning the history of its progress. This last pertains to the study of human history..."

"[A] science cannot be completely understood without a knowledge of how it arose; and... a dogmatic knowledge of any science is necessary to an understanding of its history; and therefore we shall notice, in treating of the fundamental sciences, the incidents of their origin, when distinct and illustrative; and we shall use their history, in a scientific sense, in our treatment of Social Physics; but the historical study, important, even essential, as it is, remains entirely distinct from the proper dogmatic study of science."

"Great confusion would arise from any attempt to adhere strictly to historical order in our exposition of the sciences, for they have not all advanced at the same rate; and we must be for ever borrowing from each some fact to illustrate another, without regard to priority of origin."

"Thus... in the system of the sciences, astronomy must come before physics, properly so called: and yet, several branches of physics, above all, optics, are indispensable to the complete exposition of astronomy."

"In the main... our classification agrees with the history of science; the more general and simple sciences actually occurring first and advancing best... being followed by the more complex and restricted, though all were, since the earliest times, enlarging simultaneously."

"Our problem is, then, to find the one rational order, among a host of possible systems. ...This order is determined by the degree of simplicity, or... [i.e.,] generality of their phenomena. Hence results their successive dependence, and the greater or lesser facility for being studied. ...à priori... the most simple phenomena must be the most general; for whatever is observed in the greatest number of cases is of course the most disengaged from the incidents of particular cases."

"We must begin then with the study of the most general or simple phenomena, going on successively to the more particular or complex."

"[T]he most general and simple phenomena are the furthest removed from Man's ordinary sphere, and must thereby be studied in a calmer and more rational frame of mind than those in which he is more nearly implicated; and this constitutes a new ground for the corresponding sciences being developed more rapidly."

"We are first struck by the clear division of all natural phenomena into two classes—of inorganic and of organic bodies. The organized are evidently, in fact, more complex and less general than the inorganic, and depend upon them..."

"The Concrete must depend on the character of the objects examined, and must vary when new phenomena present themselves: whereas, the Abstract is wholly independent of the nature of the objects, and is concerned only with their numerical relations."