The Positive Philosophy of Auguste Comte

"[T]he ancient Greek geometers delighted themselves with beautiful speculations on Conic Sections; those speculations wrought, after... generations, the renovation of astronomy; and out of this has the art of navigation attained a perfection which it never could have reached otherwise than through the speculative labours of Archimedes and Apollonius..."

"[T]o use Condorcet's illustration, "the sailor who is preserved from shipwreck by the exact observation of the longitude, owes his life to a theory conceived two thousand years before by men of genius who had in view simply geometrical speculations.""

"[A]n intermediate class is rising up, whose particular destination is to organize the relations of theory and practice; such as the engineers, who do not labour in the advancement of science, but who study it in its existing state, to apply it to practical purposes. Such classes are furnishing us with the elements of a future body of doctrine on the theories of the different arts."

"Monge, in his view of , has given us a general theory of the arts of . But we have as yet only a few scattered instances of this nature."

"If we remember that several sciences are implicated in every important art,—that...[e.g.,] a true theory of Agriculture requires a combination of physiological, chemical, mechanical, and even astronomical and mathematical science,—it will be evident that true theories of the arts must wait for a large and equable development of these constituent sciences."

"We must distinguish between the two classes of ;—the abstract or general, which have for their object the discovery of the laws which regulate phenomena in all conceivable cases: and the concrete, particular, or descriptive, which are sometimes called Natural sciences in a restricted sense, whose function it is to apply these laws to the actual history of existing beings."

"The first are fundamental; and our business is with them alone, as the second are derived, and however important, not rising into the rank of our subjects of contemplation."

"We shall treat of , but not of botany and zoology, which are derived from it."

"We shall treat of chemistry, but not of ... secondary to it."

"We may say of Concrete Physics, as these secondary sciences are called, the same thing that we said of theories of the arts,—that they require a preliminary knowledge of several sciences, and an advance of those sciences not yet achieved..."

"At a future time Concrete Physics will have made progress, according to the development of Abstract Physics, and will afford a mass of less incoherent materials than those which it now presents."

"At present, too few of the students of these secondary sciences appear... aware that a due acquaintance with the primary sciences is requisite..."

"We have now considered, First, that science being composed of speculative knowledge and of practical knowledge, we have to deal only with the first; and Second, that theoretical knowledge, or science properly so called, being divided into general and particular, or abstract and concrete science, we have again to deal only with the first."

"The classification of the sciences is not so easy a matter... However natural it may be, it will always involve something, if not arbitrary, at least artificial; and in so far, it will always involve imperfection."

"It is impossible to fulfil... rigorously, the object of presenting the sciences in their natural connection, and according to their mutual dependence, so as to avoid... a vicious circle."

"Every science may be exhibited under two methods or procedures, the Historical and the Dogmatic."

"These are wholly distinct from each other, and any other method can be nothing but some combination of these two."

"By the first method knowledge is presented in the same order in which it was actually obtained... together with the way in which it was obtained."

"By the second, the system of ideas is presented as it might be conceived of at this day, by a mind which, duly prepared and placed at the right point of view, should begin to reconstitute the science as a whole."

"A new science must be pursued historically, the only thing to be done being to study in chronological order the different works which have contributed to the progress..."

"But when such materials have become recast to form a general system, to meet the demand for a more natural logical order, it is because the science is too far advanced for the historical order to be practicable or suitable."

"The more discoveries are made, the greater becomes the labour of the historical method of study, and the more effectual the dogmatic, because the new conceptions bring forward the earlier ones in a fresh light."

"Thus, the education of an ancient geometer consisted simply in the study, in their due order, of the very small number of original treatises then existing on the different parts of geometry. The writings of Archimedes and Apollonius were, in fact, about all."

"On the contrary, a modern geometer commonly finishes his education without having read a single original work dating further back than the most recent discoveries, which cannot be known by any other means."

"In order to understand the true value and character of the Positive Philosophy, we must take a brief general view of the progressive course of the human mind, regarded as a whole; for no conception can be understood otherwise than through its history."