"Mathematical Analysis is... the true rational basis of the whole system of our positive knowledge."

“The positive philosophy of Auguste Comte, freely translated and condensed by Harriet Martineau, in the Cornell University Library Historical Monographs Collection”

“Social positivism only accepts duties, for all and towards all. Its constant social viewpoint cannot include any notion of rights, for such notion always rests on individuality. We are born under a load of obligations of every kind, to our predecessors, to our successors, to our contemporaries. These obligations then increase or accumulate, for it is some time before we can return any service. … Any human right is therefore as absurd as immoral. Since there are no divine rights anymore, this concept must therefore disappear completely as related only to the preliminary regime and totally inconsistent with the final state where there are only duties based on functions.”

“In the final, positive state, the mind has given over the vain search after Abolute notions, the origin and destination of the universe, and the cause of phenomenon, and applies itself to the tudy of their laws, - that is, their invariable relations of succession and resemblance. Reasoning and observation, duly combined, are the means of this knowledge. What is now understood when we speak of an explanation of the facts is simply the establishment of a connection between single phenomena and some general facts, the number of which continually diminishes with the progress of science.”

“The first condition of unity is a subjective principle; and this principle in the Positive system is the subordination of the intellect to the heart: Without this the unity that we seek can never be placed on a permanent basis, whether individually or collectively. It is essential to have some influence sufficiently powerful to produce convergence amid the heterogeneous and often antagonistic tendencies of so complex an organism as ours.”

“The principal means of realizing it will be the formation of an alliance between philosophers and the working classes, for which both are alike prepared by the negative and positive progress of the last five centuries. The direct object of their combined action will be to set in motion the force of Public Opinion.”

“Every attempt to refer chemical questions to mathematical doctrines must be considered, now and always, profoundly irrational, as being contrary to the nature of the phenomena. . . . but if the employment of mathematical analysis should ever become so preponderant in chemistry it would occasion vast and rapid retrogradation....”