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Home > Dictionary of Science Quotations > Scientist Names Index C > Auguste Comte Quotes

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Auguste Comte
(17 Jan 1798 - 5 Sep 1857)

French philosopher and mathematician who was founder of positivism, a system of thought and knowledge which avoided speculation and validated through strict scientific method. He was a founder of sociology as a systematic study, and coined the term 'altruism.'. His grounding in mathematics and science dated back to his undergraduate studies at École Polytechnique.

Science Quotes by Auguste Comte (14 quotes)

C’est donc par l’étude des mathématiques, et seulement par elle, que l’on peut se faire une idée juste et approfondie de ce que c’est qu’une science. … Toute éducation scientifique qui ne commence point par une telle étude pèche donc nécessairement par sa base.
It is therefore through the study of mathematics, and only by it, that one can form a fair and comprehensive idea of what science is. … Any scientific education which does not begin with such a study, necessarily is fundamentally flawed.
— Auguste Comte
Original French in Cours de Philosophie Positive (1830), Vol. 1, 132. English version by Webmaster using online resources. Comte believed in a hierarchy of the sciences, ordered by degree of generality and simplicity of their ideas. Mathematics he placed first, followed by astronomy, physics, chemistry, biology, and sociology in the sixth and last place. This quote was included by T.H. Huxley, in 'The Scientific Aspects of Positivism', Fortnightly Review (1869), 11, 666-667, in which Huxley strongly disagreed with ranking the abstract discipline of mathematics at the top, since education should begin with the concrete based on investigation by observation, “from the easy to the difficult.”
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All good intellects have repeated, since Bacon’s time, that there can be no real knowledge but that which is based on observed facts. This is incontestable, in our present advanced stage; but, if we look back to the primitive stage of human knowledge, we shall see that it must have been otherwise then. If it is true that every theory must be based upon observed facts, it is equally true that facts cannot be observed without the guidance of some theory. Without such guidance, our facts would be desultory and fruitless; we could not retain them: for the most part we could not even perceive them.
— Auguste Comte
The Positive Philosophy, trans. Harriet Martineau (1853), Vol. 1, 3-4.
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Confined to its true domain, mathematical reasoning is admirably adapted to perform the universal office of sound logic: to induce in order to deduce, in order to construct. … It contents itself to furnish, in the most favorable domain, a model of clearness, of precision, and consistency, the close contemplation of which is alone able to prepare the mind to render other conceptions also as perfect as their nature permits. Its general reaction, more negative than positive, must consist, above all, in inspiring us everywhere with an invincible aversion for vagueness, inconsistency, and obscurity, which may always be really avoided in any reasoning whatsoever, if we make sufficient effort.
— Auguste Comte
In Synthèse Subjective (1856), 98. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 202-203. From the original French, “Bornée à son vrai domaine, la raison mathématique y peut admirablement remplir l’office universel de la saine logique: induire pour déduire, afin de construire. … Elle se contente de former, dans le domaine le plus favorable, un type de clarté, de précision, et de consistance, dont la contemplation familière peut seule disposer l’esprit à rendre les autres conceptions aussi parfaites que le comporte leur nature. Sa réaction générale, plus négative que positive, doit surtout consister à nous inspirer partout une invincible répugnance pour le vague, l’incohérence, et l’obscurité, que nous pouvons réellement éviter envers des pensées quelconques, si nous y faisons assez d’efforts.”
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In mathematics we find the primitive source of rationality; and to mathematics must the biologists resort for means to carry out their researches.
— Auguste Comte
The Positive Philosophy, trans. Harriet Martineau (1853), Vol. 1, 388.
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In the final, the positive, state, the mind has given over the vain search after absolute notions, the origin and destination of the universe, and the causes of phenomena, and applies itself to the study 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 facts is simply the establishment of a connection between single phenomena and some general facts.
— Auguste Comte
The Positive Philosophy, trans. Harriet Martineau (1853), Vol. 1, 2.
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Induction for deduction, with a view to construction.
— Auguste Comte
Attributed in John Arthur Thomson, quote at heading of chapter 'Scientific Method', Introduction to Science (1911), 57, but without further citation. Webmaster has found no primary source for confirmation. Please contact if you can help.
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It needs scarcely be pointed out that in placing Mathematics at the head of Positive Philosophy, we are only extending the application of the principle which has governed our whole Classification. We are simply carrying back our principle to its first manifestation. Geometrical and Mechanical phenomena are the most general, the most simple, the most abstract of all,— the most irreducible to others, the most independent of them; serving, in fact, as a basis to all others. It follows that the study of them is an indispensable preliminary to that of all others. Therefore must Mathematics hold the first place in the hierarchy of the sciences, and be the point of departure of all Education whether general or special.
— Auguste Comte
In Auguste Comte and Harriet Martineau (trans.), The Positive Philosophy (1858), Introduction, Chap. 2, 50.
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Positivism is a theory of knowledge according to which the only kind of sound knowledge available to human kind is that if science grounded in observation.
— Auguste Comte
(1891). As given as an epigraph in M.J. Vinod and Meena Deshpande, Contemporary Political Theory (2013), 3.
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The business of concrete mathematics is to discover the equations which express the mathematical laws of the phenomenon under consideration; and these equations are the starting-point of the calculus, which must obtain from them certain quantities by means of others.
— Auguste Comte
In Positive Philosophy, Bk. 1, chap. 2.
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The law is this: that each of our leading conceptions—each branch of our knowledge—passes successively through three different theoretical conditions: the Theological, or fictitious; the Metaphysical, or abstract; and the Scientific, or positive.
— Auguste Comte
The Positive Philosophy, trans. Harriet Martineau (1853), Vol. 1, 1-2.
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The progress of the individual mind is not only an illustration, but an indirect evidence of that of the general mind. The point of departure of the individual and of the race being the same, the phases of the mind of a man correspond to the epochs of the mind of the race. Now, each of us is aware, if he looks back upon his own history, that he was a theologian in his childhood, a metaphysician in his youth, and a natural philosopher in his manhood. All men who are up to their age can verify this for themselves.
— Auguste Comte
The Positive Philosophy, trans. Harriet Martineau (1853), Vol. 1, 3.
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To understand a science it is necessary to know its history.
— Auguste Comte
From Cours de Philosophie Positive (1830), Tome 1, 82, as often seen in English, by an unidentified translator. From the original French, “Je pense même qu’on ne connaît pas complétement une science tant qu’on n’eu sait pas l’histoire”, which translates more literally as, “I even think that one does not completely understand a science completely as long as one did not know the history”. Other translations include, for example, “A science can not be completely understood without a knowledge of how it arose”, in Auguste Comte and Harriet Martineau (trans.), A Course of Positive Philosophy (1832-1842), Vol. 1, 43.
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[Engineers are] the direct and necessary instrument of coalition by which alone the new social order can commence.
— Auguste Comte
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[Mathematics] has for its object the indirect measurement of magnitudes, and it proposes to determine magnitudes by each other, according to the precise relations which exist between them.
— Auguste Comte
In The Positive Philosophy of Auguste Comte, translated by Harriet Martineau, (1896), Vol. 1, 40.
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Quotes by others about Auguste Comte (7)

The scientist who recognizes God knows only the God of Newton. To him the God imagined by Laplace and Comte is wholly inadequate. He feels that God is in nature, that the orderly ways in which nature works are themselves the manifestations of God's will and purpose. Its laws are his orderly way of working.
The Human Meaning of Science (1940), 69.
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The only occasion when Comte
Is known to have romped
Was when the multitude roared “Vive La Philosophie Positive!”
E. C. Bentley, Biography for Beginners (1905). Collected in Complete Clerihews (2008), 32.

A hundred years ago, Auguste Compte, … a great philosopher, said that humans will never be able to visit the stars, that we will never know what stars are made out of, that that's the one thing that science will never ever understand, because they're so far away. And then, just a few years later, scientists took starlight, ran it through a prism, looked at the rainbow coming from the starlight, and said: “Hydrogen!” Just a few years after this very rational, very reasonable, very scientific prediction was made, that we'll never know what stars are made of.
Quoted in Nina L. Diamond, Voices of Truth (2000), 332.
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The mathematical intellectualism is henceforth a positive doctrine, but one that inverts the usual doctrines of positivism: in place of originating progress in order, dynamics in statics, its goal is to make logical order the product of intellectual progress. The science of the future is not enwombed, as Comte would have had it, as Kant had wished it, in the forms of the science already existing; the structure of these forms reveals an original dynamism whose onward sweep is prolonged by the synthetic generation of more and more complicated forms. No speculation on number considered as a category a priori enables one to account for the questions set by modern mathematics … space affirms only the possibility of applying to a multiplicity of any elements whatever, relations whose type the intellect does not undertake to determine in advance, but, on the contrary, it asserts their existence and nourishes their unlimited development.
As translated in James Byrnie Shaw, Lectures on the Philosophy of Mathematics (1918), 193. From Léon Brunschvicg, Les Étapes de La Philosophie Mathématique (1912), 567-568, “L’intellectualisme mathématique est désormais une doctrine positive, mais qui intervertira les formules habituelles du positivisme: au lieu de faire sortir le progrès de l’ordre, ou le dynamique du statique, il tend à faire de l'ordre logique le produit du progrès intellectuel. La science à venir n'est pas enfermée, comme l’aurait voulu Comte, comme le voulait déjà Kant, dans les formes de la science déjà faite; la constitution de ces formes révèle un dynamisme originel dont l’élan se prolonge par la génération synthétique de notions de plus en plus compliquées. Aucune spéculation sur le nombre, considéré comme catégorie a priori, ne permet de rendre compte des questions qui se sont posées pour la mathématique moderne … … l’espace ne fait qu'affirmer la possibilité d'appliquer sur une multiplicité d’éléments quelconques des relations dont l’intelligence ne cherche pas à déterminer d’avance le type, dont elle constate, au contraire, dont elle suscite le développement illimité.”
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[Comte] may truly be said to have created the philosophy of higher mathematics.
In System of Logic (1846), 369.
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These specimens, which I could easily multiply, may suffice to justify a profound distrust of Auguste Comte, wherever he may venture to speak as a mathematician. But his vast general ability, and that personal intimacy with the great Fourier, which I most willingly take his own word for having enjoyed, must always give an interest to his views on any subject of pure or applied mathematics.
In R. Graves, Life of W. R. Hamilton (1882-89), Vol. 3, 475.
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It has been asserted … that the power of observation is not developed by mathematical studies; while the truth is, that; from the most elementary mathematical notion that arises in the mind of a child to the farthest verge to which mathematical investigation has been pushed and applied, this power is in constant exercise. By observation, as here used, can only be meant the fixing of the attention upon objects (physical or mental) so as to note distinctive peculiarities—to recognize resemblances, differences, and other relations. Now the first mental act of the child recognizing the distinction between one and more than one, between one and two, two and three, etc., is exactly this. So, again, the first geometrical notions are as pure an exercise of this power as can be given. To know a straight line, to distinguish it from a curve; to recognize a triangle and distinguish the several forms—what are these, and all perception of form, but a series of observations? Nor is it alone in securing these fundamental conceptions of number and form that observation plays so important a part. The very genius of the common geometry as a method of reasoning—a system of investigation—is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds. So characteristic of common geometry is this method of investigation, that Comte, perhaps the ablest of all writers upon the philosophy of mathematics, is disposed to class geometry, as to its method, with the natural sciences, being based upon observation. Moreover, when we consider applied mathematics, we need only to notice that the exercise of this faculty is so essential, that the basis of all such reasoning, the very material with which we build, have received the name observations. Thus we might proceed to consider the whole range of the human faculties, and find for the most of them ample scope for exercise in mathematical studies. Certainly, the memory will not be found to be neglected. The very first steps in number—counting, the multiplication table, etc., make heavy demands on this power; while the higher branches require the memorizing of formulas which are simply appalling to the uninitiated. So the imagination, the creative faculty of the mind, has constant exercise in all original mathematical investigations, from the solution of the simplest problems to the discovery of the most recondite principle; for it is not by sure, consecutive steps, as many suppose, that we advance from the known to the unknown. The imagination, not the logical faculty, leads in this advance. In fact, practical observation is often in advance of logical exposition. Thus, in the discovery of truth, the imagination habitually presents hypotheses, and observation supplies facts, which it may require ages for the tardy reason to connect logically with the known. Of this truth, mathematics, as well as all other sciences, affords abundant illustrations. So remarkably true is this, that today it is seriously questioned by the majority of thinkers, whether the sublimest branch of mathematics,—the infinitesimal calculus—has anything more than an empirical foundation, mathematicians themselves not being agreed as to its logical basis. That the imagination, and not the logical faculty, leads in all original investigation, no one who has ever succeeded in producing an original demonstration of one of the simpler propositions of geometry, can have any doubt. Nor are induction, analogy, the scrutinization of premises or the search for them, or the balancing of probabilities, spheres of mental operations foreign to mathematics. No one, indeed, can claim preeminence for mathematical studies in all these departments of intellectual culture, but it may, perhaps, be claimed that scarcely any department of science affords discipline to so great a number of faculties, and that none presents so complete a gradation in the exercise of these faculties, from the first principles of the science to the farthest extent of its applications, as mathematics.
In 'Mathematics', in Henry Kiddle and Alexander J. Schem, The Cyclopedia of Education, (1877.) As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-book (1914), 27-29.
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