A History of European Thought in the Nineteenth Century

"The object of the book is philosophical, in the sense now accepted by many and by divergent schools—i.e., it desires to contribute something towards a unification of thought."

"Such a survey seemed to me indispensable. ...Like every survey it can claim to be merely an approximation. It gives outlines which closer scrutiny will have to correct and fill up."

"I... decided to complete the first part of the history which deals with scientific thought in two volumes..."

"The two last chapters of this volume, which treat of the astronomical and of the atomic views of Nature, will be followed in the second volume by similar chapters on the mechanical, the physical, the biological, the statistical, and the psychophysical views of Nature... it is my intention to close the first part of my subject by an attempt to trace concisely the development of mathematical thought in this century."

"One indeed to whom I am... more indebted, perhaps, than to any one else—whom to have known has meant, for many, a revelation of the power of mind and the reality of spirit—is no more: Ernst Curtius. ...But she who was nearest and dearest to him is still with us—a true priestess of the higher life, who has kept burning in the soul of many a youthful friend the spiritual fire when it was in danger of being quenched by the growing materialism of our age."

"Behind the panorama of external events and changes which history unfolds before our view there lies the hidden world of desires and motives, of passions and energies, which produced or accompanied them; behind the busy scenes of Life lie the inner regions of Thought."

"Only when facts and events cease to be unconnected, when they appear to us linked together according to some design and purpose, leading us back to some originating cause or forward to some defined end, can we speak of History... and similarly do the hidden motives, desires, and energies which underlie or accompany the external events require to be somehow connected, to present themselves in some order and continuity, before we are able to grasp and record them."

"Take away thought, and monotony becomes the order."

"Motion and change would be as monotonous as absolute rest, were they merely to repeat themselves endlessly, did the whole movement not produce something more, and were this something more not greater or better than the beginning. But greater and better are terms which imply comparison by a thinking beholder..."

"The pendulum which swings backwards and forwards in endless monotony, the planet which moves round the sun in unceasing repetition, the atom of matter which vibrates in the same path, have for us no interest beyond the mathematical formulae which govern their motions, and which permit us mentally to reproduce, i.e., to think them."

"As it was enough to point to the existence of the two worlds of Life and Thought, so it will be enough to notice that thought does not mean merely defined, clear, methodical thought, but likewise the great region of desire, impulse, feeling, and imagination, all of which play, we must admit, a great part in the inner life of the soul as well as in that of the outer world."

"As every person is his own best biographer, so... every age is... its own best historian."

"It is hardly doubtful that, after hundreds or thousands of years have passed, the simple, detailed, and perhaps contradictory, narratives of contemporary witnesses will outlive those more elaborate and artistic efforts of the historian which are so largely inspired and coloured by the convictions of another—viz., his own—age. For as Goethe has remarked: "History must from time to time be rewritten, not because many new facts have been discovered, but because new aspects come into view, because the participant in the progress of an age is led to standpoints from which the past can be regarded and judged in a novel manner.""

"Most of the great historians whom our age has produced will, centuries hence, probably be more interesting as exhibiting special methods of research, special views... than as faithful and reliable chroniclers of events; and the objectivity on which some of them pride themselves will be looked upon not as freedom from, but as unconsciousness on their part, of the preconceived notions which have governed them."

"But where the facts recorded and the mind which records them both belong to the same age, we have a double testimony regarding that age."

"Historians like Thucydides, Tacitus, and Machiavelli are looked upon as perfect models in the art of writing history, and the memoirs of many modern statesmen are more lastingly valuable than the more elaborate and connected narratives of remote and secluded scholars."

"A large portion of this hidden life is known only to those who have taken part in it. The vague yearnings of thousands who never succeed either in satisfying or expressing them, the hundreds of failures which never become known, the numberless desires which live only in the hearts of men or are painted only in their living features, the uncounted strivings after solutions of practical problems dictated by ambition or by want, the many hours spent by labourers of science in unsuccessful attempts to solve the riddles of nature,—all these hidden and forgotten efforts form indeed the bulk of a nation's thought, of which only a small fraction comes to the surface, or shows itself in the literature, science, poetry, art, and practical achievements of the age."

"This large body of forgotten thought has nevertheless been... the great propelling force which, stored up, awaits the time and aid of individual talent or genius to set it free."

"Philosophers tell us of the wastefulness of organic life, of the thousands of germs which perish, of the huge volume of seed scattered uselessly. A similar fate seems to fall on the larger portion of intellectual and moral effort; but here a deeper conviction tells us that it is not the sacrifice but the cooperation of the many which makes the few succeed, that excellence is the prize of united effort, that many must run so that one may reach a higher goal."

"We who live in the expectation of the light which is to come, surrounded by the shadows, difficulties, and obstacles; we who belong to the army, and are not leaders, who live in, not after, the fight,—we claim to be better able to tell the tale of endless hopes and endeavours, of efforts common to many, of the hidden intellectual and moral work of our age."

"Certain it is that in our parents and immediate forefathers we have known the representatives of a generation which witnessed and laboured in the interests of the great Anti-Slavery, the Reform, and the Anti-Corn Law movements, who experienced the revolutions worked by the introduction of steam-power and gas, who took part in the great work of national and popular education abroad and in the reform of school-life in England. They themselves went through the enthusiasm of the anti-Napoleonic Revolution in Germany, came under the influence of Goethe's mature manhood, were fascinated by the stories from the pen of the Wizard of the North, partook of the spirit of the Romantic School, felt the electrical touch of Lord Byron's verse, listened to the great orators of the third French Revolution, and could tell us of the now forgotten spell which Napoleon I exercised over millions of reluctant admirers."

"It is the object of these volumes to fix, if possible, this possession; to rescue from oblivion that which appears to me to be our secret property; in the last and dying hour of a remarkable age to throw the light upon the fading outlines of its mental life; to try to trace them, and with the aid of all possible information, gained from the written testimonies or the records of others, to work them into a coherent picture, which may give those who follow some idea of the peculiar manner in which our age looked upon the world and life, how it intellectualised and spiritualised them."

"Of European thought itself I am forced to select... only the central portion the thought embodied in French, German, and English Literature. ...languages unknown and interests foreign to me have made it impossible to identify myself ever so superficially with the new life that is contained in them."

"National peculiarities still exist, but are mainly to be sought in those remoter and more hidden recesses of thought, where the finer shades, the untranslatable idioms, of language suggest, rather than clearly express, a struggling but undefined idea. Thought has its dawn and twilight, its chiaroscuro as well as its open day; but the daylight has grown wider and clearer and more diffused in the course of our century, and so far as the greater volume of ideas is concerned, we can speak now of European thought, when at one time we should have had to distinguish between French, German, and English thought."

"At the end of the century no extension or analogue of the Newtonian gravitation formula has been generally accepted, and it still stands there as almost the only firmly established mathematical relation, expressive of a property of all matter, to which the progress of more than two centuries has added nothing, from which it has taken nothing away."

"The value, however, of all those partial attempts in another direction has been enormous; for with the aim of applying, extending, or modifying a rigorous mathematical formula, those philosophers have carried out a series of the most exact observations and measurements of physical quantities, very greatly extended our knowledge of natural phenomena and their mutual relations, and founded that general system of physical measurement which is now universally adopted. The names of Gauss and Weber stand out prominently as leaders in this work."

"Although no mathematical relation equal in value and definiteness to the gravitation formula marks the introduction of the Atomic theory in Chemistry, it nevertheless owes its success to similar qualities—viz., to the fact that it led natural philosophers to make definite measurements, and put exact research in the place of vague reasoning."

"We are... bound to attach the greatest importance to the preliminary step taken by Lavoisier, who is even more justly called the father of modern chemistry than Kepler is called the father of modern astronomy. The exact claims of Lavoisier to this important place in the history of chemistry have been variously stated: ...since his time, and greatly through his labours, the quantitative method has been established as the ultimate test of chemical facts; the principle of this method being the rule that in all changes of combination and reaction, the total weight of the various ingredients—be they elementary bodies or compounds—remains unchanged. The science of chemistry was thus established upon an exact, a mathematical basis. By means of this method Lavoisier, utilising and analysing the results gained by himself and others before him, notably those of Priestley, Cavendish, and Black, succeeded in destroying the older theory of combustion, the so-called phlogistic theory."

"In the time of Lavoisier, and preeminently through his exertions, this vague and unmeasurable principle phlogiston was eliminated from the laboratory and the textbooks: quantities took the place of indefinable qualities, and numerical determinations increased in frequency and accuracy. The vague phlogistic theory, which contained a germ of truth, but one which at that time could not be put into definite terms, had helped to gather up many valuable facts and observations: these were collected and restated in a new and precise language. It has been said that every science must pass through three periods of development. The first is that of presentiment, or faith; the second is that of sophistry; and the third is that of sober research."

"Liebig states the case somewhat more correctly when he says: "To investigate the essence of a natural phenomenon, three conditions are necessary: We must first study and know the phenomenon itself, from all sides; we must then determine in what relation it stands to other natural phenomena; and lastly, when we have ascertained all these relations, we have to solve the problem of measuring these relations and the laws of mutual dependence—that is, of expressing them in numbers. In the first period of chemistry, all the powers of men's minds were devoted to acquiring a knowledge of the properties of bodies; it was necessary to discover, observe, and ascertain their peculiarities. This is the alchemistical period. The second period embraces the determination of the mutual relations or connections of these properties; this is the period of phlogistic chemistry. In the third period, in which we now are, we ascertain by weight and measure and express in numbers the degree in which the properties of bodies are mutually dependent. The inductive sciences begin with the substance itself, then come just ideas, and lastly, mathematics are called in, and with the aid of numbers, complete the work.""

"In the study of inanimate nature, astronomy—the mechanics of the heavens—deals with the simplest relations; chemistry—the science of the changes which bodies undergo when being combined or separated—deals with the most complicated side of reality. Physics occupy an intermediate position, and thus we can also trace in the history of physical research the twofold influence of the astronomical method of inquiry on one side, and the chemical on the other."

"Jeremias Benjamin Richter—a name possessed of no popular celebrity—published in 1792 to 1794, in three parts, his "Stœchiometry," or the art of measuring chemical elements. From his data, Fischer calculated in 1802 the first table of chemical equivalents, taking sulphuric acid as the standard with the figure 1000."

"The conviction that chemical substances combine according to fixed and simple proportions gained ground on the Continent, chiefly during the discussion in which Proust finally disproved and defeated Berthollet's theory of chemical affinity; but it is to Dalton that the doctrine of fixed and multiple proportions is indebted for a consistent exposition. Dalton based it upon a mental representation which ever since has been the soul of all chemical reasoning."

"Dalton adopted what was known as the atomic view of matter. The conception of matter as made up of Independent particles, which for our means and methods prove not only indestructible but likewise indivisible... Combined with the Newtonian view that weight is a universal property of all matter, it made the two fundamental rules of chemical action intelligible: the two facts—first, that the total weight of substances remains always the same, be they combined in ever so many different ways; and secondly, that all substances, be they in large or in small quantities, combine with each other, or separate from each other, in definite and fixed proportions. This view could not be consistently maintained, except it was referred to the smallest particles into which matter is practically divisible: the figures expressing the combining numbers were viewed by Dalton as representing the relative weights of the actual atoms or elements of matter. That the ultimate particles of matter have definite weights is the reason why substances combine in fixed proportions, and why the combining weight of the compound is the sum of the combining weights of the constituents."

"Berzelius, ...by a great number of very accurate determinations confirmed inductively the correctness of Dalton's theory. And even more important than the confirmation of the theory was the great harvest of actual knowledge of the things and processes of nature which was collaterally gathered, whilst chemists were trying to prove or to refute existing opinions."

"The number of elements or simple bodies, which in Lavoisier's time hardly exceeded thirty, increased before the year 1830 to more than double: the number of new compounds, unknown before, has probably never been counted."

"We now live about as long after the reform of chemistry through Lavoisier and Dalton as Laplace lived after the reform of physical astronomy through Newton. But who could compare the state of chemistry at the present day with that of astronomy in the age of Laplace? There every step had tended to show that the one Newtonian formula sufficed to comprehend all cosmic phenomena; here, the simplification introduced by Dalton has had to give way to a series of modifications which have rendered the atomic theory one of the most complicated machineries ever introduced into science."

"Wollaston prophetically foretold that if once an accurate knowledge were gained of the relative weights of elementary atoms, philosophers would not rest satisfied with the determination of mere numbers, but would have to gain a geometrical conception of how the elementary particles were placed in space. Van't Hoff's 'La Chimie dans l'Espace'—published at Rotterdam in 1875—was the first practical realisation of this prophecy."

"In the gradual development and clearer definition of... conceptions a general rule of thought seems to have unconsciously guided philosophers probably more than in any other department of knowledge. It is the rule of simplicity. How the human mind should have arrived at the old formula of "simplex sigillum veri" [simplicity is the sign of truth] is difficult to understand on any other ground than that of convenience and expediency. The prevailing impression, indeed, which the world of phenomena makes on the mind of an unbiassed observer must be the very reverse of simplicity or unity of law and purpose. That, nevertheless, the knowledge of some simple relations in time, number, and space would enable the human intellect to acquire a considerable insight into the course of events and the order of Nature's processes must have come to philosophers as a kind of revelation, and it is not surprising that it came late in the course of civilisation."

"Nothing can have tended more in this direction than the success of the Newtonian gravitation formula, and of the simple laws of motion, which, at the time of the birth oi modern chemistry, stood firmly established as the key to all problems of physical astronomy. No wonder that men were on the look-out for correspondingly simple—perhaps analogous—relations in the world of molecular phenomena."

"The age... witnessed the decomposition of many compounds into their two constituents by Davy's successful use of the galvanic battery, at the poles of which the two elements of substances made their separate appearance. Substances which had always been considered as elemental and permanent, such as many oxides and earths, came to be ranged among the list of binary compounds. This lent plausibility to the idea that even the supposed elements themselves might ultimately prove to be aggregates—differing in number and figure—of the elementary particles of one and the same primary substance."

"The identity or difference of chemical substances seemed in the early part of the century to be fixed by the constituent elements and their quantitative proportions determined by a qualitative and quantitative analysis. This simple view had to be abandoned when Wöhler in 1823, Liebig in 1824, and Faraday in 1825 found that entirely different qualities, indicating a different constitution, could belong to bodies having the same elements in the same numerical proportions. ...It took forty years before the great variety of views which were brought forward with the purpose of explaining how composition and constitution of the same aggregate of elements might differ, could be approximately brought into line and order. This period was filled by the development of the chemistry of organic compounds."

"A new term had to be coined for those constituents which might comprise both elementary bodies and... primary compounds which behaved like elements in organic substances. This was the term "Radicle." A radicle might be an element or a compound. For a long time it was thought that these complex radicles, as distinguished from the elements, were produced mainly—if not exclusively—in the organism of the plant or of the animal. Liebig himself, who favoured this view, and who first brought organic chemistry in its application to agriculture and physiology under the notice of a large circle of readers, introduced this branch of the subject with the designation of the chemistry of compound radicles, inorganic or mineral chemistry being termed the chemistry of simple radicles."

"It was about the year 1840 that the idea of "substitution" entered the list of formula by which chemical philosophers attempted to systematise and simplify the ever growing number of definite compounds supplied mainly by organic analysis. It was found that one or more atoms in an organic compound, notably of hydrogen, might be replaced by an equal number of atoms of other elements, and that such products of substitution retained similar qualities, and could be mutually converted into each other, the type of the compound remaining the same."

"The process of substitution led to the conception of "Types," which remained the same whilst the individual compounds varied according to the different elements which were introduced."

"Whilst the Radicle theory of Berzelius and Liebig sought to simplify the study of chemical compounds by reducing them to a definite number of complex atoms the Type theory of Laurent and Gerhardt sought to attain the same object by establishing a small number of simple formulæ corresponding to well known simple substances under which the vast number of organic compounds could be grouped."

"The conception of a "type" exhibiting certain stable qualities with a multitude of varieties was a notion familiar to other branches of history. The idea of substituting one element for another gave the death-blow to the theory of Berzelius, which assumed that elements paired with each other, according to some polar contrast. It was found, for instance, that the element chlorine, which stood on one side of the scale—the electro-negative—could take the place of the opposite electro-positive element hydrogen."

"In the course of time the conception of types was much changed, and became more and more complicated; it had, however, the effect of finally destroying the binary view of chemical composition, and restoring in its place the older unitary conception."

"A variety of circumstances combined to bring into prominence, and subsequently into general acceptance, the modern view of the "atomicity" or "valency" of chemical substances—be they elements or compounds. This most recent development of chemical systematisation originated in England, whereas the "radicle" theory belonged more to the German, and the "type" theory to the French, school of chemists."

"The idea of the "atomicity" and "valency" or saturating capacity of the element of any substance was not possible without the clear notion of the "molecule" as distinct from the "atom." This idea had lain dormant in the now celebrated but long forgotten law of Avogadro, which was established in the year 1811, almost immediately after the appearance of Dalton's atomic theory."