History of the Inductive Sciences

History of the Inductive Sciences from the Earliest Times to the Present (1837) is one of William Whewell's two best-known works. It is his attempt to map and systematize the development of the sciences through time. Second and third editions were published in 1847 and in 1859. The last edition was published in two volumes, and the first two editions were published in three volumes.

• A very important advantage would be gained, if any light could be thrown upon the modes of discovering truth, the powers that we possess for this end, and the points to which these may most profitably be applied.

• The Great Reform of Philosophy and Method, in which Bacon so eloquently called upon men to unite their exertions in his day, has, even in ours, been very imperfectly carried into effect. And even if his plan had been fully executed, it would now require to be pursued and extended.

• If Bacon had weighed well all that Science had achieved in his time, and had laid down a complete scheme of rules for scientific research, so far as they could be collected from the lights of that age, it would still be incumbent upon the philosophical world to augment as well as preserve the inheritance which he left; by combining with his doctrines such new views as the advances of later times cannot fail to produce or suggest; and by endeavouring to provide, for every kind of truth, methods of research as effective as those to which we owe the clearest and surest portions of our knowledge. Such a renovation and extension of the reform of philosophy appears to belong peculiarly to our own time.

• The Novum Organon of Bacon was suitably ushered into the world by his Advancement of Learning; and any attempt to continue and extend his Reform of the Methods and Philosophy of Science may, like his, be most fitly preceded by, and founded upon, a comprehensive Survey of the existing state of human knowledge. The wish to contribute something, however little it may be, to such a Reform, gave rise to that study of the History of Science of which the present Work is the fruit.

• The effect of these researches has been, a persuasion, that we need not despair of seeing, even in our own time, a renovation of sound philosophy, directed by the light which the History of Science sheds. Such a reform, when its Epoch shall arrive, will not be the work of any single writer, but the result of the intellectual tendencies of the age.

• To balance... disadvantages, and to enable us to judge of the characters who must figure in our history, we may recollect that we have before us, not the record only of their actions, but the actions themselves, for the acts of a philosopher are his writings. We do not receive his exploits on tradition, but by sight; we do not read of him, we read him.

• Having... lived with some of the great intellects of the past and the present, I had found myself capable of rejoicing in their beauties, of admiring their endowments, and, I trusted, also, of understanding their discoveries and views, their hopes and aims. I did not, therefore, turn aside from the responsibility which the character of the Historian of Science imposed upon me.

• I trusted... that my study of the philosophers of former times had enabled me to appreciate the discoveries of the present, and that I should be able to speak of persons now alive, with the same impartiality and in the same spirit as if they were already numbered with the great men of the past. Seeking encouragement in these reflections, and in the labour and thought which I was conscious of having bestowed upon my task, I have conducted my history from the earliest ages of the speculative world up to our own days.

• If there be branches of knowledge which regard Morals, or Politics, or the Fine Arts, and which may properly be called Inductive (an opinion which I by no means gainsay); still it must be allowed, I think, that the processes of collecting general truths from assemblages of special facts, and of ascending from propositions of a limited to those of a larger generality, which the term Induction peculiarly implies, have hitherto been far more clearly exhibited in the physical sciences which form the subject of the present work, than in those hyper physical sciences to which I have not extended my history.

• All who venture upon such tasks [as this work] must gather trust and encouragement from reflections like those by which their great forerunner prepared himself for his endeavours;—by recollecting that they are aiming to advance the best interests and privileges of man; and that they may expect all the best and wisest of men to join them in their aspirations and to aid them in their labours. "Concerning ourselves we speak not; but as touching the matter which we have in hand, this we ask;—that men deem it not to be the setting up of an Opinion, but the performing of a Work; and that they receive this as a certainty; that we are not laying the foundations of any sect or doctrine, but of the profit and dignity of mankind:—Furthermore, that being well disposed to what shall advantage themselves, and putting off factions and prejudices, they take common counsel with us, to the end that being by these our aids and appliances freed and defended from wanderings and impediments, they may lend their hands also to the labours which remain to be performed:—And yet, further, that they be of good hope; neither feign and imagine to themselves this our Reform as something of infinite dimension and beyond the grasp of mortal man, when, in truth, it is of infinite errour, the end and true limit; and is by no means unmindful of the condition of mortality and humanity, not confiding that such a thing can be carried to its perfect close in the space of one single age, but assigning it as a task to a succession of generations."
  • Quoting Francis Bacon's Preface to The Great Instauration

• The attempt to throw the histories of all the Sciences into Inductive Epochs, each Epoch having its Prelude and its Sequel, and thus to combine the persons and the events which fill these histories into intelligible groups, was so far as I know, new.

• The Epochs here marked out, are the cardinal points of scientific history.

• The main object of the work was to present such a survey of the advances already made in physical knowledge, and of the mode in which they have been made, as might serve as a real and firm basis for our speculations concerning the progress of human knowledge, and the processes by which sciences are formed. And an attempt to frame such speculations on this basis was made in the Philosophy of the Inductive Sciences, which was published shortly after this History. To that work I must refer, for a further explanation of any views respecting the nature and progress of science which may here appear defective or obscure.

• The completeness of historical view... consists, not in accumulating all the details of the cultivation of each science, but in marking clearly the larger features of its formation.

• The present generation finds itself the heir of a vast patrimony of science; and it must needs concern us to know the steps by which these possessions were acquired, and the documents by which they are secured to us and our heirs for ever.

• Our species, from the time of its creation, has been travelling onwards in pursuit of truth; and now that we have reached a lofty and commanding position, with the broad light of day around us, it must be grateful to look back on the line of our past progress;—to review the journey.

• The eminence on which we stand may enable us to see the land of promise, as well as the wilderness through which we have passed.

• The examination of the steps by which our ancestors acquired our intellectual estate, may make us acquainted with our expectations as well as our possessions;—may not only remind us of what we have, but may teach us how to improve and increase our store.

• It is not possible, without entering into... philosophy, to explain adequately how science which is Inductive differs from that which is not so; or why some portions of knowledge may properly be selected from the general mass and termed Science. It will be sufficient at present to say, that the sciences of which we have here to treat, are those which are commonly known as the Physical Sciences; and that by Induction is to be understood that process of collecting general truths from the examination of particular facts, by which such sciences have been formed.

• To the formation of science, two things are requisite;—Facts and Ideas; observation of Things without, and an inward effort of Thought; or, in other words, Sense and Reason. Neither of these elements, by itself, can constitute substantial general knowledge.

• The impressions of sense, unconnected by some rational and speculative principle, can only end in a practical acquaintance with individual objects; the operations of the rational faculties, on the other hand, if allowed to go on without a constant reference to external things, can lead only to empty abstraction and barren ingenuity.

• Real speculative knowledge demands the combination of the two ingredients;—right reason, and facts to reason upon.

• True knowledge is the interpretation of nature; and thus it requires both the interpreting mind, and nature for its subject; both the document, and the ingenuity to read it aright.

• Invention, acuteness, and connexion of thought, are necessary on the one hand, for the progress of philosophical knowledge; and on the other hand, the precise and steady application of these faculties to facts well known and clearly conceived. It is easy to point out instances in which science has failed to advance, in consequence of the absence of one or other of these requisites; indeed, by far the greater part of the course of the world, the history of most times and most countries, exhibits a condition thus stationary with respect to knowledge.

• We have no lack of proof that mere activity of thought is... inefficient in producing real knowledge. Almost the whole of the career of the Greek schools of philosophy; of the schoolmen of Europe in the middle ages; of the Arabian and Indian philosophers; shows us that we may have extreme ingenuity and subtlety, invention and connexion, demonstration and method; and yet that out of these germs, no physical science may be developed. We may obtain, by such means, logic and metaphysics, and even geometry and algebra; but out of such materials we shall never form mechanics and optics, chemistry and physiology. How impossible the formation of these sciences is without a constant and careful reference to observation and experiment;—how rapid and prosperous their progress may be when they draw from such sources the materials on which the mind of the philosopher employs itself;—the history of those branches of knowledge for the last three hundred years abundantly teaches us.

• Whenever any material step in general knowledge has been made,—whenever any philosophical discovery arrests our attention;—some man or men came before us, who have possessed, in an eminent degree, a clearness of the ideas which belong to the subject in question, and who have applied such ideas in a vigorous and distinct manner to ascertained facts and exact observations. We shall never proceed through any considerable range of our narrative, without having occasion to remind the reader of this reflection.

• Such sciences as we have here to do with, are, commonly, not formed by a single act;—they are not completed by the discovery of one great principle. On the contrary, they consist in a long-continued advance; a series of changes; a repeated progress from one principle to another, different and often apparently contradictory. Now it is important to remember that this contradiction is apparent only.

• The principles which constituted the triumph of the preceding stages of the science, may appear to be subverted and ejected by the later discoveries, but in fact they are, (so far as they were true,) taken up into the subsequent doctrines and included in them. They continue to be an essential part of the science.

• The earlier truths are not expelled but absorbed, not contradicted but extended; and the history of each science, which may thus appear like a succession of revolutions, is, in reality, a series of developements.

• In the intellectual, as in the material world,—
  
  Omnia mutantur nil interit...
  Nee manet ut fuerat nee formas servat easdem,
  Sed tamen ipsa eadem est.
  
  All changes, nought is lost; the forms are changed,
  And that which has been, is not what it was,
  Yet that which has been, is.
  
  Nothing which was done was useless or unessential, though it ceases to be conspicuous and primary.
  • Refer to Ovid, Metamorphoses Lib. XV. 153-237

• The final form of each science contains the substance of each of its preceding modifications; and all that was at any antecedent period discovered and established, ministers to the ultimate developement of its proper branch of knowledge. Such previous doctrines may require to be made precise and definite, to have their superfluous and arbitrary portions expunged, to be expressed in new language, to be taken up into the body of science by various processes;—but they do not on such accounts cease to be true doctrines, or [cease] to form a portion of the essential constituents of our knowledge.

• We shall frequently have to notice the manner in which great discoveries... stamp their impress upon the terms of a science; and like great political revolutions, are recorded by the change of the current coin which has accompanied them.

• The great changes which... take place in the history of science, the revolutions of the intellectual world... are steps of generalization;—transitions from particular truths to others of a wider extent, in which the former are included. This progress of knowledge, from individual facts to universal laws,—from particular propositions to general ones,—and from these to others still more general...—is so far familiar to men's minds, that... its nature will be understood sufficiently to prepare the reader to recognise the exemplifications of such a process, which he will find at every step of our advance.

• It is the progress of knowledge only which we have to attend to. ...Our narrative will therefore consist mainly of successive steps of generalization.

• Primary movements, when the Inductive process, by which science is formed, has been exercised in a more energetic and powerful manner, may be distinguished as the Inductive Epochs of scientific history; and they deserve our more express and pointed notice. They are, for the most part, marked by the great discoveries and the great philosophical names which all civilized nations have agreed in admiring. But... we find that these epochs have not occurred suddenly and without preparation. They have been preceded by a period, which we may call their Prelude, during which the ideas and facts on which they turned were called into action;—were gradually evolved into clearness and connexion, permanency and certainty; till at last the discovery which marks the Epoch, seized and fixed for ever the truth which had till then been obscurely and doubtfully discerned.

• There may generally be observed another period, which we may call the Sequel of the Epoch, during which the discovery has acquired a more perfect certainty and a more complete developement among the leaders of the advance; has been diffused to the wider throng of the secondary cultivators of such knowledge, and traced into its distant consequences. This is a work, always of time and labour, often of difficulty and conflict.

• To distribute the History of science into such Epochs, with their Preludes and Sequels... must needs make the series and connexion of its occurrences more distinct and intelligible. Such periods form resting-places, where we pause till the dust of the confused march is laid, and the prospect of the path is clear.

• We might form a Chart, or Table, of the progress of each science, by setting down the particular facts which have thus been combined, so as to form general truths, and by marking the further union of these general truths into others more comprehensive. The Table of the progress of any science would thus resemble the Map of a River, in which the waters from separate sources unite and make rivulets... and thus go on forming by their junction trunks of a higher and higher order. ...the last and most advanced generalization would have in such a scheme its proper place and the evidence of its validity. ...no merely arbitrary division of the events could satisfy such conditions.

• Though I have constructed... charts to direct the course of the present history, I shall not insert them in the work, reserving them for the illustration of the philosophy of the subject; for to this they more properly belong, being a part of the Logic of Induction.

• In order to understand the conditions of the progress of knowledge, we must attend, in some measure, to the failures as well as the successes by which such attempts have been attended.

• When we reflect during how small a portion of the whole history of human speculations, science has really been, in any marked degree, progressive, we must needs feel some curiosity to know what was doing in these stationary periods; what field could be found which admitted of so wide a deviation, or at least so protracted a wandering.

• It is highly necessary to our purpose, to describe the baffled enterprises as well as the achievements of human speculation.

• During a great part of... stationary periods we shall find that the process which we have spoken of as essential to the formation of real science, the conjunction of clear ideas with distinct facts, was interrupted; and, in such cases, men dealt with ideas alone.

• This process of drawing conclusions from our principles, by rigorous and unimpeachable trains of demonstration, is termed Deduction. In its due place, it is a highly important part of every science; but it has no value when the fundamental principles, on which the whole of the demonstration rests, have not first been obtained by the induction of facts, so as to supply the materials of substantial truth. Without such materials, a series of demonstrations resembles physical science only as a shadow.

• To give a real significance to our propositions, Induction must provide what Deduction cannot supply. From a pictured hook we can hang only a pictured chain.

• Scientific Ideas and common Notions differ in this, that the former are precise and stable, the latter vague and variable; the former are possessed with clear insight, and employed in a sense rigorously limited, and always identically the same; the latter have grown up in the mind from a thousand dim and diverse suggestions, and the obscurity and incongruity which belongs to their origin hangs about all their applications.

• All attempts to reason by means of Definitions from common Notions, lead to empty forms or entire confusion.

• The mind cannot but claim a right to speculate concerning all its own acts and creations; yet, when it exercises this right upon its common practical notions, we find that it runs into barren abstractions and ever recurring cycles of subtlety. Such Notions are like waters naturally stagnant; however much we urge and agitate them, they only revolve in stationary whirlpools.

• When our speculations are duly fed from the spring-heads of observation, and frequently drawn off into the region of applied science, we may have a living stream of consistent and progressive knowledge. That science may be both real as to its import, and logical as to its form, the examples of many existing sciences sufficiently prove.

• I do not include in the phrase "Inductive Sciences," the branches of Pure Mathematics, (Geometry, Arithmetic, Algebra, and the like,) because as I have elsewhere stated these are not Inductive but Deductive Sciences: they do not infer true theories from observed facts, and more general from more limited laws: but they trace the conditions of all theory, the properties of space and number; and deduce results from ideas without the aid of experience.
  • Notes to the Introduction

• All the first attempts to comprehend the operations of nature, led to the introduction of abstract conceptions, often vague, indeed, but not, therefore, unmeaning... And the next step in philosophizing, necessarily was to endeavour to make these vague abstractions more clear and fixed, so that the logical faculty should be able to employ them securely and coherently. But there were two ways of making this attempt; the one, by examining the words only, and the thoughts which they call up; the other, by attending to the facts and things which bring these abstract terms into use. The latter, the method of real inquiry, was the way to success; but the Greeks followed the former, the verbal or notional course, and failed.

• They ought to have collected clear Fundamental Ideas from the world of things by inductive acts of thought; they only derived results by Deduction from one or other of their familiar Conceptions.

• The physical philosophy of the Greek Schools was formed by looking at the material world through the medium of that common language which men employ to answer the common occasions of life... adopting, arbitrarily... notions more abstract and large than those with which men are practically familiar, but not less vague and obscure. Such a philosophy, however much it might be systematized, by classifying and analyzing the conceptions which it involves, could not overcome the vices of its fundamental principle.

• Thales, the founder of Greek philosophy... When he was asked "What is the greatest thing?" he replied, "Place; for all other things are in the world, but the world is in it. In Aristotle we have the consummation of this mode of speculation. ...Proceeding then to the question of a void, he, as usual, examines the different senses in which the term is used, and adopts, as the most proper, place without matter; with no useful result.

• Again, we find the Greek philosophers applying themselves to extract their dogmas from the most general and abstract notions which they could detect; for example,—from the conception of the Universe as One or as Many things. They tried to determine how far we may, or must, combine with these conceptions that of a whole, of parts, of number, of limits, of place, of beginning or end, of full or void, of rest or motion, of cause and effect, and the like. The analysis of such conceptions with such a view, occupies, for instance, almost the whole of Aristotle's Treatise on the Heavens.

• The Dialogue of Plato, which is entitled Parmenides, appears at first as if its object were to show the futility of this method of philosophizing; for... arguing with an Athenian named Aristotle, and, by a process of metaphysical analysis, reducing him at least to this conclusion, "that whether One exist, or do not exist, it follows that both it and other things, with reference to themselves and to each other, all and in all respects, both are and are not, both appear and appear not." Yet the method of Plato, so far as concerns truth of that kind with which we are here concerned, was little more efficacious than that of his rival. It consists mainly,... and especially in the Timæus, in the application of notions as loose as those of the Peripatetics; for example, the conceptions of the Good, the Beautiful, the Perfect; and these are rendered still more arbitrary, by assuming an acquaintance with the views of the Creator of the universe. The philosopher is thus led to maxims which agree with those of the Aristotelians, that there can be no void, that things seek their own place, and the like.

• Another mode of reasoning... was the doctrine of contrarieties, in which it was assumed, that adjectives or substantives which are in common language, or in some abstract mode of conception, opposed to each other, must point to some fundamental antithesis in nature, which it is important to study. Thus Aristotle says, that the Pythagoreans, from the contrasts which number suggests, collected ten principles,—Limited and Unlimited, Odd and Even, One and Many, Right and Left, Male and Female, Rest and Motion, Straight and Curved, Light and Darkness, Good and Evil, Square and Oblong. ...Aristotle himself deduced the doctrine of Four Elements, and other dogmas, by oppositions of the same kind.

• Such a mode of discussion as this, led to no [physical] truths of real or permanent value. The whole mass of the Greek philosophy... shrinks into an almost imperceptible compass, when viewed with reference to the progress of physical knowledge.

• It is said, that Alexander the Great wrote to his former tutor to this effect; "You have not done well in publishing these lectures; for how shall we, your pupils, excel other men, if you make that public to all, which we learnt from you." To this Aristotle is said to have replied; "My Lectures are published and not published; they will be intelligible to those who heard them, and to none beside." This may very easily be a story invented and circulated among those who found the work beyond their comprehension; and it cannot be denied, that to make out the meaning and reasoning of every part, would be a task very laborious and difficult, if not impossible.

• The progress made by the ancients in Optics was nearly proportional to that which they made in Statics. As they discovered the true grounds of the doctrine of Equilibrium, without obtaining any sound principles concerning Motion, so they discovered the law of the Reflection of light, but had none but the most indistinct notions concerning Refraction.

• They knew that vision is performed by rays which proceed in straight lines, and that these rays are reflected by certain surfaces (mirrors) in such manner that the angles which they make with the surface on each side are equal. They drew various conclusions from these premises by the aid of geometry; as for instance the convergence of rays which fall on a concave speculum.

• We are told in the Proem [of Euclid's Treatise on Optics], "In explaining what concerns the sight, he adduced certain arguments from which he inferred that all light is carried in straight lines. The greatest proof of this is shadows, and the bright spots which are produced by light coming through windows and cracks.

• Euclid, and the Platonists, maintained that vision is exercised by rays proceeding from the eye, not to it; so that when we see objects, we learn their form as a blind man would do, by feeling it out with his staff. This mistake, however... was neither very discreditable nor very injurious; for the mathematical conclusions on each supposition are necessarily the same.

• Another curious, and false assumption is, that these visual rays [emanating from the eyes] are not close together, but separated by intervals, like the fingers when the hand is spread. The motive for this invention was the wish to account for the fact, that in looking for a small object, as a needle, we often cannot see it when it is under our nose; which it was conceived would be impossible if the visual rays reached to all points of the surface before us.

• Aristotle's views led him to try to describe the kind of causation by which vision is produced, instead of the laws by which it is exercised; and the attempt consisted, as in other subjects, of indistinct principles, and ill-combined facts.

• According to [Aristotle], vision must be produced by a Medium,—by something between the object and the eye,—for if we press the object on the eye, we do not see it; this Medium is Light, or "the transparent in action."

• [A] new and peculiar element was introduced into the Greek philosophy which occupied the attention of the Alexandrian school; and... this element tinged a large portion of the speculations of succeeding ages. We may speak of this peculiar element as Mysticism.
  • Ch.3 Of the Mysticism of the Middle Ages

• [I]nstead of referring the events of the external world to space and time, to sensible connexion and causation, men attempted to reduce such occurrences under spiritual and supersensual relations and dependencies; they referred them to superior intelligences, to theological conditions, to past and future events in the moral world, to states of mind and feelings, to the creatures of an imaginary mythology or demonology. And thus their physical Science became Magic, their Astronomy became Astrology, the study of the Composition of bodies became Alchemy, Mathematics became the contemplation of the Spiritual Relations of number and figure, and Philosophy became Theosophy. ...By its direct operation it gave rise to the newer Platonic philosophy among the Greeks, and to corresponding doctrines among the Arabians; and by calling into a prominent place astrology, alchemy, and magic, it long occupied most of the real observers of the material world. In this manner it delayed and impeded the progress of true science...

• [H]uman knowledge lost more by the perversion of men's minds and the misdirection of their efforts, than it gained by any increase of zeal arising from the peculiar hopes and objects of the mystics.

• Some of its [mysticism's] characters... illustrate those tendencies of thought which accompanied the retrogradation of inductive science. And of these, the leading feature which demands our notice is... the practice of referring things and events not to clear and distinct relations obviously applicable to such cases;—not to general rules capable of direct verification; but to notions vague, distant, and vast, which we cannot bring into contact with facts, because they belong to a different region from the facts; as when we connect natural events with moral or historical causes, or seek spiritual meanings in the properties of number and figure.

• The character of Mysticism is, that it refers particulars, not to generalizations homogeneous and immediate, but to such as are heterogeneous and remote; to which we must add, that the process of this reference is not a calm act of the intellect, but is accompanied with a glow of enthusiastic feeling.

• The Newer Platonism is the... doctrine of an Intellectual World resulting from the act of the Divine Mind, as the only reality; and the aspiration after the union of the human soul with this Divine Mind, as the object of human existence.

• The "Ideas" of Plato were forms of our knowledge; but among the Neoplatonists they became... the only really existing, objects; and the inaccessible scheme of the universe which these ideas constitute, was offered as the great subject of philosophical contemplation. The desire of the human mind to approach towards its Creator and Preserver, and to obtain a spiritual access to Him, leads to an employment of the thoughts which is well worth the notice of the religious philosopher; but such an effort, even when founded on revelation and well regulated, is not a means of advance in physics: and when it is the mere result of natural enthusiasm, it may easily obtain such a place in men's minds as to unfit them for the successful prosecution of natural philosophy.

• The temper... which introduces... supernatural communion into the general course of its speculations, may be properly treated as mystical, and as one of the causes of the decline of science in the Stationary Period.

• "Plotinus, the philosopher of our time," Porphyry thus begins his biography, "appeared like a person ashamed that he was in the body. In consequence of this disposition, he could not bear to talk concerning his family, or his parents, or his country. He would not allow himself to be represented by a painter or statuary; and... said, 'Is it not enough for us to carry this image in which nature has enclosed us, but we must also try to leave a more durable image of this image, as if it were so great a sight?'... When he was dying he said, 'I am trying to bring the divinity which is in us to the divinity which is in the universe." He was looked upon by his successors with extraordinary admiration and reverence; and his disciple Porphyry collected... the six Enneads of his doctrines... which he arranged and annotated.

• To the Intelligible World, man's mind ascends, by a triple road which Plotinus figuratively calls that of the Musician, the Lover, the Philosopher. The activity of the human soul is identified by analogy with the motion of the heavens. "This activity is about a middle point, and thus it is circular... and as the sphere revolves about its center, the soul revolves about God through its affections."

• The conclusion of the work [Enneads] is... upon the approach to, union with, and fruition of God. The author refers again to the analogy between the movements of the soul and those of the heavens. "We move round him like a choral dance; even when we look from him we revolve about him; we do not always look at him, but when we do, we have satisfaction and rest, and the harmony which belongs to that divine movement. In this movement, the mind beholds the fountain of life, the fountain of mind, the origin of being, the cause of good, the root of the soul. ...There will be a time when this vision shall be continual; the mind being no more interrupted, nor suffering any perturbation from the body. Yet that which beholds is not that which is disturbed; and when this vision becomes dim, it does not obscure the knowledge which resides in demonstration, and faith, and reasoning; but the vision itself is not reason, but greater than reason, and before reason."

• The fifth book of the third Ennead, has for its subject the Daemon which belongs to each man. It is entitled "Concerning Love;" and the doctrine appears to be, that the Love, or common source of the passions which is in each man's mind, is "the Daemon which they say accompanies each man." ...This imagination soon produced pretensions to the power of making these daemons or genii visible.

• It is unnecessary for us to dwell on the... growth of the Theurgy which thus arose or to describe the attempts to claim a high antiquity for this system, and to make Orpheus, the poet, the first promulgator of its doctrines. The system, like all mystical systems, assumed the character rather of a religion than of a theory. The opinions of its disciples materially influenced their lives. It gave the world the spectacle of an austere morality, a devotional exaltation, combined with the grossest superstitions of Paganism. The successors of Iamblichus appeared rather to hold a priesthood, than the chair of a philosophical school. They were persecuted by Constantine and Constantius, as opponents of Christianity.

• Proclus was one of the greatest of the teachers of this school; and was both in his life and doctrines, a worthy successor of Plotinus, Porphyry, and Iamblichus. We possess a... panegyric of him by his disciple Marinus, in which he is exhibited as a representation of the ideal perfection of the philosophic character, according to the views of the Neoplatonists. ... He appears before us rather as a hierophant than a philosopher. A large portion of his life was spent in evocations, purifications, fastings, prayers, hymns, intercourse with apparitions, and with the gods, and in the celebration of the festivals of Paganism, especially those which were held in honour of the Mother of the Gods. His religious admiration extended to all forms of mythology. The philosopher, said he, is not the priest of a single religion, but of all the religions in the world. Accordingly, he composed hymns in honour of all the divinities of Greece, Rome, Egypt, Arabia;—Christianity alone was excluded from his favour.

• Mystical Arithmetic... Like all the kinds of Mysticism, this consists in the attempt to connect our conceptions of external objects by general and inappropriate notions of goodness, perfection, and relation to the divine essence and government; instead of referring such conceptions to those appropriate ideas, which, by due attention, become perfectly distinct, and capable of being positively applied and verified.

• Number... tempts men into these visionary speculations more naturally than any other. For number is really applicable to moral notions,—to emotions and feelings, and to their objects,—as well as to the things of the material world. Moreover, by the discovery of the principle of musical concords, it had been found, probably most unexpectedly, that numerical relations were closely connected with sounds which could hardly be distinguished from the expression of thought and feeling; and a suspicion might easily arise, that the universe, both of matter and of thought, might contain many general and abstract truths of some analogous kind. The relations of number have so wide a bearing, that the ramifications of such a suspicion could not easily be exhausted, supposing men willing to follow them into darkness and vagueness; which it is precisely the mystical tendency to do.

• [T]his kind of speculation appeared very early, and showed itself first among the Pythagoreans, as we might have expected from the attention which they gave to the theory of harmony: and this, as well as some other of the doctrines of the Pythagorean philosophy, was adopted by the later Platonists, and indeed by Plato himself, whose speculations concerning number have decidedly a mystical character.

• The mere mathematical relations of numbers,—as odd and even, perfect and imperfect, abundant and defective,—were, by a willing submission to an enthusiastic bias, connected with the notions of good and beauty, which were suggested by the terms expressing their relations; and principles resulting from such a connexion were woven into a wide and complex system.

• Archytas is said to have written a treatise on the number ten: Telaugé, the daughter of Pythagoras, wrote on the number four. This number... known by the name of the Tetractys, was very celebrated in the school of Pythagoras. It is mentioned in the "Golden Verses," which are ascribed to him: the pupil is conjured to be virtuous...
  By him who stampt The Four upon the mind,
  The Four, the fount of nature's endless stream.
  In Plato's works we have evidence of a similar belief in religious relations of Number; and in the New Platonists this doctrine was established as a system.

• Proclus... founds his philosophy, in a great measure, on the relation of Unity and Multiple; from this, he is led to represent the causality of the Divine Mind by three Triads of abstractions; and in the developement of one part of this system, the number seven is introduced. "The intelligible and intellectual gods produce all things triadically; for the monads in these latter are divided according to number; and what the monad was in the former, the number is in these latter. And the intellectual gods produce all things hebdomically; for they evolve the intelligible, and at the same time intellectual triads, into intellectual hebdomads, and expand their contracted powers into intellectual variety."

• Seven is what is called by arithmeticians a prime number, that is, it cannot be produced by the multiplication of other numbers. In the language of the New Platonists, the number seven is said to be a virgin, and without a mother, and it is therefore sacred to Minerva. The number six is a perfect number, and is consecrated to Venus.
  • Ch.3 Of the Mysticism of the Middle Ages, Sect.2 Mystical Arithmetic

• The relations of space were dealt with in like manner, the geometrical properties being associated with such physical and metaphysical notions as vague thought and lively feeling could anyhow connect with them. We may consider, as an example of this, Plato's opinion concerning the particles of the four elements. He gave to each kind of particle one of the five regular solids, about which, the geometrical speculations of himself and his pupils had been employed. The particles of fire were pyramids, because they are sharp, and tend upwards; those of earth are cubes, because they are stable, and fill space; the particles of air are octahedral, as most nearly resembling those of fire; those of water are icositetrahedron, as most nearly spherical. The dodecahedron is the figure of the element of the heavens, and shows its influence in other things, as in the twelve signs of the zodiac. In such examples we see how loosely space and number are combined or confounded by these mystical visionaries.

• Like other kinds of Mysticism, Alchemy seems to have grown out of the notions of moral, personal, and mythological qualities, which men associated with terms, of which the primary application was to physical properties. This is the form in which the subject is presented to us in the earliest writings... those of Geber of Seville, who is supposed to have lived in the eighth or ninth century.

• The very titles of Geber's works show the notions on which this pretended science proceeds. They are, "Of the Search of Perfection;" "Of the Sum of Perfection, or of the Perfect Magistery;" "Of the Invention of Verity, or Perfection." The basis of this phraseology is the distinction of metals into more or less perfect; gold being the most perfect, as being the most valuable, most beautiful, most pure, most durable; silver the next; and so on. The "Search of Perfection," was, therefore, the attempt to convert other metals into gold; and doctrines were adopted which represented the metals as all compounded of the same elements, so that this was theoretically possible.

• But the mystical trains of association were pursued much further than this; gold and silver were held to be the most noble of metals; gold was their King, and silver their Queen. Mythological associations were called in aid of these fancies, as had been done in astrology.

• Gold was Sol, the sun; silver was Luna, the moon; copper, iron, tin, lead, were assigned to Venus, Mars, Jupiter, Saturn.

• The processes of mixture and heat were spoken of as personal actions and relations, struggles and victories. Some elements were conquerors, some conquered; there existed preparations which possessed the power of changing the whole of a body into a substance of another kind: these were called magisteries.

• When gold and quicksilver are combined, the king and the queen are married, to produce children of their own kind. It will easily be conceived, that when chemical operations were described in phraseology of this sort, the enthusiasm of the fancy would be added to that of the hopes, and observation would not be permitted to correct the delusion, or to suggest sounder and more rational views.

to the 1837 edition

• We enter now upon a new region of the human mind. In passing from Astronomy to Mechanics we make a transition from the formal to the physical sciences;—from time and space to force and matter;—from phenomena to causes.

• [W]e must consider the history of the speculations concerning motion in general, terrestrial as well as celestial.

• In the same way in which the developement of Pure Mathematics which began with the Greeks, was a necessary condition of the progress of Formal Astronomy, the creation of the science of Mechanics now became necessary to the formation and progress of Physical Astronomy.

• Geometry and Mechanics were cultivated for their own sakes; but they also supplied ideas, language, and reasoning to other sciences. If the Greeks had not cultivated Conic Sections, Kepler could not have superseded Ptolemy; if the Greeks had cultivated Dynamics, Kepler might have anticipated Newton.

—Central Forces

• The reader will recollect that we are here speaking of the Principia as a mechanical treatise only... As a work on dynamics, its merit is, that it contains a wonderful store of refined and beautiful mathematical artifices, applied to solve all the most general problems which the subject offered. It can hardly be said to contain any new inductive discovery respecting the principles of mechanics; for though Newton's "Axioms or Laws of Motion," which stand at the beginning of the book, are a much clearer and more general statement of the grounds of mechanics than had yet appeared, it can hardly be said that they contain any doctrines which had not been previously stated or taken for granted by other mathematicians.

• We have now to contemplate the last and most splendid period of the progress of Astronomy... the first great example of a wide and complex assemblage of phenomena indubitably traced to their single simple cause... the first example of the formation of a perfect Inductive Science.
  • Ref: Bacon, "Description of the Intellectual Globe" Vol. ix, p. 221.

• In his attempts to suggest a right physical view of the starry heavens and their relation to the earth, Bacon failed, along with all the writers of his time. ...[T]he main cause of this failure was the want of a knowledge of the true theory of motion;—the non-existence of the science of Dynamics.

• At the time of Bacon and Kepler, it was only just beginning to be possible to trace the heavenly motions to the laws of earthly motion, because the [laws] were only just then divulged. Accordingly, we have seen that the whole of Kepler's physical speculations proceed upon an ignorance of the first law of motion, and assume it to be the main problem of the physical astronomer to assign the cause which keeps up the motions of the planets.

• Kepler's doctrine is, that a certain Force or Virtue resides in the sun, by which all bodies within his influence are carried round him. He illustrates the nature of this Virtue in various ways, comparing it to Light, and to the Magnetic Power, which it resembles in the circumstances of operating at a distance, and also in exercising a feebler influence as the distance becomes greater.

• But it was obvious that these comparisons were very imperfect; for they do not explain how the sun produces in a body at a distance a motion athwart the line of emanation; and though Kepler introduced an assumed rotation of the sun on his axis as the cause of this effect, that such a cause could produce the result could not be established by any analogy of terrestrial motions.

• But another image to which [Kepler] referred, suggested a much more substantial and conceivable kind of mechanical action by which the celestial motions might be produced, namely, a current of fluid matter circulating round the sun, and carrying the planet with it, like a boat in a stream. In the Table of Contents of the work on the planet Mars, the purport of the chapter... is stated... "A physical speculation, in which it is demonstrated that the vehicle of that Virtue which urges the planets, circulates through the spaces of the universe after the manner of a river or whirlpool (vortex,) moving quicker than the planets." ...Kepler's phrases concerning the moving force,—the magnetic nature,—the immaterial virtue of the sun... convey no distinct conception, except so far as they are interpreted by the expressions just quoted. A vortex of fluid constantly whirling round the sun, kept in this whirling motion by the rotation of the sun himself, and carrying the planets round the sun by its revolution, as a whirlpool carries straws, could be readily understood; and though it appears to have been held by Kepler that this current and vortex was immaterial, he ascribes to it the power of overcoming the inertia of bodies, and of putting them and keeping them in motion, the only material properties with which he had anything to do.

• Nor... was it easy for any one at Kepler's time to devise a more plausible theory than the theory of vortices... It was only with the formation and progress of the science of mechanics that this theory became untenable.

• But if Kepler might be excused, or indeed admired, for propounding the theory of vortices at his time, the case was different when the laws of motion had been fully developed, and when those who knew the state of mechanical science ought to have learned to consider the motions of the stars as a mechanical problem, subject to the same conditions as other mechanical problems, and capable of the same exactness of solution. And there was an especial inconsistency in the circumstance of the Theory of Vortices being put forwards by Descartes, who pretended, or was asserted by his admirers, to have been one of the discoverers of the true laws of motion. It... shows both great conceit and great shallowness, that he should have proclaimed with much pomp this crude invention of the ante-mechanical period, at the time when the best mathematicians of Europe, as Borelli in Italy, Hooke and Wallis in England, Huyghens in Holland, were patiently labouring to bring the mechanical problem of the universe into its most distinct form, in order that it might be solved at last and for ever.

• I do not mean to assert that Descartes borrowed his doctrines from Kepler, or from any of his predecessors; for the theory was sufficiently obvious...

Discovery of the Universal Gravitation of Matter, According to the Law of the Inverse Square of the Distance.

• Reflections on the Discovery.—Such, then, is the great Newtonian induction of universal gravitation, and such its history. It is indisputably and incomparably the greatest scientific discovery ever made, whether we look at the advance which it involved, the extent of the truth disclosed, or the fundamental and satisfactory nature of this truth.

• Galvani appears never to have acquired much general knowledge of electricity: Volta, on the other hand, had laboured at this branch of knowledge from the age of eighteen, through a period of nearly thirty years; and had invented an electrophorus and an electrical condenser, which showed great experimental skill. When he turned his attention to the experiments made by Galvani, he observed that the author of them had been far more surprized than he needed to be, at those results in which an electrical spark was produced; and that it was only in the cases in which no such apparatus was employed, that the observations could justly be considered as indicating a new law, or a new kind of electricity. He soon satisfied himself (about 1794) that the essential conditions of this kind of action depended on the metals;—that it is brought into play most decidedly when two different metals touch each other, and are connected by any moist body;—and that the parts of animals which had been used discharged the office both of such moist bodies, and of very sensitive electrometers. The animal electricity of Galvani might, he observed, be with more propriety called metallic electricity. ...The term "animal electricity" has been superseded by others, of which galvanism is perhaps the most familiar.

• [T]he voltaic pile, which Volta described in the Philosophical Transactions for 1800... was, in fact, a more important step in the history of electricity than the Leyden jar had been.

• [I]t was discovered by Nicholson and Carlisle, in 1800, that water was decomposed by the pile of Volta; that is, it was found that when the wires of the pile were placed with their ends near each other in the fluid, a stream of bubbles of air arose from each wire, and these airs were found on examination to be oxygen and hydrogen; which... had already been found to be the constituents of water. This was as Davy says, the true origin of all that has been done in electro-chemical science. ...Cruickshank in pursuing these experiments added to them many important new results such as the decomposition of muriates of magnesia soda and ammonia by the pile and the general observation that the alkaline matter always appeared at the negative and the acid at the positive pole.

• Humphry Davy was... in 1801, appointed lecturer at the Royal Institution in London, (then recently established,) he was soon put in possession of a galvanic apparatus of great power; and with this he was not long in obtaining the most striking results.

• He [Davy] had already conjectured, in 1802, that all decompositions might be polar; that is, that in all cases of chemical decomposition, the elements might be related to each other as electrically positive and negative... At this period such a view was far from obvious; and it was contended by many, on the contrary, that the elements which the voltaic apparatus brought to view, were not liberated from combinations, but generated.

• [A]s he [Davy] says, "referring to my experiments of 1800, 1801, and 1802, and to a number of new facts, which showed that inflammable substances and oxygen, alkalies and acids, and oxidable and noble metals, were in electrical relations of positive and negative, I drew the conclusion, that the combinations and decompositions by electricity were referrible to the law of electrical attractions and repulsions," and advanced the hypothesis, "that chemical and electrical attractions mere produced by the same cause, acting in the one case on particles, in the other on masses; ...and that the same property, under different modifications, was the cause of all the phenomena exhibited by different voltaic combinations." Although this is the enunciation... of the great discovery of this epoch... neither Davy nor his followers, for a considerable period, apprehended it with that distinctness which makes a discovery complete.

• By a happy chance, the first edition of Whewell's 'History of the Inductive Sciences' was published in 1837, and it affords a very useful view of the state of things at the commencement of the Victorian epoch.
  • Thomas Henry Huxley, The Advance of Science in the Last Half-Century (1889)

• Those who still repeat the once favorible objection that Darwin's 'Origin of Species' is nothing but a new version of the 'Philosophie zoologique' will find that so late as 1844, Whewell had not the slightest suspicion of Darwin's main theorem, even as a logical possibility. In fact, the publication of that theorem by Darwin and Wallace, in 1859, took all the biological world by surprise.
  • Thomas Henry Huxley, The Advance of Science in the Last Half-Century (1889)

• Even the second edition of the 'History of the Inductive Sciences,' which was published in 1846, contains no allusion either to the general view of the 'Correlation of Forces' published in England in 1842, or to the publication in 1843 of the first of the series of experiments by which the mechanical equivalent of heat was correctly ascertained. Such a failure on the part of a contemporary, of great acquirements and remarkable intellectual powers, to read the signs of the times, is a lesson and a warning worthy of being deeply pondered by anyone who attempts to prognosticate the course of scientific progress.
  • Thomas Henry Huxley, The Advance of Science in the Last Half-Century (1889)

• Whewell... claimed to be inferring his philosophy of science from his study of the history and practice of science. His large-scale History of the Inductive Sciences was a survey of science from ancient to modern times. He insisted upon completing this work before writing his Philosophy of the Inductive Sciences, founded upon their history.
  • Laura J. Snyder, "William Whewell," (2000) (Nov 12, 2012 substantive revision) Stanford Encyclopedia of Philosophy

• History of the Inductive Sciences from the Earliest to the Present Time (1837) Vol.1, Vol.2, Vol.3 (1847) Vol.1, Vol.2, Vol.3; (1859) Vol.1, Vol.2