NOVUM ORGANON
RENOVATUM.

By WILLIAM WHEWELL, D.D.,

MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND
CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.

BEING THE SECOND PART OF THE PHILOSOPHY
OF THE INDUCTIVE SCIENCES.

THE THIRD EDITION, WITH LARGE ADDITIONS.

ΛΑΜΠΑΔIΑ ΕΧΟΝΤΕΣ ΔIΑΔΩΣΟΥΣIΝ ΑΛΛΗΛΟIΣ

LONDON:
JOHN W. PARKER AND SON, WEST STRAND.
1858.

It is to our immortal countryman; Bacon, that we owe the broad announcement of this grand and fertile principle; and the developement of the idea, that the whole of natural philosophy consists entirely of a series of inductive generalizations, commencing with the most circumstantially stated particulars, and carried up to universal laws, or axioms, which comprehend in their statements every subordinate degree of generality; and of a corresponding series of inverted reasoning from generals to particulars, by which these axioms are traced back into their remotest consequences, and all particular propositions deduced from them; as well those by whose immediate considerations we rose to their discovery, as those of which we had no previous knowledge.

Herschel, Discourse on Natural Philosophy, Art. 96.

CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.

PREFACE.

Even if Bacon’s Novum Organon had possessed the character to which it aspired as completely as was possible in its own day, it would at present need renovation: and even if no such book had ever been written, it would be a worthy undertaking to determine the machinery, intellectual, social and material, by which human knowledge can best be augmented. Bacon could only divine how sciences might be constructed; we can trace, in their history, how their construction has taken place. However sagacious were his conjectures, the facts which have really occurred must give additional instruction: however large were his anticipations, the actual progress of science since his time has illustrated them in all their extent. And as to the structure and operation of the Organ by which truth is to be collected from nature,—that is, the Methods by which science is to be promoted—we know that, though Bacon’s general maxims are sagacious and animating, his particular precepts failed in his hands, and are now practically useless. This, perhaps, was not wonderful, seeing that they were, as I have said, mainly derived from conjectures respecting knowledge and the progress of knowledge; but at iv the present day, when, in several provinces of knowledge, we have a large actual progress of solid truth to look back upon, we may make the like attempt with the prospect of better success, at least on that ground. It may be a task, not hopeless, to extract from the past progress of science the elements of an effectual and substantial method of Scientific Discovery. The advances which have, during the last three centuries, been made in the physical sciences;—in Astronomy, in Physics, in Chemistry, in Natural History, in Physiology;—these are allowed by all to be real, to be great, to be striking; may it not be that the steps of progress in these different cases have in them something alike? May it not be that in each advancing movement of such knowledge there is some common principle, some common process? May it not be that discoveries are made by an Organ which has something uniform in its working? If we can shew that this is so, we shall have the New Organ, which Bacon aspired to construct, renovated according to our advanced intellectual position and office.

It was with the view of opening the way to such an attempt that I undertook that survey of the past progress of physical knowledge, of which I have given the results in the History of the Sciences, and the History of Scientific Ideas[1]; the former containing the history of the sciences, so far as it depends on v observed Facts; the latter containing the history of those Ideas by which such Facts are bound into Theories.

[1] Published in two former editions as part of the Philosophy of the Inductive Sciences (b. i–x.).

It can hardly happen that a work which treats of Methods of Scientific Discovery, shall not seem to fail in the positive results which it offers. For an Art of Discovery is not possible. At each step of the investigation are needed Invention, Sagacity, Genius,—elements which no art can give. We may hope in vain, as Bacon hoped, for an Organ which shall enable all men to construct Scientific Truths, as a pair of compasses enables all men to construct exact circles[2]. This cannot be. The practical results of the Philosophy of Science must be rather classification and analysis of what has been done, than precept and method for future doing. Yet I think that the methods of discovery which I have to recommend, though gathered from a wider survey of scientific history, both as to subjects and as to time, than (so far as I am aware) has been elsewhere attempted, are quite as definite and practical as any others which have been proposed; with the great additional advantage of being the methods by which all great discoveries in science have really been made. This may be said, for instance, of the Method of Gradation and the Method of Natural Classification, spoken of [b. iii. c. viii]; and in a narrower sense, of the Method of Curves, the Method of vi Means, the Method of Least Squares and the Method of Residues, spoken of in [chap. vii.] of the same Book. Also the Remarks on the Use of Hypotheses and on the Tests of Hypotheses ([b. ii. c. v.]) point out features which mark the usual course of discovery.

[2] Nov. Org. lib. i. aph. 61.

But one of the principal lessons resulting from our views is undoubtedly this:—that different sciences may be expected to advance by different modes of procedure, according to their present condition; and that in many of these sciences, an Induction performed by any of the methods which have just been referred to is not the next step which we may expect to see made. Several of the sciences may not be in a condition which fits them for such a Colligation of Facts; (to use the phraseology to which the succeeding analysis has led me). The Facts may, at the present time, require to be more fully observed, or the Idea by which they are to be colligated may require to be more fully unfolded.

But in this point also, our speculations are far from being barren of practical results. The examination to which we have subjected each science, gives us the means of discerning whether what is needed for the further progress of the science, has its place in the Observations, or in the Ideas, or in the union of the two. If observations be wanted, the Methods of Observation, given in [b. iii. c. ii.] may be referred to. If those who are to make the next discoveries need, for that purpose, a developement of their Ideas, the modes in which such a developement has usually taken vii place are treated of in Chapters [iii.] and [iv.] of that Book.

No one who has well studied the history of science can fail to see how important a part of that history is the explication, or as I might call it, the clarification of men’s Ideas. This, the metaphysical aspect of each of the physical sciences, is very far from being, as some have tried to teach, an aspect which it passes through at an early period of progress, and previously to the stage of positive knowledge. On the contrary, the metaphysical movement is a necessary part of the inductive movement. This, which is evidently so by the nature of the case, was proved by a copious collection of historical evidences, in the History of Scientific Ideas. The ten Books of that History contain an account of the principal philosophical controversies which have taken place in all the physical sciences, from Mathematics to Physiology. These controversies, which must be called metaphysical if anything be so called, have been conducted by the greatest discoverers in each science, and have been an essential part of the discoveries made. Physical discoverers have differed from barren speculators, not by having no metaphysics in their heads, but by having good metaphysics in their heads while their adversaries had bad; and by binding their metaphysics to their physics, instead of keeping the two asunder. I trust that the History of Scientific Ideas is of some value, even as a record of a number of remarkable controversies; but I conceive that it also contains an indisputable proof that there viii is, in progressive science, a metaphysical as well as a physical element;—ideas as well as facts;—thoughts as well as things. Metaphysics is the process of ascertaining that thought is consistent with itself: and if it be not so, our supposed knowledge is not knowledge.

In [Chapter vi.] of the Second Book, I have spoken of the Logic of Induction. Several writers[3] have quoted very emphatically my assertion that the Logic of Induction does not exist in previous writers: using it as an introduction to Logical Schemes of their own. They seem to have overlooked the fact that at the same time that I noted the deficiency, I offered a scheme which I think fitted to supply this want. And I am obliged to say that I do not regard the schemes proposed by any of those gentlemen as at all satisfactory for the purpose. But I must defer to a future occasion any criticism of authors who have written on the subjects here treated. A critical notice of such authors formed the Twelfth Book of the former edition of the Philosophy of the Sciences. I have there examined the opinions concerning the Nature of Real Knowledge and the mode of acquiring it, which have been promulgated in all ages, from Plato and Aristotle, to Roger Bacon, to Francis Bacon, to Newton, to Herschel. Such a survey, with the additions which I should now have to make to it, may hereafter be put forth as a separate book: but I ix have endeavoured to confine the present volume to such positive teaching regarding Knowledge and Science as results from the investigations pursued in the other works of this series. But with regard to this matter, of the Logic of Induction, I may venture to say, that we shall not find anything deserving the name explained in the common writers on Logic, or exhibited under the ordinary Logical Forms. That in previous writers which comes the nearest to the notice of such a Logic as the history of science has suggested and verified, is the striking declaration of Bacon in two of his Aphorisms (b. i. aph. civ. cv.).

[3] Apelt Die Theorie der Induction: Gratry Logique.

“There will be good hopes for the Sciences then, and not till then, when by a true scale or Ladder, and by successive steps, following continuously without gaps or breaks, men shall ascend from particulars to the narrower Propositions, from those to intermediate ones, rising in order one above another, and at last to the most general.

“But in establishing such propositions, we must devise some other Form of Induction than has hitherto been in use; and this must be one which serves not only to prove and discover Principles, (as very general Propositions are called,) but also the narrower and the intermediate, and in short, all true Propositions.”

And he elsewhere speaks of successive Floors of Induction.

All the truths of an extensive science form a Series of such Floors, connected by such Scales or Ladders; and a part of the Logic of Induction consists, as I x conceive, in the construction of a Scheme of such Floors. Converging from a wide basis of various classes of particulars, at last to one or a few general truths, these schemes necessarily take the shape of a Pyramid. I have constructed such Pyramids for Astronomy and for Optics[4]; and the illustrious Von Humboldt in speaking of the former subject, does me the honour to say that my attempt in that department is perfectly successful[5]. The Logic of Induction contains other portions, which may be seen in the following work, [b. ii. c. vi.]

[4] See the Tables at the end of book ii.

[5] Cosmos, vol. ii. n. 35.

I have made large additions to the present edition, especially in what regards the Application of Science, ([b. iii. c. ix.]) and the Language of Science. The former subject I am aware that I have treated very imperfectly. It would indeed, of itself, furnish material for a large work; and would require an acquaintance with practical arts and manufactures of the most exact and extensive kind. But even a general observer may see how much more close the union of Art with Science is now than it ever was before; and what large and animating hopes this union inspires, both for the progress of Art and of Science. On another subject also I might have dilated to a great extent,—what I may call (as I have just now called it) the social machinery for the advancement of science. There can be no doubt that at certain stages of sciences, xi Societies and Associations may do much to promote their further progress; by combining their observations, comparing their views, contributing to provide material means of observation and calculation, and dividing the offices of observer and generalizer. We have had in Europe in general, and especially in this country, very encouraging examples of what may be done by such Associations. For the present I have only ventured to propound one Aphorism on the subject, namely this; (Aph. LV.) That it is worth considering whether a continued and connected system of observation and calculation, like that of Astronomy, might not be employed in improving our knowledge of other subjects; as Tides, Currents, Winds, Clouds, Rain, Terrestrial Magnetism, Aurora Borealis, composition of crystals, and the like. In saying this, I have mentioned those subjects which are, as appears to me, most likely to profit by continued and connected observations.

I have thrown the substance of my results into Aphorisms, as Bacon had done in his Novum Organum. This I have done, not in the way of delivering dogmatic assertions or oracular sentences; for the Aphorisms are all supported by reasoning, and were, in fact, written after the reasoning, and extracted from it. I have adopted this mode of gathering results into compact sentences, because it seems to convey lessons with additional clearness and emphasis.

I have only to repeat what I have already said; that this task of adapting the Novum Organum to the xii present state of Physical Science, and of constructing a Newer Organ which may answer the purposes at which Bacon aimed, seems to belong to the present generation; and being here founded upon a survey of the past history and present condition of the Physical Sciences, will I hope, not be deemed presumptuous.

Trinity Lodge,

1 November, 1858.

TABLE OF CONTENTS.

NOVUM ORGANON
RENOVATUM.

De Scientiis tum demum bene sperandum est, quando per Scalam veram et per gradus continuos, et non intermissos aut hiulcos, a particularibus ascendetur ad Axiomata minora, et deinde ad media, alia aliis superiora, et postremo demum ad generalissima.

In constituendo autem Axiomate, Forma Inductionis alia quam adhuc in usu fuit, excogitanda est; et quæ non ad Principia tantum (quæ vocant) probanda et invenienda, sed etiam ad Axiomata minora, et media, denique omnia.

Bacon, Nov. Org., Aph. civ. cv.

NOVUM ORGANON RENOVATUM.

The name Organon was applied to the works of Aristotle which treated of Logic, that is, of the method of establishing and proving knowledge, and of refuting errour, by means of Syllogisms. Francis Bacon, holding that this method was insufficient and futile for the augmentation of real and useful knowledge, published his Novum Organon, in which he proposed for that purpose methods from which he promised a better success. Since his time real and useful knowledge has made great progress, and many Sciences have been greatly extended or newly constructed; so that even if Bacon’s method had been the right one, and had been complete as far as the progress of Science up to his time could direct it, there would be room for the revision and improvement of the methods of arriving at scientific knowledge.

Inasmuch as we have gone through the Histories of the principal Sciences, from the earliest up to the present time, in a previous work, and have also traced the History of Scientific Ideas in another work, it may perhaps be regarded as not too presumptuous if we attempt this revision and improvement of the methods by which Sciences must rise and grow. This 4 is our task in the present volume; and to mark the reference of this undertaking to the work of Bacon, we name our book Novum Organon Renovatum.

Bacon has delivered his precepts in Aphorisms, some of them stated nakedly, others expanded into dissertations. The general results at which we have arrived by tracing the history of Scientific Ideas are the groundwork of such Precepts as we have to give: and I shall therefore begin by summing up these results in Aphorisms, referring to the former work for the historical proof that these Aphorisms are true.

NOVUM ORGANON RENOVATUM.

BOOK I.

APHORISMS CONCERNING IDEAS DERIVED FROM THE HISTORY OF IDEAS.

I.

MAN is the Interpreter of Nature, Science the right interpretation. (History of Scientific Ideas: Book i. Chapter 1.)

II.

The Senses place before us the Characters of the Book of Nature; but these convey no knowledge to us, till we have discovered the Alphabet by which they are to be read. (Ibid. i. 2.)

III.

The Alphabet, by means of which we interpret Phenomena, consists of the Ideas existing in our own minds; for these give to the phenomena that coherence and significance which is not an object of sense. (i. 2.)

IV.

The antithesis of Sense and Ideas is the foundation of the Philosophy of Science. No knowledge can exist without the union, no philosophy without the separation, of these two elements. (i. 2.) 6

V.

Fact and Theory correspond to Sense on the one hand, and to Ideas on the other, so far as we are conscious of our Ideas: but all facts involve ideas unconsciously; and thus the distinction of Facts and Theories is not tenable, as that of Sense and Ideas is. (i. 2.)

VI.

Sensations and Ideas in our knowledge are like Matter and Form in bodies. Matter cannot exist without Form, nor Form without Matter: yet the two are altogether distinct and opposite. There is no possibility either of separating, or of confounding them. The same is the case with Sensations and Ideas. (i. 2.)

VII.

Ideas are not transformed, but informed Sensations; for without ideas, sensations have no form. (i. 2.)

VIII.

The Sensations are the Objective, the Ideas the Subjective part of every act of perception or knowledge. (i. 2.)

IX.

General Terms denote Ideal Conceptions, as a circle, an orbit, a rose. These are not Images of real things, as was held by the Realists, but Conceptions: yet they are conceptions, not bound together by mere Name, as the Nominalists held, but by an Idea. (i. 2.)

X.

It has been said by some, that all Conceptions are merely states or feelings of the mind, but this assertion only tends to confound what it is our business to distinguish. (i. 2.)

XI.

Observed Facts are connected so as to produce new truths, by superinducing upon them an Idea: and such truths are obtained by Induction. (i. 2.) 7

XII.

Truths once obtained by legitimate Induction are Facts: these Facts may be again connected, so as to produce higher truths: and thus we advance to Successive Generalizations. (i. 2.)

XIII.

Truths obtained by Induction are made compact and permanent by being expressed in Technical Terms. (i. 3.)

XIV.

Experience cannot conduct us to universal and necessary truths:—Not to universal, because she has not tried all cases:—Not to necessary, because necessity is not a matter to which experience can testify. (i. 5.)

XV.

Necessary truths derive their necessity from the Ideas which they involve; and the existence of necessary truths proves the existence of Ideas not generated by experience. (i. 5.)

XVI.

In Deductive Reasoning, we cannot have any truth in the conclusion which is not virtually contained in the premises. (i. 6.)

XVII.

In order to acquire any exact and solid knowledge, the student must possess with perfect precision the ideas appropriate to that part of knowledge: and this precision is tested by the student’s perceiving the axiomatic evidence of the axioms belonging to each Fundamental Idea. (i. 6.)

XVIII.

The Fundamental Ideas which it is most important to consider, as being the Bases of the Material Sciences, are the Ideas of Space, Time (including Number), Cause (including Force and Matter), Outness of Objects, and Media of Perception of Secondary Qualities, Polarity (Contrariety), 8 Chemical Composition and Affinity, Substance, Likeness and Natural Affinity, Means and Ends (whence the Notion of Organization), Symmetry, and the Ideas of Vital Powers. (i. 8.)

XIX.

The Sciences which depend upon the Ideas of Space and Number are Pure Sciences, not Inductive Sciences: they do not infer special Theories from Facts, but deduce the conditions of all theory from Ideas. The Elementary Pure Sciences, or Elementary Mathematics, are Geometry, Theoretical Arithmetic and Algebra. (ii. 1.)

XX.

The Ideas on which the Pure Sciences depend, are those of Space and Number; but Number is a modification of the conception of Repetition, which belongs to the Idea of Time. (ii. 1.)

XXI.

The Idea of Space is not derived from experience, for experience of external objects presupposes bodies to exist in Space, Space is a condition under which the mind receives the impressions of sense, and therefore the relations of space are necessarily and universally true of all perceived objects. Space is a form of our perceptions, and regulates them, whatever the matter of them may be. (ii. 2.)

XXII.

Space is not a General Notion collected by abstraction from particular cases; for we do not speak of Spaces in general, but of universal or absolute Space. Absolute Space is infinite. All special spaces are in absolute space, and are parts of it. (ii. 3.)

XXIII.

Space is not a real object or thing, distinct from the objects which exist in it; but it is a real condition of the existence of external objects. (ii. 3.) 9

XXIV.

We have an Intuition of objects in space; that is, we contemplate objects as made up of spatial parts, and apprehend their spatial relations by the same act by which we apprehend the objects themselves. (ii. 3.)

XXV.

Form or Figure is space limited by boundaries. Space has necessarily three dimensions, length, breadth, depth; and no others which cannot be resolved into these. (ii. 3.)

XXVI.

The Idea of Space is exhibited for scientific purposes, by the Definitions and Axioms of Geometry; such, for instance, as these:—the Definition of a Right Angle, and of a Circle;—the Definition of Parallel Lines, and the Axiom concerning them;—the Axiom that two straight lines cannot inclose a space. These Definitions are necessary, not arbitrary; and the Axioms are needed as well as the Definitions, in order to express the necessary conditions which the Idea of Space imposes. (ii. 4.)

XXVII.

The Definitions and Axioms of Elementary Geometry do not completely exhibit the Idea of Space. In proceeding to the Higher Geometry, we may introduce other additional and independent Axioms; such as that of Archimedes, that a curve line which joins two points is less than any broken line joining the same points and including the curve line. (ii. 4.)

XXVIII.

The perception of a solid object by sight requires that act of mind by which, from figure and shade, we infer distance and position in space. The perception of figure by sight requires that act of mind by which we give an outline to each object. (ii. 6.) 10

XXIX.

The perception of Form by touch is not an impression on the passive sense, but requires an act of our muscular frame by which we become aware of the position of our own limbs. The perceptive faculty involved in this act has been called the muscular sense. (ii. 6.)

XXX.

The Idea of Time is not derived from experience, for experience of changes presupposes occurrences to take place in Time. Time is a condition under which the mind receives the impressions of sense, and therefore the relations of time are necessarily and universally true of all perceived occurrences. Time is a form of our perceptions, and regulates them, whatever the matter of them may be. (ii. 7.)

XXXI.

Time is not a General Notion collected by abstraction from particular cases. For we do not speak of particular Times as examples of time in general, but as parts of a single and infinite Time. (ii. 8.)

XXXII.

Time, like Space, is a form, not only of perception, but of Intuition. We consider the whole of any time as equal to the sum of the parts; and an occurrence as coinciding with the portion of time which it occupies. (ii. 8.)

XXXIII.

Time is analogous to Space of one dimension: portions of both have a beginning and an end, are long or short. There is nothing in Time which is analogous to Space of two, or of three, dimensions, and thus nothing which corresponds to Figure. (ii. 8.)

XXXIV.

The Repetition of a set of occurrences, as, for example, strong and weak, or long and short sounds, according to a 11 steadfast order, produces Rhythm, which is a conception peculiar to Time, as Figure is to Space. (ii. 8.)

XXXV.

The simplest form of Repetition is that in which there is no variety, and thus gives rise to the conception of Number. (ii. 8.)

XXXVI.

The simplest numerical truths are seen by Intuition; when we endeavour to deduce the more complex from these simplest, we employ such maxims as these:—If equals be added to equals the wholes are equal:—If equals be subtracted from equals the remainders are equal:—The whole is equal to the sum of all its parts. (ii. 9.)

XXXVII.

The Perception of Time involves a constant and latent kind of memory, which may be termed a Sense of Succession. The Perception of Number also involves this Sense of Succession, although in small numbers we appear to apprehend the units simultaneously and not successively. (ii. 10.)

XXXVIII.

The Perception of Rhythm is not an impression on the passive sense, but requires an act of thought by which we connect and group the strokes which form the Rhythm. (ii. 10.)

XXXIX.

Intuitive is opposed to Discursive reason. In intuition, we obtain our conclusions by dwelling upon one aspect of the fundamental Idea; in discursive reasoning, we combine several aspects of the Idea, (that is, several axioms,) and reason from the combination. (ii. 11.)

XL.

Geometrical deduction (and deduction in general) is called Synthesis, because we introduce, at successive steps, the 12 results of new principles. But in reasoning on the relations of space, we sometimes go on separating truths into their component truths, and these into other component truths; and so on: and this is geometrical Analysis. (ii. 11.)

XLI.

Among the foundations of the Higher Mathematics, is the Idea of Symbols considered as general Signs of Quantity. This idea of a Sign is distinct from, and independent of other ideas. The Axiom to which we refer in reasoning by means of Symbols of quantity is this:—The interpretation of such symbols must be perfectly general. This Idea and Axiom are the bases of Algebra in its most general form. (ii. 12.)

XLII.

Among the foundations of the Higher Mathematics is also the Idea of a Limit. The Idea of a Limit cannot be superseded by any other definitions or Hypotheses, The Axiom which we employ in introducing this Idea into our reasoning is this:—What is true up to the Limit is true at the Limit. This Idea and Axiom are the bases of all Methods of Limits, Fluxions, Differentials, Variations, and the like. (ii. 12.)

XLIII.

There is a pure Science of Motion, which does not depend upon observed facts, but upon the Idea of motion. It may also be termed Pure Mechanism, in opposition to Mechanics Proper, or Machinery, which involves the mechanical conceptions of force and matter. It has been proposed to name this Pure Science of Motion, Kinematics. (ii. 13.)

XLIV.

The pure Mathematical Sciences must be successfully cultivated, in order that the progress of the principal Inductive Sciences may take place. This appears in the case of Astronomy, in which Science, both in ancient and in modern times, each advance of the theory has depended upon the 13 previous solution of problems in pure mathematics. It appears also inversely in the Science of the Tides, in which, at present, we cannot advance in the theory, because we cannot solve the requisite problems in the Integral Calculus. (ii. 14.)

XLV.

The Idea of Cause, modified into the conceptions of mechanical cause, or Force, and resistance to force, or Matter, is the foundation of the Mechanical Sciences; that is, Mechanics, (including Statics and Dynamics,) Hydrostatics, and Physical Astronomy. (iii. 1.)

XLVI.

The Idea of Cause is not derived from experience; for in judging of occurrences which we contemplate, we consider them as being, universally and necessarily, Causes and Effects, which a finite experience could not authorize us to do. The Axiom, that every event must have a cause, is true independently of experience, and beyond the limits of experience. (iii. 2.)

XLVII.

The Idea of Cause is expressed for purposes of science by these three Axioms:—Every Event must have a Cause:—Causes are measured by their Effects:—Reaction is equal and opposite to Action. (iii. 4.)

XLVIII.

The Conception of Force involves the Idea of Cause, as applied to the motion and rest of bodies. The conception of force is suggested by muscular action exerted: the conception of matter arises from muscular action resisted. We necessarily ascribe to all bodies solidity and inertia, since we conceive Matter as that which cannot be compressed or moved without resistance. (iii. 5.)

XLIX.

Mechanical Science depends on the Conception of Force; and is divided into Statics, the doctrine of Force preventing 14 motion, and Dynamics, the doctrine of Force producing motion. (iii. 6.)

L.

The Science of Statics depends upon the Axiom, that Action and Reaction are equal, which in Statics assumes this form:—When two equal weights are supported on the middle point between them, the pressure on the fulcrum is equal to the sum of the weights. (iii. 6.)

LI.

The Science of Hydrostatics depends upon the Fundamental Principle that fluids press equally in all directions. This principle necessarily results from the conception of a Fluid, as a body of which the parts are perfectly moveable in all directions. For since the Fluid is a body, it can transmit pressure; and the transmitted pressure is equal to the original pressure, in virtue of the Axiom that Reaction is equal to Action. That the Fundamental Principle is not derived from experience, is plain both from its evidence and from its history. (iii. 6.)

LII.

The Science of Dynamics depends upon the three Axioms above stated respecting Cause. The First Axiom,—that every change must have a Cause,—gives rise to the First Law of Motion,—that a body not acted upon by a force will move with a uniform velocity in a straight line. The Second Axiom,—that Causes are measured by their Effects,—gives rise to the Second Law of Motion,—that when a force acts upon a body in motion, the effect of the force is compounded with the previously existing motion. The Third Axiom,—that Reaction is equal and opposite to Action,—gives rise to the Third Law of Motion, which is expressed in the same terms as the Axiom; Action and Reaction being understood to signify momentum gained and lost. (iii. 7.) 15

LIII.

The above Laws of Motion, historically speaking, were established by means of experiment: but since they have been discovered and reduced to their simplest form, they have been considered by many philosophers as self-evident. This result is principally due to the introduction and establishment of terms and definitions, which enable us to express the Laws in a very simple manner. (iii. 7.)

LIV.

In the establishment of the Laws of Motion, it happened, in several instances, that Principles were assumed as self-evident which do not now appear evident, but which have since been demonstrated from the simplest and most evident principles. Thus it was assumed that a perpetual motion is impossible;—that the velocities of bodies acquired by falling down planes or curves of the same vertical height are equal;—that the actual descent of the center of gravity is equal to its potential ascent. But we are not hence to suppose that these assumptions were made without ground: for since they really follow from the laws of motion, they were probably, in the minds of the discoverers, the results of undeveloped demonstrations which their sagacity led them to divine. (iii. 7.)

LV.

It is a Paradox that Experience should lead us to truths confessedly universal, and apparently necessary, such as the Laws of Motion are. The Solution of this paradox is, that these laws are interpretations of the Axioms of Causation. The axioms are universally and necessarily true, but the right interpretation of the terms which they involve, is learnt by experience. Our Idea of Cause supplies the Form, Experience, the Matter, of these Laws. (iii. 8.)

LVI.

Primary Qualities of Bodies are those which we can conceive as directly perceived; Secondary Qualities are those 16 which we conceive as perceived by means of a Medium. (iv. 1.)

LVII.

We necessarily perceive bodies as without us; the Idea of Externality is one of the conditions of perception. (iv. 1.)

LVIII.

We necessarily assume a Medium for the perceptions of Light, Colour, Sound, Heat, Odours, Tastes; and this Medium must convey impressions by means of its mechanical attributes. (iv. 1.)

LIX.

Secondary Qualities are not extended but intensive: their effects are not augmented by addition of parts, but by increased operation of the medium. Hence they are not measured directly, but by scales; not by units, but by degrees. (iv. 4.)

LX.

In the Scales of Secondary Qualities, it is a condition (in order that the scale may be complete,) that every example of the quality must either agree with one of the degrees of the Scale, or lie between two contiguous degrees. (iv. 4.)

LXI.

We perceive by means of a medium and by means of impressions on the nerves: but we do not (by our senses) perceive either the medium or the impressions on the nerves. (iv. 1.)

LXII.

The Prerogatives of the Sight are, that by this sense we necessarily and immediately apprehend the position of its objects: and that from visible circumstances, we infer the distance of objects from us, so readily that we seem to perceive and not to infer. (iv. 2.) 17

LXIII.

The Prerogatives of the Hearing are, that by this sense we perceive relations perfectly precise and definite between two notes, namely, Musical Intervals (as an Octave, a Fifth); and that when two notes are perceived together, they are comprehended as distinct, (a Chord,) and as having a certain relation, (Concord or Discord.) (iv. 2.)

LXIV.

The Sight cannot decompose a compound colour into simple colours, or distinguish a compound from a simple colour. The Hearing cannot directly perceive the place, still less the distance, of its objects: we infer these obscurely and vaguely from audible circumstances. (iv. 2.)

LXV.

The First Paradox of Vision is, that we see objects upright, though the images on the retina are inverted. The solution is, that we do not see the image on the retina at all, we only see by means of it. (iv. 2.)

LXVI.

The Second Paradox of Vision is, that we see objects single, though there are two images on the retinas, one in each eye. The explanation is, that it is a Law of Vision that we see (small or distant) objects single, when their images fall on corresponding points of the two retinas. (iv. 2.)

LXVII.

The law of single vision for near objects is this:—When the two images in the two eyes are situated, part for part, nearly but not exactly, upon corresponding points, the object is apprehended as single and solid if the two objects are such as would be produced by a single solid object seen by the eyes separately. (iv. 2.)

LXVIII.

The ultimate object of each of the Secondary Mechanical Sciences is, to determine the nature and laws of the processes 18 by which the impression of the Secondary Quality treated of is conveyed: but before we discover the cause, it may be necessary to determine the laws of the phenomena; and for this purpose a Measure or Scale of each quality is necessary. (iv. 4.)

LXIX.

Secondary qualities are measured by means of such effects as can be estimated in number or space. (iv. 4.)

LXX.

The Measure of Sounds, as high or low, is the Musical Scale, or Harmonic Canon. (iv. 4.)

LXXI.

The Measures of Pure Colours are the Prismatic Scale; the same, including Fraunhofer’s Lines; and Newton’s Scale of Colours. The principal Scales of Impure Colours are Werner’s Nomenclature of Colours, and Merimée’s Nomenclature of Colours. (iv. 4.)

LXXII.

The Idea of Polarity involves the conception of contrary properties in contrary directions:—the properties being, for example, attraction and repulsion, darkness and light, synthesis and analysis; and the contrary directions being those which are directly opposite, or, in some cases, those which are at right angles. (v. 1.)

LXXIII. (Doubtful.)

Coexistent polarities are fundamentally identical. (v. 2.)

LXXIV.

The Idea of Chemical Affinity, as implied in Elementary Composition, involves peculiar conceptions. It is not properly expressed by assuming the qualities of bodies to resemble those of the elements, or to depend on the figure of the elements, or on their attractions. (vi. 1.) 19

LXXV.

Attractions take place between bodies, Affinities between the particles of a body. The former may be compared to the alliances of states, the latter to the ties of family. (vi. 2.)

LXXVI.

The governing principles of Chemical Affinity are, that it is elective; that it is definite; that it determines the properties of the compound; and that analysis is possible. (vi. 2.)

LXXVII.

We have an idea of Substance: and an axiom involved in this Idea is, that the weight of a body is the sum of the weights of all its elements. (vi. 3.)

LXXVIII.

Hence Imponderable Fluids are not to be admitted as chemical elements. (vi. 4.)

LXXIX.

The Doctrine of Atoms is admissible as a mode of expressing and calculating laws of nature; but is not proved by any fact, chemical or physical, as a philosophical truth. (vi. 5.)

LXXX.

We have an Idea of Symmetry; and an axiom involved in this Idea is, that in a symmetrical natural body, if there be a tendency to modify any member in any manner, there is a tendency to modify all the corresponding members in the same manner. (vii. 1.)

LXXXI.

All hypotheses respecting the manner in which the elements of inorganic bodies are arranged in space, must be constructed with regard to the general facts of crystallization. (vii. 3.) 20

LXXXII.

When we consider any object as One, we give unity to it by an act of thought. The condition which determines what this unity shall include, and what it shall exclude, is this;—that assertions concerning the one thing shall be possible. (viii. 1.)

LXXXIII.

We collect individuals into Kinds by applying to them the Idea of Likeness. Kinds of things are not determined by definitions, but by this condition:—that general assertions concerning such kinds of things shall be possible. (viii. 1.)

LXXXIV.

The Names of kinds of things are governed by their use; and that may be a right name in one use which is not so in another. A whale is not a fish in natural history, but it is a fish in commerce and law. (viii. 1.)

LXXXV.

We take for granted that each kind of things has a special character which may be expressed by a Definition. The ground of our assumption is this;—that reasoning must be possible. (viii. 1.)

LXXXVI.

The “Five Words,” Genus, Species, Difference, Property, Accident, were used by the Aristotelians, in order to express the subordination of Kinds, and to describe the nature of Definitions and Propositions. In modern times, these technical expressions have been more referred to by Natural Historians than by Metaphysicians. (viii. 1.)

LXXXVII.

The construction of a Classificatory Science includes Terminology, the formation of a descriptive language;—Diataxis, the Plan of the System of Classification, called 21 also the Systematick;—Diagnosis, the Scheme of the Characters by which the different Classes are known, called also the Characteristick. Physiography is the knowledge which the System is employed to convey. Diataxis includes Nomenclature. (viii. 2.)

LXXXVIII.

Terminology must be conventional, precise, constant; copious in words, and minute in distinctions, according to the needs of the science. The student must understand the terms, directly according to the convention, not through the medium of explanation or comparison. (viii. 2.)

LXXXIX.

The Diataxis, or Plan of the System, may aim at a Natural or at an Artificial System. But no classes can be absolutely artificial, for if they were, no assertions could be made concerning them. (viii. 2.)

XC.

An Artificial System is one in which the smaller groups (the Genera) are natural; and in which the wider divisions (Classes, Orders) are constructed by the peremptory application of selected Characters; (selected, however, so as not to break up the smaller groups.) (viii. 2.)

XCI.

A Natural System is one which attempts to make all the divisions natural, the widest as well as the narrowest; and therefore applies no characters peremptorily. (viii. 2.)

XCII.

Natural Groups are best described, not by any Definition which marks their boundaries, but by a Type which marks their center. The Type of any natural group is an example which possesses in a marked degree all the leading characters of the class. (viii. 2.) 22

XCIII.

A Natural Group is steadily fixed, though not precisely limited; it is given in position, though not circumscribed; it is determined, not by a boundary without, but by a central point within;—not by what it strictly excludes, but by what it eminently includes;—by a Type, not by a Definition. (viii. 2.)

XCIV.

The prevalence of Mathematics as an element of education has made us think Definition the philosophical mode of fixing the meaning of a word: if (Scientific) Natural History were introduced into education, men might become familiar with the fixation of the signification of words by Types; and this process agrees more nearly with the common processes by which words acquire their significations. (viii. 2.)

XCV.

The attempts at Natural Classification are of three sorts; according as they are made by the process of blind trial, of general comparison, or of subordination of characters. The process of Blind Trial professes to make its classes by attention to all the characters, but without proceeding methodically. The process of General Comparison professes to enumerate all the characters, and forms its classes by the majority. Neither of these methods can really be carried into effect. The method of Subordination of Characters considers some characters as more important than others; and this method gives more consistent results than the others. This method, however, does not depend upon the Idea of Likeness only, but introduces the Idea of Organization or Function. (viii. 2.)

XCVI.

A Species is a collection of individuals, which are descended from a common stock, or which resemble such a collection as much as these resemble each other: the resemblance being opposed to a definite difference. (viii. 2.) 23

XCVII.

A Genus is a collection of species which resemble each other more than they resemble other species: the resemblance being opposed to a definite difference. (viii. 2.)

XCVIII.

The Nomenclature of a Classificatory Science is the collection of the names of the Species, Genera, and other divisions. The binary nomenclature, which denotes a species by the generic and specific name, is now commonly adopted in Natural History. (viii. 2.)

XCIX.

The Diagnosis, or Scheme of the Characters, comes, in the order of philosophy, after the Classification. The characters do not make the classes, they only enable us to recognize them. The Diagnosis is an Artificial Key to a Natural System. (viii. 2.)

C.

The basis of all Natural Systems of Classification is the Idea of Natural Affinity. The Principle which this Idea involves is this:—Natural arrangements, obtained from different sets of characters, must coincide with each other. (viii. 4.)

CI.

In order to obtain a Science of Biology, we must analyse the Idea of Life. It has been proved by the biological speculations of past time, that Organic Life cannot rightly be solved into Mechanical or Chemical Forces, or the operation of a Vital Fluid, or of a Soul. (ix. 2.)

CII.

Life is a System of Vital Forces; and the conception of such Forces involves a peculiar Fundamental Idea. (ix. 3.) 24

CIII.

Mechanical, chemical, and vital Forces form an ascending progression, each including the preceding. Chemical Affinity includes in its nature Mechanical Force, and may often be practically resolved into Mechanical Force. (Thus the ingredients of gunpowder, liberated from their chemical union, exert great mechanical Force: a galvanic battery acting by chemical process does the like.) Vital Forces include in their nature both chemical Affinities and mechanical Forces: for Vital Powers produce both chemical changes, (as digestion,) and motions which imply considerable mechanical force, (as the motion of the sap and of the blood.) (ix. 4.)

CIV.

In voluntary motions, Sensations produce Actions, and the connexion is made by means of Ideas: in reflected motions, the connexion neither seems to be nor is made by means of Ideas: in instinctive motions, the connexion is such as requires Ideas, but we cannot believe the Ideas to exist. (ix. 5.)

CV.

The Assumption of a Final Cause in the structure of each part of animals and plants is as inevitable as the assumption of an Efficient Cause for every event. The maxim that in organized bodies nothing is in vain, is as necessarily true as the maxim that nothing happens by chance. (ix. 6.)

CVI.

The Idea of living beings as subject to disease includes a recognition of a Final Cause in organization; for disease is a state in which the vital forces do not attain their proper ends. (ix. 7.)

CVII.

The Palætiological Sciences depend upon the Idea of Cause: but the leading conception which they involve is that of historical cause, not mechanical cause. (x. 1.) 25

CVIII.

Each Palætiological Science, when complete, must possess three members: the Phenomenology, the Ætiology, and the Theory. (x. 2.)

CIX.

There are, in the Palætiological Sciences, two antagonist doctrines: Catastrophes and Uniformity. The doctrine of a uniform course of nature is tenable only when we extend the nation of Uniformity so far that it shall include Catastrophes. (x. 3.)

CX.

The Catastrophist constructs Theories, the Uniformitarian demolishes them. The former adduces evidence of an Origin, the latter explains the evidence away. The Catastrophist’s dogmatism is undermined by the Uniformitarian’s skeptical hypotheses. But when these hypotheses are asserted dogmatically they cease to be consistent with the doctrine of Uniformity. (x. 3.)

CXI.

In each of the Palætiological Sciences, we can ascend to remote periods by a chain of causes, but in none can we ascend to a beginning of the chain. (x. 3.)

CXII.

Since the Palætiological sciences deal with the conceptions of historical cause, History, including Tradition, is an important source of materials for such sciences. (x. 4.)

CXIII.

The history and tradition which present to us the providential course of the world form a Sacred Narrative; and in reconciling the Sacred Narrative with the results of science, arise inevitable difficulties which disturb the minds of those who reverence the Sacred Narrative. (x. 4.) 26

CXIV.

The disturbance of reverent minds, arising from scientific views, ceases when such views become familiar, the Sacred Narrative being then interpreted anew in accordance with such views. (x. 4.)

CXV.

A new interpretation of the Sacred Narrative, made for the purpose of reconciling it with doctrines of science, should not be insisted on till such doctrines are clearly proved; and when they are so proved, should be frankly accepted, in the confidence that a reverence for the Sacred Narrative is consistent with a reverence for the Truth. (x. 4.)

CXVI.

In contemplating the series of causes and effects which constitutes the world, we necessarily assume a First Cause of the whole series. (x. 5.)

CXVII.

The Palætiological Sciences point backwards with lines which are broken, but which all converge to the same invisible point: and this point is the Origin of the Moral and Spiritual, as well as of the Natural World. (x. 5.)

NOVUM ORGANON RENOVATUM.

BOOK II.

OF THE CONSTRUCTION OF SCIENCE.

CHAPTER I.
Of two principal Processes by which Science is constructed.

Aphorism I.

THE two processes by which Science is constructed are the Explication of Conceptions, and the Colligation of Facts.

TO the subject of the present and next Book all that has preceded is subordinate and preparatory. In former works we have treated of the History of Scientific Discoveries and of the History of Scientific Ideas. We have now to attempt to describe the manner in which discoveries are made, and in which Ideas give rise to knowledge. It has already been stated that Knowledge requires us to possess both Facts and Ideas;—that every step in our knowledge consists in applying the Ideas and Conceptions furnished by our minds to the Facts which observation and experiment offer to us. When our Conceptions are clear and distinct, when our Facts are certain and sufficiently numerous, and when the Conceptions, being suited to the nature of the 28 Facts, are applied to them so as to produce an exact and universal accordance, we attain knowledge of a precise and comprehensive kind, which we may term Science. And we apply this term to our knowledge still more decidedly when, Facts being thus included in exact and general Propositions, such Propositions are, in the same manner, included with equal rigour in Propositions of a higher degree of Generality; and these again in others of a still wider nature, so as to form a large and systematic whole.

But after thus stating, in a general way, the nature of science, and the elements of which it consists, we have been examining with a more close and extensive scrutiny, some of those elements; and we must now return to our main subject, and apply to it the results of our long investigation. We have been exploring the realm of Ideas; we have been passing in review the difficulties in which the workings of our own minds involve us when we would make our conceptions consistent with themselves: and we have endeavoured to get a sight of the true solutions of these difficulties. We have now to inquire how the results of these long and laborious efforts of thought find their due place in the formation of our Knowledge. What do we gain by these attempts to make our notions distinct and consistent; and in what manner is the gain of which we thus become possessed, carried to the general treasure-house of our permanent and indestructible knowledge? After all this battling in the world of ideas, all this struggling with the shadowy and changing forms of intellectual perplexity, how do we secure to ourselves the fruits of our warfare, and assure ourselves that we have really pushed forwards the frontier of the empire of Science? It is by such an appropriation, that the task which we have had in our hands during the two previous works, (the History of the Inductive Sciences and the History of Scientific Ideas,) must acquire its real value and true place in our design.

In order to do this, we must reconsider, in a more definite and precise shape, the doctrine which has already been laid down;—that our Knowledge consists 29 in applying Ideas to Facts; and that the conditions of real knowledge are that the ideas be distinct and appropriate, and exactly applied to clear and certain facts. The steps by which our knowledge is advanced are those by which one or the other of these two processes is rendered more complete;—by which Conceptions are made more clear in themselves, or by which the Conceptions more strictly bind together the Facts. These two processes may be considered as together constituting the whole formation of our knowledge; and the principles which have been established in the History of Scientific Ideas bear principally upon the former of these two operations;—upon the business of elevating our conceptions to the highest possible point of precision and generality. But these two portions of the progress of knowledge are so clearly connected with each other, that we shall deal with them in immediate succession. And having now to consider these operations in a more exact and formal manner than it was before possible to do, we shall designate them by certain constant and technical phrases. We shall speak of the two processes by which we arrive at science, as the Explication of Conceptions and the Colligation of Facts: we shall show how the discussions in which we have been engaged have been necessary in order to promote the former of these offices; and we shall endeavour to point out modes, maxims, and principles by which the second of the two tasks may also be furthered.

CHAPTER II.
Of the Explication of Conceptions.