Novum organon renovatum / Being the second part of the philosophy of the inductive sciences

by William Whewell

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.

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				PAGE
Preface				[iii]
BOOK I.
APHORISMS CONCERNING IDEAS.
Aphorisms I.	—	XVIII.	Ideas in general	[5]—7
XIX.	—	XLIV.	Ideas in the Pure Sciences	[8]—12
XLV.	—	LV.	Ideas in the Mechanical Sciences	[13]—15
LVI.	—	LXXI.	Ideas in the Secondary MechanicalSciences	[15]—18
LXXII.	—	LXXIII.	Ideas in the Mechanico-chemicalSciences	[18]
LXXIV.	—	LXXIX.	Ideas in Chemistry	[18]
LXXX.	—	LXXXI.	Ideas in Morphology	[19]
LXXXII.	—	C.	Ideas in Classificatory Science	[20]—23
CI.	—	CVI.	Ideas in Biology	[23]—24
CVII.	—	CXVII.	Ideas in Palæontology	[24]—26
BOOK II.
OF KNOWLEDGE.
Chap. I.	Of Two Principal Processes by which Science isconstructed			[27]
Chap. II.	Of the Explication of Conceptions			[30]
Sect. I.	The Historical Progress.
Art.	[1.]	The Explication of Conceptions,
[2.]		Has taken place historically by discussions.
{xiv}
Art.	[3.]	False Doctrines when exposed appear impossible:
[4.]		But were plausible before
[5.]		Men’s Minds gradually cleared.
Sect. II.	Use of definitions.
Art.	[6.]	Controversies about Definitions.
[7.]		Not arbitrary Definitions.
[8.]		Attention to Facts requisite.
[9.]		Definition is not essential.
[10.]		The omission of Definition not always blameable.
Sect. III.	Use of Axioms.
Art.	[11.]	Axioms serve to express Ideas.
Sect. IV.	Clear and appropriate Ideas.
Art.	[12.]	We must see the Axioms clearly.
[13.]		Inappropriate Ideas cannot lead to Truth.
[14.]		The fault is in the Conceptions.
[15.]		Rules cannot teach Discovery;
[16.]		But are not useless.
[17.]		Discussion as well as Facts needed.
Sect. V.	Accidental Discoveries.
Art.	[18.]	No Scientific Discovery is accidental.
[19.]		Such accidents do not happen to common Men.
[20.]		Examples.
[21.]		So far Explication of Conceptions.
Chap. III.	Of Facts as the Materials of Science			[50]
Art.	[1.]	Facts must be true.
[2.]		Facts not separable from Ideas.
[3.]		The Ideas must be distinct.
[4.]		Conceptions of the Intellect only to be admitted.
[5.]		Facts are to be observed with reference toSpace and Time:
[6.]		And also to other Ideas.
[7.]		The Decomposition of Facts.
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Art.	[8.]	This step is not sufficient.
[9.]		It introduces Technical Terms,
[10.]		And Classification.
[11.]		The materials of Science.
Chap. IV.	Of the Colligation of Facts			[59]
Art.	[1.]	Facts are colligated by Conceptions.
[2.]		Science begins with common Observation.
[3.]		Facts must be decomposed.
[4.]		What Ideas first give Sciences.
[5.]		Facts must be referred to Ideas.
[6.]		Sagacity needed.
[7.]		Discovery made by Guesses.
[8.]		False Hypotheses preluding to true ones.
[9.]		New Hypotheses not mere modifications of old ones.
[10.]		Hypotheses may have superfluous parts.
[11.]		Hypotheses to be compared with Facts.
[12.]		Secondary Steps.
Chap. V.	Of certain Characteristics of Scientific Induction			[70]
Sect. I.	Invention a part of Induction.
Art.	[1.]	Induction the source of Knowledge.
[2.]		Induction involves a New Element.
[3.]		Meaning of Induction.
[4.]		The New Element is soon forgotten.
[5.]		Induction includes a Definition and a Proposition.
Sect. II.	Use of Hypotheses.
Art.	[6.]	Discoveries made by Guesses,
[7.]		Which must be compared with Facts.
[8.]		Hypotheses are suspected.
[9.]		Hypotheses may be useful though inaccurate.
Sect. III.	Tests of Hypotheses.
Art.	[10.]	True Hypotheses foretel Phenomena,
[11.]		Even of different kinds.—Consilience ofInductions.
{xvi}
Art.	[12.]	True Theories tend to Simplicity.
[13.]		Connexion of the last Tests.
Chap. VI.	Of the Logic of Induction			[97]
Art.	[1.]	Steps of Generalization,
[2.]		May be expressed by Tables.
[3.]		Which exhibit Inductive Steps;
[4.]		And the Consilience of Inductions;
[5.]		And the tendency to Simplicity;
[6.]		And the names of Discoverers;
[7.]		And the Verifications of Theory;
[8.]		By means of several easy steps.
[9.]		This resembles Book-keeping.
[10.]		The Logic of Induction.
[11.]		Attention at each step required.
[12.]		General Truths are not mere additions ofparticulars:
[13.]		But a new view is introduced.
[14.]		Formula of Inductive Logic:
[15.]		May refer to Definition.
[16.]		Formula inadequate.
[17.]		Deductive Connexion of Steps.
[18.]		Relation of Deductive and Inductive Reasoning.
[19.]		The Criterion of Truth.
[20.]		Theory and Fact.
[21.]		Higher and Lower Generalizations.
Chap. VII.	Of Laws of Phenomena and of Causes			[118]
Art.	[1.]	Knowledge of Laws of Phenomena.
[2.]		Formal and Physical Sciences.
[3.]		Causes in Astronomy.
[4.]		Different Mechanical Causes in other Sciences.
[5.]		Chemical and Vital Forces as Causes.
[6.]		Difference of these kinds of Force.
[7.]		Difficulty of conceiving new Causes.
[8.]		Men willingly take old Causes.
[9.]		Is the Magnetic Fluid real?
[10.]		Are Causes to be sought? (Comte’s Doctrine.)
[11.]		Both Laws and Causes to be studied.
{xvii}
Chap. VIII.	Of Art and Science			[129]
Art.	[1.]	Art precedes Science.
[2.]		Contrast of Art and Science.
[3.]		Instinct and Insight.
[4.]		Difference of Art and Instinct.
[5.]		Does Art involve Science?
[6.]		Science unfolds Principles.
[7.]		Science may improve Art.
[8.]		Arts not classified with Sciences.
Chap. IX.	Of the Classification of Sciences			[136]
Art.	[1.]	Use and Limits of such Classification.
[2.]		Classification depends on the Ideas.
[3.]		This points out Transitions.
[4.]		The Classification.
Inductive Table of Astronomy				[140]
Inductive Table of Optics				[140]
BOOK III.
OF METHODS EMPLOYED IN THE FORMATION OF SCIENCE.
Chap. I.	Introduction			[141]
Art.	[1.]	Object of this Book.
[2.]		An Art of Discovery not possible.
[3.]		Use of Methods.
[4.]		Series of Six Processes.
[5.]		Methods of Observation and Induction.
Chap. II.	Of Methods of Observation			[145]
Art.	[1.]	Referring to Number, Space, and Time.
[2.]		Observations are never perfect.
[3.]		(I.) Number is naturally exact.
[4.]		(II.) Measurement of Space.
[5.]		Instruments Invented in Astronomy,
[6.]		And improved.
{xviii}
Art.	[7.]	Goniometer.
[8.]		Standard of Length.
[10.]		(III.) Measurement of Time.
[11.]		Unit of Time.
[12.]		Transit Instrument.
[13.]		Chronometers.
[14.]		(IV.) Conversion of Space and Time.
[15.]		Space may Measure Time.
[16.]		Time may Measure Space.
[17.]		(V.) The Method of Repetition.
[18.]		The Method of Coincidences.
[19.]		Applied to Pendulums.
[20.]		(VI.) Measurement of Weight.
[21.]		Standard of Weight.
[22.]		(VII.) Measurement of Secondary Qualities.
[23.]		“The Howl” in Harmonics.
[24.]		(VIII.) Manipulation.
[25.]		Examples in Optics.
[26.]		(IX.) The Education of the Senses,
[27.]		By the Study of Natural History.
[28.]		Preparation for Ideas.
Chap. III.	Of Methods of Acquiring clear Scientific Ideas; and first of Intellectual Education			[164]
Art.	[1.]	(I.) Idea of Space.
[2.]		Education by Geometry.
[3.]		(II.) Idea of Number.
[4.]		Effect of the usual Education.
[5.]		(III.) Idea of Force.
[6.]		Study of Mechanics needed,
[7.]		To make Newton intelligible.
[8.]		No Popular Road.
[9.]		(IV.) Chemical Ideas.
[10.]		(V.) Natural History Ideas.
[11.]		Natural Classes to be taught.
[12.]		Mathematical Prejudices,
[13.]		To be corrected by Natural History.
[14.]		Method of Natural History,
[15.]		Resembles common language.
{xix}
Art.	[16.]	Its Lessons.
[17.]		(VI.) Well-established Ideas alone to be used.
[18.]		How are Ideas cleared?
Chap. IV.	Of Methods of Acquiring Clear Scientific Ideas, continued.—Of the Discussion of Ideas			[180]
Art.	[1.]	Successive Clearness,
[2.]		Produced by Discussion.
[3.]		Examples.
4.		Disputes not useless,
[5.]		Although “metaphysical.”
[6.]		Connected with Facts.
Chap. V.	Analysis of the Process of Induction			[186]
Sect. I.	The Three Steps of Induction.
Art.	[1.]	Methods may be useful.
[2.]		The three Steps.
[3.]		Examples.
[4.]		Mathematical names of the Steps.
Sect. II.	Of the Selection of the Fundamental Idea.
Art.	[5.]	Examples.
[6.]		The Idea to be found by trying,
[7.]		Till the Discovery is made;
[8.]		Preluded by Guesses.
[9.]		Idea and Facts homogeneous.
[10.]		Idea tested by the Facts.
Chap. VI.	General Rules for the Construction of theConception			[195]
Art.	[1.]	First: for Quantity.
[2.]		Formula and Coefficients found together.
[3.]		Example. Law of Cooling.
[4.]		Determined by Experiment.
[5.]		Progressive Series of Numbers.
[6.]		Recurrent Series.
[7.]		Use of Hypotheses.
[8.]		Even with this there are difficulties.
{xv}
Chap. VII.	Special Methods of Induction Applicable toQuantity			[202]
Sect. I.	The Method of Curves.
Art.	[1.]	Its Process.
[2.]		Its Use.
[3.]		With imperfect Observations.
[4.]		It corrects Observations.
[5.]		Obstacles. (I.) Ignorance of the argument.
[6.]		(II.) Combination of Laws.
Sect. II.	The Method of Means.
Art.	[7.]	Its Relation to the Method of Curves.
[8.]		Its process.
[9.]		Argument required to be known.
[10.]		Use of the Method.
[11.]		Large masses of Observations used.
[12.]		Proof of the Use of the Method.
Sect. III.	The Method of Least Squares.
Art.	[13.]	Is a Method of Means.
[14.]		Example.
Sect. IV.	The Method of Residues.
Art.	[15.]	Occasion for its Use.
[16.]		Its Process.
[17.]		Examples.
[18.]		Its Relation to the Method of Means.
[19.]		Example.
[20.]		“Residual Phenomena.”
Chap. VIII.	Methods of Induction Depending on Resemblance			[220]
Sect. I.	The Law of Continuity.
Art.	[1.]	Its Nature and Application,
[2.]		To Falling Bodies,
[3.]		To Hard Bodies,
[4.]		To Gravitation.
[5.]		The Evidence.
{xxi}
Sect. II.	The Method of Gradation.
Art.	[6.]	Occasions of its Use.
[7.]		Examples.
[8.]		Not enjoined by Bacon.
[9.]		Other Examples.
[10.]		Its Value in Geology.
[11.]		Limited Results.
Sect. III.	The Method of Natural Classification.
Art.	[12.]	Examples of its Use.
[13.]		Its Process.
[14.]		Negative Results.
[15.]		Is opposed to Arbitrary Definitions.
[16.]		Propositions and Definitions correlative.
[17.]		Definitions only provisional.
Chap. IX.	Of the Application of Inductive Truths			[233]
Art.	[1.]	This forms the Sequel of Discovery.
[2.]		Systematic Verification of Discoveries.
[3.]		Correction of Coefficients.
[4.]		Astronomy a Model.
[5.]		Verification by new cases.
[6.]		Often requires fresh calculation.
[7.]		Cause of Dew.
[8.]		Useful Applications.
Chap. X.	Of the Induction of Causes			[247]
Art.	[1.]	Is to be pursued.
[2.]		Induction of Substance.
[3.]		Induction of Force.
[4.]		Induction of Polarity.
[5.]		Is Gravity Polar?
[6.]		Induction of Ulterior Causes.
[7.]		Of the Supreme Cause.
{xxii}
BOOK IV.
OF THE LANGUAGE OF SCIENCE.
Introduction				[257]
Aphorisms concerning the Language of Science.
Aphorism I.		Relative to the Ancient Period		[258]
Art.	[1.]	Common Words.
[2.]		Descriptive Terms.
[3.]		Theoretical Terms.
Aphorism II.		Relative to the Modern Period		[269]
Art.	[1.]	Systematic Nomenclature.
[2.]		Systematic Terminology.
[3.]		Systematic Modification.
Aphorisms (III. IV. V. VI. VII.) relative to theApplication of Common Words				[278]
Aphorisms (VIII. IX. X. XI. XII. XIII.) relative to theConstruction of New Terms				[285]
Aphorism XIV.		Binary Nomenclature		[307]
XV.		Linnæan Maxims		[308]
XVI.		Numerical Names		[309]
XVII.		Names of more than two Steps		[310]
XVIII.		No arbitrary Terms		[311]
XIX.		Forms fixed by Convention		[314]
XX.		Form of Terms		[318]
Art.	[1.]	Terms derived from Latin and Greek.
[2.]		German Terms.
[3.]		Descriptive Terms.
[4.]		Nomenclature. Zoology.
[5.]		—————— Mineralogy.
[6.]		—————— Botany.
[7.]		—————— Chemistry.
[8.]		—————— Crystallography.
{xxiii}
Aphorism XXI.		Philological Rules		[328]
Art.	[1.]	Hybrids.
[2.]		Terminations of Substantives.
[3.]		Formations of Substantives (names of things).
[4.]		Abstract Substantives.
[5.]		Rules of derivation from Greek and Latin.
[6.]		Modification of Terminations.
Aphorism XXII.		Introduction of Changes		[341]
FURTHER ILLUSTRATIONS OF THE APHORISMS ON SCIENTIFICLANGUAGE, FROM THE RECENT COURSE OF SCIENCES.
1. Botany.
Aphorism XXIII.		Multiplication of Genera		[346]
2. Comparative Anatomy.
Aphorism XXIV.		Single Names to be used		[353]
XXV.		The History of Science is the Historyof its Language		[355]
XXVI.		Algebraical Symbols		[357]
XXVII.		Algebraical Analogies		[364]
XXVIII.		Capricious Derivations		[365]
XXIX.		Inductions are our Definitions		[368]

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.