William Whewell

Every failure is a step to success. Every detection of what is false directs us towards what is true: every trial exhausts some tempting form of error.

William Whewell (May 24, 1794 – March 6, 1866) was an English polymath, scientist, Anglican priest, philosopher, theologian and historian of science.

See also: History of the Inductive Sciences

Quotes

No force however great can stretch a cord however fine into an horizontal line which is accurately straight.

• And so no force however great can stretch a cord however fine into an horizontal line which is accurately straight.
  • Elementary Treatise on Mechanics, The Equilibrium of Forces on a Point (1819)

• We cannot observe external things without some degree of Thought; nor can we reflect upon our Thoughts, without being influenced in the course of our reflection by the Things which we have observed.
  • The Elements of Morality, Book 1, ch. 1. (1845)

• Every failure is a step to success. Every detection of what is false directs us towards what is true: every trial exhausts some tempting form of error. Not only so; but scarcely any attempt is entirely a failure; scarcely any theory, the result of steady thought, is altogether false; no tempting form of Error is without some latent charm derived from Truth.
  • Lectures on the History of Moral Philosophy in England, Lecture 7. (1852)

Philosophy of the Inductive Sciences (1840)

The part of a man’s knowledge which belongs to his own mind, is subjective: that which flows in upon him from the world external to him, is objective.

In art, truth is a means to an end; in science, it is the only end.

It is a test of true theories not only to account for but to predict phenomena.

• According to the technical language of old writers, a thing and its qualities are described as subject and attributes; and thus a man’s faculties and acts are attributes of which he is the subject. The mind is the subject in which ideas inhere. Moreover, the man’s faculties and acts are employed upon external objects; and from objects all his sensations arise. Hence the part of a man’s knowledge which belongs to his own mind, is subjective: that which flows in upon him from the world external to him, is objective.
  • Part I Of Ideas, Book I Of Ideas in General, Chap. 4 Of the Difference and Opposition of Sensation and Ideas

• We unfold out of the Idea of Space the propositions of geometry, which are plainly truths of the most rigorous necessity and universality. But if the idea of space were merely collected from observation of the external world, it could never enable or entitle us to assert such propositions: it could never authorize us to say that not merely some lines, but all lines, not only have, but must have, those properties which geometry teaches. Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but half comprehends the meaning.
  • Part I Of Ideas, Book I Of Ideas in General, Chap. 12 The Fundamental Ideas Are Not Derived From Experience

• By speaking of space as an Idea, I intend to imply the apprehension of objects as existing in space, and of the relations of position prevailing among them, is not a consequence of experience but a result of a peculiar constitution and activity of the mind which is independent of all experience in its origin, though constantly combined with experience in its exercise.
  • Part I Of Ideas, Book II The Philosophy of the Pure Sciences, Chap. 2 Of the Idea of Space

• A scientific writer of modern times appears to wonder that men did not at once divine the weight of the air from which the phenomena formerly ascribed to the 'fuga vacui' really result. “Loaded, compressed by the atmosphere,” he says, “they did not recognize its action. In vain all Nature testified that air was elastic and heavy; they shut their eyes to her testimony. The water rose in pumps and flowed in siphons at that time as it does at this day. They could not separate the boards of a pair of bellows of which the holes were stopped; and they could not bring together the same boards without difficulty if they were at first separated. Infants sucked the milk of their mothers; air entered rapidly into the lungs of animals at every inspiration; cupping-glasses 'produced tumours on the skin; and in spite of all these striking proofs of the weight and elasticity of the air, the ancient philosophers maintained resolutely that air was light, and explained all these phenomena by the horror which they said Nature had for a vacuum.” It is curious that it should not have occurred to the author while writing this, that if these facts, so numerous and various, can all be accounted for by one principle, there is a strong presumption that the principle is not altogether baseless. And in reality is it not true that Nature does abhor a vacuum, and do all she can to avoid it? No doubt this power is not unlimited; and we can trace it to a mechanical cause, the pressure of the circumambient air. But the tendency, arising from this pressure, which the bodies surrounding a space void of air have to rush into it, may be expressed, in no extravagant or unintelligible manner, by saying that Nature has a repugnance to a vacuum.
  • Part II Of Knowledge, Book XI Of the Construction of Science, Chap. 5 Of Certain Characteristics of Scientific Induction

• Our assent to the hypothesis implies that it is held to be true of all particular instances. That these cases belong to past or to future times, that they have or have not already occurred, makes no difference in the applicability of the rule to them. Because the rule prevails, it includes all cases.
  • Part II Of Knowledge, Book XI Of the Construction of Science, Chap. 5 Of Certain Characteristics of Scientific Induction

• The system becomes more coherent as it is further extended. The elements which we require for explaining a new class of facts are already contained in our system. Different members of the theory run together, and we have thus a constant convergence to unity. In false theories, the contrary is the case.
  • Part II Of Knowledge, Book XI Of the Construction of Science, Chap. 5 Of Certain Characteristics of Scientific Induction

Aphorisms

Respecting Ideas

I

• Man, servant and interpreter of Nature, does and understands only as much as he has observed of the order of Nature, either in reality or in mind; he neither knows nor can do more.

IV

• The antithesis of 'Sense' & '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.

VIII

• The Sensations are the 'Objective', the Ideas the 'Subjective' part of every act of perception or knowledge.

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'.

XIII

• Truths obtained by Induction are made compact and permanent by being expressed in 'Technical Terms'.

XVI

• In Deductive Reasoning, we cannot have any truth in the conclusion which is not virtually contained in the premises.

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'.

XXV

• 'Form' or 'figure' is space limited by boundaries. Space has necessarily 'three' dimensions, length, breadth, depth; and no ethers which cannot be resolved into these.

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.

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

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.

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'.

XLIX

• Mechanical Science depends on the Conception of Force; and is divided into 'Statics', the doctrine of Force preventing motion, and 'Dynamics', the doctrine of Force producing motion.

L

• '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.'

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.

LVII

• We necessarily perceive bodies as 'without' us: the Idea of 'Externality' is one of the conditions of perception.

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'.

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.

LXIV

• The Sight cannot decompose a compound colour into simple colours, or distinguish a compound from a simple colour

LXV

• The solution is, that we do not see the image on the retina at all, we only see by means of it.

LXXIII

• Coexistent polarities are fundamentally identical.

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.

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.

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.

LXXXIII

• We collect individuals into 'kinds' by applying to them the Idea of Likeness.

LXXXIV

• A whale is not a fish in natural history, but it is a fish in commerce and law. A plea that human laws which mention fish do not apply to whales, would be rejected at once by an intelligent judge.

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.

LXXXIX

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

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

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'.

XCII

• Natural Groups are best described, not by any definition which marks their boundaries, but by a 'Type' which marks their centre. The Type of any natural group is an example which possesses in a marked degree all the leading characters of the class.

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.

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.

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.

CI

• It has been proved by the biological speculations of past time, that organic Life cannot rightly be resolved into mechanical or chemical forces, or the operation of a vital fluid, or of a soul.

CII

• Life is a System of Vital Forces ; and the conception of such Forces involves a peculiar Fundamental Idea.

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, (digestion,) and motions which imply considerable mechanical force, (as the motion of the sap and of the blood.)

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.

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'.

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'.

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.

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 notion of uniformity so far that it shall include catastrophes.

CX

• The Catastrophist constructs theories, the Uniformitarian Demolishes them.

CXI

• [W]e can ascend to remote periods by a chain of causes, but in none can we ascend to a 'beginning' of the chain.

CXIII

• The Palaetiological 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.

Respecting Knowledge

I

• The two processes by which Science is constructed are the 'Explication of Conceptions' and the 'Colligation of Facts'.

IV

• Discovery depends upon the previous cultivation or natural clearness of the appropriate Idea, and therefore no discovery is the work of accident.

• Facts are the materials of science, but all Facts involve Ideas. Since, in observing Facts, we cannot exclude Ideas, we must, for the purposes of science, take care that the Ideas are clear and rigorously applied.

VIII

• The resolution of complex Facts into precise and measured partial Facts, we call the 'Decomposition of Facts'. This process is requisite for the progress of science, but does not necessarily lead to progress. The Conceptions by which Facts are bound together, are suggested by the sagacity of discoverers. But a supply of appropriate hypotheses cannot be constructed by rule, nor without inventive talent. The truth of tentative hypotheses must be tested by their application to facts. The discoverer must be ready, carefully to try his hypotheses in this manner, and to reject them if they will not bear the test, in spite of indolence and vanity.

XII

• When a series of progressive numbers is given as the result of observation, it may generally be reduced to law by combinations of arithmetical and geometrical progressions. A true formula for a progressive series of numbers cannot commonly be obtained from a narrow range of observations.

XIII

• 'Induction' is a term applied to describe the 'process' of a true Colligation of Facts by means of an exact and appropriate Conception. 'An Induction' is also employed to denote the 'proposition' which results from this process. An Induction is not the mere sum of the Facts which are colligated. The Facts are not only brought together, but seen in a new point of view. 'The Consilience of Inductions' takes place when an Induction, obtained from one class of facts, coincides with an Induction, obtained from another different class.

XVII

• The 'Logic of Induction' consists in stating the Facts and the Inference in such a manner, that the evidence of the Inference is manifest; just as the Logic of Deduction consists in stating the Premises and the Conclusion in such a manner that the Evidence of the Conclusion is manifest.

XXV

• The Logic of Induction is the 'Criterion of Truth' inferred from Facts, as the Logic of Deduction is the 'Criterion of Truth' deduced from necessary Principle. In Art, Truth is a means to an end; in Science, it is the only end.

XXXVII

• The distinction of Fact and Theory is only relative. Brute animals have a practical knowledge of relations of space and force; but they have no knowledge of Geometry or Mechanicks.

XXXIX

• The Methods of Observation of Quantity in general, are 'Numeration', which is precise by the nature of Number; the 'Measurement of Space' and 'of Time', which are easily made precise; the 'Conversion of Space and Time', by which each aids the measurement of the other. The Idea of Space becomes more clear by studying 'Geometry'; the Idea of Force, by studying 'Mechanics'; the Ideas of Likeness, of Kind, of subordination of Classes, by studying 'Natural History'.

XLII

• 'Natural History' ought to form a part of intellectual education, in order to correct certain prejudices which arise from cultivating the intellect by means of mathematics alone and in order to lead the student to see that the division of things into kinds, and the attribution and use of names, are processes susceptible of great precision.

XLVII

• The Process of Induction may be resolved into three steps ; the 'Selection of the Idea', the 'Construction of the Conception', and the 'Determination of the Magnitudes'. These three steps correspond to the determination of the 'Independent Variable', the 'formula', and the 'coefficients', in mathematical investigations; or to the 'Argument', the 'Law', and the 'Numerical Data', in a Table of an Inequality. The conceptions involved in scientific truths have attained the requisite degree of clearness by means of the Discussions respecting ideas which have taken place among discoverers and their followers. Such discussions are very far from being unprofitable

XLIX

• The Construction of the Conception very often includes, in a great measure, the Determination of the Magnitudes. The true construction of the conception is frequently suggested by some hypothesis; and in these cases, the hypothesis may be useful, though containing superfluous parts.

L

• 'The Law of Continuity' is this:—that a quantity cannot pass from one amount to another by any change of conditions, without passing through all intermediate magnitudes according to the intermediate conditions. It may often be employed to disprove distinctions which have no real foundation. 'The Method of Gradation' consists in taking a number of stages of a property in question, intermediate between two extreme cases which appear to be different. It is employed to determine whether the extreme cases are really distinct or not. 'The Method of Gradation', applied to decide the question, whether the existing phenomena arise from existing causes, leads to this result:—That the phenomena do appear to arise from existing causes, but that the action of existing causes have transgressed their recorded Limits of Intensity. 'The Method of Natural Classification' consists in classing cases, not according to any assumed definition, but according to the connexion of the facts themselves.

LIV

• In the 'Induction of Causes' the principal maxim is, that we must be careful to possess, and to apply, with perfect clearness, the Fundamental Idea on which the Induction depends. The Induction of Substance, of Force, of Polarity, go beyond mere laws of phenomena, and may be considered as the Induction cf Causes. The Cause of certain phenomena being inferred, we are led to inquire into the Cause of this Cause, which inquiry must be conducted in the same manner as the previous one; and thus we have the Induction of Ulterior Causes.

Respecting the Language of Science

I

• In the Ancient Period of Science, Technical Terms were formed in three different ways:—by appropriating common words and fixing their meaning;—by constructing terms containing a description;—by constructing terms containing reference to a theory.

III

• In framing scientific terms, the appropriation of old words is preferable to the invention of new ones.

IV

• When common words are appropriated as technical terms, their meaning and relations in common use should be retained as far as can conveniently be done.

V

• When common words are appropriated as technical terms, their meaning may be modified, and must be rigorously fixed.

VI

• When common words are appropriated as technical terms, this must be done so that they are not ambiguous in their application.

VII

• It is better to form new words as technical terms, than to employ old ones in which the last three Aphorisms cannot be complied with.

VIII

• Terms must be constructed and appropriated so as to be fitted to enunciate simply and clearly true general propositions.

The word Force has been appropriated in the science of Mechanics in two senses: as indicating the cause of motion; and again, as expressing certain measures of the effects of this cause, in the phrases accelerating force and moving force. Hence we might have occasion to speak of the accelerating or moving force of a certain force; for instance, if we were to say that the centre of force which governs the motions of the planets resides in the sun; and that the accelerating force of this force varies only with the distance, but its moving force varies as the product of the mass of the sun and the planet. This is a harsh and incongruous mode of expression; and might have been avoided, if, instead of accelerating force and moving force, single abstract terms had been introduced by Newton: if, for instance, he had said that the velocity generated in a second measures the accelerativity of the force which produces it, and the momentum produced in a second measures the motivity of the force.

The science which treats of heat has hitherto had no special designation : treatises upon it have generally been termed treatises On Heat. But this practice of employing the same term to denote the property and the science which treats of it, is awkward and often ambiguous. And it is further attended with this inconvenience, that we have no adjective derived from the name of the science, as we have in other cases, when we speak of acoustical experiments and optical theories. This inconvenience has led various persons to suggest names for the Science of Heat. M. Le Comte terms it Thermology. In the History of the Sciences, I have named it Thermotics, which appears to me to agree better with the analogy of the names of other corresponding sciences, Acoustics and Optics.

Electricity is in the same condition as heat ; having only one word to express the property and the science. M. Le Comte proposes Electrology : for the same reason as before, I should conceive Electrics more agreeable to analogy. The coincidence of the word with the plural of Electric would not give rise to ambiguity ; for Electrics ', taken as the name of a science, would be singular, like Optics and Mechanics. But a term offers itself to express common or machine Electrics, which appears worthy of admission, though involving a theoretical view. The received doctrine of the difference between voltaic and common electricity is, that in the former case the fluid must be considered as in motion, in the latter as at rest. The science which treats of the former class of subjects is commonly termed Electrodynamics, which obviously suggests the name Electrostatics for the latter.

The subject of the Tides is, in like manner, destitute of any name which designates the science concerned about it. I have ventured to employ the term Tidology, having been much engaged in tidological researches.

Many persons possess a peculiarity of vision, which disables them from distinguishing certain colours. On examining many such cases, we find that in all such persons the peculiarities are the same ; all of them confounding scarlet with green, and pink with blue. Hence they form a class, which, for the convenience of physiologists and others, ought to have a fixed designation. Instead of calling them, as has usually been done, "persons having a peculiarity of vision," we might take a Greek term implying this meaning, and term them idiopts.

x

• New terms and changes of terms, which are not needed in order to express truth, are to be avoided.

XI

• Terms which imply theoretical views are admissible, as far as the theory is proved.

And hence the rule which we must follow is, not that our terms must involve no theory, but that they imply the theory only in that sense in which it is the interpretation of the facts. For example, the term polarization of light was objected to, as involving a theory. Perhaps the term was at first suggested by conceiving light to consist of particles having poles turned in a particular manner. But among intelligent speculators, the notion of polarization soon reduced itself to the simple conception of opposite properties in opposite positions, which is a bare statement of the fact: and the term being understood to have this meaning, is a perfectly good term, and indeed the best which we can imagine for designating what is intended. I need hardly add the caution, that names involving theoretical views not in accordance with facts are to be rejected.

XII

• If terms are systematically good, they are not to be rejected because they are etymologically inaccurate.

XIII

• The fundamental terms of a system of Nomenclature may "be conveniently borrowed from casual or arbitrary circumstances.

XIV

• In forming a Terminology, words may be invented when necessary, but they cannot be conveniently borrowed from casual or arbitrary circumstances.

It will be recollected that Terminology is a language employed for describing objects. Nomenclature, a body of names of the objects themselves. The names, as was stated in the last maxim, may be arbitrary; but the descriptive terms must be borrowed from words of suitable meaning in the modern or the classical languages. The extension of arbitrary names in scientific terminology is by no means to be encouraged. I may mention a case in which it was very properly avoided. When Mr. Faraday's researches on Voltaic electricity had led him to perceive the great impropriety of the term poles, as applied to the apparatus, since the processes have not reference to any opposed points, but to two opposite directions of a path, he very suitably wished to substitute for the phrases positive pole and negative pole two words ending in ode. Zincode and Platinode, terms derived from the metal which, in one modification of the apparatus, forms what was previously termed the pole, are to be avoided, because in their origin too much is casual; and they are not a good basis for derivative terms. The pole at which the zinc is, is the Anode or Cathode, according as it is associated with different metals. Either the Zincode must sometimes mean the pole at which the Zinc is, and at other times that at which the Zinc is not, or else we must have as many names for poles as there are metals. Anode and Cathode were free from these objections; for they refer to a natural standard of the direction of the voltaic current. Anode and Cathode, the rising and the setting way, are the directions which correspond to east and west in that voltaic current to which we must ascribe terrestrial magnetism. And with these words it was easy to connect anïon and cathïon, to designate the opposite elements which are separated and liberated at the two 'electrodes'.

XVI

• [P]hilological analogies are to be preserved if possible, but modified according to scientific convenience.

XVII

• When alterations in technical terms become necessary, it is desirable that the new term should contain in its form some memorial of the old one.

Quotes about Whewell

• Many glaring errors of the Greeks will have to be noticed ... few of them can be referred to the cause assigned by Dr. Whewell.
  • George Henry Lewes, Aristotle: a Chapter from the History of Science (1864) with reference to Whewell's "Cause of the failure of the Greek Philosophy" in his History of the Inductive Sciences (1837)

External links

• Profile at Stanford Encyclopedia of Philosophy
• Profile from History of Economic Thought
• The philosophy of the inductive sciences, founded upon their history (1847)
• Papers of Wlliam Whewell
• Six Lectures on Political Economy (1861)