The Project Gutenberg EBook of A System of Logic: Ratiocinative and Inductive, by John Stuart Mill This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: A System of Logic: Ratiocinative and Inductive 7th Edition, Vol. II Author: John Stuart Mill Release Date: February 27, 2011 [EBook #35421] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, VOL II *** Produced by David Clarke, Stephen H. Sentoff and the Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/Canadian Libraries) A SYSTEM OF LOGIC RATIOCINATIVE AND INDUCTIVE VOL. II. A SYSTEM OF LOGIC RATIOCINATIVE AND INDUCTIVE BEING A CONNECTED VIEW OF THE PRINCIPLES OF EVIDENCE AND THE METHODS OF SCIENTIFIC INVESTIGATION BY JOHN STUART MILL IN TWO VOLUMES VOL. II. SEVENTH EDITION LONDON: LONGMANS, GREEN, READER, AND DYER MDCCCLXVIII CONTENTS OF THE SECOND VOLUME. BOOK III. ON INDUCTION.—(Continued.) Chapter XIV. Of the Limits to the Explanation of Laws of Nature; and of Hypotheses. § 1. Can all the sequences in nature be resolvable into one law? 3 2. Ultimate laws cannot be less numerous than the distinguishable feelings of our nature 4 3. In what sense ultimate facts can be explained 7 4. The proper use of scientific hypotheses 8 5. Their indispensableness 16 6. Legitimate, how distinguished from illegitimate hypotheses 18 7. Some inquiries apparently hypothetical are really inductive 25 Chapter XV. Of Progressive Effects; and of the Continued Action of Causes. § 1. How a progressive effect results from the simple continuance of the cause 29 2. —and from the progressiveness of the cause 33 3. Derivative laws generated from a single ultimate law 36 Chapter XVI. Of Empirical Laws. § 1. Definition of an empirical law 38 2. Derivative laws commonly depend on collocations 39 3. The collocations of the permanent causes are not reducible to any law 41 4. Hence empirical laws cannot be relied on beyond the limits of actual experience 41 5. Generalizations which rest only on the Method of Agreement can only be received as empirical laws 43 6. Signs from which an observed uniformity of sequence may be presumed to be resolvable 44 7. Two kinds of empirical laws 47 [Pg v] [Pg vi] Chapter XVII. Of Chance, and its Elimination. § 1. The proof of empirical laws depends on the theory of chance 49 2. Chance defined and characterized 50 3. The elimination of chance 55 4. Discovery of residual phenomena by eliminating chance 57 5. The doctrine of chances 59 Chapter XVIII. Of the Calculation of Chances. § 1. Foundation of the doctrine of chances, as taught by mathematics 61 2. The doctrine tenable 63 3. On what foundation it really rests 64 4. Its ultimate dependence on causation 68 5. Theorem of the doctrine of chances which relates to the cause of a given event 72 6. How applicable to the elimination of chance 74 Chapter XIX. Of the Extension of Derivative Laws to Adjacent Cases. § 1. Derivative laws, when not casual, are almost always contingent on collocations 78 2. On what grounds they can be extended to cases beyond the bounds of actual experience 80 3. Those cases must be adjacent cases 82 Chapter XX. Of Analogy. § 1. Various senses of the word analogy 86 2. Nature of analogical evidence 87 3. On what circumstances its value depends 91 Chapter XXI. Of the Evidence of the Law of Universal Causation. § 1. The law of causality does not rest on an instinct 95 2. But on an induction by simple enumeration 100 3. In what cases such induction is allowable 102 4. The universal prevalence of the law of causality, on what grounds admissible 105 Chapter XXII. Of Uniformities of Coexistence not dependent on Causation. § 1. Uniformities of coexistence which result from laws of sequence 110 2. The properties of Kinds are uniformities of coexistence 111 3. Some are derivative, others ultimate 113 4. No universal axiom of coexistence 114 5. The evidence of uniformities of coexistence, how measured 117 6. When derivative, their evidence is that of empirical laws 117 7. So also when ultimate 119 8. The evidence stronger in proportion as the law is more general 120 9. Every distinct Kind must be examined 121 [Pg vii] Chapter XXIII. Of Approximate Generalizations, and Probable Evidence. § 1. The inferences called probable, rest on approximate generalizations 124 2. Approximate generalizations less useful in science than in life 124 3. In what cases they may be resorted to 126 4. In what manner proved 127 5. With what precautions employed 130 6. The two modes of combining probabilities 131 7. How approximate generalizations may be converted into accurate generalizations equivalent to them 136 Chapter XXIV. Of the Remaining Laws of Nature. § 1. Propositions which assert mere existence 139 2. Resemblance, considered as a subject of science 141 3. The axioms and theorems of mathematics comprise the principal laws of resemblance 143 4. —and those of order in place, and rest on induction by simple enumeration 145 5. The propositions of arithmetic affirm the modes of formation of some given number 146 6. Those of algebra affirm the equivalence of different modes of formation of numbers generally 151 7. The propositions of geometry are laws of outward nature 154 8. Why geometry is almost entirely deductive 156 9. Function of mathematical truths in the other sciences, and limits of that function 158 Chapter XXV. Of the Grounds of Disbelief. § 1. Improbability and impossibility 161 2. Examination of Hume's doctrine of miracles 162 3. The degrees of improbability correspond to differences in the nature of the generalization with which an assertion conflicts 166 4. A fact is not incredible because the chances are against it 170 5. Are coincidences less credible than other facts? 172 6. An opinion of Laplace examined 175 BOOK IV. OF OPERATIONS SUBSIDIARY TO INDUCTION. Chapter I. Of Observation and Description. § 1. Observation, how far a subject of logic 183 2. A great part of what seems observation is really inference 184 3. The description of an observation affirms more than is contained in the observation 187 4. —namely an agreement among phenomena; and the comparison of phenomena to ascertain such agreements is a preliminary to induction 190 Chapter II. Of Abstraction, or the Formation of Conceptions. § 1. The comparison which is a preliminary to induction implies general conceptions 193 2. —but these need not be pre-existent 194 [Pg viii] [Pg ix] 3. A general conception, originally the result of a comparison, becomes itself the type of comparison 198 4. What is meant by appropriate conceptions 200 5. —and by clear conceptions 203 6. Further illustration of the subject 205 Chapter III. Of Naming, as subsidiary to Induction. § 1. The fundamental property of names as an instrument of thought 209 2. Names are not indispensable to induction 210 3. In what manner subservient to it 211 4. General names not a mere contrivance to economize the use of language 213 Chapter IV. Of the Requisites of a Philosophical Language, and the Principles of Definition. § 1. First requisite of philosophical language, a steady and determinate meaning for every general name 215 2. Names in common use have often a loose connotation 215 3. —which the logician should fix, with as little alteration as possible 218 4. Why definition is often a question not of words but of things 220 5. How the logician should deal with the transitive applications of words 224 6. Evil consequences of casting off any portion of the customary connotation of words 229 Chapter V. On the Natural History of the Variations in the Meaning of Terms. § 1. How circumstances originally accidental become incorporated into the meaning of words 236 2. —and sometimes become the whole meaning 238 3. Tendency of words to become generalized 240 4. —and to become specialized 243 Chapter VI. The Principles of a Philosophical Language further considered. § 1. Second requisite of philosophical language, a name for every important meaning 248 2. —viz. first, an accurate descriptive terminology 248 3. —secondly, a name for each of the more important results of scientific abstraction 252 4. —thirdly, a nomenclature, or system of the names of Kinds 255 5. Peculiar nature of the connotation of names which belong to a nomenclature 257 6. In what cases language may, and may not, be used mechanically 259 Chapter VII. Of Classification, as subsidiary to Induction. § 1. Classification as here treated of, wherein different from the classification implied in naming 266 2. Theory of natural groups 267 3. Are natural groups given by type, or by definition? 271 4. Kinds are natural groups 274 5. How the names of Kinds should be constructed 280 Chapter VIII. Of Classification by Series. § 1. Natural groups should be arranged in a natural series 284 [Pg x] 2. The arrangement should follow the degrees of the main phenomenon 285 3. —which implies the assumption of a type-species 287 4. How the divisions of the series should be determined 288 5. Zoology affords the completest type of scientific classification 289 BOOK V. ON FALLACIES. Chapter I. Of Fallacies in General. § 1. Theory of fallacies a necessary part of logic 295 2. Casual mistakes are not fallacies 297 3. The moral sources of erroneous opinion, how related to the intellectual 297 Chapter II. Classification of Fallacies. § 1. On what criteria a classification of fallacies should be grounded 301 2. The five classes of fallacies 302 3. The reference of a fallacy to one or another class is sometimes arbitrary 305 Chapter III. Fallacies of Simple Inspection, or à priori Fallacies. § 1. Character of this class of Fallacies 309 2. Natural prejudice of mistaking subjective laws for objective, exemplified in popular superstitions 310 3. Natural prejudices, that things which we think of together must exist together, and that what is inconceivable must be false 314 4. Natural prejudice, of ascribing objective existence to abstractions 321 5. Fallacy of the Sufficient Reason 322 6. Natural prejudice, that the differences in nature correspond to the distinctions in language 325 7. Prejudice, that a phenomenon cannot have more than one cause 329 8. Prejudice, that the conditions of a phenomenon must resemble the phenomenon 332 Chapter IV. Fallacies of Observation. § 1. Non-observation, and Mal-observation 341 2. Non-observation of instances, and non-observation of circumstances 341 3. Examples of the former 342 4. —and of the latter 347 5. Mal-observation characterized and exemplified 352 Chapter V. Fallacies of Generalization. § 1. Character of the class 356 2. Certain kinds of generalization must always be groundless 356 3. Attempts to resolve phenomena radically different into the same 357 4. Fallacy of mistaking empirical for causal laws 359 5. Post hoc, ergo propter hoc; and the deductive fallacy corresponding to it 364 [Pg xi] [Pg xii] 6. Fallacy of False Analogies 366 7. Function of metaphors in reasoning 373 8. How fallacies of generalization grow out of bad classification 375 Chapter VI. Fallacies of Ratiocination. § 1. Introductory Remarks 377 2. Fallacies in the conversion and æquipollency of propositions 377 3. Fallacies in the syllogistic process 379 4. Fallacy of changing the premises 379 Chapter VII. Fallacies of Confusion. § 1. Fallacy of Ambiguous Terms 384 2. Fallacy of Petitio Principii 396 3. Fallacy of Ignoratio Elenchi 405 BOOK VI. ON THE LOGIC OF THE MORAL SCIENCES. Chapter I. Introductory Remarks. § 1. The backward state of the Moral Sciences can only be remedied by applying to them the methods of Physical Science, duly extended and generalized 413 2. How far this can be attempted in the present work 415 Chapter II. Of Liberty and Necessity. § 1. Are human actions subject to the law of causality? 417 2. The doctrine commonly called Philosophical Necessity, in what sense true 418 3. Inappropriateness and pernicious effect of the term Necessity 420 4. A motive not always the anticipation of a pleasure or a pain 424 Chapter III. That there is, or may be, a Science of Human Nature. § 1. There may be sciences which are not exact sciences 426 2. To what scientific type the Science of Human Nature corresponds 429 Chapter IV. Of the Laws of Mind. § 1. What is meant by Laws of Mind 432 2. Is there a science of Psychology? 433 3. The principal investigations of Psychology characterized 435 4. Relation of mental facts to physical conditions 440 Chapter V. Of Ethology, or the Science of the Formation of Character. § 1. The Empirical Laws of Human Nature 445 [Pg xiii] 2. —are merely approximate generalizations. The universal laws are those of the formation of character 447 3. The laws of the formation of character cannot be ascertained by observation and experiment 449 4. —but must be studied deductively 454 5. The Principles of Ethology are the axiomata media of mental science 455 6. Ethology characterized 459 Chapter VI. General Considerations on the Social Science. § 1. Are Social Phenomena a subject of Science? 461 2. Of what nature the Social Science must be 463 Chapter VII. Of the Chemical, or Experimental, Method in the Social Science. § 1. Characters of the mode of thinking which deduces political doctrines from specific experience 466 2. In the Social Science experiments are impossible 468 3. —the Method of Difference inapplicable 469 4. —and the Methods of Agreement, and of Concomitant Variations, inconclusive 471 5. The Method of Residues also inconclusive, and presupposes Deduction 472 Chapter VIII. Of the Geometrical, or Abstract Method. § 1. Characters of this mode of thinking 476 2. Examples of the Geometrical Method 478 3. The interest-philosophy of the Bentham school 479 Chapter IX. Of the Physical, or Concrete Deductive Method. § 1. The Direct and Inverse Deductive Methods 486 2. Difficulties of the Direct Deductive Method in the Social Science 489 3. To what extent the different branches of sociological speculation can be studied apart. Political Economy characterized 492 4. Political Ethology, or the science of national character 497 5. The Empirical Laws of the Social Science 500 6. The Verification of the Social Science 502 Chapter X. Of the Inverse Deductive, or Historical Method. § 1. Distinction between the general Science of Society, and special sociological inquiries 506 2. What is meant by a State of Society? 506 3. The Progressiveness of Man and Society 508 4. The laws of the succession of states of society can only be ascertained by the Inverse Deductive Method 511 5. Social Statics, or the science of the Coexistences of Social Phenomena 513 6. Social Dynamics, or the science of the Successions of Social Phenomena 521 7. Outlines of the Historical Method 522 8. Future prospects of Sociological Inquiry 525 Chapter XI. Additional Elucidations of the Science of History. [Pg xiv] [Pg xv] § 1. The subjection of historical facts to uniform laws is verified by statistics 529 2. —does not imply the insignificance of moral causes 532 3. —nor the inefficacy of the characters of individuals and of the acts of governments 535 4. The historical importance of eminent men and of the policy of governments illustrated 540 Chapter XII. Of the Logic of Practice, or Art; including Morality and Policy. § 1. Morality not a science, but an Art 544 2. Relation between rules of art and the theorems of the corresponding science 544 3. What is the proper function of rules of art? 546 4. Art cannot be Deductive 548 5. Every Art consists of truths of Science, arranged in the order suitable for some practical use 549 6. Teleology, or the Doctrine of Ends 550 7. Necessity of an ultimate standard, or first principle of Teleology 552 8. Conclusion 554 BOOK III. CONTINUED. OF INDUCTION. "In such cases the inductive and deductive methods of inquiry may be said to go hand in hand, the one verifying the conclusions deduced by the other; and the combination of experiment and theory, which may thus be brought to bear in such cases, forms an engine of discovery infinitely more powerful than either taken separately. This state of any department of science is perhaps of all others the most interesting, and that which promises the most to research."—Sir J. Herschel, Discourse on the Study of Natural Philosophy. CHAPTER XIV. OF THE LIMITS TO THE EXPLANATION OF LAWS OF NATURE; AND OF HYPOTHESES. § 1. The preceding considerations have led us to recognise a distinction between two kinds of laws, or observed uniformities in nature: ultimate laws, and what may be termed derivative laws. Derivative laws are such as are deducible from, and may, in any of the modes which we have pointed out, be resolved into, other and more general ones. Ultimate laws are those which cannot. We are not sure that any of the uniformities with which we are yet acquainted are ultimate laws; but we know that there must be ultimate laws; and that every resolution of a derivative law into more general laws, brings us nearer to them. Since we are continually discovering that uniformities, not previously known to be other than ultimate, are derivative, and resolvable into more general laws; since (in other words) we are continually discovering the explanation of some sequence which was previously known only as a fact; it becomes an interesting question whether there are any necessary limits to this philosophical operation, or whether it may proceed until all the uniform sequences in nature are resolved into some one universal law. For this seems, at first sight, to be the ultimatum towards which the progress of induction, by the Deductive Method resting on a basis of observation and experiment, is tending. Projects of this kind were universal in the infancy of philosophy; any speculations which held out a less brilliant prospect, being in those early times deemed not worth pursuing. And the idea receives so much apparent countenance from the nature of the most remarkable achievements of modern science, that speculators are even now frequently appearing, who profess either to have solved the problem, or to suggest modes in which it may one day be solved. Even where pretensions of this magnitude are not made, the character of the solutions which are given or sought of particular classes of phenomena, [Pg 1] [Pg 2] [Pg 3] [Pg 4] often involves such conceptions of what constitutes explanation, as would render the notion of explaining all phenomena whatever by means of some one cause or law, perfectly admissible. § 2. It is therefore useful to remark, that the ultimate Laws of Nature cannot possibly be less numerous than the distinguishable sensations or other feelings of our nature;—those, I mean, which are distinguishable from one another in quality, and not merely in quantity or degree. For example; since there is a phenomenon sui generis, called colour, which our consciousness testifies to be not a particular degree of some other phenomenon, as heat or odour or motion, but intrinsically unlike all others, it follows that there are ultimate laws of colour; that though the facts of colour may admit of explanation, they never can be explained from laws of heat or odour alone, or of motion alone, but that however far the explanation may be carried, there will always remain in it a law of colour. I do not mean that it might not possibly be shown that some other phenomenon, some chemical or mechanical action for example, invariably precedes, and is the cause of, every phenomenon of colour. But though this, if proved, would be an important extension of our knowledge of nature, it would not explain how or why a motion, or a chemical action, can produce a sensation of colour; and however diligent might be our scrutiny of the phenomena, whatever number of hidden links we might detect in the chain of causation terminating in the colour, the last link would still be a law of colour, not a law of motion, nor of any other phenomenon whatever. Nor does this observation apply only to colour, as compared with any other of the great classes of sensations; it applies to every particular colour, as compared with others. White colour can in no manner be explained exclusively by the laws of the production of red colour. In any attempt to explain it, we cannot but introduce, as one element of the explanation, the proposition that some antecedent or other produces the sensation of white. The ideal limit, therefore, of the explanation of natural phenomena (towards which as towards other ideal limits we are constantly tending, without the prospect of ever completely attaining it) would be to show that each distinguishable variety of our sensations, or other states of consciousness, has only one sort of cause; that, for example, whenever we perceive a white colour, there is some one condition or set of conditions which is always present, and the presence of which always produces in us that sensation. As long as there are several known modes of production of a phenomenon, (several different substances, for instance, which have the property of whiteness, and between which we cannot trace any other resemblance,) so long it is not impossible that one of these modes of production may be resolved into another, or that all of them may be resolved into some more general mode of production not hitherto recognised. But when the modes of production are reduced to one, we cannot, in point of simplification, go any further. This one may not, after all, be the ultimate mode; there may be other links to be discovered between the supposed cause and the effect; but we can only further resolve the known law, by introducing some other law hitherto unknown; which will not diminish the number of ultimate laws. In what cases, accordingly, has science been most successful in explaining phenomena, by resolving their complex laws into laws of greater simplicity and generality? Hitherto chiefly in cases of the propagation of various phenomena through space: and, first and principally, the most extensive and important of all facts of that description, the fact of motion. Now this is exactly what might be expected from the principles here laid down. Not only is motion one of the most universal of all phenomena, it is also (as might be expected from that circumstance) one of those which, apparently at least, are produced in the greatest number of ways; but the phenomenon itself is always, to our sensations, the same in every respect but degree. Differences of duration, or of velocity, are evidently differences in degree only; and differences of direction in space, which alone has any semblance of being a distinction in kind, entirely disappear (so far as our sensations are concerned) by a change in our own position; indeed the very same motion appears to us, according to our position, to take place in every variety of direction, and motions in every different direction to take place in the same. And again, motion in a straight line and in a curve are no otherwise distinct than that the one is motion continuing in the same direction, the other is motion which at each instant changes its direction. There is, therefore, according to the principles I have stated, no absurdity in supposing that all motion may be produced in one and the same way; by the same kind of cause. Accordingly, the greatest achievements in physical science have consisted in resolving one observed law of the production of motion into the laws of other known modes of production, or the laws of several such modes into one more general mode; as when the fall of bodies to the earth, and the motions of the planets, were brought under the one law of the mutual attraction of all particles of matter; when the motions said to be produced by magnetism were shown to be produced by electricity; when the motions of fluids in a lateral direction, or even contrary to the direction of gravity, were shown to be produced by gravity; and the like. There is an abundance of distinct causes of motion still unresolved into one another; gravitation, heat, electricity, chemical action, nervous action, and so forth; but whether the efforts of the present generation of savans to resolve all these different modes of production into one, are ultimately successful or not, the attempt so to resolve them is perfectly legitimate. For though these various causes produce, in other respects, sensations intrinsically different, and are not, therefore, capable of being resolved into one another, yet in so far as they all produce motion, it is quite possible that the immediate antecedent of the motion may in all these different cases be the same; nor is it impossible that these various agencies themselves may, as the new doctrines assert, all of them have for their own immediate antecedent, modes of molecular motion. We need not extend our illustration to other cases, as for instance to the propagation of light, sound, heat, electricity, &c. through space, or any of the other phenomena which have been found susceptible of explanation by the resolution of their observed laws into more general laws. Enough has been said to display the difference between the kind of explanation and resolution of laws which is chimerical, and that of which the accomplishment is the great aim of science; [Pg 5] [Pg 6] [Pg 7] and to show into what sort of elements the resolution must be effected, if at all. § 3. As, however, there is scarcely any one of the principles of a true method of philosophizing which does not require to be guarded against errors on both sides, I must enter a caveat against another misapprehension, of a kind directly contrary to the preceding. M. Comte, among other occasions on which he has condemned, with some asperity, any attempt to explain phenomena which are "evidently primordial," (meaning, apparently, no more than that every peculiar phenomenon must have at least one peculiar and therefore inexplicable law,) has spoken of the attempt to furnish any explanation of the colour belonging to each substance, "la couleur élémentaire propre à chaque substance," as essentially illusory. "No one," says he, "in our time attempts to explain the particular specific gravity of each substance or of each structure. Why should it be otherwise as to the specific colour, the notion of which is undoubtedly no less primordial?"[1] Now although, as he elsewhere observes, a colour must always remain a different thing from a weight or a sound, varieties of colour might nevertheless follow, or correspond to, given varieties of weight, or sound, or some other phenomenon as different as these are from colour itself. It is one question what a thing is, and another what it depends on; and though to ascertain the conditions of an elementary phenomenon is not to obtain any new insight into the nature o f the phenomenon itself, that is no reason against attempting to discover the conditions. The interdict against endeavouring to reduce distinctions of colour to any common principle, would have held equally good against a like attempt on the subject of distinctions of sound; which nevertheless have been found to be immediately preceded and caused by distinguishable varieties in the vibrations of elastic bodies: though a sound, no doubt, is quite as different as a colour is from any motion of particles, vibratory or otherwise. We might add, that, in the case of colours, there are strong positive indications that they are not ultimate properties of the different kinds of substances, but depend on conditions capable of being superinduced upon all substances; since there is no substance which cannot, according to the kind of light thrown upon it, be made to assume almost any colour; and since almost every change in the mode of aggregation of the particles of the same substance, is attended with alterations in its colour, and in its optical properties generally. The real defect in the attempts which have been made to account for colours by the vibrations of a fluid, is not that the attempt itself is unphilosophical, but that the existence of the fluid, and the fact of its vibratory motion, are not proved; but are assumed, on no other ground than the facility they are supposed to afford of explaining the phenomena. And this consideration leads to the important question of the proper use of scientific hypotheses; the connexion of which with the subject of the explanation of the phenomena of nature, and of the necessary limits to that explanation, needs not be pointed out. § 4. An hypothesis is any supposition which we make (either without actual evidence, or on evidence avowedly insufficient) in order to endeavour to deduce from it conclusions in accordance with facts which are known to be real; under the idea that if the conclusions to which the hypothesis leads are known truths, the hypothesis itself either must be, or at least is likely to be, true. If the hypothesis relates to the cause, or mode of production of a phenomenon, it will serve, if admitted, to explain such facts as are found capable of being deduced from it. And this explanation is the purpose of many, if not most, hypotheses. Since explaining, in the scientific sense, means resolving an uniformity which is not a law of causation, into the laws of causation from which it results, or a complex law of causation into simpler and more general ones from which it is capable of being deductively inferred; if there do not exist any known laws which fulfil this requirement, we may feign or imagine some which would fulfil it; and this is making an hypothesis. An hypothesis being a mere supposition, there are no other limits to hypotheses than those of the human imagination; we may, if we please, imagine, by way of accounting for an effect, some cause of a kind utterly unknown, and acting according to a law altogether fictitious. But as hypotheses of this sort would not have any of the plausibility belonging to those which ally themselves by analogy with known laws of nature, and besides would not supply the want which arbitrary hypotheses are generally invented to satisfy, by enabling the imagination to represent to itself an obscure phenomenon in a familiar light; there is probably no hypothesis in the history of science in which both the agent itself and the law of its operation were fictitious. Either the phenomenon assigned as the cause is real, but the law according to which it acts, merely supposed; or the cause is fictitious, but is supposed to produce its effects according to laws similar to those of some known class of phenomena. An instance of the first kind is afforded by the different suppositions made respecting the law of the planetary central force, anterior to the discovery of the true law, that the force varies as the inverse square of the distance; which also suggested itself to Newton, in the first instance, as an hypothesis, and was verified by proving that it led deductively to Kepler's laws. Hypotheses of the second kind are such as the vortices of Descartes, which were fictitious, but were supposed to obey the known laws of rotatory motion; or the two rival hypotheses respecting the nature of light, the one ascribing the phenomena to a fluid emitted from all luminous bodies, the other (now generally received) attributing them to vibratory motions among the particles of an ether pervading all space. Of the existence of either fluid there is no evidence, save the explanation they are calculated to afford of some of the phenomena; but they are supposed to produce their effects according to known laws; the ordinary laws of continued locomotion in the one case, and in the other, those of the propagation of undulatory movements among the particles of an elastic fluid. According to the foregoing remarks, hypotheses are invented to enable the Deductive Method to be earlier applied to [Pg 8] [Pg 9] [Pg 10] phenomena. But[2] in order to discover the cause of any phenomenon by the Deductive Method, the process must consist of three parts; induction, ratiocination, and verification. Induction, (the place of which, however, may be supplied by a prior deduction,) to ascertain the laws of the causes; ratiocination, to compute from those laws, how the causes will operate in the particular combination known to exist in the case in hand; verification, by comparing this calculated effect with the actual phenomenon. No one of these three parts of the process can be dispensed with. In the deduction which proves the identity of gravity with the central force of the solar system, all the three are found. First, it is proved from the moon's motions, that the earth attracts her with a force varying as the inverse square of the distance. This (though partly dependent on prior deductions) corresponds to the first, or purely inductive, step, the ascertainment of the law of the cause. Secondly, from this law, and from the knowledge previously obtained of the moon's mean distance from the earth, and of the actual amount of her deflexion from the tangent, it is ascertained with what rapidity the earth's attraction would cause the moon to fall, if she were no further off, and no more acted upon by extraneous forces, than terrestrial bodies are: that is the second step, the ratiocination. Finally, this calculated velocity being compared with the observed velocity with which all heavy bodies fall, by mere gravity, towards the surface of the earth, (sixteen feet in the first second, forty-eight in the second, and so forth, in the ratio of the odd numbers, 1, 3, 5, &c.,) the two quantities are found to agree. The order in which the steps are here presented, was not that of their discovery; but it is their correct logical order, as portions of the proof that the same attraction of the earth which causes the moon's motion, causes also the fall of heavy bodies to the earth: a proof which is thus complete in all its parts. Now, the Hypothetical Method suppresses the first of the three steps, the induction to ascertain the law; and contents itself with the other two operations, ratiocination and verification; the law which is reasoned from, being assumed, instead of proved. This process may evidently be legitimate on one supposition, namely, if the nature of the case be such that the final step, the verification, shall amount to, and fulfil the conditions of, a complete induction. We want to be assured that the law we have hypothetically assumed is a true one; and its leading deductively to true results will afford this assurance, provided the case be such that a false law cannot lead to a true result; provided no law, except the very one which we have assumed, can lead deductively to the same conclusions which that leads to. And this proviso is often realized. For example, in the very complete specimen of deduction which we just cited, the original major premise of the ratiocination, the law of the attractive force, was ascertained in this mode; by this legitimate employment of the Hypothetical Method. Newton began by an assumption, that the force which at each instant deflects a planet from its rectilineal course, and makes it describe a curve round the sun, is a force tending directly towards the sun. He then proved that if this be so, the planet will describe, as we know by Kepler's first law that it does describe, equal areas in equal times; and, lastly, he proved that if the force acted in any other direction whatever, the planet would not describe equal areas in equal times. It being thus shown that no other hypothesis would accord with the facts, the assumption was proved; the hypothesis became an inductive truth. Not only did Newton ascertain by this hypothetical process the direction of the deflecting force; he proceeded in exactly the same manner to ascertain the law of variation of the quantity of that force. He assumed that the force varied inversely as the square of the distance; showed that from this assumption the remaining two of Kepler's laws might be deduced; and finally, that any other law of variation would give results inconsistent with those laws, and inconsistent, therefore, with the real motions of the planets, of which Kepler's laws were known to be a correct expression. I have said that in this case the verification fulfils the conditions of an induction: but an induction of what sort? On examination we find that it conforms to the canon of the Method of Difference. It affords the two instances, A B C, a b c, and B C, b c. A represents central force; A B C, the planets plus a central force; B C, the planets apart from a central force. The planets with a central force give a, areas proportional to the times; the planets without a central force give b c (a set of motions) without a, or with something else instead of a. This is the Method of Difference in all its strictness. It is true, the two instances which the method requires are obtained in this case, not by experiment, but by a prior deduction. But that is of no consequence. It is immaterial what is the nature of the evidence from which we derive the assurance that A B C will produce a b c, and B C only b c; it is enough that we have that assurance. In the present case, a process of reasoning furnished Newton with the very instances, which, if the nature of the case had admitted of it, he would have sought by experiment. It is thus perfectly possible, and indeed is a very common occurrence, that what was an hypothesis at the beginning of the inquiry, becomes a proved law of nature before its close. But in order that this should happen, we must be able, either by deduction or experiment, to obtain both the instances which the Method of Difference requires. That we are able from the hypothesis to deduce the known facts, gives only the affirmative instance, A B C, a b c. It is equally necessary that we should be able to obtain, as Newton did, the negative instance B C, b c; by showing that no antecedent, except the one assumed in the hypothesis, would in conjunction with B C produce a. Now it appears to me that this assurance cannot be obtained, when the cause assumed in the hypothesis is an unknown cause, imagined solely to account for a. When we are only seeking to determine the precise law of a cause already ascertained, or to distinguish the particular agent which is in fact the cause, among several agents of the same kind, one or other of which it is already known to be, we may then obtain the negative instance. An inquiry, which of the bodies of the solar system causes by its attraction some particular irregularity in the orbit or periodic time of some satellite or comet, would be a case of the second description. Newton's was a case of the first. If it had not been previously known that the planets were hindered from moving in straight lines by some force tending towards the interior of their orbit, though the exact direction was doubtful; or if it had not been known that the force increased in some proportion or [Pg 11] [Pg 12] [Pg 13] other as the distance diminished, and diminished as it increased; Newton's argument would not have proved his conclusion. These facts, however, being already certain, the range of admissible suppositions was limited to the various possible directions of a line, and the various possible numerical relations between the variations of the distance, and the variations of the attractive force: now among these it was easily shown that different suppositions could not lead to identical consequences. Accordingly, Newton could not have performed his second great scientific operation, that of identifying terrestrial gravity with the central force of the solar system, by the same hypothetical method. When the law of the moon's attraction had been proved from the data of the moon itself, then on finding the same law to accord with the phenomena of terrestrial gravity, he was warranted in adopting it as the law of those phenomena likewise; but it would not have been allowable for him, without any lunar data, to assume that the moon was attracted towards the earth with a force as the inverse square of the distance, merely because that ratio would enable him to account for terrestrial gravity: for it would have been impossible for him to prove that the observed law of the fall of heavy bodies to the earth could not result from any force, save one extending to the moon, and proportional to the inverse square. It appears, then, to be a condition of a genuinely scientific hypothesis, that it be not destined always to remain an hypothesis, but be of such a nature as to be either proved or disproved by comparison with observed facts. This condition is fulfilled when the effect is already known to depend on the very cause supposed, and the hypothesis relates only to the precise mode of dependence; the law of the variation of the effect according to the variations in the quantity or in the relations of the cause. With these may be classed the hypotheses which do not make any supposition with regard to causation, but only with regard to the law of correspondence between facts which accompany each other in their variations, though there may be no relation of cause and effect between them. Such were the different false hypotheses which Kepler made respecting the law of the refraction of light. It was known that the direction of the line of refraction varied with every variation in the direction of the line of incidence, but it was not known how; that is, what changes of the one corresponded to the different changes of the other. In this case any law, different from the true one, must have led to false results. And, lastly, we must add to these, all hypothetical modes of merely representing, or describing, phenomena; such as the hypothesis of the ancient astronomers that the heavenly bodies moved in circles; the various hypotheses of excentrics, deferents, and epicycles, which were added to that original hypothesis; the nineteen false hypotheses which Kepler made and abandoned respecting the form of the planetary orbits; and even the doctrine in which he finally rested, that those orbits are ellipses, which was but an hypothesis like the rest until verified by facts. In all these cases, verification is proof; if the supposition accords with the phenomena there needs no other evidence of it. But in order that this may be the case, I conceive it to be necessary, when the hypothesis relates to causation, that the supposed cause should not only be a real phenomenon, something actually existing in nature, but should be already known to exercise, or at least to be capable of exercising, an influence of some sort over the effect. In any other case, it is no evidence of the truth of the hypothesis that we are able to deduce the real phenomena from it. Is it, then, never allowable, in a scientific hypothesis, to assume a cause; but only to ascribe an assumed law to a known cause? I do not assert this. I only say, that in the latter case alone can the hypothesis be received as true merely because it explains the phenomena: in the former case it is only useful by suggesting a line of investigation which may possibly terminate in obtaining real proof. For this purpose, as is justly remarked by M. Comte, it is indispensable that the cause suggested by the hypothesis should be in its own nature susceptible of being proved by other evidence. This seems to be the philosophical import of Newton's maxim, (so often cited with approbation by subsequent writers,) that the cause assigned for any phenomenon must not only be such as if admitted would explain the phenomenon, but must also be a vera causa. What he meant by a vera causa Newton did not indeed very explicitly define; and Dr. Whewell, who dissents from the propriety of any such restriction upon the latitude of framing hypotheses, has had little difficulty in showing[3] that his conception of it was neither precise nor consistent with itself: accordingly his optical theory was a signal instance of the violation of his own rule. It is certainly not necessary that the cause assigned should be a cause already known; else how could we ever become acquainted with any new cause? But what is true in the maxim is, that the cause, though not known previously, should be capable of being known thereafter; that its existence should be capable of being detected, and its connexion with the effect ascribed to it should be susceptible of being proved, by independent evidence. The hypothesis, by suggesting observations and experiments, puts us on the road to that independent evidence if it be really attainable; and till it be attained, the hypothesis ought not to count for more than a conjecture. § 5. This function, however, of hypotheses, is one which must be reckoned absolutely indispensable in science. When Newton said, "Hypotheses non fingo," he did not mean that he deprived himself of the facilities of investigation afforded by assuming in the first instance what he hoped ultimately to be able to prove. Without such assumptions, science could never have attained its present state: they are necessary steps in the progress to something more certain; and nearly everything which is now theory was once hypothesis. Even in purely experimental science, some inducement is necessary for trying one experiment rather than another; and though it is abstractedly possible that all the experiments which have been tried, might have been produced by the mere desire to ascertain what would happen in certain circumstances, without any previous conjecture as to the result; yet, in point of fact, those unobvious, delicate, and often cumbrous and tedious processes of experiment, which have thrown most light upon the general constitution of nature, would hardly ever have been undertaken by the persons or at the time they were, unless it had seemed to depend on [Pg 14] [Pg 15] [Pg 16] them whether some general doctrine or theory which had been suggested, but not yet proved, should be admitted or not. If this be true even of merely experimental inquiry, the conversion of experimental into deductive truths could still less have been effected without large temporary assistance from hypotheses. The process of tracing regularity in any complicated, and at first sight confused set of appearances, is necessarily tentative: we begin by making any supposition, even a false one, to see what consequences will follow from it; and by observing how these differ from the real phenomena, we learn what corrections to make in our assumption. The simplest supposition which accords with the more obvious facts, is the best to begin with; because its consequences are the most easily traced. This rude hypothesis is then rudely corrected, and the operation repeated; and the comparison of the consequences deducible from the corrected hypothesis, with the observed facts, suggests still further correction, until the deductive results are at last made to tally with the phenomena. "Some fact is as yet little understood, or some law is unknown: we frame on the subject an hypothesis as accordant as possible with the whole of the data already possessed; and the science, being thus enabled to move forward freely, always ends by leading to new consequences capable of observation, which either confirm or refute, unequivocally, the first supposition." Neither induction nor deduction would enable us to understand even the simplest phenomena, "if we did not often commence by anticipating on the results; by making a provisional supposition, at first essentially conjectural, as to some of the very notions which constitute the final object of the inquiry."[4] Let any one watch the manner in which he himself unravels a complicated mass of evidence; let him observe how, for instance, he elicits the true history of any occurrence from the involved statements of one or of many witnesses: he will find that he does not take all the items of evidence into his mind at once, and attempt to weave them together: he extemporises, from a few of the particulars, a first rude theory of the mode in which the facts took place, and then looks at the other statements one by one, to try whether they can be reconciled with that provisional theory, or what alterations or additions it requires to make it square with them. In this way, which has been justly compared to the Methods of Approximation of mathematicians, we arrive, by means of hypotheses, at conclusions not hypothetical.[5] § 6. It is perfectly consistent with the spirit of the method, to assume in this provisional manner not only an hypothesis respecting the law of what we already know to be the cause, but an hypothesis respecting the cause itself. It is allowable, useful, and often even necessary, to begin by asking ourselves what cause may have produced the effect, in order that we may know in what direction to look out for evidence to determine whether it actually did. The vortices of Descartes would have been a perfectly legitimate hypothesis, if it had been possible, by any mode of exploration which we could entertain the hope of ever possessing, to bring the reality of the vortices, as a fact in nature, conclusively to the test of observation. The hypothesis was vicious, simply because it could not lead to any course of investigation capable of converting it from an hypothesis into a proved fac...