CHAPTER VIII.Methods of Induction depending on Resemblance.AphorismXLIX.The Law of Continuityis 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. This Law may often be employed to disprove distinctions which have no real foundation.AphorismL.The Method of Gradationconsists in taking a number of stages of a property in question, intermediate between two extreme cases which appear to be different. This Method is employed to determine whether the extreme cases are really distinct or not.AphorismLI.The Method of Gradation, applied to decide the question, whether the existinggeologicalphenomena 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 may, in past times, have transgressed, to any extent, theirrecordedlimits of intensity.AphorismLII.The Method of Natural Classificationconsists in classing cases, not according to anyassumedDefinition, but according to the connexion of the facts themselves, so as to make them the means of asserting general truths.221Sect.I.—The Law of Continuity.1.THE Law of Continuity is applicable to quantity primarily, and therefore might be associated with the methods treated of in the last chapter: but inasmuch as its inferences are made by a transition from one degree to another among contiguous cases, it will be found to belong more properly to the Methods of Induction of which we have now to speak.TheLaw of Continuityconsists in this proposition,—That a quantity cannot pass from one amount to another by any change of conditions, without passing through all intermediate degrees of magnitude according to the intermediate conditions. And this law may often be employed to correct inaccurate inductions, and to reject distinctions which have no real foundation in nature. For example, the Aristotelians made a distinction between motions according to nature, (as that of a body falling vertically downwards,) and motions contrary to nature, (as that of a body moving along a horizontal plane:) the former, they held, became naturally quicker and quicker, the latter naturally slower and slower. But to this it might be replied, that a horizontal line may pass, by gradual motion, through various inclined positions, to a vertical position: and thus the retarded motion may pass into the accelerated; and hence there must be some inclined plane on which the motion downwards is naturally uniform: which is false, and therefore the distinction of such kinds of motion is unfounded. Again, the proof of the First Law of Motion depends upon the Law of Continuity: for since, by diminishing the resistance to a body moving on a horizontal plane, we diminish the retardation, and this without limit, the law of continuity will bring us at the same time to the case of no resistance and to the case of no retardation.2. The Law of Continuity is asserted by Galileo in a particular application; and the assertion which it222suggests is by him referred to Plato;—namely36that a moveable body cannot pass from rest to a determinate degree of velocity without passing through all smaller degrees of velocity. This law, however, was first asserted in a more general and abstract form by Leibnitz37: and was employed by him to show that the laws of motion propounded by Descartes must be false. The Third Cartesian Law of Motion was this38: that when one moving body meets another, if the first body have a less momentum than the second, it will be reflected with its whole motion: but if the first have a greater momentum than the second, it will lose a part of its motion, which it will transfer to the second. Now each of these cases leads, by the Law of Continuity, to the case in which the two bodies haveequalmomentums: but in this case, by the first part of the law the body wouldretain allits motion; and by the second part of the law it wouldlosea portion of it: hence the Cartesian Law is false.36Dialog.iii. 150. iv. 32.37Opera, i. 366.38Cartes,Prin.p. 35.3. I shall take another example of the application of this Law from Professor Playfair’s Dissertation on the History of Mathematical and Physical Science39. ‘The Academy of Sciences at Paris having (in 1724) proposed, as a Prize Question, the Investigation of the Laws of the Communication of Motion, John Bernoulli presented an Essay on the subject very ingenious and profound; in which, however, he denied the existence of hard bodies, because in the collision of such bodies, a finite change of motion must take place in an instant: an event which, on the principle just explained, he maintained to be impossible.’ And this reasoning was justifiable: for we can form acontinuoustransition from cases in which the impact manifestly occupies a finite time, (as when we strike a large soft body) to cases in which it is apparently instantaneous. Maclaurin and others are disposed, in order to avoid the conclusion of Bernoulli, to reject the Law of223Continuity. This, however, would not only be, as Playfair says, to deprive ourselves of an auxiliary, commonly useful though sometimes deceptive; but what is much worse, to acquiesce in false propositions, from the want of clear and patient thinking. For the Law of Continuity, when rightly interpreted, isneverviolated in actual fact. There are not really any such bodies as have been termedperfectly hard: and if we approach towards such cases, we must learn the laws of motion which rule them by attending to the Law of Continuity, not by rejecting it.39In theEncyc. Brit.p. 537.4. Newton used the Law of Continuity to suggest, but not to prove, the doctrine of universal gravitation. Let, he said, a terrestrial body be carried as high as the moon: will it not still fall to the earth? and does not the moon fall by the same force40? Again: if any one says that there is a material ether which does not gravitate41, this kind of matter, by condensation, may be gradually transmuted to the density of the most intensely gravitating bodies: and these gravitating bodies, by taking the internal texture of the condensed ether, may cease to gravitate; and thus the weight of bodies depends, not on their quantity of matter, but on their texture; which doctrine Newton conceived he had disproved by experiment.40Principia, lib. iii. prop. 6.41Ib.cor. 2.5. The evidence of the Law of Continuity resides in the universality of those Ideas, which enter into our apprehension of Laws of Nature. When, of two quantities, one depends upon the other, the Law of Continuity necessarily governs this dependence. Every philosopher has the power of applying this law, in proportion as he has the faculty of apprehending the Ideas which he employs in his induction, with the same clearness and steadiness which belong to the fundamental ideas of Quantity, Space and Number. To those who possess this faculty, the Law is a Rule of very wide and decisive application. Its use, as has appeared in the above examples, is seen rather in the disproof of erroneous views, and in the correction of false propositions,224than in the invention of new truths. It is a test of truth, rather than an instrument of discovery.Methods, however, approaching very near to the Law of Continuity may be employed as positive means of obtaining new truths; and these I shall now describe.Sect.II.—The Method of Gradation.6. To gather together the cases which resemble each other, and to separate those which are essentially distinct, has often been described as the main business of science; and may, in a certain loose and vague manner of speaking, pass for a description of some of the leading procedures in the acquirement of knowledge. The selection of instances which agree, and of instances which differ, in some prominent point or property, are important steps in the formation of science. But when classes of things and properties have been established in virtue of such comparisons, it may still be doubtful whether these classes are separated by distinctions of opposites, or by differences of degree. And to settle such questions, theMethod of Gradationis employed; which consists in taking intermediate stages of the properties in question, so as to ascertain by experiment whether, in the transition from one class to another, we have to leap over a manifest gap, or to follow a continuous road.7. Thus for instance, one of the earlyDivisionsestablished by electrical philosophers was that ofElectricsandConductors. But this division Dr. Faraday has overturned as an essential opposition. He takes42aGradationwhich carries him from Conductors to Non-conductors. Sulphur, or Lac, he says, are held to be non-conductors, but are not rigorously so. Spermaceti is a bad conductor: ice or water better than spermaceti: metals so much better that they are put in a different class. But even in metals the transit of the electricity is not instantaneous: we have in them proof of a retardation of the electric current: ‘and what225reason,” Mr. Faraday asks, “why this retardation should not be of the same kind as that in spermaceti, or in lac, or sulphur? But as, in them, retardation is insulation, [and insulation is induction43] why should we refuse the same relation to the same exhibitions of force in the metals?”42Researches, 12th series, art. 1328.43These words refer to another proposition, also established by the Method of Gradation.The process employed by the same sagacious philosopher to show theidentityof Voltaic and Franklinic electricity, is another example of the same kind44. Machine [Franklinic] electricity was made to exhibit the same phenomena as Voltaic electricity, by causing the discharge to pass through a bad conductor, into a very extensive discharging train: and thus it was clearly shown that Franklinic electricity, not so conducted, differs from the other kinds, only in being in a state of successive tension and explosion instead of a state of continued current.44Hist. Ind. Sc.b. xiv. c. ix. sect. 2.Again; to show that the decomposition of bodies in the Voltaic circuit was not due to theAttractionof the Poles45, Mr. Faraday devised a beautiful series of experiments, in which these supposedPoleswere made to assume all possible electrical conditions:—in some cases the decomposition took place against air, which according to common language is not a conductor, nor is decomposed;—in others, against the metallic poles, which are excellent conductors but undecomposable;—and so on: and hence he infers that the decomposition cannot justly be considered as due to the Attraction, or Attractive Powers, of the Poles.45Ibid. Researches, art. 497.8. The reader of theNovum Organonmay perhaps, in looking at such examples of the Rule, be reminded of some of Bacon’s Classes of Instances, as hisinstantiæ absentiæ in proximo, and hisinstantiæ migrantes. But we may remark that Instances classed and treated as Bacon recommends in those parts of his work, could hardly lead to scientific truth. His226processes are vitiated by his proposing to himself theformorcauseof the property before him, as the object of his inquiry; instead of being content to obtain, in the first place, thelaw of phenomena. Thus his example46of a Migrating Instance is thus given. “Let theNature inquired intobe that of Whiteness; an Instance Migrating to the production of this property is glass, first whole, and then pulverized; or plain water, and water agitated into a foam; for glass and water are transparent, and not white; but glass powder and foam are white, and not transparent. Hence we must inquire what has happened to the glass or water in that Migration. For it is plain that theForm of Whitenessis conveyed and induced by the crushing of the glass and shaking of the water.” No real knowledge has resulted from this line of reasoning:—from taking the Natures and Forms of things and of their qualities for the primary subject of our researches.46Nov. Org.lib. ii. Aph. 28.9. We may easily give examples from other subjects in which the Method of Gradation has been used to establish, or to endeavour to establish, very extensive propositions. Thus Laplace’s Nebular Hypothesis,—that systems like our solar system are formed by gradual condensation from diffused masses, such as the nebulæ among the stars,—is founded by him upon an application of this Method of Gradation. We see, he conceives, among these nebulæ, instances of all degrees of condensation, from the most loosely diffused fluid, to that separation and solidification of parts by which suns, and satellites, and planets are formed: and thus we have before us instances of systems in all their stages; as in a forest we see trees in every period of growth. How far the examples in this case satisfy the demands of the Method of Gradation, it remains for astronomers and philosophers to examine.Again; this method was used with great success by Macculloch and others to refute the opinion, put in currency by the Wernerian school of geologists, that227the rocks calledtrap rocksmust be classed with those to which asedimentaryorigin is ascribed. For it was shown that a gradualtransitionmight be traced from those examples in which trap rocks most resembled stratified rocks, to the lavas which have been recently ejected from volcanoes: and that it was impossible to assign a different origin to one portion, and to the other, of this kind of mineral masses; and as the volcanic rocks were certainly not sedimentary, it followed, that the trap rocks were not of that nature.Again; we have an attempt of a still larger kind made by Sir C. Lyell, to apply this Method of Gradation so as to disprove all distinction between the causes by which geological phenomena have been produced, and the causes which are now acting at the earth’s surface. He has collected a very remarkable series of changes which have taken place, and are still taking place, by the action of water, volcanoes, earthquakes, and other terrestrial operations; and he conceives he has shown in these agradationwhich leads, with no wide chasm or violent leap, to the state of things of which geological researches have supplied the evidence.10. Of the value of this Method in geological speculations, no doubt can be entertained. Yet it must still require a grave and profound consideration, in so vast an application of the Method as that attempted by Sir C. Lyell, to determine what extent we may allow to the steps of ourgradation; and to decide how far the changes which have taken place in distant parts of the series may exceed those of which we have historical knowledge, without ceasing to be of thesame kind. Those who, dwelling in a city, see, from time to time, one house built and another pulled down, may say that suchexisting causes, operating through past time, sufficiently explain the existing condition of the city. Yet we arrive at important political and historical truths, by considering theoriginof a city as an event of adifferent orderfrom those daily changes. The causes which are now working to produce geological results, may be supposed to have been, at some former epoch, so far exaggerated in their operation, that the changes228should be paroxysms, not degrees;—that they should violate, not continue, the gradual series. And we have no kind of evidence whether the duration of our historical times is sufficient to give us a just measure of the limits of such degrees;—whether the terms which we have under our notice enable us to ascertain the average rate of progression.11. The result of such considerations seems to be this:—that we may apply the Method of Gradation in the investigation of geological causes, provided we leave the Limits of the Gradation undefined. But, then, this is equivalent to the admission of the opposite hypothesis: for a continuity of which the successive intervals are not limited, is not distinguishable from discontinuity. The geological sects of recent times have been distinguished asuniformitariansandcatastrophists: the Method of Gradation seems to prove the doctrine of the uniformitarians; but then, at the same time that it does this, it breaks down the distinction between them and the catastrophists.There are other exemplifications of the use of gradations in Science which well deserve notice: but some of them are of a kind somewhat different, and may be considered under a separate head.Sect.III.The Method of Natural Classification.12. The Method of Natural Classification consists, as we have seen, in grouping together objects, not according to any selected properties, but according to their most important resemblances; and in combining such grouping with the assignation of certain marks of the classes thus formed. The examples of the successful application of this method are to be found in the Classificatory Sciences through their whole extent; as, for example, in framing the Genera of plants and animals. The same method, however, may often be extended to other sciences. Thus the classification of Crystalline Forms, according to their Degree of Symmetry, (which is really an important distinction,) as introduced by Mohs and Weiss, was a great improvement229upon Haüy’s arbitrary division according to certain assumed primary forms. Sir David Brewster was led to the same distinction of crystals by the study of their optical properties; and the scientific value of the classification was thus strongly exhibited. Mr. Howard’s classification of Clouds appears to be founded in their real nature, since it enables him to express the laws of their changes and successions. As we have elsewhere said, the criterion of a true classification is, that it makes general propositions possible. One of the most prominent examples of the beneficial influence of a right classification, is to be seen in the impulse given to geology by the distinction of strata according to the organic fossils which they contain47: which, ever since its general adoption, has been a leading principle in the speculations of geologists.47Hist. Ind. Sc.b. xviii. c. ii. sect. 3.13. The mode in which, in this and in other cases, the Method of Natural Classification directs the researches of the philosopher, is this:—his arrangement being adopted, at least as an instrument of inquiry and trial, he follows the course of the different members of the classification, according to the guidance which Nature herself offers; not prescribing beforehand the marks of each part, but distributing the facts according to the total resemblances, or according to those resemblances which he finds to be most important. Thus, in tracing the course of a series of strata from place to place, we identify each stratum, not by any single character, but by all taken together;—texture, colour, fossils, position, and any other circumstances which offer themselves. And if, by this means, we come to ambiguous cases, where different indications appear to point different ways, we decide so as best to preserve undamaged those general relations and truths which constitute the value of our system. Thus although we consider the organic fossils in each stratum as its most important characteristic, we are not prevented, by the disappearance of some fossils, or the addition of others, or by the total absence of fossils,230from identifying strata in distant countries, if the position and other circumstances authorize us to do so. And by this Method of Classification, the doctrine ofGeological Equivalents48has been applied to a great part of Europe.48Hist. Ind. Sc.b. xviii. c. iii. sect. 4.14. We may further observe, that the same method of natural classification which thus enables us to identify strata in remote situations, notwithstanding that there may be great differences in their material and contents, also forbids us to assume the identity of the series of rocks which occur in different countries, when this identity has not been verified by such a continuous exploration of the component members of the series. It would be in the highest degree unphilosophical to apply the special names of the English or German strata to the rocks of India, or America, or even of southern Europe, till it has appeared that in those countries the geological series of northern Europe really exists. In each separate country, the divisions of the formations which compose the crust of the earth must be made out, by applying the Method of Natural Arrangementto that particular case, and not by arbitrarily extending to it the nomenclature belonging to another case. It is only by such precautions, that we can ever succeed in obtaining geological propositions, at the same time true and comprehensive; or can obtain any sound general views respecting the physical history of the earth.15. The Method of Natural Classification, which we thus recommend, falls in with those mental habits which we formerly described as resulting from the study of Natural History. The method was then termed theMethod of Type, and was put in opposition to theMethod of Definition.The Method of Natural Classification is directly opposed to the process in which we assume and applyarbitrarydefinitions; for in the former Method, we find our classes in nature, and do not make them by marks of our own imposition. Nor can any advantage231to the progress of knowledge be procured, by laying down our characters when our arrangements are as yet quite loose and unformed. Nothing was gained by the attempts todefineMetals by their weight, their hardness, their ductility, their colour; for to all these marks, as fast as they were proposed, exceptions were found, among bodies which still could not be excluded from the list of Metals. It was only when elementary substances were divided intoNatural Classes, of which classes Metals were one, that a true view of their distinctive characters was obtained. Definitions in the outset of our examination of nature are almost always, not only useless, but prejudicial.16. When we obtain a Law of Nature by induction from phenomena, it commonly happens, as we have already seen, that we introduce, at the same time, a Proposition and a Definition. In this case, the two are correlative, each giving a real value to the other. In such cases, also, the Definition, as well as the Proposition, may become the basis of rigorous reasoning, and may lead to a series of deductive truths. We have examples of such Definitions and Propositions in the Laws of Motion, and in many other cases.17. When we have established Natural Classes of objects, we seek for Characters of our classes; and these Characters may, to a certain extent, be called theDefinitionsof our classes. This is to be understood, however, only in a limited sense: for these Definitions are not absolute and permanent. They are liable to be modified and superseded. If we find a case which manifestly belongs to our Natural Class, though violating our Definition, we do not shut out the case, but alter our definition. Thus, when we have made it part of our Definition of theRosefamily, that they havealternate stipulate leaves, we do not, therefore, exclude from the family the genusLowæa, which hasno stipulæ. In Natural Classifications, our Definitions are to be considered as temporary and provisional only. When Sir C. Lyell established the distinctions of the tertiary strata, which he termedEocene,Miocene, andPliocene, he took a numerical criterion232(the proportion of recent species of shells contained in those strata) as the basis of his division. But now that those kinds of strata have become, by their application to a great variety of cases, a series of Natural Classes, we must, in our researches, keep in view the natural connexion of the formations themselves in different places; and must by no means allow ourselves to be governed by the numerical proportions which were originally contemplated; or even by any amended numerical criterion equally arbitrary; for however amended, Definitions in natural history are never immortal. The etymologies ofPlioceneandMiocenemay, hereafter, come to have merely an historical interest; and such a state of things will be no more inconvenient, provided the natural connexions of each class are retained, than it is to call a rockooliteorporphyry, when it has no roelike structure and no fiery spots.The Methods of Induction which are treated of in this and the preceding chapter, and which are specially applicable to causes governed by relations of Quantity or of Resemblance, commonly lead us toLaws of Phenomenaonly. Inductions founded upon other ideas, those of Substance and Cause for example, appear to conduct us somewhat further into a knowledge of the essential nature and real connexions of things. But before we speak of these, we shall say a few words respecting the way in which inductive propositions, once obtained, may be verified and carried into effect by their application.
CHAPTER VIII.Methods of Induction depending on Resemblance.
AphorismXLIX.
The Law of Continuityis 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. This Law may often be employed to disprove distinctions which have no real foundation.
AphorismL.
The Method of Gradationconsists in taking a number of stages of a property in question, intermediate between two extreme cases which appear to be different. This Method is employed to determine whether the extreme cases are really distinct or not.
AphorismLI.
The Method of Gradation, applied to decide the question, whether the existinggeologicalphenomena 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 may, in past times, have transgressed, to any extent, theirrecordedlimits of intensity.
AphorismLII.
The Method of Natural Classificationconsists in classing cases, not according to anyassumedDefinition, but according to the connexion of the facts themselves, so as to make them the means of asserting general truths.221
Sect.I.—The Law of Continuity.
1.THE Law of Continuity is applicable to quantity primarily, and therefore might be associated with the methods treated of in the last chapter: but inasmuch as its inferences are made by a transition from one degree to another among contiguous cases, it will be found to belong more properly to the Methods of Induction of which we have now to speak.
TheLaw of Continuityconsists in this proposition,—That a quantity cannot pass from one amount to another by any change of conditions, without passing through all intermediate degrees of magnitude according to the intermediate conditions. And this law may often be employed to correct inaccurate inductions, and to reject distinctions which have no real foundation in nature. For example, the Aristotelians made a distinction between motions according to nature, (as that of a body falling vertically downwards,) and motions contrary to nature, (as that of a body moving along a horizontal plane:) the former, they held, became naturally quicker and quicker, the latter naturally slower and slower. But to this it might be replied, that a horizontal line may pass, by gradual motion, through various inclined positions, to a vertical position: and thus the retarded motion may pass into the accelerated; and hence there must be some inclined plane on which the motion downwards is naturally uniform: which is false, and therefore the distinction of such kinds of motion is unfounded. Again, the proof of the First Law of Motion depends upon the Law of Continuity: for since, by diminishing the resistance to a body moving on a horizontal plane, we diminish the retardation, and this without limit, the law of continuity will bring us at the same time to the case of no resistance and to the case of no retardation.
2. The Law of Continuity is asserted by Galileo in a particular application; and the assertion which it222suggests is by him referred to Plato;—namely36that a moveable body cannot pass from rest to a determinate degree of velocity without passing through all smaller degrees of velocity. This law, however, was first asserted in a more general and abstract form by Leibnitz37: and was employed by him to show that the laws of motion propounded by Descartes must be false. The Third Cartesian Law of Motion was this38: that when one moving body meets another, if the first body have a less momentum than the second, it will be reflected with its whole motion: but if the first have a greater momentum than the second, it will lose a part of its motion, which it will transfer to the second. Now each of these cases leads, by the Law of Continuity, to the case in which the two bodies haveequalmomentums: but in this case, by the first part of the law the body wouldretain allits motion; and by the second part of the law it wouldlosea portion of it: hence the Cartesian Law is false.
36Dialog.iii. 150. iv. 32.
37Opera, i. 366.
38Cartes,Prin.p. 35.
3. I shall take another example of the application of this Law from Professor Playfair’s Dissertation on the History of Mathematical and Physical Science39. ‘The Academy of Sciences at Paris having (in 1724) proposed, as a Prize Question, the Investigation of the Laws of the Communication of Motion, John Bernoulli presented an Essay on the subject very ingenious and profound; in which, however, he denied the existence of hard bodies, because in the collision of such bodies, a finite change of motion must take place in an instant: an event which, on the principle just explained, he maintained to be impossible.’ And this reasoning was justifiable: for we can form acontinuoustransition from cases in which the impact manifestly occupies a finite time, (as when we strike a large soft body) to cases in which it is apparently instantaneous. Maclaurin and others are disposed, in order to avoid the conclusion of Bernoulli, to reject the Law of223Continuity. This, however, would not only be, as Playfair says, to deprive ourselves of an auxiliary, commonly useful though sometimes deceptive; but what is much worse, to acquiesce in false propositions, from the want of clear and patient thinking. For the Law of Continuity, when rightly interpreted, isneverviolated in actual fact. There are not really any such bodies as have been termedperfectly hard: and if we approach towards such cases, we must learn the laws of motion which rule them by attending to the Law of Continuity, not by rejecting it.
39In theEncyc. Brit.p. 537.
4. Newton used the Law of Continuity to suggest, but not to prove, the doctrine of universal gravitation. Let, he said, a terrestrial body be carried as high as the moon: will it not still fall to the earth? and does not the moon fall by the same force40? Again: if any one says that there is a material ether which does not gravitate41, this kind of matter, by condensation, may be gradually transmuted to the density of the most intensely gravitating bodies: and these gravitating bodies, by taking the internal texture of the condensed ether, may cease to gravitate; and thus the weight of bodies depends, not on their quantity of matter, but on their texture; which doctrine Newton conceived he had disproved by experiment.
40Principia, lib. iii. prop. 6.
41Ib.cor. 2.
5. The evidence of the Law of Continuity resides in the universality of those Ideas, which enter into our apprehension of Laws of Nature. When, of two quantities, one depends upon the other, the Law of Continuity necessarily governs this dependence. Every philosopher has the power of applying this law, in proportion as he has the faculty of apprehending the Ideas which he employs in his induction, with the same clearness and steadiness which belong to the fundamental ideas of Quantity, Space and Number. To those who possess this faculty, the Law is a Rule of very wide and decisive application. Its use, as has appeared in the above examples, is seen rather in the disproof of erroneous views, and in the correction of false propositions,224than in the invention of new truths. It is a test of truth, rather than an instrument of discovery.
Methods, however, approaching very near to the Law of Continuity may be employed as positive means of obtaining new truths; and these I shall now describe.
Sect.II.—The Method of Gradation.
6. To gather together the cases which resemble each other, and to separate those which are essentially distinct, has often been described as the main business of science; and may, in a certain loose and vague manner of speaking, pass for a description of some of the leading procedures in the acquirement of knowledge. The selection of instances which agree, and of instances which differ, in some prominent point or property, are important steps in the formation of science. But when classes of things and properties have been established in virtue of such comparisons, it may still be doubtful whether these classes are separated by distinctions of opposites, or by differences of degree. And to settle such questions, theMethod of Gradationis employed; which consists in taking intermediate stages of the properties in question, so as to ascertain by experiment whether, in the transition from one class to another, we have to leap over a manifest gap, or to follow a continuous road.
7. Thus for instance, one of the earlyDivisionsestablished by electrical philosophers was that ofElectricsandConductors. But this division Dr. Faraday has overturned as an essential opposition. He takes42aGradationwhich carries him from Conductors to Non-conductors. Sulphur, or Lac, he says, are held to be non-conductors, but are not rigorously so. Spermaceti is a bad conductor: ice or water better than spermaceti: metals so much better that they are put in a different class. But even in metals the transit of the electricity is not instantaneous: we have in them proof of a retardation of the electric current: ‘and what225reason,” Mr. Faraday asks, “why this retardation should not be of the same kind as that in spermaceti, or in lac, or sulphur? But as, in them, retardation is insulation, [and insulation is induction43] why should we refuse the same relation to the same exhibitions of force in the metals?”
42Researches, 12th series, art. 1328.
43These words refer to another proposition, also established by the Method of Gradation.
The process employed by the same sagacious philosopher to show theidentityof Voltaic and Franklinic electricity, is another example of the same kind44. Machine [Franklinic] electricity was made to exhibit the same phenomena as Voltaic electricity, by causing the discharge to pass through a bad conductor, into a very extensive discharging train: and thus it was clearly shown that Franklinic electricity, not so conducted, differs from the other kinds, only in being in a state of successive tension and explosion instead of a state of continued current.
44Hist. Ind. Sc.b. xiv. c. ix. sect. 2.
Again; to show that the decomposition of bodies in the Voltaic circuit was not due to theAttractionof the Poles45, Mr. Faraday devised a beautiful series of experiments, in which these supposedPoleswere made to assume all possible electrical conditions:—in some cases the decomposition took place against air, which according to common language is not a conductor, nor is decomposed;—in others, against the metallic poles, which are excellent conductors but undecomposable;—and so on: and hence he infers that the decomposition cannot justly be considered as due to the Attraction, or Attractive Powers, of the Poles.
45Ibid. Researches, art. 497.
8. The reader of theNovum Organonmay perhaps, in looking at such examples of the Rule, be reminded of some of Bacon’s Classes of Instances, as hisinstantiæ absentiæ in proximo, and hisinstantiæ migrantes. But we may remark that Instances classed and treated as Bacon recommends in those parts of his work, could hardly lead to scientific truth. His226processes are vitiated by his proposing to himself theformorcauseof the property before him, as the object of his inquiry; instead of being content to obtain, in the first place, thelaw of phenomena. Thus his example46of a Migrating Instance is thus given. “Let theNature inquired intobe that of Whiteness; an Instance Migrating to the production of this property is glass, first whole, and then pulverized; or plain water, and water agitated into a foam; for glass and water are transparent, and not white; but glass powder and foam are white, and not transparent. Hence we must inquire what has happened to the glass or water in that Migration. For it is plain that theForm of Whitenessis conveyed and induced by the crushing of the glass and shaking of the water.” No real knowledge has resulted from this line of reasoning:—from taking the Natures and Forms of things and of their qualities for the primary subject of our researches.
46Nov. Org.lib. ii. Aph. 28.
9. We may easily give examples from other subjects in which the Method of Gradation has been used to establish, or to endeavour to establish, very extensive propositions. Thus Laplace’s Nebular Hypothesis,—that systems like our solar system are formed by gradual condensation from diffused masses, such as the nebulæ among the stars,—is founded by him upon an application of this Method of Gradation. We see, he conceives, among these nebulæ, instances of all degrees of condensation, from the most loosely diffused fluid, to that separation and solidification of parts by which suns, and satellites, and planets are formed: and thus we have before us instances of systems in all their stages; as in a forest we see trees in every period of growth. How far the examples in this case satisfy the demands of the Method of Gradation, it remains for astronomers and philosophers to examine.
Again; this method was used with great success by Macculloch and others to refute the opinion, put in currency by the Wernerian school of geologists, that227the rocks calledtrap rocksmust be classed with those to which asedimentaryorigin is ascribed. For it was shown that a gradualtransitionmight be traced from those examples in which trap rocks most resembled stratified rocks, to the lavas which have been recently ejected from volcanoes: and that it was impossible to assign a different origin to one portion, and to the other, of this kind of mineral masses; and as the volcanic rocks were certainly not sedimentary, it followed, that the trap rocks were not of that nature.
Again; we have an attempt of a still larger kind made by Sir C. Lyell, to apply this Method of Gradation so as to disprove all distinction between the causes by which geological phenomena have been produced, and the causes which are now acting at the earth’s surface. He has collected a very remarkable series of changes which have taken place, and are still taking place, by the action of water, volcanoes, earthquakes, and other terrestrial operations; and he conceives he has shown in these agradationwhich leads, with no wide chasm or violent leap, to the state of things of which geological researches have supplied the evidence.
10. Of the value of this Method in geological speculations, no doubt can be entertained. Yet it must still require a grave and profound consideration, in so vast an application of the Method as that attempted by Sir C. Lyell, to determine what extent we may allow to the steps of ourgradation; and to decide how far the changes which have taken place in distant parts of the series may exceed those of which we have historical knowledge, without ceasing to be of thesame kind. Those who, dwelling in a city, see, from time to time, one house built and another pulled down, may say that suchexisting causes, operating through past time, sufficiently explain the existing condition of the city. Yet we arrive at important political and historical truths, by considering theoriginof a city as an event of adifferent orderfrom those daily changes. The causes which are now working to produce geological results, may be supposed to have been, at some former epoch, so far exaggerated in their operation, that the changes228should be paroxysms, not degrees;—that they should violate, not continue, the gradual series. And we have no kind of evidence whether the duration of our historical times is sufficient to give us a just measure of the limits of such degrees;—whether the terms which we have under our notice enable us to ascertain the average rate of progression.
11. The result of such considerations seems to be this:—that we may apply the Method of Gradation in the investigation of geological causes, provided we leave the Limits of the Gradation undefined. But, then, this is equivalent to the admission of the opposite hypothesis: for a continuity of which the successive intervals are not limited, is not distinguishable from discontinuity. The geological sects of recent times have been distinguished asuniformitariansandcatastrophists: the Method of Gradation seems to prove the doctrine of the uniformitarians; but then, at the same time that it does this, it breaks down the distinction between them and the catastrophists.
There are other exemplifications of the use of gradations in Science which well deserve notice: but some of them are of a kind somewhat different, and may be considered under a separate head.
Sect.III.The Method of Natural Classification.
12. The Method of Natural Classification consists, as we have seen, in grouping together objects, not according to any selected properties, but according to their most important resemblances; and in combining such grouping with the assignation of certain marks of the classes thus formed. The examples of the successful application of this method are to be found in the Classificatory Sciences through their whole extent; as, for example, in framing the Genera of plants and animals. The same method, however, may often be extended to other sciences. Thus the classification of Crystalline Forms, according to their Degree of Symmetry, (which is really an important distinction,) as introduced by Mohs and Weiss, was a great improvement229upon Haüy’s arbitrary division according to certain assumed primary forms. Sir David Brewster was led to the same distinction of crystals by the study of their optical properties; and the scientific value of the classification was thus strongly exhibited. Mr. Howard’s classification of Clouds appears to be founded in their real nature, since it enables him to express the laws of their changes and successions. As we have elsewhere said, the criterion of a true classification is, that it makes general propositions possible. One of the most prominent examples of the beneficial influence of a right classification, is to be seen in the impulse given to geology by the distinction of strata according to the organic fossils which they contain47: which, ever since its general adoption, has been a leading principle in the speculations of geologists.
47Hist. Ind. Sc.b. xviii. c. ii. sect. 3.
13. The mode in which, in this and in other cases, the Method of Natural Classification directs the researches of the philosopher, is this:—his arrangement being adopted, at least as an instrument of inquiry and trial, he follows the course of the different members of the classification, according to the guidance which Nature herself offers; not prescribing beforehand the marks of each part, but distributing the facts according to the total resemblances, or according to those resemblances which he finds to be most important. Thus, in tracing the course of a series of strata from place to place, we identify each stratum, not by any single character, but by all taken together;—texture, colour, fossils, position, and any other circumstances which offer themselves. And if, by this means, we come to ambiguous cases, where different indications appear to point different ways, we decide so as best to preserve undamaged those general relations and truths which constitute the value of our system. Thus although we consider the organic fossils in each stratum as its most important characteristic, we are not prevented, by the disappearance of some fossils, or the addition of others, or by the total absence of fossils,230from identifying strata in distant countries, if the position and other circumstances authorize us to do so. And by this Method of Classification, the doctrine ofGeological Equivalents48has been applied to a great part of Europe.
48Hist. Ind. Sc.b. xviii. c. iii. sect. 4.
14. We may further observe, that the same method of natural classification which thus enables us to identify strata in remote situations, notwithstanding that there may be great differences in their material and contents, also forbids us to assume the identity of the series of rocks which occur in different countries, when this identity has not been verified by such a continuous exploration of the component members of the series. It would be in the highest degree unphilosophical to apply the special names of the English or German strata to the rocks of India, or America, or even of southern Europe, till it has appeared that in those countries the geological series of northern Europe really exists. In each separate country, the divisions of the formations which compose the crust of the earth must be made out, by applying the Method of Natural Arrangementto that particular case, and not by arbitrarily extending to it the nomenclature belonging to another case. It is only by such precautions, that we can ever succeed in obtaining geological propositions, at the same time true and comprehensive; or can obtain any sound general views respecting the physical history of the earth.
15. The Method of Natural Classification, which we thus recommend, falls in with those mental habits which we formerly described as resulting from the study of Natural History. The method was then termed theMethod of Type, and was put in opposition to theMethod of Definition.
The Method of Natural Classification is directly opposed to the process in which we assume and applyarbitrarydefinitions; for in the former Method, we find our classes in nature, and do not make them by marks of our own imposition. Nor can any advantage231to the progress of knowledge be procured, by laying down our characters when our arrangements are as yet quite loose and unformed. Nothing was gained by the attempts todefineMetals by their weight, their hardness, their ductility, their colour; for to all these marks, as fast as they were proposed, exceptions were found, among bodies which still could not be excluded from the list of Metals. It was only when elementary substances were divided intoNatural Classes, of which classes Metals were one, that a true view of their distinctive characters was obtained. Definitions in the outset of our examination of nature are almost always, not only useless, but prejudicial.
16. When we obtain a Law of Nature by induction from phenomena, it commonly happens, as we have already seen, that we introduce, at the same time, a Proposition and a Definition. In this case, the two are correlative, each giving a real value to the other. In such cases, also, the Definition, as well as the Proposition, may become the basis of rigorous reasoning, and may lead to a series of deductive truths. We have examples of such Definitions and Propositions in the Laws of Motion, and in many other cases.
17. When we have established Natural Classes of objects, we seek for Characters of our classes; and these Characters may, to a certain extent, be called theDefinitionsof our classes. This is to be understood, however, only in a limited sense: for these Definitions are not absolute and permanent. They are liable to be modified and superseded. If we find a case which manifestly belongs to our Natural Class, though violating our Definition, we do not shut out the case, but alter our definition. Thus, when we have made it part of our Definition of theRosefamily, that they havealternate stipulate leaves, we do not, therefore, exclude from the family the genusLowæa, which hasno stipulæ. In Natural Classifications, our Definitions are to be considered as temporary and provisional only. When Sir C. Lyell established the distinctions of the tertiary strata, which he termedEocene,Miocene, andPliocene, he took a numerical criterion232(the proportion of recent species of shells contained in those strata) as the basis of his division. But now that those kinds of strata have become, by their application to a great variety of cases, a series of Natural Classes, we must, in our researches, keep in view the natural connexion of the formations themselves in different places; and must by no means allow ourselves to be governed by the numerical proportions which were originally contemplated; or even by any amended numerical criterion equally arbitrary; for however amended, Definitions in natural history are never immortal. The etymologies ofPlioceneandMiocenemay, hereafter, come to have merely an historical interest; and such a state of things will be no more inconvenient, provided the natural connexions of each class are retained, than it is to call a rockooliteorporphyry, when it has no roelike structure and no fiery spots.
The Methods of Induction which are treated of in this and the preceding chapter, and which are specially applicable to causes governed by relations of Quantity or of Resemblance, commonly lead us toLaws of Phenomenaonly. Inductions founded upon other ideas, those of Substance and Cause for example, appear to conduct us somewhat further into a knowledge of the essential nature and real connexions of things. But before we speak of these, we shall say a few words respecting the way in which inductive propositions, once obtained, may be verified and carried into effect by their application.