The Method Of Science And Its Application To Metaphysics
27. A MOMENT'S reflection will show that the Experiential Method is by no means restricted to that enumeration of particulars and classification of sensations which is assumed to be its scope by those philosophers who vilify it under the name of Empiricism, and those rhetors who declaim against it as dealing with nothing but what can be seen and felt. It is the methodizing of what is known. The range of the known embraces much more than the sensible. (See Prob. I., Ch. IV.) Not only the direct presentations to Sense, but the indirect representations, — the verifiable Inferences from Sense, — constitute its elements. Not only the individual experiences, slowly acquired, but the accumulated Experience of the race, organized in Language, condensed in Instruments and Axioms, and in what may be called the inherited Intuitions, — these form the multiple unity which is expressed in the abstract term Experience. This being stated once for all by way of forestalling hasty criticism, let us now proceed with our exposition.
28. Whether the object of research be Nature, Man, or Society in general, or some special group of their phenomena, we always find it presenting three aspects : 1°, the positive or known ; 2°, the speculative or unknown though knowable ; 3°, the unknowable. The two first are empirical ; the third is metempirical. The two first rest either, on direct Sensation and verified Inference,* or, 2 on Intuition and logical deductions from Intuition, which are verifiable by direct or indirect reduction to Sensation. The third rests on no such bases, and is therefore distinguishable from the two former in kind, not simply in degree.
29. By way of illustration, suppose the object investigated is the motion of the heavenly bodies. The first step is to determine the positive, or known, elements of the question, namely, that all the planets move round the sun in the same direction and in nearly the same plane, and that, inasmuch as their orbits are nearly circular, they describe paths which are parallel. This general plane of circulation is very nearly the plane of the sun's equator. The same facts are ascertained respecting the motion of the satellites round their planets, although their equators have various inclinations to the plane of the sun's equator. This leads to the inference that the two circulations of planets and satellites, although independent as facts, depend on the same principle, and have a common origin. What is that? This question brings forward the speculative aspect. The principle sought cannot be seen, it must be deduced. Speculation is seeing with the mind's eye what is not present to Sense or to Intuition. It is ideal construction, and begins with conjecture, - too often, alas ! ending where it began.
The satellites present also another remarkable law, their rotation on their own axes being executed in the same time as their rotation round their planets (hence we always see the same face of the moon). This law is positive ; it is the observed order. But the cause, i. e. that it depends on tidal friction in the satellite while it was still in motion, is at present speculative.
Suppose now the astronomer, after expounding the positive and speculative aspects of the planetary motions, is led to expound his conception of the purpose which these laws were intended to fulfil in creation, and his estimate of the wisdom and benevolence in so disposing them, and not otherwise, — is it not obvious that in this teleological explanation he quits the ground of Experience to enter on that region where all sensible data and all verifiable inferences vanish ? His conjectures on this point may be approximately right or absurdly wrong ; no possible means of determining whether they are right or wrong exist. If he regard them as no more than subjective fancies wherewith to satisfy his own feelings, we cannot object. But if he regard them as in any degree entering into astronomical science, and if he permit any deductions from them to modify the positive and speculative data or in any way to modify the course of astronomical thought, he violates the first principle of Method, by suffering the empirical to be controlled by the met-empirical, and allowing the unknowable to distort the known.
30. Having thus sharply defined the three aspects which every question may present, and which every one would always present had not men long ago quietly set aside the metempirical aspect in most questions of practical aim and most questions of scientific research, I need scarcely insist that in dealing with the speculative we ought to follow the same canons as in dealing with the positive, except that we are forced to substitute analogies for perceptions, forced to employ hypotheses and rely on inferences. When a platinum wire is raised gradually to a white heat, we see a succession of combinations of more and more of the primitive colors, but we do not see the motions of the wire which successively determine these colors, nor the tremors of the optic tract which are deter-mined by these motions and produce these colors. We only see the changing colors. We infer the rest. But these inferences have been verified a thousand times, and are but reproductions of analogical experiences. Our mental vision is a reproduction of the past and application to the present. It is Experience — our own or that of others — on which we rest. We are not at liberty to invent Experience, nor to infer anything contrary to it, only to extend it analogically. Speculation to be valid must be simply the extension of Experience by the analogies of experiences.
31. The speculative begins where the positive ends ; and where the speculative quits the ground of Sense and Verification, the region of the Metempirical begins. It is possible to move securely on the ground of Speculation so long as we carefully pick our way, and consider each position insecure till what was merely probable becomes proven. But in the metempirical region we have not even probability as a guide ; it is a morass of uncertainty where all footing yields and all tests fail. In this region, conjectures, however fantastic, are as valid as conceptions which seem rational. They maintain their ascendency over the mind which has once admitted them, because being, by the nature of the case, incapable of proof, they are incapable of refutation; they never approach near enough to the truths of Experience for us to show how widely they diverge from or contradict it.
32. Whenever a question is couched in terms that ignore Experience, reject known truths, and invoke inaccessible data, — i. e. data inaccessible through our present means, or through any conceivable extension of those means, — it is metempirical, and Philosophy can have nothing to do with it. We need not trouble ourselves with it, until in possession of the requisite means ; it is adjourned, not suppressed. Perilous it may be to set bounds to human possibilities, and to forejudge what future inquiries may disclose ; but there is no peril in standing inflexibly by the rule which declares all questions to be unanswerable when the means of answering them are not at hand. He who propounds an answer is called upon to show that he has the requisite means. What is invisible to the naked eye may be made visible by microscope or telescope. Let these be produced, and their powers demonstrated. No assertion, however confident, will suffice ; no "inner vision" which dispenses with verification. Roger Bacon passionately declared that he could construct an instrument which would make objects visible at a distance of many miles; and because such instruments have been constructed, he is believed to have anticipated the discovery, whereas, in point of fact, he not only made no such discovery, but showed, in his very statement of the conception he had formed, that he had not mastered the elementary principles which were requisite. The theories of many speculators are in this not unlike the telescope of Roger Bacon.
33. While no question which cannot be couched in terms of Experience, and answered on its data, ought for a moment to be entertained, any question which can be so asked and answered is admissible. In Science this has long been understood ; in Metaphysics it is ignored. No geologist, no biologist, would listen patiently if asked, What is the succession of strata in Sirius ? What are the leading characters of the flora and fauna of Saturn ? Yet metaphysicians patiently listen to questions of equal irrelevance ; nay, confidently give answers to them.
Without travelling so far as Sirius, suppose we present a new substance to the chemist, and ask him what are its properties, and what reactions it will exhibit, under given conditions. He will decline to answer until he has sufficiently examined the substance and classed it among substances already known ; because he is aware that any guess he may make before trial must be valueless unless guided by analogy ; in as far as it is like known substances he will infer that it has like properties. Guessing is only fertile in proportion to the fertility of the experiences it reproduces. If a man knows little, he can infer but little. All knowledge is reproduction of experiences, the direct or indirect assimilation (making like) of the new phenomena to phenomena resembling them, formerly experimented on. Ask the profoundest analyst to re-solve an equation numerically, and he is silent unless the values of the coefficients are assigned; nor can the child tell the result of multiplying 5 by 5, until he has learned the multiplication-table.
34. Must not this be equally true in Metaphysics ? To ask the metaphysician to answer questions respecting things per se (or what is usually understood by them), and to tell us their nature and properties, is asking him to resolve equations numerically without assigning their several values to the coefficients. Nay more, these values cannot be assigned, for the symbols profess to be symbols of what was never presented in Experience. But if instead of this irrational procedure we give the metaphysician verifiable data, he can deal with them as the physicist and chemist deal with theirs ; and his answers will be as valid as theirs, if his data and method be like theirs.
35. Hitherto metaphysicians have asked, What is Mat-ter ? What is Force ? What is Cause ? And these words are symbols of an imaginary class of Noumena, Dinge-ansich, Things as they are and underlying the Things which appear, — a world behind phenomena, incapable of being sensibly grasped, but supposed to have a more perfect reality than the phenomenal world. Because questions thus irrationally put are found to yield no rational answers, one class of thinkers hurries to the conclusion that this impotence proves all metaphysical inquiries to be idle ; another class infers that knowledge of this superior world must be gained through another source than that relied on in the investigation of phenomena. But we may urge that all inquiries are not idle because some are improperly conceived ; nor is any special organ needed for the interpretation of questions rationally put. Since it is a fact that we have ideas of Matter, Force, Cause, etc., and that these words are symbols of sensible experiences, the genesis of such ideas and the interpretation of such symbols are not less legitimate objects of inquiry than the genesis and interpretation of our ideas of Animal, Plant, Planet, or Cosmos. I shall hereafter endeavor to make clear that these abstract ideas are integrant parts of what I call the Logic of Feeling, before they are raised into terms of the Logic of Signs. They are threads woven into the web of Experience ; and because they have this warp and woof they are capable of being raised into the tissue of Abstraction, — they are experiences before they are signs. The Method which enables us to unravel the complex threads in the one case will aid us in the other.
36. As already hinted, the chief source of perplexity is the irrationality of the terms in which the questions are propounded. But although this defect. is specially flagrant in the case of Metaphysics, it is frequently noticeable in Physics. Take, for example, the puzzle concerning the communication of motion from one body to another, either through impact or " action at a distance." This communication is accepted as a fact, and declared to be beyond our comprehension. The inconceivability of the statement is not allowed to suggest a doubt respecting its certainty. But the inconceivability, when closely examined, will be found to rest entirely on the irrational mode of expressing the fact observed ; instead of stating what is observed in simple terms, the statement is made in terms of an hypothesis which cannot be steadily conceived. What is observed is that one body in motion— that is to say, in changing space relations — is succeeded by changes in. the space relations of another, and that there is a constancy in this sequence. This not being held sufficient, there is invented a hypothetical Motion (not an abstract symbol, but a physical entity), which is passed from one body to another like so much milk poured from one jug into another ; and to complete the hypothesis, this Motion is imagined under the control of the body moving, — since this body divides its quantity of Motion, keeping one portion to itself and communicating the other portion to the other body ! Is it strange that having travestied the observed phenomena in this way, and accepted our metaphorical language as exact, Ive marvel that the entity thus created is beyond comprehension ? Instead of throwing the onus on human incompetence, suppose we ask whether it may not rest on the illusory statement. Analyze the real data, and it will then be seen that the " communication of Motion" is one of those metaphorical phrases which (as Lagrange remarks, on a somewhat similar occasion *) are, supposed to reveal the essence of Nature's laws, and which can "par quelque vertu secrète ériger en causes finales, de simples résultats des lois con nues de la mécanique. We first raise a dust and then exclaim, " Impossible to see through it !"
37. Of a similar kind is the puzzle respecting Force inherent in Matter. Neither abstraction, is reduced to its concretes, neither term accurately defined; and then such questions as the following are asked (which I cite from a distinguished mathematician and physicist, Maupertius) : " Qu'est-ce que cette force impulsive ? comment réside-t-elle dans les corps ? qui eut pu deviner qu'elle y réside avant que d'avoir vu des corps se choquer? La résidence des autres propriétés. n'est pas plus claire. Comment l'impénétrabilité et les autres propriétés viennent elles se joindre h. l'étendue ? "
When such questions are detached from a work and seriously considered, it seems difficult to understand how any thinking mind could have propounded them. Yet, having puzzled himself with irrational questions, Maupertius evades them with the customary formula : "These must ever remain mysteries for us." Mysteries no doubt ; but mysteries quite needlessly fabricated.
38. Examples need not be multiplied ; enough if we understand that every problem is mysterious when irrationally stated ; but, when rationally stated, there is no greater mystery in the existence of an external world, or the relation between Object and Subject, than in the relation between activity and waste in the tissues, the relation between heat and expansion, or the relation between an are and its chord. The successful interrogation of Nature mainly depends on the selection of the question to be put, and the ability with which it is expressed in terms that admit of an answer. Hence the first operation in dealing with any metaphysical problem must be this: —To disengage the metempirical elements, and proceed to treat the empirical elements with the view of deducing from them the unknown elements, if that be practicable, or, if the deduction be impracticable, of registering the unknown elements as transcendental.
This procedure seems very simple. It is the ordinary procedure' of the analyst, whose first operation is to disengage the unknown quantity, — and of the physicist, who always seeks to eliminate whatever is irrelevant or indeterminate, replacing it by exact data, so that nothing finally remains for exploration but what is expressible in calculable terms. Yet simple as the procedure may seem, it has rarely been adopted by metaphysicians and never, I believe, avowedly stated as a principle of research. On the contrary, there has been a confused mingling of empirical and metempirical elements, sensations and abstractions, inferences and traditions, exact quantitative data, and imaginary unquantitative data, facts and phrases, phenomena' and phantoms, — and then it is thought marvellous that such a network of cordage and cobweb should let everything run through !
39. Our first operation must be to disengage the unknown quantity, and endeavor to ascertain whether it is knowable or unknowable ; and this will determine whether it is empirical or metempirical.
In every question, from that presented by the growth of a blade of grass to that presented, in the evolution of a social organism, from the chemical union of two gases to the formation of ideal types, there must necessarily be certain transcendental elements, not determinable by us, unexplored remainders after the most exhaustive exploration. These may be grouped under three heads :
1. Elements known to be present in the phenomena, but not yet quantitatively appreciable, and therefore now incalculable ;
2. Elements not certainly known to be present, but assumed hypothetically for the sake of provisional explanation ;
3. Elements which, lying beyond all possible' appreciation, because incapable of being brought within the range of Sense and Inference, are to be set aside, and not allowed in any way to enter into the explanation.
40. An illustration or two may here be useful. Geometers agree that the exact ratio of the circumference of a circle to its diameter cannot be accurately expressed in ordinary finite numbers, although the real value may be approached as nearly as we please. They indicate this ratio by the sign — a sign which dispenses with a long series of figures and an unexplored remainder. This sign, although entering into the expression of the quantities compared, does not enter into the expression of their ratios, but vanishes from the final equation. Thus the surface of a sphere, and the surface of a great circle of that sphere, are two quantities which cannot be accurately expressed in numbers, because enters into both, and this 7r containing an unexplored remainder must remain transcendental. Nevertheless the presence of this transcendental element produces no disturbance in the calculation ; for we are certain that the first quantity is exactly the quadruple of the second, whatever values these may have. Thus the transcendental element, which exists in both quantities, disappears from the ratio of the one to the other.
We thus lay down the important formula :
The existence of an unknown quantity does not necessarily disturb ,the accuracy of calculations founded on the known functions of that quantity.
41. If in Mathematics we can thus deal with transcendentals Without peril to the exactness of our deductions, the question arises whether in other sciences and even in Metaphysics the same procedure may not be adopted with similar effect. My purpose is to show that this procedure can be followed ; and that in all inquiries, unexplored remainders must be eliminated, and our deductions be confined to the known functions of these unknown quantities. The profitless discussions upon Space and Time have been profitless, because of the non-recognition of the transcendental elements and their consequent separation from the positive elements. What is Time ? This philosopher holds it to be an objective existence, which must be accepted as ultimate. Another holds it to be a purely subjective Form of Sense. A third says it is a Form of Sense because it is a Form of Things. Others are fascinated by Lagrange's definition of it, "a fourth dimension of Space." Mathematicians are content with Newton's conception of it as a fluent which has no variable fluxion, the only independent variable which "flows equally without regard to anything external and by another name is called-Duration."
Without pausing to choose between these conceptions, or to trace the genesis of the abstraction and its relations to the concretes it expresses, we simply note that each conception leaves something indeterminate, none accurately conveys all that is meant by Time. A mystery always remains unexplained, unexplorable, Let this be granted, let the presence of a transcendent element be insisted on, how you will, the truth is, that in the only use we ever make of the conception of Time — e. in its known functions, the measurement of intervals—this transcendent disappears, the mystery vanishes. What-ever Time may be, the intervals, which are all we deal with, are equal or unequal, and our equations are rigorously exact.
42. It is the same with Space. Whether we are to regard it as an entity or an abstraction, is a question for . Psychology. What Space is may be left undetermined. The vulgar imagine it to be pure Nothing, which nevertheless does mysteriously contain all things, holding them like a vessel They speak of it as of an infinite air-pump, empty of all contents. They do not ask them-selves what need Being has of Non-Being to contain it, what need Existence has for another Existence in which to exist. The psychologist may be called upon to explain the genesis of such conceptions, but Science and Practice detach themselves from such puzzles, and without endeavoring to lay hold of the transcendental element in Space, are content to measure spaces with rigorous precision.
43. Matter and Motion, Force and Cause, have also their transcendental elements, and it is the province of Metaphysics to demarcate these from the known and knowable elements. Character, again, involves many incalculable elements, organic, historic, social ; yet this does not prevent our comparison of one character with another, or with the different manifestations of one character under different conditions, Vitality, again, presents certain aspects which, if only from their speciality, must always distinguish organic from inorganic existence.
Although many vital phenomena have 'been assigned to physical and chemical conditions, there still remain unexplored remainders after all our analysis. These we may assign either to some special Agent, the supposed vital Force, or to some special Agency, some peculiar combination of physical forces, not yet determined. Whichever hypothesis we adopt, the presence of the transcendental need in no way disturb the accuracy of our calculations, if we deal with it properly, and eliminate it from the equations. We may compare one vital phenomenon with another, or with its conditions, as we compare one sphere with another, or any one function of an unknown quantity with another ; and the comparison may yield exact results, although we remain eternally ignorant of the excluded elements.
44. The initial defect in transcendental Philosophy and all metempirical inquiry is not the admission of transcendental elements * as facts and mysteries, but the admission of them among the calculable elements ; and the supposition that by means of guesses and constructions in which these incalculable data enter as components, man can reach a higher truth than is attainable through Experience. It will indeed be urged by metaphysicians that although the transcendental elements are not calculable from data furnished by Sense and Understanding, they are directly knowable and calculable through the so-called Vernunft, or Intellectual Intuition, which deals with them as Understanding deals with the data of Sense. I do not pause here to consider this argument which will occupy us further on, but continue my exposition of the Method by which metaphysical problems may be treated without the assumption of any such special faculty for the discernment of the transcendental. If I can succeed in extricating such questions from the confusion which results when two diametrically opposite Methods are employed, and if I can thus confine the metempirical Method to the metempirical aspects of each question, it will then be time to examine the pretensions of the Intellectual Intuition.
45. Our first step then is to state each question in such a way that the "unexplored remainder" is disengaged from the positive and speculative aspects, and carefully kept apart as a transcendental, not allowed to enter into the equations.
The second step is the analysis by which we ascertain whether this unknown quantity is to be accepted as an ultimate fact, a fiction, or a phrase. We inquire, 1°, whether it is ultimate, as in itself beyond analysis, incapable of reduction to some more general fact ; 2°, whether it might possibly be analyzed were certain data secured ; but, these not being secured, we make a provisional guess, throwing out some hypothesis which, if correct, would link the phenomena into intelligible unity ; 3°, or failing even this speculative aid, we adopt a phrase which, although explaining nothing, serves at least to baptize the unknown, and is thus often of advantage (sometimes the reverse) in keeping under one rubric phenomena which have essential points of similarity along with manifold differences.
46. These three modes of dealing with the unknown quantity may be thus exemplified. A biologist having ascertained that organic phenomena always require special combinations of oxygen, carbon, hydrogen, and nitrogen for their basis, and are never found where these are absent, accepts the ultimate fact of Vitality dependent on this combination. It is a fact no more explicable by reduction to some other fact, than why the ratio of I is the ratio of 4/6 or 8/12. The fact is so, is observed to be so ; why it is so admits no further answer (for the present) than that whatever is is.
46a. The speculative biologist is dissatisfied, and thinks this dependence may be explained by the introduction of an Agent, visible to his speculative eye. He creates the fiction of a Vital Principle, which no one has seen, which no one can connect with positive data ; and endows it with whatever properties are needed for the results observed. He invents an Imponderable, a Force, which has the power of fashioning the Ponderable, — which can select and combine physical and chemical elements, and can animate lifeless matter. -
We see that this is a fiction ; but we do not on that account reject it. Fictions are potent; and all are welcome if they can justify themselves by bringing speculative insight within the range of positive vision. What then must be our attitude with respect to this Vital Principle ? We must submit it to all the tests by which hypotheses are controlled, — tests which, while allowing the freest scope to the energy of Imagination, prevent that energy from degenerating into license.
This fiction has been tested, and has proved a failure : it explains nothing. Nevertheless it has left behind it a convenient phrase ; and now positive biologists are quite ready to speak of Vital Force, or the vital forces, as brief ways of designating phenomena. There is indeed always danger in thus appropriating the phrases of rejected fictions, — the danger lest insufficient vigilance allow the phrases to be interpreted in their old meanings ; and an immense service to Science would be effected by some notation which would always accompany hypotheses and hypothetic phrases, — a sort of algebraic x, keeping alive our sense of the presence of an unknown quantity.*
47. The metaphysical problems of Matter, Force, Cause, Law, Soul, etc., likewise present elements positively known, elements speculatively knowable, and elements that lie beyond all reduction to Experience, positive or speculative. The novelty of the procedure followed in this work consists in treating these problems on the same Method as that followed in Science, first separating the three aspects, and then seeing how far inductions will carry us,
No one can have studied the history of physical investigation without seeing that progress has been mainly effected by the habit of more or less consciously eliminating from each question the metempirical aspect. It is strikingly manifest in the labors of Galileo and Newton, when compared with those of Kepler and Descartes. But in instituting this comparison we must guard against the common confusion of the speculative with the met-empirical point of view, — a confusion explicable enough when no sharp definition of the metempirical had been given, It is a. serious error to imagine that the true scientific spirit is opposed to the speculative, because it is opposed to the metempirical. The error arises partly because the Logic of Speculation has not yet been organized with sufficient precision, its tests and canons are left undisciplined ; hence, because Speculation is conterminous at one side with Metempirics, it has frequently been carried by its ardor over its own lawful boundaries into that nebulous region where all tests fail ; and thus the speculative thinker is regarded with distrust by positive thinkers. Nor is the distrust surprising, when we see the discordant mingling of unprovable fictions with provable conjectures in the writings of even such splendid workers as Kepler and Descartes.
48. To confirm our vindication of the speculative procedure, it is enough to glance at the labors of the two supreme positive inquirers, Galileo and Newton. Illustrious judges have declared that Galileo's conception of the laws of Motion is his greatest achievement.* If we examine his famous dialogue we find that it is mainly theoretical ; experiment is rarely invoked, though every-where implied. Let us, he says, conceive the simplest and most perfect rule, and we shall form the most probable hypothesis. If we follow out the consequences . of this rule, and express them in mathematical theorems, we may do so without peril. " Geometry has already studied numerous curves never met with in reality, and detected in them wonderful properties ; and to geometry our conclusion also will belong even if experiment is unable to confirm them." Here there is an explicit announcement of the deepest conception of scientific Method, and the conjunction of the principle of Ideal Construction (on which see Prob. I. Chap. V.) with the principle of Sensible Verification. The separation and co-operation of the speculative and positive points of view could not be more clearly stated. Galileo knew that such a conception as Velocity was ideal and that the proportionality between the velocity of a falling body and the time of its fall could never be directly verified in experiment ; but he knew also that it could be indirectly verified through consequences accessible to observation and experiment. His laws of Motion would have been speculatively true, like those of geometry, even could they never have received positive verification ; and I shall hereafter show that they are only rigorously true in the region of Abstraction, and are not true of actual motions.
49. The reader was perhaps somewhat incredulous on finding Newton cited as an example of speculative greatness. The veneration which consecrates the name of Newton has so far failed to dignify his practice, that the simple characterizing of that practice wears the air of paradox. Was he not the ideal of a positive thinker ? Did he not protest against Speculation ? It is true. But although Newton's language is sometimes directly counter to his practice, and is vitiated by the misplaced alarm which he shared in common with all the reformers of that day, at the chaotic consequences of speculative ingenuity, this was mainly due to the absence of a clear discrimination between speculative and metempirical inquiry. At any rate; it is the fact that Newton's glory is founded quite as much on the purely speculative as on the purely positive part of his labors ; while nearly all his popularity, outside the mathematical circle, is due to it.
He who declared that he made no hypotheses—insisting that they could have no place in experimental philosophy —has raised his name out of the very small circle of mathematicians, where he must ever occupy a glorious position, into its leadership among philosophers, by virtue of his splendid speculative insight, the daring keenness of his venturesome imagination in creating hypotheses. It was an hypothesis, and a daring one, by which he instituted the Infinitesimal Calculus, introducing velocities, under the name of Fluxions, whereby the correlative values of two variables were supposed to increase together. The element of Velocity was as pure an hypothesis as the element of Ether in the explanation of Light, or of Electricity or Nervous Fluid in the explanation of Neuxility: it was, moreover, an accessory hypothesis,— an artifice, not an inference. Again, his identification of celestial and terrestrial motions was an hypothesis ; so was the extension of gravitation beyond the solar system; an hypothesis his conception of the attraction exercised by spherical bodies on a point beyond or within their spheres ;* an hypothesis his conception of attractive and repulsive forces similar to positive and negative quantities in Algebra, the former vanishing where the latter be-gin ; an hypothesis that Motion is constantly destroyed, and consequently that the universe requires active Principles, " such as the cause of gravity, by which planets and comets keep their orbits, and ,bodies acquire great motion in falling ; and the cause of fermentation by which the heart and blood of animals is kept in constant motion and heat "; an hypothesis that Light consists of corpuscles emitted from the luminous source ; an hypothesis that "the Senses are not for enabling the soul to perceive the species of things in its sensorium, but only for conveying them thither ";— these, and several other queries propounded in the Optics, are surely strange contradictions to the often-quoted and much-misunderstood hypotheses nom fingo.
49a. It may be objected that some of these hypotheses he himself brought so near to demonstration that they have taken place among established truths, and that they were legitimate constructions on mathematical principles. This does not alter their speculative character. And while we know that some of his illustrious contemporaries regarded these hypotheses as revivals of a scholastic spirit, rejecting Attraction because it was an occult quality,* we also know that Science, which has accepted some of the hypotheses, has recognized others as non-verifiable, and some as false, nay, even absurd. Be this as it may, our purpose is simply to recognize the large latitude given by this mighty investigator to the operation of that speculative imagination which he is commonly supposed to have discredited. In this connection it is piquant to. observe that in the very passage which follows his famous denunciation of hypotheses, he has no hesitation in propounding, a view which in these days must startle the most speculative by its wildness —
"And now we might add something concerning a most subtle Spirit which pervades and lies hid in all gross bodies; by the force and action of which Spirit the particles of bodies mutually attract one another at near distances, and cohere if contiguous ; and electric bodies operate to greater distances, as well repelling as attracting the neighboring corpuscles ; and light is emitted, reflected, refracted, inflected, and heats bodies ; and all sensation is excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this Spirit, mutually propagated along the solid filaments of the nerves from the outward organs of sense to the brain, and from the brain into the muscles. But these are things that cannot be explained in few words, nor are we furnished with that sufficiency of experiments which is required to an accurate determination and demonstration of the laws by which this electric and elastic spirit operates."
50. In presence of evidence like this one may well ask, What meaning is to be attached to the famous dictum, and what is the vindication of Newton's practice which so obviously departs from that dictum ? The answer is, that Newton had thoroughly grasped scientific Method ; and his magisterial superiority is nowhere more lucent than in its clear and careful distinction between the positive and speculative aspects of each question. The positive part of his work always consists of geometrical and dynamical facts and deductions. The precision and reach of this are uncontested, incontestable. Then comes a speculative part, brilliant, seductive, and peculiarly acceptable, because it fulfils the primary condition of affording facilities to calculation. But this part is always questionable, hypothetical. Observe how clearly he separates these very different aspects in the declaration which opens the exposition of the system of the world in Book III.: —
" In the preceding books I have laid down the principles of philosophy, principles not philosophical but mathematical; such, to wit, as we may build our reasonings upon in philosophical inquiries. These principles are the laws and conditions of certain motions and powers or forces, which chiefly have respect to philosophy. But lest they should have appeared of themselves dry and barren, I have illustrated them here and there with some philosophical scholiums, giving an account of such things as are of more general nature, and which philosophy seems chiefly to be founded on."
And towards the close of the general scholium he says : " Hitherto we have explained the phenomena of the heavens and the sea by the power of gravity, but have not yet assigned the cause of this power.. . I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses. To us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of our celestial bodies and our sea."
From this alone it would be evident that he did not, as is often said, discourage inquiries into the cause of gravity, but simply discouraged the facile and illusory explanations which were constructed out of arbitrary suppositions, instead of out of observed phenomena.
Physics, beware of Metaphysics," was his warning. He was ready enough to speculate as to the cause of gravity, but well knew that his speculations were mere gropings in the dark, not to be placed beside the positive principles he had so laboriously brought to bear on the facts observed. The cause, whatsoever it might be, he declared was an active Principle, not an occult quality supposed to result from the specific Forms of Things, but one of the "general Laws of Nature " by which the things themselves are formed ; " their truth appearing to us by phenomena, though their causes be not yet discovered. For these are manifest qualities, and the causes only are occult. And the Aristotelians gave the name of occult qualities not to manifest qualities, but to such only as they supposed to lie hid in bodies, and to be the unknown causes of manifest effects, — such as would be the causes of Gravity, and of magnetic and electric attractions and of fermentations, if we should suppose that these forces or actions arose from qualities unknown to us, and incapable of being discovered and made manifest. Such occult qualities put a stop to the improvement of natural philosophy, and therefore of late years have been rejected. To tell us that every species of things is endowed with an occult specific quality by which it acts and produces manifest effects, is to tell us nothing. But to derive two or three general Principles of Motion from phenomena, and afterwards to tell us how the properties and actions of all corporeal things follow from these manifest Principles, would be a very great step in philosophy, though their causes were not discovered.” *
In the preface to the Principia he says : "For all the difficulty of philosophy seems to consist in this, — from the phenomena of Motion to investigate the forces of Nature, and then from these forces to demonstrate the other phenomena. And to this end the general propositions in the first and second books are directed. In the third book is given an example in the explanation of the System of the World. For by the propositions mathematically demonstrated in the first book, we there derive from the celestial phenomena the forces of Gravity with which bodies tend to the sun and the several planets. Then from these forces, by other propositions, which are also mathematical, we deduce the motions of the Planets, the Comets, the Moon, and the Sea. I wish we could derive the rest of the phenomena of Nature by the same kind of reasoning from mathematical principles. For I am induced by many reasons to suspect that they may all depend upon certain forces 'by which the particles of bodies by some causes hitherto unknown are either mutually impelled towards each other and cohere in regular figures, or are repelled and recede from each other which forces being unknown, philosophers have hitherto attempted the search in vain. But I hope the principles here laid down will afford some light either to that or some true method of philosophy."
And again, towards the close of the Optics, he says: "As in Mathematics, so in Natural Philosophy the investigation of difficult things by the method of analysis ought ever to precede the method of composition. This. analysis consists in making experiments and observations, and in drawing general conclusions from them by induction, and admitting of no objections against the conclusions, but such as are taken from experiments or other certain truths. For hypotheses are not to be regarded in experimental philosophy. And although the arguing from experiments and observations by Induction be no demonstration of general conclusions, yet it is the best way of arguing which the nature of things admits of, and may be looked upon as so much the stronger by how much the Induction is more general. And if no exception occur from phenomena, the conclusion may be pronounced generally. But if at any time afterwards any exception shall occur from experiments, it may then begin to be pronounced with such exceptions as occur. By this way of analysis we may proceed from compounds to ingredients, and from motions to the forces producing them ; and in general from effects to their causes, and from particular causes to more general ones, till the argument end in the most general."
This, then, was Newton's doctrine, and it was also his practice in general ; although he sometimes so far forgot his own principles that he allowed theological and metempirical elements to mingle with the inductions of Experience.
51. The reader has already seized my drift, which is that Metaphysics can be pursued on the Method of Science, provided it accepts all the tests and conditions of that Method, and keeps within the range of Experience. Thus treated, its dangers and difficulties would be no greater than those of Science, its certainties would have the same foundation. In both we have to disengage the known and knowable from the unknown and unknowable ; and having disengaged the known quantities; we proceed to operate on them in the detection of the unknown. In every problem we have to determine, — 1°, Is there a known Agent or Agency, which will furnish the answer ? 2°, By what operations can the presence of this be made manifest ? by what tests can we assure ourselves that the Agent is the one which we have assumed, or that this Agency has the requisite law, or order ?
52. Now the common error of metaphysicians, and one not uncommon also among men of science, is hastily to assume an unknown Agent or Agency, or to assume the presence of one known, and then to operate on that assumption as on a solid basis. There is one aspect in which such a procedure is perfectly legitimate, namely, when it is avowedly conducted as a tentative hypothetical mode of establishing an equation, afterwards to be verified when the values are assigned. The procedure is fatal when this artifice is forgotten, and is made to solve the problem without verification of the assumed values. The geometer resolves his problem by deriving the properties of the figure from those already known and analogous ; having before him the laws to which the several parts of the system conform, he deduces from these the ,quantities sought, and thus constructs his figure. To obtain his equation he assumes the problem to be already solved, and constructs a figure according to the hypothetical state of the known and unknown quantities. Thus, so far from dispensing with Hypothesis, the geometer largely invokes its aid, only he never forgets the nature of the aid invoked. He is mostly guided by probabilities, which he intends reducing to certainties ; he anticipates by divination what is afterwards to be reached through demonstration. The chief distinction between his probabilities and those of the physicist or biologist lies in the greater simplicity or unequivocalness of his terms, and the consequent greater facility of their verification. Sometimes he finds his construction leads to a nugatory solution, and he here sees that the hypothetical figure does not agree with the question, and that somewhere some contradictory conditions have been introduced. In this case he constructs another, invoking fresh hypothesis, and thus he tries one after the other, until he hits upon that which will satisfy the equation.
53. The procedure of the physicist is similar. He constructs a hypothetical scheme of the dependent parts of the phenomenon from those already known, and by processes of Verification ascertains whether this scheme agrees with Observation and Deduction. If he has introduced into the scheme contradictory conditions, or has left out conditions that are co-operant, the discrepancy between Observation and Calculation warns him of his error ; and he tries another scheme. Although the task of Verification is usually more arduous and delicate than in Geometry, it is essentially the same. Dealing as the physicist does with data which are more complicated, less accurately definable, and dependent on. minute and numerous observations and inductions, he is more easily led to accept a complex condition for a simple one, and to disregard conditions which seem insignificant because he is not alive to their significance.
54. If the physicist is thus hampered, still more are the biologist, psychologist, and metaphysician hampered, because their data are excessively complex, and their definitions fatally equivocal. Yet their Method should be the same. Could they pursue it with the same rigorous regard to its tests and canons, their results would be as exact as those of the physicist and geometer. The common notion of the exclusive superiority of what are called the exact sciences I hold to be an error. There is always an admitted inaccuracy, or incompleteness, in every geometrical solution, except in the region of Abstraction, i. e. ideal construction ; and in that region the solutions of Biology or Metaphysics may have equal accuracy. In Mathematics, which consists of operations on symbols, the exactness is ideal; when the results thus obtained are applied to reality they are approximately true in as far as the symbols express real terms but mathematical operations may be equally exact when their symbols are avowedly unreal ; and it has been possible to ingenious geometers to construct a non-Euclidian geometry, on the assumption that Euclid's postulate is false. Hence we may conclude that Metaphysics, consisting of operations on symbols of Force, may be equally exact, and their results approximately true in regard to reality, the degree of approximation depending on the reality of the terms. The presence of transcendent elements need not disturb us. Every physical problem involves metempirical elements beside those which are empirical ; but Physics sets them aside, and, dealing only with the empirical, reaches conclusions which are exact, within that sphere. No disturbance in the accuracy of calculation follows from the existence, outside the calculation, of elements which are incalculable. The law of gravitation, for example, is ex-act, although its transcendental aspect — namely, what gravitation is in itself, whether Attraction, Undulation, or Pressure — is not merely left undetermined, but by the majority of physicists is not even sought. The law of Association of Ideas is equally exact, although not quantitatively expressible. The dependence of Sensation upon Stimulus is not less so, and has received a quantitative expression. The laws of Causation may be formulated with equal precision. And exact knowledge of Force, Cause, Matter, ought to be attainable, in spite of their transcendental elements, by the one procedure of eliminating these, and operating solely on the empirical Hence the conclusion : —
The scientific canon of excluding from calculation all incalculable data places Metaphysics on the same level with Physics.
( Originally Published 1874 )
Problems of Life and Mind:
The Method Of Science And Its Application To Metaphysics
The Method Of Science And Its Application To Metaphysics
The Method Of Science And Its Application To Metaphysics
The Method Of Science And Its Application To Metaphysics
The Method Of Science And Its Application To Metaphysics
The Rules Of Philosophizing
The Limitations Of Knowledge
The Sensational And A Priori Hypotheses
The Sensible, Extra-sensible, And Supra-sensible
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