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The Use And Abuse Of Hypothesis

84. COULD we observe the processes of nature we should need no Science to explain them : Perception would suffice. But we cannot observe them, or can observe them only in fragments; we must therefore imagine what 'we cannot see, and link the fragments into a whole. Explanation of phenomena is always a making visible to the mind's eye of what is invisible in the facts presented : it is the rendering conspicuous of those inconspicuous Relations of coexistence and succession through which one phenomenon co-operates with, and thus determines a change in, another. When this is seen, there is an intuition of the truth that everywhere a recurrence of these Relations, or of similar conditions, must be accompanied by this change, or a similar change. This is the intuition which rests on the assumption of homogeneity (Rule X.) and is justified by the logical principle of Equivalence (to be hereafter expounded).

85. Not only does Science pass from the consideration of isolated visible facts, to their co-ordination and consolidation in general, invisible facts ; but it necessarily tends to generalize more and more, to become more and more abstract, less and less occupied with concrete observation ; and this because every concrete observation' is limited, whereas the grasp of a few general facts enables us to anticipate an endless multitude of observations, and that in cases where Observation would be difficult, sometimes impossible. Science is fertile, not because it is a tank, but because it is a spring. The grandest discoveries, and the grandest applications to practice, have not only outstripped the slow march of Observation, but have revealed by the telescope of Imagination what the micro-scope of Observation could never have seen, although it may afterwards be employed to verify the vision.

No reader of these pages will misunderstand the reach of this remark, or suppose that it warrants any neglect of Observation through a too confident reliance on Imagination and Reason; for Imagination and Reason are only powerful as the organized results of previous Observation. If Types are to be valid they must be formed by abstraction from concrete experiences, thus enabling Prevision to be only an extension of Vision, and enabling Deduction to rest securely on a basis of Induction. It is the neglect of this single, but indispensable condition, that constitutes the danger of Hypothesis.

86. Certain facts are observed to coexist, or to succeed each other, but the process of their connection is hidden, and we seek to drag into light the facts which come between the facts which are seen. There is a gap to be filled up. How ? Not by direct vision. Then by indirect vision. We guess, and our guess has a Greek name, Hypothesis, namely, that which is placed under, and sup-ports the observed facts ; it is the imaginative arch thrown over the gap which we may traverse as a bridge. Unless this arch rests on solid supports, it will not bear our weight ; and many a visionary hypothesis turns out to be no better than the arch of the rainbow, beautiful to look upon, impossible to walk upon.

It is therefore of the utmost importance to ascertain the conditions of solid support. Guessing has a wide and capricious range; it is oftener wrong than right; but worse than all is the fatal facility with which the mind accepts a guess in lieu of vision, believing in the image it has formed out of materials from within, as if it were an image formed of materials from without ; and thus, while the probabilities of error are enormous, the pertinacity with which error once formed on very slight evidence is held, resists all but demonstrative evidence against it. Hypothesis thus becomes pernicious. It retards Science by arresting inquiry; it quiets the unrest of the mind with the anodyne of a phrase, and seems to explain what it only rebaptizes. It also retards Science by misdirecting inquiry, stimulating the mind to seek direct relations where none exist.

87. These dangers have been eloquently exposed by many writers, and need not here be illustrated. Yet while it would be difficult to express too strong a condemnation of the lax unscientific use of Imagination, which has brought Hypothesis into disrepute, it would be difficult to exaggerate the immense, the indispensable service of Hypothesis in the construction and advancement of Science. How largely Newton availed himself of its aid, and how he reprobated it, have already been indicated (Introd., § 49). When Newton said that Hypothesis had no place in experimental philosophy, he probably meant that we must not take fancies for facts, guesses for conclusions ; which is a warning not the less needed because it seems so obvious. But if we regard Hypothesis in its true light, namely, that of ideal experiment, — the tentative process of trying which among many possible conceptions hest accords with perceptions, — that experimental character will place it beside the tentative process of trying which among many physical conditions will determine a modification of the result.

Cuvier, in his dispute with Geoffroy St. Hilaire, was always insisting on the dangers of Hypothesis; and else-where proclaimed it his guiding principle to adhere simply to the " exposition of positive facts " ; a declaration which occasionally meets with the fatal objection that what he expounds as facts have been proved to be fictions ; and which may always be met by the undeniable statement of Laplace, that if men had limited their efforts to the collection of facts, Science would have been only a sterile nomenclature, and would never have revealed the great laws of Nature. Without Hypothesis no step could be taken. Our very perceptions involve it. Nay more, I venture to affirm that the wildest flights of Imagination consciously sweeping round the circle of Experience, and' alighting where it pleases, are legitimate tentatives of scientific Research, if only they submit to the one indispensable condition (unhappily too often neglected) of ultimate verification. The profound remark of Copernicus,* that the value of an hypothesis consists in reconciling Calculation with Observation, has not been duly appreciated ; so little has it been appreciated that most people would echo Bacon's sneer at Copernicus as the man who thinks nothing of introducing fictions of any kind into Nature, provided his calculations turn out well." The answer to this sneer is the triumphant achievements which are effected by the introduction of avowed fictions among the artifices of Research.

88. It is not only in Algebra that in endeavoring to form an equation we often begin by assigning any value we please to the unknown quantity, and submit this to all the operations necessary for ascertaining whether it answers the conditions or not, so that the result is to the correct one as the assumed value is to the unknown one. We may employ what materials we please for our scaffolding, on the sole proviso that since this scaffolding is not the house, it must be carefully taken away again, when the house is constructed; we must not allow the beams, ropes, and ladders, used as auxiliaries, to thrust themselves discordantly into the structure itself. No doubt great skill is needed in the selection of auxiliaries, and in avoiding the danger of thrusting parts of the scaffolding into the structure ; and the formation of true hypotheses is the severest task for the scientific imagination ; while the invention of false, or illusory, hypotheses is the sterile abundance of an untrained imagination. The principle here proclaimed is the absolute freedom of introducing any elements in the formation of an equation, on the understanding that nothing which is introduced as an auxiliary be permitted to appear in the result. On this principle we may admit the conception of Atoms, even if we regard them as pure fictions : and we may endow these Atoms with any shape, size, or qualities we please, if thereby calculation can be aided; provided always that we assume nothing absolutely contradictory of experience, but only what is in harmony with experience; that is to say, the Atoms must be Extra-sensible, not Supra-sensible. The truth, or falsity, of the existence of these Atoms is another question altogether ; and need never be raised so long as we treat them purely as auxiliaries, not realities. Thus, suppose I assume the Atoms to have the shape of an ellipsoid, and to be capable of moving only in rotation about three fixed axes, but incapable of vibration or translation. The assumption is inadmissible, because it is contradictory of experience, which rejects the idea of rotation as an exclusive form of motion. If, however, I merely assume that under given conditions the only motion possible is that of rotation, and I deduce from this some exact results, not otherwise obtainable, my assumption is valid, since it is proved thereby to represent some relation of the real agents. But- that this relation is only one among many is proved by the simple fact that bodies expand, which would be impossible unless there were internal motions, not necessarily of vibration.

89. Again, the hypothesis of an undulating Ether, so largely employed in modern inquiries, is perfectly legitimate, and is proved to be so by its results. The vast array of phenomena which it explains, and the striking anticipations of Observation which it has effected, do not indeed prove the reality of the Ether, though they render its existence highly probable. The hypothesis with its dependent calculations brings into view a larger number of conditions which must be accepted as true, even when the ether itself is rejected.

The controversy on this question is too often confused by the want of a clear recognition of the principle I am here expounding, namely, that the value of the hypothesis is one thing, its evidence for the reality of an Ether is another. We are not bound to prove the existence of the Agent, so long as we confine ourselves to the hypothesis of an Agency acting on hydrodynamic or molecular dynamic laws ; and so long as we do not allow more than the demonstrated Agency to enter into the final equation ; such as would be the case if from any assumed, but not demonstrated, properties of the Ether we deduced conclusions at variance with, or not verifiable by, experience. And the reason of this reliance on the Agency,irrespective of the reality of the Agent, is that at any rate what is thus demonstrable must be true of the relations of the Agent, be that Agent what it may. Let this Ether be only an attenuated form of ponderable Matter, or a fluid, or a solid, sui generis, we know at least that its mode of action in certain phenomena is explicable on dynamic laws. But there are phenomena which these laws have hitherto failed to explain. Hence we conclude that the Agent has other modes of action besides those already revealed, that the dynamic laws require to be supplemented by some other laws of molecular movement.

90. Some years ago I suggested a course of inquiry which was unhappily beyond my own power, but which in the hands of a powerful analyst might resolve some of the difficulties at present attending the undulatory theory. That theory only regards the movements of vibration, leaving out of sight the movement of rotation. But if the Ether be assumed as atomic, these atoms must have form ; their geometric properties entail corresponding dynamic properties ; and they cannot have movements of translation without also having rotation. Now if the mathethatical investigation of the movements of translation were supplemented by an investigation of the movements of rotation, it is eminently probable that this new analysis would disclose the equations necessary for the reduction of those phenomena which still resist mathematical analysis.

91. Be this as it may, the achieved results are ample justification of the hypothesis of an Ether. I cannot, therefore, agree with Comte in his polemic against the hypothesis, a polemic which could only avail against those who proclaimed the reality of the Ether. But he will not allow it to have even an auxiliary value. " A la vérité les physiciens se défendent vivement aujourd'hui d'attacher aucune réalité intrinsèque à ces hypothèses, qu'ils préconisent seulement comme des moyens indispensables pour faciliter la conception et la combinaison des phénomènes. Mais n'est ce point là l'illusion d'une positivité incomplète, qui sent la profonde inanité de tels systèmes et pourtant n'ose point encore s'en passer ? "

To this question I answer, No; and in so answering it, believe I am standing strictly within the sphere of positive science. But as Comte's view is shared by some eminent writers, we are bound to consider it carefully and impartially.

Hypotheses relate either to the Agents, or the Agencies, which link together the observed phenomena, i. e. the qualitative or quantitative elements which are the determinants of the phenomena. Sometimes we know the determinant (Agent, or Substance), but are ignorant of its mode of operation in effecting the change observed. Sometimes we know this mode of operation, or Agency, but are ignorant of the Agent. Thus we know that oxygen is the agent in the transformation of venous into arterial blood, and in the decomposition of the tissues necessary to the liberation of organic force ; but the mode in which this is effected, whether by direct or indirect oxidation, is still a mystery. On the other hand, we know that the agency of Light is that of wave-movement; but the moving agent is unknown. The mode of operation of what .is called chemical Affinity is known, but Affinity itself is unknown. We know as an experimental fact that Heat is Motion, and therefore the laws of Motion are laws of Heat ; but we are still unable to explain many of the phenomena, " because we do not know what is moving nor how it moves. Results of the theory in which these are not involved are experimentally verified."

92. Now, any hypothesis introduced either respecting the Agent or the Agency is justified if it facilitates Research and conforms to the test of Verification ; and it ' can only be called upon to show evidence for its reality, when we declare it to be the real Agent, and when as such it enters into the final equation. Whether the Agent which determines the orbit of a planet be an An-gel seated in the sun, or an Attraction issuing forth from the sun and the planet, is a matter of indifference, so long as we admit nothing but the law of the Agency into our final equation, and allow neither any assumed proper-ties of Angels, nor any assumed properties of an occult Attraction, to find expression. Again, whatever hypothesis we form respecting the Agent of Heat will be indifferent, so long as we confine our equation to the Agency. Thus, while assuming Heat to be Motion, we only select from all the possible forms of Motion those of Vibration and Rotation, which constitute the known Agency ; and since the results of calculation thus obtained agree rigorously with observation, we conclude that we have detected something at least of the real mode of operation, let the Agent be a peculiar substance moving amid the particles of the heated body, or simply the molecules of the body itself in a state of agitation. Comte is right in saying that it would be difficult to see how the dilatation of a body by heat is explained by the idea of an imaginary fluid interposed between its molecules, tending constantly to augment their intervals, since we should then have to inquire whence the fluid gained its elasticity, which is assuredly less intelligible than the primitive fact. But although the introduction of a fluid as an Agent explains nothing, the fluid' as an Agency — i. e. its hydrodynamic laws — explains much. Of course, any other hypothesis — that, for instance, of expansion being due to the increased oscillation of the molecules — may take the place of this hydrodynamic hypothesis ; and it will remain for the advocates of each to justify the preference by the greater sum of verified results. The two hypotheses of Light both explained many of the phenomena; and the one was finally victorious only when it succeeded in explaining what its rival stumbled over as a contradiction. The undulatory hypothesis itself, as usually stated, may perhaps have to yield the place to another.

93. Let us never forget that the agreement of observation with calculation does not prove the reality of the Ether as an Agent; it only proves that the mode of operation of the real Agent (whatever that may be) is to some extent such as we assume ; and it is only because we are in doubt of the reality that we call upon hypothesis to aid us. Were the reality proved, there would be no longer an hypothesis, the supposition would give place to a demonstration. To demand that what are avowedly fictions should be called to prove their reality, is inconsistent. Hypotheses are guesses, aids to research, and not to be treated like the results. There are good and bad guesses ; and unhappily their inventors are generally careless in verifying them. Sometimes verification is, in the nature of the case, not attainable ; we then rely on probability. Our guesses may be ranged under three classes : 1°, the Real Hypotheses, which being intrinsic are explicative ; 2°, the Auxiliary Hypotheses, which being extrinsic are merely aids in construction ; 3°, the Illusory Hypotheses.

94. A Real Hypothesis is one which explains observed phenomena, and anticipates the results of future observation, by means of some Agent or Agency known to be present among the elements of the observed phenomenon, the precise relations of which, however, as determinants, are not known. Thus the phenomenon of Expansion in gases and solids is explained as the wider sweep of the oscillating molecules. That the molecules are in a state of oscillation is known ; the laws of oscillation are sufficient to account for the phenomenon, without the intervention of any extrinsic agency. If a vibrating fluid be introduced to account for the oscillation of the particles, and be absolutely restricted to the simple office of transmitting vibrations, without any admixture of undemonstrable properties, the hypothesis still keeps within the sphere of the known; and all the demand we can make on it is that it shall explain what we observe.

95. When the x is obtained in an equation, what is known of it (its functions) must satisfy the equation, otherwise no step in advance is made. Thus, if we intro-duce a Spirit as the Agent in certain changes, how does this enlighten us, unless we know the properties of the Spirit and its laws of action? Whereas if instead of a Spirit we introduce Attraction, although we may be equally ignorant of this Agent, if we know the laws of its action, through these known laws the equation is satisfied. Newton's great hypothesis is a fine example. It was what I have called a Real Hypothesis, — what he would have put forward as legitimate because it was " deduced from the phenomena." He began by assuming that the force which at each instant deflects a planet from its tangent (the observed fact of deflection leading to the assumption of a deflecting force), and which causes the planet to move in a curve round the sun (another observation), is a force tending directly towards the sun. He then showed that, on such premises being granted, the conclusion follows that the planet will describe equal areas in equal times, — and this conclusion Kepler's first law had already established (subject to the qualification I have before noted, and accepting the law in its ideal aspect). Newton further showed that if the deflecting force did not tend towards the sun, the planet would not describe equal areas in equal times. Having thus demonstrated that the hypothesis necessarily carried the conclusion which observation disclosed, and that a contradictory hypothesis would not carry such a conclusion, his assumption was established as a truth, his guess was "deduced from the phenomena."

96. It is characteristic of all Real Hypotheses that they pass by Verification into inductive truths. Since they admit nothing extrinsic to the phenomena, directly the right guess has been intuited the process of demonstration requires no elimination of auxiliary elements. Hence it is obvious that our first aim should be to frame hypotheses of this kind, and to seek for an explanation of phenomena in Agents or Agencies already known, or surmised to be present (Rule XV.). But it is no less obvious that were we to confine Inquiry to such a procedure, the advance of Science would be extremely slow, since it is seldom that we have this solid foundation to stand on, and it mostly happens that we do not know but are forced to guess, what is the Agent or Agency in operation. Hence the employment of Auxiliary Hypotheses.

An Auxiliary Hypothesis is a conscious fiction by which Imagination pictures what would be the effect of a given Agent, or Agency, if present. It is purely a tentative process, like that of assigning an arbitrary value to an unknown quantity. The advantage of such a tentative process will of course depend on the degree in which the imagined agency resembles the actual agency; and for this purpose it must be of a character strictly analogical with those of the elements known to be present in similar phenomena (Rule XV.) For example, the complications of the planetary movements would baffle all rational theory were it not for the various fictions by which astronomers turn the difficulty and especially by that of the Type presented in the problem of two bodies, one of which is assumed to be fixed. It is to this Type, avowedly a fiction, that the real movements are reduced by successive approximations ; and its completion is Lagrange's celebrated theory of the variation of arbitrary constants, which treats the effective movement of any planet as if it were really elliptical, but with variable elements instead of constant elements.

" So many of the properties of matter," says Professor Clerk Maxwell, " can be deduced from the hypothesis that their minute parts are in rapid motion, the. velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity. Daniel Bernouilli, Herapath, Joule, Kronig, Clausius, etc., have shown that the relations between pressure, temperature, and density in a perfect gas can be explained by supposing the particles to move with uniform velocity in straight lines, striking against the sides of the containing vessel and thus producing pressure. It is not necessary to suppose each particle to travel to any great distance in the same straight line ; for the effect in producing pressure will be the same if the particles strike against each other ; so that the straight line described may be very short. Clausius has determined the mean length of path in terms of the average distance of the particles, and the distance between the centres of two particles when collision takes place. We have at present no means of ascertaining either of these distances ; but certain phenomena such as the internal friction of gases, the conduction of heat through a gas, and the diffusion of one gas through another, seem to indicate the possibility of determining accurately the mean length of path which a particle de-scribes between two successive collisions, In order to lay the foundation of such investigations on strict mechanical principles, I shall demonstrate the laws of motion of an indefinite number of small, hard, and perfectly elastic spheres acting on one another only during impact. If the properties of such a system of bodies are found to corresponde to those of gases, an important physical analogy will be established which may lead to more accurate knowledge of the properties of matter. If experiments on gases are in-consistent with the hypothesis of these propositions, then our theory, though consistent in itself, is proved to be incapable of explaining the phenomena of gases. In either case it is necessary to follow out the consequences of the hypothesis.

Instead of saying that the particles are hard, elastic, and spherical, we may, if we please, say that the particles are centres of force of which the action is insensible except at a certain small distance, when it suddenly appears as a repulsive force of very great intensity. It is evident that either assumption will lead to the same results."

97. The freedom which Imagination is here allowed in the creation of conscious fictions does not prevent these guesses being submitted to the most rigorous tests and the value of such fictions appears in the aid they furnish to calculation. We find Mr. Maxwell not only explaining the pressure of a gas by this assumption of elastic particles moving in straight lines, — the square of the velocity being proportional directly to the absolute temperature and inversely to the specific gravity of the gas at a constant temperature, — but also that the number of particles in a unit of volume is the same for all gases at the same pressure and temperature : a result in striking accordance with the chemical law that equal volumes of gases are chemically equivalent. Again, it is a pure fiction which transfers the circular nature of the Earth and all the geometrical properties of the circle to the Heavens. That the Earth is a sphere, or approximates to one, is a fact ; but that it is enclosed in a heavenly sphere is a sheer fiction ; yet it is the celestial circles by which the terrestrial latitudes and longitudes are calculated ; and were it not for this fiction, which connects Geography with Astronomy, our geographical science could not have been constructed.

98. It is necessary to insist on the strictly scientific use of the Imagination in constructing these auxiliaries, because Newton has in emphatic language condemned them, though his own practice we have seen to be a splendid vindication of them. He pronounced hypotheses il-legitimate which were not deduced from the phenomena; in fact it was these only that he called hypotheses. " Whatever is not deduced from the phenomena," he says in the famous Scholium, " is to be called an hypothesis ; and hypotheses, whether metaphysical or physical, have no place in experimental philosophy." The weight of his authority has pressed Hypothesis into the mire, where it is trodden on by the feet of writers who are by no means slow to profit by its services ; and thus, in spite of its services, Hypothesis has become the pariah of research.

99. The rival hypotheses respecting Light are manifestly auxiliary. The corpuscular is now discredited, but it was once, if erroneous, effective. Some writers declare that there was this initial defect in it, that only on the supposition of a corpuscle being visible and tangible, could the hypothesis have been justifiable. This is precisely the objection urged by Comte, Mill, and others against the undulatory hypothesis. If the Ether be admissible, although no one has seen or could see it, then surely luminous corpuscles are admissible ? Neither of these Agents is known to be present in luminous phenomena ; neither is positively known to exist. But the valid ground for the rejection of the one hypothesis is not that the Agent is proved to be absent, but that the Agency invoked as an auxiliary fails to explain the phenomena ; whereas the Agency invoked in the other case, although still incompetent to explain all the phenomena, explains so many, that its aid is more effective, and there-fore preferred.

The vortices of Descartes have long since passed into the rag-shop of worn-out finery ; and those who see the hypothesis huddled among many others equally discarded, forget that it was once a part of the furniture of Science. In estimating an opinion we must always take the historical stand-point ; for the suggestion which from a later stand-point appears inept, may be recognized as ingenious from the earlier. The vortices of Descartes thus viewed present an example of the three stages through which most hypotheses must pass, its stage of indispensable though temporary aid, its stage of application and verification, and its stage of final displacement in favor of some more successful rival. Placing ourselves for a moment at the point of view prevalent when Descartes devised the vortices, we at once see the enormous and indispensable aid it furnished, simply by the introduction of the idea of mechanical law where even the great Kepler could only conceive the action of genii. A philosophy which explained phenomena by the aid of such genii could only be set aside by a philosophy which explained the phenomena on mechanical grounds. And although when Celestial Mechanics had received a sure foundation by the discovery of gravitation, the hypothesis of Vortices was an obstruction, not an aid, its doom was not sealed until geometers and astronomers proved that it was in contradiction with known facts and known mechanical laws ; and proved that another hypothesis accomplished all it pretended, and explained what it left inexplicable. Here, as elsewhere, those who declared that it was impossible to theorize without such an aid were answered by a more effectual theorizing with another.

100. Among auxiliaries a distinction is to be made between those which relate to Agencies and those which relate to Agents. In the first class are the quantitative hypotheses of mathematical physics, where, in entire ignorance of the Agents, we can, from mathematical laws, at least deduce their mode of operation. The nature of Heat, Electricity, or Magnetism may be unknown, but some of their quantitative laws are absolutely known. Yet auxiliary hypotheses have always to be treated as auxiliary, and, when applied to physical facts, require numerous modifying and limiting considerations, such as are always requisite in passing from the abstract to the concrete. Thus Newton says : I use the words attraction and impulse not defining the species or physical qualities of forces, but investigating the quantities and mathematical proportions of them. In mathematics we are to investigate the quantities of forces with their proportions consequent upon any conditions supposed ; then when we enter upon physics we compare those proportions with the phenomena of Nature, that we may know what conditions of those forces answer to the several kinds of at-tractive bodies. And this preparation being made we may agree more safely concerning the physical species, causes, and proportions of the forces.

" The history of physical science," says Prof. Challis, " seems to show that theoretical investigation proceeds in but one course, that of deducing quantitative laws, by means of solutions of equation, from known or hypothetical principles."

101. The second class of hypotheses is of smaller value. Unless we already know the law of the Agency, our guess at the Agent is almost certain to be erroneous ; a consideration which should make us particularly cautious. Even when we know the law, there is great danger of missing the one out of many possible Agents which may be involved. For example, the Electrodynamic theory of Ampère merely expresses the law of the Agency : the experimental data of the action of closed currents on each other give expressions for the mathematical law of the action which one element must exert on another. But Weber seeks the Agent, and his hypothesis is that of an electric current formed by the motion of particles of two kinds of electricity moving in opposite directions ; an hypothesis which is open to many objections.

102. Another example is the hypothesis propounded by Young, and adopted by Helmholtz, of three special retinal fibres for the three primary colors ; or the kindred hypothesis of Helmholtz, that the auditory nerve has special fibres for notes of particular pitch. I shall examine this more in detail in a subsequent Problem. Enough for the present to remark that these different fibres are assumed Agents, and there must first be demonstrated the presence of fibres having different structure and proper-ties ; no attempt has been made to demonstrate this, and we cannot accept them merely on the ground of the Agency, i. e. merely because the known law of distinct primary colors suggests the presence of distinct fibres. The more so because the Agency may be otherwise interpreted. I shall hope to make clear that the Agency can be rigorously deduced from the general Law of Grouping which determines all sensitive phenomena, each color and each tone being simply a special group of neural units. We do .not need three different fibres, since one fibre can readily be conceived vibrating with different nodes, like a rod or cord; and the principle of the superposition of small oscillations may be applied to nerves as to rods.

103. Whether an hypothesis refers to the Agent or the Agency, the one thing needful to be steadily borne in mind is the one thing commonly neglected, namely, that while any supposition which can furnish aid is justified by the assistance we derive from it, no supposition can be accepted for more than instrumental aid, no supposition can be allowed to take the place of a truth, until it has itself been submitted to the operations which establish a truth. An hypothesis may be false, yet help us to a truth; but no demonstration of the truth of any process proves that the hypothesis which explains the process is true. The existence of Ether is not demonstrated because the hypothesis of an Ether is the most satisfactory means we have at present of explaining luminous phenomena ; all that is proved is that the hypothesis is effective. This caution is the more needful because of our tendency to consider the verification of a result as a proof of the independent truth of the hypothesis. Because the supposed Agency is adequate, is it therefore to be held as existent ? Laplace mentions an example of the danger which besets auxiliary hypotheses, "quand on les réalise au lieu de les regarder comme des moyens de soumettre les observations au calcul." Dominic Cassini, he says, in forming a table of refraction, started from the simple supposition of a constant density in the atmosphere. This table was exact at the heights at which the stars are usually observed, and was adopted by astronomers ; and the hypothesis that the refraction augments with the elevation gained universal acceptance until Bouger proved, by observations made at Quito, that the refraction at that height instead of being increased was diminished.

104. Were Newton's dictum to be followed, no auxiliary hypothesis would be permitted. If, however, we clearly understand its nature, and do not confound an instrument of construction with an element of construction, , we may allow Imagination unrestricted license. Any operation is legitimate by which we can submit observations to calculation, or by which new observations are rendered practicable. Suppose I am studying the evolution of an ovum, and unable by the microscope to see the mutual relations of its parts, which could be seen were a thin section made of it ; the delicacy of the structure prevents my making such a section ; I must therefore seek some external aid. A solution of chromic acid hardens the ovum sufficiently to enable a section to be made. Nothing can be more foreign to the organic tissue than this chromic acid ; yet by its aid I am enabled to detect certain constituent elements in that tissue ; and no one would object to my employing it, on the ground that it was extra-organic. But if, after employing chromic acid as an auxiliary, I allowed it to enter into the construction, i. e. if in treating of the chemical and physical composition of the tissue, I introduced among the constituents those results which were due to the agency of the acid, then, indeed, every one would rightly object to the procedure. And it is this error which is committed when hypotheses originally introduced as aids in bringing phenomena into appreciable relation, are finally allowed to appear in the result.

105. The Illusory Hypothesis must be broadly distinguished from the other two classes. It is not deduced from the phenomena ; it is not an aid ; it is simply a re-statement of the observed facts in a compendious, and generally ambiguous phrase. It rebaptizes an observation. Yet such is the influence of mere naming, that the rebaptism of our ignorance seems to be an illumination, and exercises a charm that is all the more obstructive to Research, because we often find a positive advantage in a phrase which condenses a multitude of details ; and the advantage of the formula leads us to confound it with a principle. To many minds the word Affinity is more than a term ; and when chemists say that oxygen unites with hydrogen because these gases have a strong Affinity, many persons accept this as an explanation. In former days a multitude of phenomena were condensed in the formula of the fuga vacui. Nature was said to " abhor a vacuum." This phrase named, and by naming linked together, observed facts of suction, breathing, the rise of water in a tube, etc. and had it been limited to the simple expression of the observed facts, it would, like the term Affinity, have been of unimpeachable advantage. The error lay in taking the formula for a principle, and supposing that it explained what it simply named. Believe to be a principle, its action was necessarily generalized beyond the sphere of observation ; and thus Mersenne imagined a siphon which should go over a mountain ; whereas the real law of suction, on which the siphon depends, is limited to drawing water to the height of 34 feet, — above that, the " horror of a vacuum " ceases.

106. In our own day writers who ridicule the fuga vacui are quite ready to invent or accept Illusory Hypotheses of the same calibre. They confidently assign phenomena to Electricity, Ozone, Polarity, Nervo-atmospheres, Repulsive atmospheres, Psychic force, Vital force, and the like. Nay, it is popularly supposed that the invention of such hypotheses is an exercise of the Imagination ; and on this ground soberer thinkers. are wont to decry Imagination, believing it to be the pest of Science. Such hypotheses are indeed a pest ; but so far from their source being Imagination, it is precisely a defect of Imagination which forms their nidus. To imagine a natural process is to see the Agents or Agencies which are really operative, or which, if present, would act so as to produce the result observed. But this mental picture of the unseen process is given only to the highest minds equipped with exact knowledge. In Science, as in Art, any feeble mind can satisfy itself by vaguely supposing that some-thing may in some way or other (not specified) determine the changes which take place; the difficulty is in precise vision. But precision is the one quality which impatient minds least appreciate ; and therefore Illusory Hypotheses spring up like mushrooms in half-cultivated minds, and are readily accepted by the uncultivated, who see no difficulties because they have no vision of the requisites : marvels are not marvellous to them, for ignorance does not marvel.

107. Whenever an hypothesis suggests itself it should be submitted to the following conditions : first, the sup-posed Agent or Agency must be a true cause. This does not mean that it should be a cause already known to be in operation here, but one known to be in operation somewhere, so that from its known properties the phenomena may be deduced. "Nature's horror" and "Psychic Force" are clearly not brought from some other part of our experience to explain a present difficulty, but are invented for the nonce. " Nature's horror " and " Psychic Force " must first be made known to us by their properties in other cases before we can explain any phenomena by their presence ; or conversely, if we assume that the present phenomena clearly suggest the presence of these agents, we must show that these agents are operative elsewhere; and this must be done by direct demonstration of their existence, or by the indirect demonstration that no other agents will suffice. Having laid hold of a vera causa, we must next render intelligible how its known properties in action agree with the phenomena it is brought in to explain. That is to say, suppose Electricity be the Agent assumed, we must show how the known laws of electrical action lead deductively to the facts observed ; or if any laws of electrical action be assumed for the nonce they must not be in contradiction with known laws, nor in contradiction with any of the observed facts. Having got thus far there remain two final conditions :it is not sufficient that the phenomena can be deduced from the hypothesis, there must be also a deduction of new phenomena not hitherto observed, or an extension of the hypothesis to other cases, thereby justifying the hypothesis as at least an aid in enlarging knowledge, and not simply a rebaptism of the known ; and, secondly, there must be proof that no other hypothesis will at once explain the old observations and lead deductively to the new. Kepler's hypothesis of the elliptical orbit of the planets did not satisfy Dominic Cassini, who proposed to replace it by a curve of the fourth degree roughly resembling an ellipse in certain cases, and in which the product of the focal distances, instead of their sum, remained invariable. But why have astronomers rejected this Cassinoïd, and retained the ellipse ? Simply because the one does not, and the other does, reconcile calculation with observation. Again, of the four hypotheses suggested to explain meteoric stones, some facts are explicable on all four; and by turns it may appear that the meteorites are products of volcanoes in the moon, volcanoes in our earth, or condensations of atmospheric particles ; but a wide survey of the facts, and comparison with these three hypotheses in all their consequences, leaves each defective, and the fourth hypothesis (of the cosmical origin of these bodies) takes their place by right of conquest over the phenomena.

108. To conclude : all hypotheses are illusory which cannot justify themselves by enlarging knowledge; and if their inventors would hesitate to put them forth until they had submitted them to the requisite tests, or shown what new results are obtainable by the hypotheses, the amplest scope would be given to their inventive powers, with-out any evil accruing.

109. Having thus described the use and abuse of Hypothesis, I must, before quitting the subject, notice a restriction on its effective range, placed by Comte and Mill, which is a departure from the principle I have adopted from Copernicus. Mr. Mill considers it allowable to assume the law of what we already know to be the cause, but not to assume the cause itself. "It is allowable, useful, and even necessary to begin by asking ourselves what cause may have produced the effect, in order that we may know in what direction to look out for evidence to deter-mine whether it actually did. The vortices of Descartes would have been a perfectly legitimate hypothesis, if it had been possible by any mode of explanation to bring the reality of the vortices as a fact in Nature conclusively to the test of observation. The hypothesis was vicious simply because it could not lead to any course of investigation capable of converting it from an hypothesis into a proved fact."

This argument is equally destructive of the Nebular Hypothesis and the Evolution Hypothesis, both of which Mr. Mill regards in the light of genuine scientific procedures. Nay, it is destructive of the hypothesis of universal Gravitation (which, indeed, Mr. Mill hesitates to accept). No one of these is capable of being brought to the test of observation, of being converted into a proved fact. Indeed the restriction placed by Comte and Mill would interdict all speculation respecting geological and astronomical phenomena which, dependent on past causations, cannot receive verification except by reflection from present causation. If such indirect evidence be inadmissible, vainly will astronomers, geologists, and biologists accumulate evidence. The various phases of the earth's evolution, the various stages of animal evolution, are explained on the assumption that causes similar to those now observed in operation were formerly the agents in bringing about the evolution ; and the assumption is admitted, but no one pretends that there is proof of the hypothesis. The Nebular Hypothesis and the Evolution Hypothesis have amply justified themselves by the aids they have furnished to Research ; but few imagine them to be demonstrable ; nor can we assert them to be final.

( Originally Published 1874 )

Problems of Life and Mind:
The Reality Of Abstractions

Ideal Construction In Science

What Are Laws Of Nature?

The Use And Abuse Of Hypothesis

The Passage From The Abstract To The Concrete

Ideal Construction In Metaphysics

The Search After Causes

Intuition And Demonstration

Axioms And Their Validity

Necessary Truths

Read More Articles About: Problems of Life and Mind

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