One can express this state of things otherwise by saying that the whole of the stimulus does not seem to be effective in giving us the perception of 'more,' and the simplest interpretation of such a state of things would be physical. The loss of effect would take place in the nervous system. If our feelings resulted from a condition of the nerve-molecules which it grew ever more difficult for the stimulus to increase, our feelings would naturally grow at a slower rate than the stimulus itself. An ever larger part of the latter's work would go to overcoming the resistances, and an ever smaller part to the realization of the feeling-bringing state. Weber's law would thus be a sort of law of friction in the neural machine.[462] Just how these inner resistances and frictions are to be conceived is a speculative question. Delbœuf has formulated them as fatigue; Bernstein and Ward, as irradiations. The latest, and probably the most 'real,' hypothesis is that of Ebbinghaus, who supposes that the intensity of sensation depends on the number of neural molecules which are disintegrated in the unit of time. There are only a certain number at any time which are capable of disintegrating; and whilst most of these are in an average condition of instability, some are almost stable and some already near to decomposition. The smallest stimuli affect these latter molecules only; and as they are but few, the sensational effect from adding a given quantity of stimulus at first is relatively small. Medium stimuli affect the majority of the molecules, but affect fewer and fewer in proportion as they have already diminished their number. The latest additions to the stimuli find all the medium molecules already disintegrated, and only affect the small relatively indecomposable remainder, thus giving rise to increments of feeling which are correspondingly small. (Pflüger's Archiv, 45, 113.)
It is surely in some such way as this that Weber's law is to be interpreted, if it ever is. The Fechnerian Maasformel and the conception of it as an ultimate 'psychophysic law' will remain an 'idol of the den,' if ever there was one. Fechner himself indeed was a German Gelehrter of the ideal type, at once simple and shrewd, a mystic and an experimentalist, homely and daring, and as loyal to facts as to his theories. But it would be terrible if even such a dear old man as this could saddle our Science forever with his patient whimsies, and, in a world so full of more nutritious objects of attention, compel all future students to plough through the difficulties, not only of his own works, but of the still drier ones written in his refutation. Those who desire this dreadful literature can find it; it has a 'disciplinary value;' but I will not even enumerate it in a foot-note. The only amusing part of it is that Fechner's critics should always feel bound, after smiting his theories hip and thigh and leaving not a stick of them standing, to wind up by saying that nevertheless to him belongs the imperishable glory, of first formulating them and thereby turning psychology into an exact science,
"'And everybody praised the duke
Who this great fight did win.'
'But what good came of it at last?'
Quoth little Peterkin.
'Why, that I cannot tell,' said he,
'But 'twas a famous victory!'"
[406] Human Understanding, ii, xi, 1, 2.
[407] Analysis, vol. i, p. 71.
[408] The Senses and the Intellect, page 411.
[409] Essays Philosophical and Theological: First Series, pp. 268-273.
[410] Montgomery in 'Mind,' x, 527. Cf. also Lipps: Grundtatsachen des Seelenlebens, p. 579 ff.; and see below, Chapter XIX.
[411] Stumpf (Tonpsychologie, i, 116 ff.) tries to prove that the theory that all differences are differences of composition leads necessarily to an infinite regression when we try to determine the unit. It seems to me that in his particular reasoning he forgets the ultimate units of the mind-stuff theory. I cannot find the completed infinite to be one of the obstacles to belief in this theory, although I fully accept Stumpf's general reasoning, and am only too happy to find myself on the same side with such an exceptionally clear thinker. The strictures by Wahle in the Vierteljsch. f. wiss. Phil. seem to me to have no force, since the writer does not discriminate between resemblance of things obviously compound and that of things sensibly simple.
[412] The belief that the causes of effects felt by us to differ qualitatively are facts which differ only in quantity (e.g. that blue is caused by so many ether-waves, and yellow by a smaller number) must not be confounded with the feeling that the effects differ quantitatively themselves.
[413] Herr G. H. Schneider, in his youthful pamphlet (Die Unterscheidung, 1877) has tried to show that there are no positively existent elements of sensibility, no substantive qualities between which differences obtain, but that the terms we call such, the sensations, are but sums of differences, loci or starting points whence many directions of difference proceed. 'Unterschiedsempfindungs-Complexe' are what he calls them. This absurd carrying out of that 'principle of relativity' which we shall have to mention in Chapter XVII may serve as a counterpoise to the mind-stuff theory, which says that there are nothing but substantive sensations, and denies the existence of relations of difference between them at all.
[414] Cf. Stumpf, Tonpsychologie, i, 121, and James Ward, Mind, i, 464.
[415] The ordinary treatment of this is to call it the result of the fusion of a lot of sensations, in themselves separate. This is pure mythology, as the sequel will abundantly show.
[416] "We often begin to be dimly aware of a difference in a sensation or group of sensations, before we can assign any definite character to that which differs. Thus we detect a strange or foreign ingredient or flavor in a familiar dish, or of tone in a familiar tune, and yet are wholly unable for a while to say what the intruder is like. Hence perhaps discrimination may be regarded as the earliest and most primordial mode of intellectual activity." (Sully: Outlines of Psychology, p. 142. Cf. also G. H. Schneider: Die Unterscheidung, pp. 9-10.)
[417] In cases where the difference is slight, we may need, as previously remarked, to get the dying phase of n as well as of m before n-different-from-m is distinctly felt. In that case the inevitably successive feelings (as far as we can sever what is so continuous) would be four, m, difference, n, n-different-from-m. This slight additional complication alters not a whit the essential features of the case.
[418] Analysis. J. S. Mill's ed., ii, 17. Cf. also pp. 12, 14.
[419] There is only one obstacle, and that is our inveterate tendency to believe that where two things or qualities are compared, it must be that exact duplicates of both have got into the mind and have matched themselves against each other there. To which the first reply is the empirical one of "Look into the mind and see." When I recognize a weight which I now lift as inferior to the one I just lifted; when, with my tooth now aching, I perceive the pain to be less intense than it was a minute ago; the two things in the mind which are compared would, by the authors I criticise, be admitted to be an actual sensation and an image in the memory. An image in the memory, by general consent of these same authors, is admitted to be a weaker thing than a sensation. Nevertheless it is in these instances judged stronger; that is, an object supposed to be known only in so far forth as this image represents it, is judged stronger. Ought not this to shake one's belief in the notion of separate representative 'ideas' weighing themselves, or being weighed by the Ego, against each other in the mind? And let it not be said that what makes us judge the felt pain to be weaker than the imagined one of a moment since is our recollection of the downward nature of the shock of difference which we felt as we passed to the present moment from the one before it. That shock does undoubtedly have a different character according as it comes between terms of which the second diminishes or increases; and it may be admitted that in cases Where the past term is doubtfully remembered, the memory of the shock as plus or minus, might sometimes enable us to establish a relation which otherwise we should not perceive. But one could hardly expect the memory of this shock to overpower our actual comparison of terms, both of which are present (as are the image and the sensation in the case supposed), and make us judge the weaker one to be the stronger.—And hereupon comes the second reply: Suppose the mind does compare two realities by comparing two ideas of its own which represent them—what is gained? The same mystery is still there. The ideas must still be known; and, as the attention in comparing oscillates from one to the other, past must be known with present just as before. If you must end by simply saying that your 'Ego,' whilst being neither the idea of m nor the idea of n, yet knows and compares both, why not allow your pulse of thought, which is neither the thing m nor the thing n, to know and compare both directly? 'Tis but a question of how to name the facts least artificially. The egoist explains them, by naming them as an Ego 'combining' or 'synthetizing' two ideas, no more than we do by naming them a pulse of thought knowing two facts.
[420] I fear that few will be converted by my words, so obstinately do thinkers of all schools refuse to admit the unmediated function of knowing a thing, and so incorrigibly do they substitute being the thing for it. E.g., in the latest utterance of the spiritualistic philosophy (Bowne's Introduction to Psychological Theory, 1887, published only three days before this writing) one of the first sentences which catch my eye is this: "What remembers? The spiritualist says, the soul remembers; it abides across the years and the flow of the body, and gathering up its past, carries it with it" (p. 28). Why, for heaven's sake, O Bowne, cannot you say 'knows it'? If there is anything our soul does not do to its past, it is to carry it with it.
[421] Sensations of Tone, 2d English Ed., p. 65.
[422] Psychology, i, 345.
[423] A Budget of Paradoxes, p. 380.
[424] The explanation I offer presupposes that a difference too faint to have any direct effect in the way of making the mind notice it per se will nevertheless be strong enough to keep its 'terms' from calling up identical associates. It seems probable from many observations that this is the case. All the facts of 'unconscious' inference are proofs of it. We say a painting 'looks' like the work of a certain artist, though we cannot name the characteristic differentiæ. We see by a man's face that he is sincere, though we can give no definite reason for our faith. The facts of sense-perception quoted from Helmholtz a few pages below will be additional examples. Here is another good one, though it will perhaps be easier understood after reading the chapter on Space-perception than now. Take two stereoscopic slides and represent on each half-slide a pair of spots, a and b, but make their distances such that the a's are equidistant on both slides, whilst the b's are nearer together on slide 1 than on slide 2. Make moreover the distance ab = ab''' and the distance ab' = ab''. Then look successively at the two slides stereoscopically, so that the a's in both are directly fixated (that is fall on the two foveæ, or centres of distinctest vision). The a's will then appear single, and so probably will the b's. But the now single-seeming b on slide 1 will look nearer, whilst that on slide 2 will look farther than the a. But, if the diagrams are rightly drawn, b and b''' must affect 'identical' spots, spots equally far to the right of the fovea, b in the left eye and b''' in the right eye. The same is true of b' and b''. Identical spots are spots whose sensations cannot possibly be discriminated as such. Since in these two observations, however, they give rise to such opposite perceptions of distance, and prompt such opposite tendencies to movement (since in slide 1 we converge in looking from a to b, whilst in slide 2 we diverge), it follows that two processes which occasion feelings quite indistinguishable to direct consciousness may nevertheless be each allied with disparate associates both of a sensorial and of a motor kind. Cf. Donders, Archiv f. Ophthalmologie, Bd. 13 (1867). The basis of his essay is that we cannot feel on which eye any particular element of a compound picture falls, but its effects on our total perception differ in the two eyes.
[425] A. W. Volkmann: Ueber den Einfluss der Uebung, etc., Leipzig Berichte, Math.-phys. Classe. x, 1858, p. 67.
[426] Ibid. Tabelle 1, p. 43.
[427] Professor Lipps accounts for the tactile discrimination of the blind in a way which (divested of its 'mythological' assumptions) seems to me essentially to agree with this. Stronger ideas are supposed to raise weaker ones over the threshold of consciousness by fusing with them, the tendency to fuse being proportional to the similarity of the ideas Cf. Grundtatsachen, etc., pp. 232-3; also pp. 118, 492, 526-7.
[428] Sensations of Tone, 2d. English Edition, p. 62.
[429] Compare as to this, however, what I said above, Chapter V, pp. 172-176.
[430] When a person squints, double images are formed in the centre of the field. As a matter of fact, most squinters are found blind of one eye, or almost so; and it has long been supposed amongst ophthalmologists that the blindness is a secondary affection superinduced by the voluntary suppression of one of the sets of double images, in other words by the positive and persistent refusal to use one of the eyes. This explanation of the blindness has, however, been called in question of late years. See, for a brief account of the matter, O. F. Wadsworth in Boston Med. and Surg. Journ., cxvi, 49 (Jan. 20, '87), and the replies by Derby and others a little later.—W. J.
[431] Tonempfindungen, Dritte Auflage, pp. 102-107.—The reader who has assimilated the contents of our Chapter V, above, will doubtless have remarked that the illustrious physiologist has fallen, in these paragraphs, into that sort of interpretation of the facts which we there tried to prove erroneous. Helmholtz, however, is no more careless than most psychologists in confounding together the object perceived, the organic conditions of the perception, and the sensations which would be excited by the several parts of the object, or by the several organic conditions, provided they came into action separately or were separately attended to, and in assuming that what is true of any one of these sorts of fact must be true of the other sorts also. If each organic condition or part of the object is there, its sensation, he thinks, must be there also, only in a 'synthetic'—which is indistinguishable from what the authors whom we formerly reviewed called an 'unconscious'—state. I will not repeat arguments sufficiently detailed in the earlier chapter (see especially pp. 170-176), but simply say that what he calls the 'fusion of many sensations into one' is really the production of one sensation by the co-operation of many organic conditions; and that what perception fails to discriminate (when it is 'synthetic') is not sensations already existent but not singled out, but new objective facts, judged truer than the facts already synthetically perceived—two views of the solid body, many harmonic tones, instead of one view and one tone, states of the eyeball-muscles thitherto unknown, and the like. These new facts, when first discovered, are known in states of consciousness never till that moment exactly realized before, states of consciousness which at the same time judge them to be determinations of the same matter of fact which was previously realized. All that Helmholtz says of the conditions which hinder and further analysis applies just as naturally to the analysis, through the advent of new feelings, of objects into their elements, as to the analysis of aggregate feelings into elementary feelings supposed to have been hidden in them all the while.
The reader can himself apply this criticism to the following passages from Lotze and Stumpf respectively, which I quote because they are the ablest expressions of the view opposed to my own. Both authors, it seems to me, commit the psychologist's fallacy, and allow their later knowledge of the things felt to be foisted into their account of the primitive way of feeling them.
Lotze says: "It is indubitable that the simultaneous assault of a variety of different stimuli on different senses, or even on the same sense, puts us into a state of confused general feeling in which we are certainly not conscious of clearly distinguishing the different impressions. Still it does not follow that in such a case we have a positive perception of an actual unity of the contents of our ideas, arising from their mixture; our state of mind seems rather to consist in (1) the consciousness of our inability to separate what really has remained diverse, and (2) in the general feeling of the disturbance produced in the economy of our body by the simultaneous assault of the stimuli.... Not that the sensations melt into one another, but simply that the act of distinguishing them is absent; and this again certainly not so far that the fact of the difference remains entirely unperceived, but only so far as to prevent us from determining the amount of the difference, and from apprehending other relations between the different impressions. Anyone who is annoyed at one and the same time by glowing heat, dazzling light, deafening noise, and an offensive smell, will certainly not fuse these disparate sensations into a single one with a single content which could be sensuously perceived; they remain for him in separation, and he merely finds it impossible to be conscious of one of them apart from the others. But, further, he will have a feeling of discomfort—what I mentioned above as the second constituent of his whole state. For every stimulus which produces in consciousness a definite content of sensation is also a definite degree of disturbance, and therefore makes a call upon the forces of the nerves; and the sum of these little changes, which in their character as disturbances are not so diverse as the contents of consciousness they give rise to, produce the general feeling which, added to the inability to distinguish, deludes us into the belief in an actual absence of diversity in our sensations. It is only in some such way as this, again, that I can imagine that state which is sometimes described as the beginning of our whole education, a state which in itself is supposed to be simple, and to be afterwards divided into different sensations by an activity of separation. No activity of separation in the world could establish differences where no real diversity existed; for it would have nothing to guide it to the places where it was to establish them, or to indicate the width it was to give them." (Metaphysic, § 260, English translation.)
Stumpf writes as follows: "Of coexistent sensations there are always a large number undiscriminated in consciousness, or (if one prefer to call what is undiscriminated unconscious) in the soul. They are, however, not fused into a simple quality. When, on entering a room, we receive sensations of odor and warmth together, without expressly attending to either, the two qualities of sensation are not, as it were, an entirely new simple quality, which first at the moment in which attention analytically steps in changes into smell and warmth.... In such cases we find ourselves in presence of an indefinable, unnamable total of feeling. And when, after successfully analyzing this total, we call it back to memory, as it was in its unanalyzed state, and compare it with the elements we have found, the latter (as it seems to me) may be recognized as real parts contained in the former, and the former seen to be their sum. So, for example, when we clearly perceive that the content of our sensation of oil of peppermint is partly a sensation of taste and partly one of temperature." (Tonpsychologie, i, 107.)
I should prefer to say that we perceive that objective fact, known to us as the peppermint taste, to contain those other objective facts known as aromatic or sapid quality, and coldness, respectively. No ground to suppose that the vehicle of this last very complex perception has any identity with the earlier psychosis—least of all is contained in it.
[432] Physiol. Psych., ii, 248.
[433] Wundt's Philos. Studien, i, 527.
[434] Ibid. p. 530.
[435] Mind, xi, 377 ff. He says: "I apparently either distinguished the impression and made the motion simultaneously, or if I tried to avoid this by waiting until I had formed a distinct impression before I began to make the motion, I added to the simple reaction, not only a perception, but a volition."—Which remark may well confirm our doubts as to the strict psychologic worth of any of these measurements.
[436] Mind, xi, 379.
[437] For other determinations of discrimination-time by this method cf. v. Kries and Auerbach, Archiv f. Physiologie, Bd. i, p. 297 ff. (these authors get much smaller figures); Friedrich, Psychologische Studien, i, 39. Chapter ix of Buccola's book, Le Legge del tempo, etc., gives a full account of the subject.
[438] If so, the reactions upon the spark would have to be slower than those upon the touch. The investigation was abandoned because it was found impossible to narrow down the difference between the conditions of the sight-series and those of the touch-series, to nothing more than the possible presence in the latter of the intervening motor-idea. Other disparities could not be excluded.
[439] Tischer gives figures from quite unpractised individuals, which I have not quoted. The discrimination-time of one of them is 22 times longer than Tischer's own! (Psychol. Studien, i, 527.)
[440] Compare Lipps's excellent passage to the same critical effect in his Grundtatsachen des Seelenlebens, pp. 390-393.—I leave my text just as it was written before the publication of Lange's and Münsterberg's results cited on pp. 92 and 432. Their 'shortened' or 'muscular' times, got when the expectant attention was addressed to the possible reactions rather than to the stimulus, constitute the minimal reaction-time of which I speak, and all that I say in the text falls beautifully into line with their results.
[441] Cf. Sully: Mind, x, 494-5; Bradley: ibid. xi, 83; Bosanquet: ibid. xi, 405.
[442] The judgment becomes easier if the two couples of terms have one member in common, if a—b and b—c, for example, are compared. This, as Stumpf says (Tonpsychologie, i, 131), is probably because the introduction of the fourth term brings involuntary cross-comparisons with it, a and b with d, b with c, etc., which confuses us by withdrawing our attention from the relations we ought alone to be estimating.
[443] J. Delbœuf: Éléments de Psychophysique (Paris, 1883), p. 64. Plateau in Stumpf, Tonpsych., i, 125. I have noticed a curious enlargement of certain 'distances' of difference under the influence of chloroform. The jingling of the bells on the horses of a horse-car passing the door, for example, and the rumbling of the vehicle itself, which to our ordinary hearing merge together very readily into a quasi-continuous body of sound, have seemed so far apart as to require a sort of mental facing in opposite directions to get from one to the other, as if they belonged in different worlds. I am inclined to suspect, from certain data, that the ultimate philosophy of difference and likeness will have to be built upon experiences of intoxication, especially by nitrous oxide gas, which lets us into intuitions the subtlety whereof is denied to the waking state. Cf. B. P. Blood: The Anæsthetic Revelation, and the Gist of Philosophy (Amsterdam, N. Y., 1874). Cf. also Mind, vii, 200.
[444] Op. cit. p. 126 ff.
[445] Stumpf, pp. 111-121.
[446] Stumpf, pp. 116-7. I have omitted, so as not to make my text too intricate, an extremely acute and conclusive paragraph, which I reproduce here: "We may generalize: Wherever a number of sensible impressions are apprehended as a series, there in the last instance must perceptions of simple likeness be found. Proof: Assume that all the terms of a series, e.g. the qualities of tone, c d e f g, have something in common,—no matter what it is, call it X; then I say that the differing parts of each of these terms must not only be differently constituted in each, but must themselves form a series, whose existence is the ground for our apprehending the original terms in serial form. We thus get instead of the original series a b c d e f ... the equivalent series Xα, Xβ, Xγ,... etc. What is gained? The question immediately arises: How is α β γ known as a series? According to the theory, these elements must themselves be made up of a part common to all, and of parts differing in each, which latter parts form a new series, and so on ad infinitum, which is absurd."
[447] The most important ameliorations of Fechner's formula are Delbœuf's in his Recherches sur la Mesure des Sensations (1873), p. 35, and Elsas's in his pamphlet Über die Psychophysik (1886) p. 16.
[448] Reversing the order is for the sake of letting the opposite accidental errors due to 'contrast' neutralize each other.
[449] Theoretically it would seem that it ought to be equal to the sum of all the additions which we judge to be increases divided by the total number of judgments made.
[450] J. Delbœuf, Éléments de Psychophysique (1883), p. 9.
[451] Philos. Studien, iv, 588.
[452] Berlin Acad. Sitzungsberichte, 1888, p. 917. Other observers (Dobrowolsky, Lamausky) found great differences in different colors.
[453] See Merkel's tables, loc. cit. p. 568.
[454] American Journal of Psychology, i, 125. The rate of decrease is small but steady, and I cannot well understand what Professor J. means by saying that his figures verify Weber's law.
[455] Philosophische Studien, v, 514-5.
[456] Cf. G. E. Müller: Zur Grundlegung der Psychophysik, §§ 68-70.
[457] Philosophische Studien, v, 287 ff.
[458] American J. of Psychology, iii, 44-7.
[459] Cf. Stumpf, Tonpsychologie, pp. 397-9. "One sensation cannot be a multiple of another. If it could, we ought to be able to subtract the one from the other, and to feel the remainder by itself. Every sensation presents itself as an indivisible unit." Professor von Kries, in the Viertejahrschrift für wiss. Philosophie, vi, 257 ff., shows very clearly the absurdity of supposing that our stronger sensations contain our weaker ones as parts. They differ as qualitative units. Compare also J. Tannery in Delbœuf's Éléments de Psychophysique (1883), p. 134 ff.; J. Ward in Mind, i, 464: Lotze, Metaphysik, § 258.
[460] F Brentano, Psychologie, i, 9, 88 ff.—Merkel thinks that his results with the method of equal-appearing intervals show that we compare considerable intervals with each other by a different law from that by which we notice barely perceptible intervals. The stimuli form an arithmetical series (a pretty wild one according to his figures) in the former case, a geometrical one in the latter—at least so I understand this valiant experimenter but somewhat obscure if acute writer.
[461] This is the formula which Merkel thinks he has verified (if I understand him aright) by his experiments by method 4.
[462] Elsas: Ueber die Psychophysik (1856), p. 41. When the pans of a balance are already loaded, but in equilibrium, it takes a proportionally larger weight added to one of them to incline the beam.