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It is a matter of popular observation that some men have sharper senses than others, and that some have acuter minds and are able to 'split hairs' and see two shades of meaning where the majority see but one. Locke long ago set apart the faculty of discrimination as one in which men differ individually. What he wrote is good enough to quote as an introduction to this chapter:

"Another faculty we may take notice of in our minds is that of discerning and distinguishing between the several ideas it has. It is not enough to have a confused perception of something in general: unless the mind had a distinct perception of different objects and their qualities, it would be capable of very little knowledge; though the bodies that affect us were as busy about us as they are now, and the mind were continually employed in thinking. On this faculty of distinguishing one thing from another depends the evidence and certainty of several even very general propositions, which have passed for innate truths; because men, overlooking the true cause why those propositions find universal assent, impute it wholly to native uniform impressions: whereas it in truth depends upon this clear discerning faculty of the mind, whereby it perceives two ideas to be the same or different. But of this more hereafter.

"How much the imperfection of accurately discriminating ideas one from another lies either in the dulness or faults of the organs of sense, or want of acuteness, exercise, or attention in the understanding, or hastiness and precipitancy natural to some tempers, I will not here examine: it suffices to take notice that this is one of the operations that the mind may reflect on and observe in itself. It is of that consequence to its other knowledge, that so far as this faculty is in itself dull, or not rightly made use of for the distinguishing one thing from another, so far our notions are confused, and our reason and judgment disturbed or misled. If in having our ideas in the memory ready at hand consists quickness of parts; in this of having them unconfused, and being able nicely to distinguish one thing from another where there is but the least difference, consists in a great measure the exactness of judgment and clearness of reason which is to be observed in one man above another. And hence, perhaps, may be given some [p. 484] reason of that common observation, -- that men who have a great deal of wit and prompt memories have not always the clearest judgment or deepest reason. For, wit lying most in the assemblage of ideas, and putting those together with quickness and variety wherein can be found any resemblance or congruity, thereby to make up pleasant pictures and agreeable visions in the fancy; judgment, on the contrary, lies quite on the other side, in separating carefully one from another ideas wherein can be found the least difference, thereby to avoid being misled by similitude and by affinity to take one thing for another. This is a way of proceeding quite contrary to metaphor and allusion, wherein for the most part lies that entertainment and pleasantry of wit which strikes so lively on the fancy, and therefore, so acceptable to all people because its beauty appears at first sight, and there is required no labor of thought to examine what truth or reason there is in it."[1]

But Locke's descendants have been slow to enter into the path whose fruitfulness was thus pointed out by their master, and have so neglected the study of discrimination that one might almost say that the classic English psychologists have, as a school, hardly recognized it to exist. 'Association' has proved itself in their hands the one all-absorbing power of the mind. Dr. Martineau, in his review of Bain, makes some very weighty remarks on this onesidedness of the Lockian school. Our mental history, says he, is, in its view,

"a perpetual formation of new compounds: and the words 'association,' 'cohesion,' 'fusion,' 'indissoluble connection,' all express the change from plurality of data to some unity of result. An explanation of the process therefore requires two things: a true enumeration of the primary constituents, and a correct statement of their laws of combination: just as, in chemistry, we are furnished with a list of the simple elements, and the with then principles of their synthesis. Now the latter of these two conditions we find satisfied by the association-psychologists: but not the former. They are not agreed upon their catalogue of elements, or the marks by which they may know the simple from the compound. The psychologic unit is not fixed; that which is called one impression by Hartley is treated as half-a-dozen or more by Mill: and the tendency of the modern teachers on this point is to recede more and more from the better chosen track of their master. Hartley, for example, regarded the whole present effect upon us of any single object -- say, an orange -- as a single sensation; and the whole vestige is left behind, as a single 'idea of sensation.' His modern disciples, [p. 485] on the other hand, consider this same effect as an aggregate from a plurality of sensations, and the ideal trace it leaves as highly compound. 'The idea of an object,' instead of being an elementary starting-point with them, is one of the elaborate results of repetition and experience; and is continually adduced as remarkably illustrating the fusing power of habitual association. Thus James Mill observes:

"'It is to this great law of association that we trace the formation of our ideas of what we call external objects; that is, the ideas of a certain number of sensations, received together so frequently that they coalesce as it were, and are spoken of under the idea of unity. Hence, what we call the idea of a tree, the idea of a stone, the idea of a horse, the idea of a man. In using the names, tree, horse, man, the names of what I call objects, I am referring, and can be referring, only to my own sensations; in fact, therefore, only naming a certain number of sensations regarded as in a particular state of combination, that is, concomitance. Particular sensations of sight, of touch, of the muscles, are the sensations to the ideas of which, color, extension, roughness, hardness, smoothness, taste, smell, so coalescing as to appear one idea, I give the name of the idea of a tree.'[2]

"To precisely the same effect Mr. Bain remarks:

"External objects usually affect us through a plurality of senses. The pebble on the sea-shore is pictured on the eye as form and color. We take it up in the hand and repeat the impression of form, with the additional feeling of touch. Knock two together, and there is a characteristic sound. To preserve the impression of an object of this kind, there must be an association of all these different effects. Such association, when matured and firm, is our idea, our intellectual grasp of the pebble. Passing to the organic world, and plucking a rose, we have the same effects of form to the eye and hand, color and touch, with new effects of odor and taste. A certain time is requisite for the coherence of all these qualities in one aggregate, so as to give us for all purposes the enduring image of the rose. When fully acquired, any one of the characteristic impressions will revive the others; the odor, the sight, the feeling of the thorny stalk -- each of these by itself will hoist the entire impression into the view.'[3]

"Now, this order of derivation, making our objective knowledge begin with plurality of impression and arrive at unity, we take to be a complete inversion of our psychological history. Hartley, we think, was perfectly right in taking no notice of the number of inlets through which an object delivers its effects upon us, and, in spite of this circumstance, treating the effect as one. . . . Even now, after life has read us so many analytic lessons, in proportion as we can fix the attitude of our scene and ourselves, the sense of plurality in our impressions retreats, and we lapse into an undivided consciousness; losing, for in- [p. 486] stance, the separate notice of any uniform hum in the ear, or light in the eye, or weight of clothes on the body, though not one of them is inoperative on the complexion of our feeling. This law, once granted, must be carried far beyond Hartley's point. Not only must each object present itself to us integrally before it shells off into its qualities, but the whole scene around us must disengage for us object after object from its still background by emergence and change; and even our self-detachment from the world over against us must wait for the start of collision between the force we issue and that which we receive. To confine ourselves to the simplest case: when a red ivory ball, seen for the first time, has been withdrawn, it will leave a mental representation of itself, in which all that it simultaneously gave us will indistinguishably coexist. Let a white ball succeed to it; now, and not before, will an attribute detach itself, and the color, by force of contrast, be shaken out into the foreground. Let the white ball be replaced by an egg: and this new difference will bring the form into notice from its previous slumber. And thus, that which began by being simply an object, cut out from the surrounding scene, becomes for us first a red object, and then a red round object; and so on. Instead, therefore, of the qualities, as separately given, subscribing together and adding themselves up to present us with the object as their aggregate, the object is beforehand with them, and from its integrity delivers them out to our knowledge, one by one. In this disintegration, the primary nucleus never loses its substantive character or name; whilst the difference which it throws off appears as a mere attribute, expressed by an adjective. Hence it is that we are compelled to think of the object as having, not as being, its qualities; and can never heartily admit the belief of any loose lot of attributes really fusing themselves into a thing. The unity of the original whole is not felt to go to pieces and be resolved into the properties which it successively gives off; it retains a residuary existence, which constitutes it a substance, as against the emerging quality, which is only its phenomenal predicate. Were it not for this perpetual process of differentiation of self from the world, of object from its scene, of attribute from object, no step of Abstraction could be taken; no qualities could fall under our notice; and had we ten thousand senses, they would all converge and meet in but one consciousness. But if this be so, it is an utter falsification of the order of nature to speak of sensations grouping themselves into aggregates, and so composing for us the objects of which we think; and the whole language of the theory, in regard to the field of synchronous existences, is a direct inversion of the truth. Experience proceeds and intellect is trained, not by Association, but by Dissociation, not by reduction of pluralities of impression to one, but by the opening out of one into many; and a true psychological history must expound itself in analytic rather than synthetic terms. Precisely those ideas -- of Substance, of Mind, of Cause, of Space -- which this system treats as infinitely complex, the last result of myriads of confluent ele- [p. 487] ments, are in truth the residuary simplicities of consciousness, whose stability the eddies and currents of phenomenal experience have left undisturbed."[4]

The truth is that Experience is trained by both association and dissociation, and that psychology must be writ both in synthetic and in analytic terms. Our original sensible totals are, on the one hand, subdivided by discriminative attention, and, on the other, united with other totals, -- either through the agency of our own movements, carrying our senses from one part of space to another, or because new objects come successively and replace those by which we were at first impressed. The 'simple impression' of Hume, the 'simple idea' of Locke are both abstractions, never realized in experience. Experience, from the very first, presents us with concreted objects, vaguely continuous with the rest of the world which envelops them in space and time, and potentially divisible into inward elements and parts. These objects we break asunder and reunite. We must treat them in both ways for our knowledge of them to grow; and it is hard to say, on the whole, which way preponderates. But since the elements with which the traditional associationism performs its constructions -- 'simple sensations,' namely -- are all products of discrimination carried to a high pitch, it seems as if we ought to discuss the subject of analytic attention and discrimination first.

The noticing of any part whatever of our object is an act of discrimination. Already on p. 404 I have described the manner in which we often spontaneously lapse into the undiscriminating state, even with regard to objects which we have already learned to distinguish. Such anæsthetics as chloroform, nitrous oxide, etc., sometimes bring about transient lapses even more total, in which numerical discrimination especially seems gone; for one sees light and hears sound, but whether one or many lights and sounds is quite impossible to tell. Where the parts of an object have already been discerned, and each made the object of a special discriminative act, we can with difficulty feel the [p. 488] object again in its pristine unity; and so prominent may our consciousness of its composition be, that we may hardly believe that it ever could have appeared undivided. But this is an erroneous view, the undeniable fact being that any number of impressions, from any number of sensory sources, falling simultaneously on a mind WHICH HAS NOT YET EXPERIENCED THEM SEPARATELY, will fuse into a single undivided object for that mind. The law is that all things fuse that can fuse, and nothing separates except what must. What makes impressions separate we have to study in this chapter. Although they separate easier if they come in through distinct nerves, yet distinct nerves are not an unconditional ground of their discrimination, as we shall presently see. The baby, assailed by eyes, ears, nose, skin, and entrails at once, feels it all as one great blooming, buzzing confusion; and to the very end of life, our location of all things in one space is due to the fact that the original extents or bignesses of all the sensations which came to our notice at once, coalesced together into one and the same space. There is no other reason than this why "the hand I touch and see coincides spatially with the hand I immediately feel."[5]

It is true that we may sometimes be tempted to exclaim, when once a lot of hitherto unnoticed details of the object lie before us, "How could we ever have been ignorant of these things and yet have felt the object, or drawn the conclusion, as if it were a continuum, a plenum? There would have been gaps -- but we felt no gaps; wherefore we must have seen and heard these details, leaned upon these steps; they must have been operative upon our minds, just as they are now, only unconsciously, or at least inattentively. Our first unanalyzed sensation was really composed of these elementary sensations, our first rapid conclusion was really based on these intermediate inferences, all the while, only we failed to note the fact." But this is nothing but the fatal 'psychologists fallacy' (p. 196) of treating an inferior state of mind as if it must somehow know implicitly all that is explicitly known [p. 489] about the same topic by superior states of mind. The thing thought of is unquestionably the same, but it is thought twice over in two absolutely different psychoses, -- once as an unbroken unit, and again as a sum of discriminated parts. It is not one thought in two editions, but two entirely distinct thoughts of one thing. And each thought is within itself a continuum, a plenum, needing no contributions from the other to fill up its gaps. As I sit here, I think objects, and I make inferences, which the future is sure to analyze and articulate and riddle with discriminations, showing me many things wherever I now notice one. Nevertheless, my thought feels quite sufficient unto itself for the time being; and ranges from pole to pole, as free, and as unconscious of having overlooked anything, as if it possessed the greatest discriminative enlightenment. We all cease analyzing the world at some point, and notice no more differences. The last units with which we stop are our objective elements of being. Those of a dog are different from those of a Humboldt; those of a practical man from those of a metaphysician. But the dog's and the practical man's thoughts feel continuous, though to the Humboldt or the metaphysician they would appear full of gaps and defects. And they are continuous, as thoughts. It is only as mirrors of things that the superior minds find them full of omissions. And when the omitted things are discovered and the unnoticed differences laid bare, it is not that the old thoughts split up, but that new thoughts supersede them, which make new judgments about the same objective world.

When we discriminate an element, we may contrast it with the case of its own absence, of its simply not being there, without reference to what is there; or we may also take the latter into account. Let the first sort of discrimination be called existential, the latter differential discrimination. A peculiarity of differential discriminations is that they result in a perception of differences which are felt as greater or less one than the other. Entire groups of differences may be ranged in series: the musical scale, the color scale, are examples. Every department of our experience [p. 490] may have its data written down in an evenly gradated order, from a lowest to a highest member. And any one datum may be a term in several such orders. A given note may have a high place in the pitch-series, a low place in the loudness-series, and a medium place in the series of agreeableness. A given tint must, in order to be fully determined, have its place assigned in the series of qualities, in the series of purities (freedom from white), and in the series of intensities or brightnesses. It may be low in one of these respects, but high in another. In passing from term to term in any such series we are conscious not only of each step of difference being equal to (or greater or less than) the last, but we are conscious of proceeding in a uniform direction, different from other possible directions. This consciousness of serial increase of differences is one of the fundamental facts of our intellectual life. More, more, MORE, of the same kind of difference, we say, as we advance from term to term, and realize that the farther on we get the larger grows the breach between the term we are at and the one from which we started. Between any two terms of such a series the difference is greater than that between any intermediate terms, or than that between an intermediate term and either of the extremes. The louder than the loud is louder than the less loud; the farther than the far is farther than the less far; the earlier than the early is earlier than the late; the higher than the high is higher than the low; the bigger than the big is bigger than the small; or, to put it briefly and universally, the more than the more is more than the less; such is the great synthetic principle of mediate comparison which is involved in the possession by the human mind of the sense of serial increase. In Chapter XX we shall see the altogether overwhelming importance of this principle in the conduct of all our higher rational operations.

Each of the differences in one of these uniform series feels like a definite sensible quantity, and each term seems like the last term with this quantity added. In many concrete objects which differ from one another we can plainly [p. 491] see that the difference does consist simply in the fact that one object is the same as the other plus something else, or that they both have an identical part, to which each adds a distinct remainder. Thus two pictures may be struck form the same block, but one of them may differ in having color added; or two carpets may show an identical pattern which in each is woven in distinct hues. Similarly, two classes of sensation may have the same emotional tone but negate each other in remaining respects -- a dark color and a deep sound, for example; or two faces may have the same shape of nose but everything else unlike. The similarity of the same note sounded by instruments of different timbre is explained by the coexistence of a fundamental tone common to both, with over-tones in one which the other lacks. Dipping my hand into water and anon into a colder water, I may then observe certain additional feelings, broader and deeper irradiations of the cold, so to speak, which were not in the earlier experience, though for aught I can tell, the feelings may be otherwise the same. 'Hefting' first one weight, and then another, new feelings may start out in my elbow-joint, wrist, and elsewhere, and make me call the second weight the heavier of the twain. In all these cases each of the differing things may be represented by two parts, one that is common to it and the others, and another that is peculiar to itself. If they form a series, A, B, C, D, etc., and the common part be called X, whilst the lowest difference be called d, then the composition of the series would be as follows:

If X itself were ultimately composed of d's we should have the entire series explained as due to the varying combination and re-combination with itself of an unvarying element; and all the apparent differences of quality would be translated into differences of quantity alone. This is the sort of reduction which the atomic theory in physics and [p. 492] the mind-stuff theory in psychology regard as their ideal. So that, following the analogy of our instances, one might easily be tempted to generalize and to say that all difference is but addition and subtraction, and that what we called 'differential' discrimination is only 'existential' discrimination in disguise; that is to say, that where A and B differ, we merely discern something in the one which the other is without. Absolute identity in things up to a certain point, then absolute non-identity, would on this theory take the place of those ultimate qualitative unlikenesses between them, in which we naturally believe; and the mental function of discrimination, ceasing to be regarded as an ultimate one, would resolve itself into mere logical affirmation and negation, or perception that a feature found in one thing, in another does not exist.

Theoretically, however, this theory is full of difficulty. If all the differences which we feel were in one direction, so that all objects could be arranged in one series (however long), it might still work. But when we consider the notorious fact that objects differ from each other in divergent directions, it grows well nigh impossible to make it do so. For then, supposing that an object differed from things in one direction by the increment d, it would have to differ from things in another direction by a different sort of increment, call it d'; so that, after getting rid of qualitative unlikeness between objects, we should have it back on our hands again between their increments. We may of course re-apply our method, and say that the difference between d and d' is not a qualitative unlikeness, but a fact of composition, one of them being the same as the other plus an increment of still higher order, d for example, added. But when we recollect that everything in the world can be compared with everything else, and that the number of directions of difference is indefinitely great, then we see that the complication of self-compoundings of the ultimate differential increment by which, on this theory, all the innumerable unlikenesses of the world are explained, in order to avoid writing any of them down as ultimate differences of kind, would beggar all conception. It is the mind-dust theory, [p. 493] with all its difficulties in a particularly uncompromising form; and all for the sake of the fantastic pleasure of being able arbitrarily to say that there is between the things in the world and between the 'ideas' in the mind nothing but absolute sameness and absolute not-sameness of elements, the not-sameness admitting no degrees.

To me it seems much wiser to turn away from such transcendental extravagances of speculation, and to abide by the natural appearances. These would leave unlikeness as an indecomposable relation amongst things, and a relation moreover of which there were all degrees. Absolute not-sameness would be the maximal degree, absolute sameness the minimal degree of this unlikeness, the discernment of which would be one of our ultimate cognitive powers.[6] Certainly the natural appearances are dead against the notion that no qualitative differences exist. With the same clearness with which, in certain objects, we do feel a difference to be a mere matter of plus and minus, in other objects we feel that this is not the case. Contrast our feeling of the difference between the length of two lines with our feeling of the difference between blue and yellow, or with that between right and left. Is right equal to left with something added? Is blue yellow plus something? If so, plus what?[7] So long as we stick to verifiable psychology, we are forced to admit that differences of simple KIND form an irreducible sort of relation between some of the elements of our experience, and forced to deny that differential discrimination [p. 494] can everywhere be reduced to the mere ascertainment that elements present in one fact, in another fail to exist. The perception that an element exists in one thing and does not exist in another and the perception of qualitative difference are, in short, entirely disconnected mental functions.[8]

But at the same time that we insist on this, we must also admit that differences of quality, however abundant, are not the only distinctions with which our mind has to deal. Differences which seem of mere composition, of number, of plus and minus, also abound.[9] But it will be best for the present to disregard all these quantitative cases and, taking the others (which, by the least favorable calculation, will still be numerous enough), to consider next the manner in which we come to cognize simple differences of kind. We cannot explain the cognition; we can only ascertain the conditions by virtue of which it occurs.

What, then, are the conditions under which we discriminate things differing in a simple way?

First, the things must BE different, either in time, or place, or quality. If the difference in any of these regards is sufficiently great, then we cannot overlook it, except by not noticing the things at all. No one can help singling out a black stripe on a white ground, or feeling the contrast between a bass note and a high one sounded immediately after it. Discrimination is here involuntary. But where the objective difference is less, discrimination need not so inevitably occur, and may even require considerable effort of attention to be performed at all.

[p. 495] Another condition which then favors it is that the sensations excited by the differing objects should not come to us simultaneously but fall in immediate SUCCESSION upon the same organ. It is easier to compare successive than simultaneous sounds, easier to compare two weights or two temperatures by testing one after the other with the same hand, than by using both hands and comparing both at once. Similarly it is easier to discriminate shades of light or color by moving the eye from one to the other, so that they successively stimulate the same retinal tract. In testing the local discrimination of the skin, by applying compass-points, it is found that they are felt to touch different spots much more readily when set down one after the other than when both are applied at once. In the latter case they may be two or three inches apart on the back, thighs, etc., and still feel as if they were set down in one spot. Finally, in the case of smell and taste it is well-nigh impossible to compare simultaneous impressions at all. The reason why successive impression so much favors the result seems to be that there is a real sensation of difference, aroused by the shock of transition from one perception to another which is unlike the first. This sensation of difference has its own peculiar quality, as difference, which remains sensible, no matter of what sort the terms may be, between which it obtains. It is, in short, one of those transitive feelings, or feelings of relation, of which I treated in a former place (pp. 245 ff.); and, when once aroused, its object lingers in the memory along with the substantive terms which precede and follow, and enables our judgments of comparison to be made. We shall soon see reason to believe that no two terms can possibly be simultaneously perceived to differ, unless, in a preliminary operation, we have successively attended to each, and, in so doing, had the transitional sensation of difference between them aroused. A field of consciousness, however complex, is never analyzed unless some of its ingredients have changed. We now discern, 'tis true, a multitude of coexisting things about us at every moment: but this is because we have had a long education, and each thing we now see distinct has been already differentiated from its neighbors by repeated [p. 496] appearances in successive order. To the infant, sounds, sights, touches, and pains, form probably one unanalyzed bloom of confusion.[10]

Where the difference between the successive sensations is but slight, the transition between them must be made as immediate as possible, and both must be compared in memory, in order to get the best results. One cannot judge accurately of the difference between two similar wines, whilst the second is still in one's mouth. So of sounds, warmths, etc. -- we must get the dying phases of both sensations of the pair we are comparing. Where, however, the difference is strong, this condition is immaterial, and we can then compare a sensation actually felt with another carried in memory only. The longer the interval of time between the sensations, the more uncertain is their discrimination.

The difference, thus immediately felt between two terms, is independent of our ability to identify either of the terms by itself. I can feel two distinct spots to be touched on my skin, yet not know which is above and which below. I can observe two neighboring musical tones to differ, and still not know which of the two is the higher in pitch. Similarly I may discriminate two neighboring tints, whilst remaining uncertain which is the bluer or the yellower, or how either differs from its mate.[11]

With such direct perceptions of difference as this, we must not confound those entirely unlike cases in which we infer that two things must differ because we know enough about each of them taken by itself to warrant our classing [p. 497] them under distinct heads. It often happens, when the interval is long between two experiences, that our judgments are guided, not so much by a positive image or copy of the earlier one, as by our recollection of certain facts about it. Thus I know that the sunshine to-day is less bright than on a certain day last week, because I then said it was quite dazzling, a remark I should not now care to make. Or I know myself to feel better now than I was last summer, because I can now psychologize, and then I could not. We are constantly busy comparing feelings with whose quality our imagination has no sort of acquaintance at the time -- pleasures, or pains, for example. It is notoriously hard to conjure up in imagination a lively image of either of these classes of feeling. The associationists may prate of an idea of pleasure being a pleasant idea, of an idea of pain being a painful one, but the unsophisticated sense of mankind is against them, agreeing with Homer that the memory of griefs when past may be a joy, and with Dante that there is no greater sorrow than, in misery, to recollect one's happier time.

Feelings remembered in this imperfect way must be compared with present or recent feelings by the aid of what we know about them. We identify the remote experience in such a case by conceiving it. The most perfect way of conceiving it is by defining it in terms of some standard scale. If I know the thermometer to stand at zero to-day and to have stood at 32^o last Sunday, I know to-day to be colder, and I know just how much colder, than it was last Sunday. If I know that a certain note was c, and that this note is d, I know that this note must be the higher of the two.

The inference that two things differ because their concomitants, effects, names, kinds, or -- to put it generally -- their signs, differ, is of course susceptible of unlimited complication. The sciences furnish examples, in the way in which men are led, by noticing differences in effects, to assume new hypothetical causes, differing from any known heretofore. But no matter how many may be the steps by which such inferential discriminations are made, they all end in a direct intuition of difference somewhere. The last [p. 498] ground for inferring that A and B differ must be that, whilst A is an m, B is an n, and that m and n are seen to differ. Let us then neglect the complex cases, the A's and the B's, and go back to the study of the unanalyzable perception of difference between their signs, the m's and the n's, when these are seemingly simple terms.
 
I said that in their immediate succession the shock of their difference was felt. It is felt repeatedly when we go back and forth from m to n; and we make a point of getting it thus repeatedly (by alternating our attention at least) whenever the shock is so slight as to be with difficulty perceived. But in addition to being felt at the brief instant of transition, the difference also feels as if incorporated and taken up into the second term, which feels 'different-from-the-first' even while it lasts. It is obvious that the 'second term' of the mind in this case is not bald n, but a very complex object; and that the sequence is not simply first 'm,' then 'difference,' then 'n'; but first 'm,' then 'difference,' then 'n-different-from-m.' The several thoughts, however, to which these three several objects are revealed, are three ordinary 'segments' of the mental 'stream.'

As our brains and minds are actually made, it is impossible to get certain m's and n's in immediate sequence and to keep them pure. If kept pure, it would mean that they remained uncompared. With us, inevitably, by a mechanism which we as yet fail to understand, the shock of difference is felt between them, and the second object is not n pure, but n-as-different-from-m.[12] It is no more a paradox that under these conditions this cognition of m and n in mutual relation should occur, than that under other condtitions the cognition of m's or n's simple quality should occur. But as it has been treated as a paradox, and as a spiritual agent, not itself a portion of the stream, has been [p. 499] invoked to account for it, a word of further remark seems desirable.

My account, it will be noted, is merely a description of the facts as they occur: feelings (or thoughts) each knowing something, but the later one knowing, if preceded by a certain earlier one, a more complicated object than it would have known had the earlier one not been there. I offer no explanation of such a sequence of cognitions. The explanation (I devoutly expect) will be found some day to depend on cerebral conditions. Until it is forthcoming, we can only treat the sequence as a special case of the general law that every experience undergone by the brain leaves in it a modification which is one factor in determining what manner of experiences the following ones shall be (cf. pp. 232-236). To anyone who denies the possibility of such a law I have nothing to say, until he brings his proofs.

The sentationalists and the spiritualists meanwhile (filled both of them with their notion that the mind must in some fashion contain what it knows) begin by giving a cooked account of the facts. Both admit that for m and n to be known in any way whatever, little rounded and finished off duplicates of each must be contained in the mind as separate entities. These pure ideas, so called, of m and n respectively, succeed each other there. And since they are distinct, say the sensationalists, they are eo ipso distinguished. "To have ideas different and ideas distinguished, are synonymous expressions; different and distinguished meaning exactly the same thing," says James Mill.[13] "Distinguished!" say the spiritualists, "distinguished by what, forsooth? Truly the respective ideas of m and of n in the mind are distinct. But for that very reason neither can distinguish itself from the other, for to do that it would have to be aware of the other, and thus for the time being become the other, and that would be to get mixed up with the other and to lose its own distinctness. Distinctness of ideas and idea of distinctness, are not one thing, but two. This last is a relation. Only a relating principle, opposed in nature to all facts of feeling, an Ego, Soul, or [p. 500] Subject, is competent, by being present to both of the ideas alike, to hold them together and at the same time to keep them distinct."

But if the plain facts be admitted that the pure idea of 'n' is never in the mind at all, when 'm' has once gone before; and that the feeling 'n-different-from-m' is itself an absolutely unique pulse of thought, the bottom of this precious quarrel drops out and neither party is left with anything to fight about. Surely such a consummation ought to be welcomed, especially when brought about, as here, by a formulation of the facts which offers itself so naturally and unsophistically.[14]

[p. 501] We may, then, conclude our examination of the manner in which simple involuntary discrimination comes about, by saying, 1) that its vehicle is a thought possessed of a knowledge of both terms compared and of their difference; 2) that the necessary and sufficient condition (as the human mind goes) for arousing this thought is that a thought or feeling of one of the terms discriminated should, as immediately as possible, precede that in which the other term is known; and 3) and that the thought which knows the second term will then also know the difference (or in more difficult cases will be continously succeeded by one which does know the difference) and both of the terms between which it holds.

This last thought need, however, not be these terms with their difference, nor contain them. A man's thought can know and mean all sorts of things without those things getting bodily into it -- the distant, for example, the future, and the past.[15] The vanishing term in the case which occupies us vanishes; but because it is the specific term it is and nothing else, it leaves a specific influence behind it when it vanishes, the effect of which is to determine the succeeding pulse of thought in a perfectly characteristic way. Whatever consciousness comes next must know the vanished term and call it different from the one now there.

Here we are at the end of our tether about involuntary discrimination of successively felt simple things; and must drop the subject, hopeless of seeing any deeper into it for [p. 502] the present, and turn to discriminations of a less simple sort.

And first, of the discrimination of simultaneously felt impressions! Our first way of looking at a reality is often to suppose it simple, but later we may learn to perceive it as compound. This new way of knowing the same reality may conveniently be called by the name of Analysis. It is manifestly one of the most incessantly performed of all our mental processes, so let us examine the conditions under which it occurs.

I think we may safely lay down at the outset this fundamental principle, that any total impression made on the mind must be unanalyzable, whose elements are never experienced apart. The components of an absolutely changeless group of not-elsewhere-occurring attributes could never be discriminated. If all cold things were wet and all wet things cold, if all hard things pricked our skin, and no other things did so; is it likely that we should discriminate between coldness and wetness, and hardness and pungency respectively? If all liquids were transparent and no non-liquid were transparent, it would be long before we had separate names for liquidity and transparency. If heat were a function of position above the earth's surface, so that the higher a thing was the hotter it became, one word would serve for hot and high. We have, in fact, a number of sensations whose concomitants are almost invariably the same, and we find it, accordingly, almost impossible to analyze them out from the totals in which they are found. The contraction of the diaphragm and the expansion of the lungs, the shortening of certain muscles and the rotation of certain joints, are examples. The converging of the eyeballs and the accommodation for near objects are, for each distance of the object (in the common use of the eyes) inseparably linked, and neither can (without a sort of artificial training which shall presently be mentioned) be felt by itself. We learn that the causes of such groups of feelings are multiple, and therefore we frame theories about the composition of the feelings themselves, by 'fusion,' [p. 503] 'integration,' 'synthesis,' or what not. But by direct introspection no analysis of them is ever made. A conspicuous case will come to view when we treat of the emotions. Every emotion has its 'expression,' of quick breathing, palpitating heart, flushed face, or the like. The expression gives rise to bodily feelings; and the emotion is thus necessarily and invariably accompanied by these bodily feelings. The consequence is that it is impossible to apprehend  it as a spiritual state by itself, or to analyze it away from the lower feelings in question. It is in fact impossible to prove that it exists as a distinct psychic fact. The present writer strongly doubts that it does so exist. But those who are most firmly persuaded of its existence must wait, to prove their point, until they can quote some as yet unfound pathological case of an individual who shall have emotions in a body in which either complete paralysis will have prevented their expression, or complete anæsthesia will have made the latter unfelt.

In general, then, if an object affects us simultaneously in a number of ways, abcd, we get a peculiar integral impression, which thereafter characterizes to our mind the individuality of that object, and becomes the sign of its presence; and which is only resolved into a, b, c, d, respectively by the aid of farther experiences. These we now may turn to consider.

If any single quality or constituent, a, of such an object, have previously been known by us isolatedly, or have in any other manner already become an object of separate acquaintance on our part, so that we have an image of it, distinct or vague, in our mind, disconnected with bcd, then that constituent a may be analyzed out from the total impression. Analysis of a thing means separate attention to each of its parts. In Chapter XI we saw that one condition of attending to a thing was the formation from within of a separate image of that thing, which should, as it were, go out to meet the impression received. Attention being the condition of analysis, and separate imagination being the condition of attention, it follows also that separate imagination is the condition of analysis. Only such elements as we are acquainted with, and can imagine, separately, can be discriminated within a total [p. 504] sense-impression. The image seems to welcome its own mate from out of the compound, and to heighten the feeling thereof; whereas it dampens and opposes the feeling of the other constituents; and thus the compound becomes broken for our consciousness into parts.

All the facts cited in Chapter XI, to prove that attention involves inward reproduction, go to prove this point as well. In looking for any object in a room, for a book in a library, for example, we detect it the more readily if, in addition to merely knowing its name, etc., we carry in our mind a distinct image of its appearance. The assafœtida in 'Worcestershire sauce' is not obvious to anyone who has not tasted assafœtida per se. In a 'cold' color an artist would never be able to analyze out the pervasive presence of blue, unless he had previously made acquaintance with the color blue by itself. All the colors we actually experience are mixtures. Even the purest primaries always come to us with some white. Absolutely pure red or green or violet is never experienced, and so we can never be discerned in the so-called primaries with which we have to deal: the latter consequently pass for pure. -- The reader will remember how an overtone can only be attended to in the midst of its consorts in the voice of a musical instrument, by sounding it previously alone. The imagination, being then full of it, hears the like of it in the compound tone. Helmholtz, whose account of this observation we formerly quoted, goes on to explain the difficulty of the case in a way which beautifully corroborates the point I now seek to prove. He says:

"The ultimate simple elements of the sensation of tone, simple tones themselves, are rarely heard alone. Even those instruments by which they can be produced (as tuning-forks before resonance-chambers), when strongly excited, give rise to weak harmonic upper partials, partly within and partly without the ear. . . . Hence the opportunities are very scanty for impressing on our memory an exact and sure image of these simple elementary tones. But if the constituents are only indefinitely and vaguely known, the analysis of their sum into them must be correspondingly uncertain. If we do not know with certainty how much of the musical tone under consideration is to be attributed to its prime, we cannot but be uncertain as to what belongs to the partials. Consequently we must begin by making the individual elements which [p. 505] have to be distinguished individually audible, so as to obtain an entirely fresh recollection of the corresponding sensation, and the whole business requires undisturbed and concentrated attention. We are even without the ease that can be obtained by frequent repetitions of the experiment, such as we possess in the analysis of musical chords into their individual notes. In that case we hear the individual notes sufficiently often by themselves, whereas we rarely hear simple tones, and may almost be said never to hear the building up of a compound from its simple tones."[16]

Very few elements of reality are experienced by us in absolute isolation. The most that usually happens to a constituent a, of a compound phenomenon abcd, is that its strength relatively to bcd varies from a maximum to a minimum; or that it appears linked with other qualities, in other compounds, as aefg, or ahik. Either of these vicissitudes in the mode of our experiencing a may, under favorable circumstances, lead us to feel the difference between it and its concomitants, and to single it out -- not absolutely, it is true, but approximately -- and so to analyze the compound of which it is a part. The act of singling out is then called abstraction, and the element disengaged is an abstract.

Consider the case of fluctuations of relative strength or intensity first. Let there be three grades of the compound, as Abcd, abcd, and abcD. In passing between these compounds, the mind will feel shocks of difference. The differences, moreover, will serially increase, and their direction will be felt as of a distinct sort. The increase from abcd to Abcd is on the a side; that to abcD is on the d side. And these two differences of direction are differently felt. I do not say that this discernment of the a-direction from the d-direction will give us an actual intuition either of a or of d in the abstract. But it leads us to conceive or postulate each of these qualities, and to define it as the extreme of a certain direction. 'Dry' wines and 'sweet' wines, for example, differ, and form a series. It happens that we have an experience of sweetness pure and simple in the taste of sugar; and this we can [p. 506] analyze out of this wine-taste. But no one knows what 'dryness' tastes like, all by itself. It must, however, be something extreme in the dry direction; and we should probably not fail to recognize it as the original of our abstract conception, in case we ever did come across it. In some such way we get to form notions of the flavor of meats, apart from their feeling to the tongue, or of that of fruits apart from their acidity, etc., and we abstract the touch of bodies as distinct from their temperature. We may even apprehend the quality of muscle's contraction as distinguished from its extent, or one muscle's contraction from another's, as when, by practising with prismatic glasses, and varying our eyes' convergence whilst our accommodation remains the same, we learn the direction in which our feeling of the convergence differs from that of the accommodation.

But the fluctuation in a quality's intensity is a less efficient aid to our abstracting of it than the diversity of the other qualities in whose company it may appear. What is associated now with one thing and now with another tends to become dissociated from either, and to grow into an object of abstract contemplation by the mind. One might call this the law of dissociation by varying concomitants. The practical result of it will be to allow the mind which has thus dissociated and abstracted a character to analyze it out of a total, whenever it meets with it again. The law has been frequently recognized by psychologists, though I know of none who has given it the emphatic prominence in our mental history which it deserves. Mr. Spencer says:

"If the property A occurs here along with the properties B, C, D, there along with C, F, H, and again with E, G, B, . . . it must happen that by multiplication of experiences the impressions produced by these properties on the organism will be disconnected and rendered so far independent in the organism as the properties are in the environment, whence must eventually result a power to recognize attributes in themselves, apart from particular bodies."[17]

And still more to the point Dr. Martineau, in the passage I have already quoted, writes:

"When a red ivory ball, seen for the first time, has been withdrawn, it will leave a mental representation of itself, in which all that
[p. 507] it simultaneously gave us will indistinguishably coexist. Let a white ball succeed to it; now, and not before, will an attribute detach itself, and the color, by force of contrast, be shaken out into the foreground. Let the white ball be replaced by an egg, and this new difference will bring the form into notice from its previous slumber, and thus that which began by being simply an object cut out from the surrounding scene becomes for us first a red object, then a red round object, and so on."

Why the repetition of the character in combination with different wholes will cause it thus to break up its adhesion with any one of them, and roll out, as it were, alone upon the table of consciousness, is a little of a mystery. One might suppose the nerve-processes of the various concomitants to neutralize or inhibit each other more or less and to leave the process of the common term alone distinctly active. Mr. Spencer appears to think that the mere fact that the common term is repeated more often than any one of its associates will, of itself, give it such a degree of intensity that its abstraction must needs ensue.

This has a plausible sound, but breaks down when examined closely. For it is not always the often-repeated character which is first noticed when its concomitants have varied a certain number of times; it is even more likely to be the most novel of all the concomitants, which will arrest the attention. If a boy has seen nothing all his life but sloops and schooners, he will probably never distinctly have singled out in his notion of 'sail' the character of being hung lengthwise. When for the first time he sees a square-rigged ship, the opportunity of extracting the lengthwise mode of hanging as a special accident, and of dissociating it from the general notion of sail, is offered. But there are twenty chances to one that that will not be the form of the boy's consciousness. What he notices will be the new and exceptional character of being hung crosswise. He will go home and speak of that, and perhaps never consciously formulate what the more familiar peculiarity consists in.

This mode of abstraction is realized on a very wide scale, because the elements of the world in which we find ourselves appear, as a matter of fact, here, there, and everywhere, and are changing their concomitants all the while. [p. 508] But on the other hand the abstraction is, so to speak, never complete, the analysis of a compound never perfect, because no element is ever given to us absolutely alone, and we can never therefore approach a compound with the image in our mind of any one of its components in a perfectly pure form. Colors, sounds, smells, are just as much entangled with other matter as are more formal elements of experience, such as extension, intensity, effort, pleasure, difference, likeness, harmony, badness, strength, and even consciousness itself. All are embedded in one world. But by the fluctuations and permutations of which we have spoken, we come to form a pretty good notion of the direction in which each element differs from the rest, and so we frame the notion of it as a terminus, and continue to mean it as an individual thing. In the case of many elements, the simple sensibles, like heat, cold, the colors, smells, etc., the extremes of the directions are almost touched, and in these instances we have a comparatively exact perception of what it is we mean to abstract. But even this is only an approximation; and in literal mathematical strictness all our abstracts must be confessed to be but imperfectly imaginable things. At bottom the process is one of conception, and is everywhere, even in the sphere of simple sensible qualities, the same as that by which we are usually understood to attain to the notions of abstract goodness, perfect felicity, absolute power, and the like; the direct perception of a difference between compounds, and the imaginary prolongation of the direction of the difference to an ideal terminus, the notion of which we fix and keep as one of our permanent subjects of discourse.

This is all that I can say usefully about abstraction, or about analysis, to which it leads.

In all the cases considered hitherto I have supposed the differences involved to be so large as to be flagrant, and the discrimination, where successive, was treated as involuntary. But, so far from being always involuntary, discriminations are often difficult in the extreme, and by most men never performed. Professor de Morgan, thinking, it [p. 509] is true, rather of conceptual than of perceptive discrimination, wrote, wittily enough:

"The great bulk of the illogical part of the educated community -- whether majority or minority I know not; perhaps six of one and half a dozen of the other -- have not power to make a distinction, and of course cannot be made to take a distinction, and of course never attempt to shake a distinction. With them all such things are evasions, subterfuges, come-offs, loop-holes, etc. They would hang a man for horse-stealing under a statute against sheep-stealing; and would laugh at you if you quibbled about the distinction between a horse and a sheep."[18]

Any personal or practical interest, however, in the results to be obtained by distinguishing, makes one's wits amazingly sharp to detect differences. The culprit himself is not likely to overlook the difference between a horse and a sheep. And long training and practice in distinguishing has the same effect as personal interest. Both of these agencies give to small amounts of objective difference the same effectiveness upon the mind that, under other circumstances, only large ones would have. Let us seek to penetrate the modus operandi of their influence -- beginning with that of practice and habit.

That 'practice makes perfect' is notorious in the field of motor accomplishments. But motor accomplishments depend in part on sensory discrimination. Billiard-playing, rifle-shooting, tight-rope-dancing, demand the most delicate appreciation of minute disparities of sensation, as well as the power to make accurately graduated muscular response thereto. In the purely sensorial field we have the well-known virtuosity displayed by the professional buyers and testers of various kinds of goods. One man will distinguish by taste between the upper and the lower half of a bottle of old Madeira. Another will recognize, by feeling the flour in a barrel, whether the wheat was grown in Iowa or Tennessee. The blind deaf-mute, Laura Bridgman, has so improved her touch as to recognize, after a year's interval, the hand of a person who once has shaken hers; and her sister in misfortune, Julia Brace, is said to have been employed in the Hartford Asylum to sort [p. 510] the linen of its multitudinous inmates, after it came from the wash, by her wonderfully educated sense of smell.

The fact is so familiar that few, if any, psychologists have even recognized it as needing explanation. They have seemed to think that practice must, in the nature of things, improve the delicacy of discernment, and have let the matter rest. At most they have said: "Attention accounts for it; we attend more to habitual things, and what we attend to we perceive more minutely." This answer is true, but too general; it seems to me that we can be a little more precise.

There are at least two distinct causes which we can see at work whenever experience improves discrimination:

First, the terms whose difference comes to be felt contract disparate associates and these help to drag them apart.

Second, the difference reminds us of larger differences of the same sort, and these help us to notice it.

Let us study the first cause first, and begin by supposing two compounds, of ten elements apiece. Suppose no one element of either compound to differ from the corresponding element of the other compound enough to be distinguished from it if the two are compared alone, and let the amount of this imperceptible difference be called equal to 1. The compounds will differ from each other, however, in ten different ways; and, although each difference by itself might pass unperceived, the total difference, equal to 10, may very well be sufficient to strike the sense. In a word, increasing the number of 'points' involved in a difference may excite our discrimination as effectually as increasing the amount of difference at any one point. Two men whose mouth, nose, eyes, cheeks, chin, and hair, all differ slightly, will be as little confounded by us, as two appearances of the same man one with, and the other without, a false nose. The only contrast in the cases is that we can easily name the point of difference in the one, whilst in the other we cannot.

Two things, then, B and C, indistinguishable when compared together alone, may each contract adhesions with different associates, and the compounds thus formed [p. 511] may, as wholes, be judged very distinct. The effect of practice in increasing discrimination must then, in part, be due to the reinforcing effect, upon an original slight difference between the terms, of additional differences between the diverse associates which they severally affect. Let B and C be the terms: If A contract adhesions with B, and C with D, AB may appear very distinct from CD, though B and C per se might have been almost identical.

To illustrate, how does one learn to distinguish claret from burgundy? Probably they have been drunk on different occasions. When we first drank claret we heard it called by that name, we were eating such and such a dinner, etc. Next time we drink it, a dim reminder of all those things chimes through us as we get the taste of the wine. When we try burgundy our first impression is that it is a kind of claret; but something falls short of full identification, and presently we hear it called burgundy. During the next few experiences, the discrimination may still be uncertain -- "which," we ask ourselves, "of the two wines is this present specimen?" But at last the claret-flavor recalls pretty distinctly its own name, 'claret,' "that wine I drank at So-and-so's table," etc.; and the burgundy-flavor recalls the name burgundy and some one else's table. And only when this different SETTING has come to each is our discrimination between the two flavors solid and stable. After a while the tables and other parts of the setting, besides the name, grow so multifarious as not to come up distinctly into consciousness; but pari passu with this, the adhesion of each wine with its own name becomes more and more inveterate, and at last each flavor suggests instantly and certainly its own name and nothing else. The names differ far more than the flavors, and help to stretch these latter farther apart. Some such process as this must go on in all our experience. Beef and mutton, strawberries and raspberries, odor of rose and odor of violet, contract different adhesions which reinforce the differences already felt in the terms.

The reader may say that this has nothing to do with making us feel the difference between the two terms. It is merely fixing, identifying, and so to speak substantializing, [p. 512] the terms. But what we feel as their difference, we should feel, even though we were unable to name or otherwise identify the terms.

To which I reply that I believe that the difference is always concreted and made to seem more substantial by recognizing the terms. I went out for instance the other day and found that the snow just fallen had a very odd look, different from the common appearance of snow. I presently called it a 'micaceous' look; and it seemed to me as if, the moment I did so, the difference grew more distinct and fixed than it was before. The other connotations of the word 'micaceous' dragged the snow farther away from ordinary snow and seemed even to aggravate the peculiar look in question. I think some such effect as this on our way of feeling a difference will be very generally admitted to follow from naming the terms between which it obtains; although I admit myself that it is difficult to show coercively that naming or otherwise identifying any given pair of hardly distinguishable terms is essential to their being felt as different at first.[19]

[p. 513] I offer the explanation only as a partial one: it certainly is not complete. Take the way in which practice refines our local discrimination on the skin, for example. Two compass-points touching the palm of the hand must be kept, say, half an inch asunder in order not to be mistaken for one point. But at the end of an hour or so of practice with them we can distinguish them as two, even when less than a quarter of an inch apart. If the same two regions of the skin were constantly touched, in this experience, the explanation we have been considering would perfectly apply. Suppose a line a b c d e f of points upon the skin. Suppose the local difference of feeling between a and f to be so strong as to be instantly recognized when the points are simultaneously touched, but suppose that between c and d to be at first too small for this purpose. If we began by putting the compasses on a and f and gradually contracted their opening, the strong doubleness recognized at first would still be suggested, as the compass-points approached the positions c and d; for the point e would be so near f, and so like it, as not to be aroused without f also coming to mind. Similarly d would recall e and, more remotely, f. In such wise c - d would no longer be bare c - d, but something more like abc - def, -- palpably differing impressions. But in actual experience the education can take place in a much less methodical way, and we learn at last to discriminate c  and d without any constant adhesion being contracted between [p. 514] one of these spots and ab, and the other and ef. Volkmann's experiments show this. He and Fechner, prompted by Czermak's observation that the skin of the blind was twice as discriminative as that of seeing folks, sought by experiment to show the effects of practice upon themselves. They discovered that even within the limits of a single sitting the distances at which points were felt double might fall at the end to considerably less than half of their magnitude at the beginning; and that some, though not all, of this improved sensibility was retained next day. But they also found that exercising one part of the skin in this way improved the discrimination not only of the corresponding part of the opposite side of the body, but of the neighboring parts as well. Thus, at the beginning of an experimental sitting, the compass-points had to be a Paris line asunder, in order to be distinguished by the little-finger-tip. But after exercising the other fingers, it was found that the little-finger-tip could discriminate points only half a line apart.[20] The same relation existed betwixt divers points of the arm and hand.[21]

Here it is clear that the cause which I first suggested fails to apply, and that we must invoke another.

What are the exact experimental phenomena? The spots, as such, are not distinctly located, and the difference, as such, between their feelings, is not distinctly felt, until the interval is greater than the minimum required for the mere perception of their doubleness. What we first feel is a bluntness, then a suspicion of doubleness, which presently becomes a distinct doubleness, and at last two different-feeling and differently placed spots with a definite tract of space between them. Some of the places we try give us this latest stage of the perception immediately; some only give us the earliest; and between them are intermediary places. But as soon as the image of the doubleness as it is felt in the more discriminative places gets lodged in our memory, it helps us to find its like in places where otherwise we might have missed it, much as the recent hearing of [p. 515] an 'overtone' helps us to detect the latter in a compound sound (supra, pp. 439-40). A dim doubleness grows clearer by being assimilated to the image of a distincter doubleness felt a moment before. It is interpreted by means of the latter. And so is any difference, like any other sort of impression, more easily perceived when we carry in our mind to meet it a distinct image of what sort of a thing we are to look for, of what its nature is likely to be.[22]

These two processes, the reinforcement of the terms by disparate associates, and the filling of the memory with past differences, of similar direction with the present one, but of more conspicuous amount, are the only explanations I can offer of the effects of education in this line. What is accomplished by both processes is essentially the same thing: they make small differences affect us as if they were large ones -- that large differences should affect us as they do remains an inexplicable fact. In principle these two processes ought to be sufficient to account for all possible cases. Whether in fact they are sufficient, whether there be no residual factor which we have failed to detect and analyze out, I will not presume to decide.

It will be remembered that on page 509 personal interest was named as a sharpener of discrimination alongside of practice. But personal interest probably acts through attention and not in any immediate or specific way. A distinction in which we have a practical stake in one which we concentrate our minds upon and which we are on the look-out for. We draw it frequently, and we get all the benefits of so doing, benefits which have just been explained. Where, on the other hand, a distinction has no practical interest, where we gain nothing by analyzing a feature from out of the compound total of which it forms a [p. 516] part, we contract a habit of leaving it unnoticed, and at last grow callous to its presence. Helmholtz was the first psychologist who dwelt on these facts as emphatically as they deserve, and I can do no better than quote his very words.

"We are accustomed," he says, "in a large number of cases where sensations of different kinds, or in different parts of the body, exist simultaneously, to recognize that they are distinct as soon as they are perceived, and to direct our attention at will to any one of them separately. Thus at any moment we can be separately conscious of what we see, of what we hear, of what we feel; and distinguish what we feel in a finger or in the great toe, whether pressure, gentle touch, or warmth. So also in the field of vision. Indeed, as I shall endeavor to show in what follows, we readily distinguish our sensations from one another when we have a precise knowledge that they are composite, as, for example, when we have become certain, by frequently repeated and invariable experience, that our present sensation arises from the simultaneous action of many independent stimuli, each of which usually excites an equally well-known individual sensation."

This, it will be observed, is only another statement of our law, that the only individual components which we can pick out of compounds are those of which we have independent knowledge in a separate form.

"This induces us to think that nothing can be easier, when a number of different sensations are simultaneously excited, than to distinguish them individually from each other, and that this is an innate faculty of our minds.

"Thus we find, among other things, that it is quite a matter of course to hear separately the different musical tones which come to our sense collectively; and we expect that in every case when two of them occur together, we shall be able to do the like.

"The matter becomes very different when we set to work to investigate the more unusual cases of perception, and seek more completely to understand the conditions under which the above-mentioned distinction can or cannot be made, as is the case in the physiology of the senses. We then become aware that two different kinds or grades must be distinguished in our becoming conscious of a sensation. The lower grade of this consciousness is that in which the influence of the sensation in question makes itself felt only in the conceptions we form of external things and processes, and assists in determining them. This can take place without our needing, or indeed being able, to ascertain to what particular part of our sensations we owe this or that circumstance in our perceptions. In this case we will say that the impression of the sensation in question is perceived synthetically. The second higher grade is when we immediately distinguish the sensation in question as [p. 517] an existing part of the sum of the sensations excited in us. We will say, then, that the sensation is perceived analytically. The two cases must be carefully distinguished from each other."[23]

By the sensation being perceived synthetically, Helmholtz means that it is not discriminated at all, but only felt in a mass with other simultaneous sensations. That it is felt there he thinks is proved by the fact that our judgment of the total will change if anything occurs to alter the outer cause of the sensation.[24] The following pages from an earlier edition show what the concrete cases of synthetic perception and what those of analytic perception are wont to be:

"In the use of our senses, practice and experience play a much larger part than we ordinarily suppose. Our sensations are in the first instance important only in so far as they enable us to judge rightly of the world about us; and our practice in discriminating between them usually goes only just far enough to meet this end. We are, however, too much disposed to think that we must be immediately conscious of every ingredient of our sensations. This natural prejudice is due to the fact that we are indeed conscious, immediately and without effort, of everything in our sensations which has a bearing upon those practical purposes, for the sake of which we wish to know the outer world. Daily and hourly, during our whole life, we keep our senses in training for this end exclusively, and for its sake our experiences are accumulated. But even within the sphere of these sensations, which do correspond to outer things, training and practice make themselves felt. It is well known how much finer and quicker the painter is in discriminating colors and illuminations than one whose eye is not trained in these matters; how the musician and the musical-instrument maker perceive with ease and certainty differences of pitch and tone which for the ear of the layman do not exist; and how even in the inferior realms of cookery and wine-judging it takes a long habit of comparing to make a master. But more strikingly still is seen the effect of practice when we pass to sensations which depend only on inner conditions of our organs, and which, not corresponding at all to outer things or to their effects upon us, are therefore of no value in giving us information about the outer world. The physiology of the sense-organs has, in recent times, made us acquainted with a number of such phenomena, discovered partly in consequence of theoretic speculations and questionings, partly by individuals, like Goethe and Purkinje, specially endowed by nature with talent for this sort of observation. These so-called subjec- [p. 518] tive phenomena are extraordinarily hard to find; and when they are once found, special aids for the attention are almost always required to observe them. It is usually hard to notice the phenomenon again even when one knows already the description of the first observer. The reason is that we are not only unpractised in singling out these subjective sensations, but that we are, on the contrary, most thoroughly trained in abstracting our attention from them, because they would only hinder us in observing the outer world. Only when their intensity is so strong as actually to hinder us in observing the outer world do we begin to notice them; or they may sometimes, in dreaming and delirium, form the starting point of hallucinations.

"Let me give a few well-known cases, taken from physiological optics, as examples. Every eye probably contains muscœ volitantes, so called; these are fibres, granules, etc., floating in the vitreous humor, throwing their shadows on the retina, and appearing in the field of vision as little dark moving spots. They are most easily detected by looking attentively at a broad, bright, blank surface like the sky. Most persons who have not had their attention expressly called to the existence of these figures are apt to notice them for the first time when some ailment befalls their eyes and attracts their attention to the subjective state of these organs. The usual complaint then is that the muscœ volitantes came in with the malady; and this often makes the patients very anxious about these harmless things, and attentive to all their peculiarities. It is then hard work to make them believe that these figures have existed throughout all their previous life, and that all healthy eyes contain them. I knew an old gentleman who once had occasion to cover one of his eyes which had accidentally become diseased, and who was then in no small degree shocked at finding that his other eye was totally blind; with a sort of blindness, moreover, which must have lasted years, and yet he never was aware of it.

"Who, besides, would believe without performing the appropriate experiments, that when one of his eyes is closed there is a great gap, the so-called 'blind spot,' not far from the middle of the field of the open eye, in which he sees nothing at all, but which he fills out with his imagination? Mariotte, who was led by theoretic speculations to discover this phenomenon, awakened no small surprise when he showed it at the court of Charles II. of England. The experiment was at that time repeated with many variations, and became a fashionable amusement. The gap is, in fact, so large that seven full moons alongside of each other would not cover its diameter, and that a man's face 6 or 7 feet off disappears within it. In our ordinary use of vision this great hole in the field fails utterly to be noticed; because our eyes are constantly wandering, and the moment an object interests us we turn them full upon it. So it follows that the object which at any actual moment excites our attention never happens to fall upon this gap, and thus it is that we never grow conscious of the blind spot in the field. In order to notice it, we must first purposely rivet our gaze upon one object and [p. 519] then move about a second object in the neighborhood of the blind spot, striving meanwhile to attend to this latter without moving the direction of our gaze from the first object. This runs counter to all our habits, and is therefore a difficult thing to accomplish. With some people it is even an impossibility. But only when it is accomplished do we see the second object vanish and convince ourselves of the existence of this gap.

"Finally, let me refer to the double images of ordinary binocular vision. Whenever we look at a point with both eyes, all objects on this side of it or beyond appear double. It takes but a moderate effort of observation to ascertain this fact; and from this we may conclude that we have been seeing the far greater part of the external world double all our lives, although numbers of persons are unaware of it, and are in the highest degree astonished when it is brought to their attention. As a matter of fact, we never have seen in this double fashion any particular object upon which our attention was directed at the time; for upon such objects we always converge both eyes. In the habitual use of our eyes, our attention is always withdrawn from such objects as give us double images at the time; this is the reason why we so seldom learn that these images exist. In order to find them we must set our attention a new and unusual task; we must make it explore the lateral parts of the field of vision, not, as usual, to find what objects are there, but to analyze our sensations. Then only do we notice this phenomenon.[25]

"The same difficulty which is found in the observation of subjective sensations to which no external object corresponds is found also in the analysis of compound sensations which correspond to a single object. Of this sort are many of our sensations of sound. When the sound of a violin, no matter how often we hear it, excites over and over again in our ear the same sum of partial tones, the result is that our feeling of this sum of tones ends by becoming for our mind a mere sign for the voice of the violin. Another combination of partial tones becomes the sensible sign of the voice of a clarionet, etc. And the oftener any such combination is heard, the more accustomed we grow to perceiving it as an integral total, and the harder it becomes to analyze it by immediate observation. I believe that this is one of the principal reasons why the analysis of the notes of the human voice in singing is relatively so [p. 520] difficult. Such fusions of many sensations into what, to conscious perception, seems a simple whole, abound in all our senses.

"Physiological optics affords other interesting examples. The perception of the bodily form of a near object comes about through the combination of two diverse pictures which the eyes severally receive from it, and whose diversity is due to the different position of each eye, altering the perspective view of what is before it. Before the invention of the stereoscope this explanation could only be assumed hypothetically; but it can now be proved at any moment by the use of the instrument. Into the stereoscope we insert two flat drawings, representing the two perspective views of the two eyes, in such a manner that each eye sees its own view in the proper place; and we obtain, in consequence, the perception of a single extended solid, as complete and vivid as if we had the real object before us.

"Now we can, it is true, by shutting one eye after the other and attending to the point, recognize the difference in the pictures -- at least when it is not too small. But, for the stereoscopic perception of solidity, pictures suffice whose difference is so extraordinarily slight as hardly to be recognized by the most careful comparison; and it is certain that, in our ordinary careless observing of bodily objects, we never dream that the perception is due to two perspective views fused into one, because it is an entirely different kind of perception from that of either flat perspective view by itself. It is certain, therefore, that two different sensations of our two eyes fuse into a third perception entirely different from either. Just as partial tones fuse into the perception of a certain instrument's voice; and just as we learn to separate the partial tones of a vibrating string by pinching a nodal point and letting them sound in isolation; so we learn to separate the images of the two eyes by opening and closing them alternately.

"There are other much more complex instances of the way in which many sensations may combine to serve as the basis of a quite simple perception. When, for example we perceive an object in a certain direction, we must somehow be impressed by the fact that certain of our optic nerve-fibres, and no others, are impressed by its light. Furthermore, we must rightly judge the position of our eyes in our head, and of our head upon our body, by means of feelings in our eye-muscles and our neck-muscles respectively. If any of these processes is disturbed we get a false perception of the object's position. The nerve-fibers can be changed by a prism before the eye; or the eyeball's position changed by pressing the organ towards one side; and such experiments show that, for the simple seeing of the position of an object, sensations of these two sorts must concur. But it would be quite impossible to gather this directly from the sensible impression which the object makes. Even when we have made experiments and convinced ourselves in every possible manner that such must be the fact, it still remains hidden from our immediate introspective observation.

"These examples" [of synthetic perception,' perception in which [p. 521] each contributory sensation is felt in the whole, and is a co-determinant of what the whole shall be, but does not attract the attention to its separate self] "may suffice to show the vital part which the direction of attention and practice in observing play in sense-perception. To apply this now to the ear. The ordinary task which our ear has to solve when many sounds assail it at once is to discern the voices of the several sounding bodies or instruments engaged; beyond this it has no objective interest in analyzing. We wish to know, when many men are speaking together, what each one says, when many instruments and voices combine, which melody is executed by each. Any deeper analysis, such as that of each separate note into its partial tones (although it might be performed by the same means and faculty of hearing as the first analysis) would tell us nothing new about the sources of sound actually present, but might lead us astray as to their number. For this reason we confine our attention in analyzing a mass of sound to the several instruments' voices, and expressly abstain, as it were, from discriminating the elementary components of the latter. In this last sort of discrimination we are as unpractised as we are, on the contrary, well trained in the former kind."[26]

[p. 522] After all we have said, no comment seems called for upon these interesting and important facts and reflections of Helmholtz.

[p. 523] REACTION-TIME AFTER DISCRIMINATION.

The time required for discrimination has been made a subject of experimental measurement. Wundt calls it Unterscheidungszeit. His subjects (whose simple reaction-time -- see p. 85 ff. -- had previously been determined) were required to make a movement, always the same, the instant they discerned which of two or more signals they received. The exact time of the signal and that of the movement were automatically registered by a galvanic chronoscope. The particular signal to be received was unknown in advance, and the excess of time occupied by those reactions in which its character had first to be discerned, over the simple reaction-time, measured, according to Wundt, the time required for the act of discrimination. It was found longer when four different signals were irregularly used than when only two were used. In the former case it averaged, for three observers respectively (the signals being the sudden appearance of a black or of a white object),

[p. 524] In the latter case, a red and a green signal being added to the former ones, it became, for the same observers,

Later, in Wundt's Laboratory, Herr Tischer made many careful experiments after the same method, where the facts to be discriminated were the different degrees of loudness in the sound which served as a signal. I subjoin Herr Tischer's table of results, explaining that each vertical column after the first gives the average results obtained from a distinct individual, and that the figure in the first column stands for the number of possible loudnesses that might be expected in the particular series of reactions made. The times are expressed in thousandths of a second.[28]

The interesting points here are the great individual variations, and the rapid way in which the time for discrimination increases with the number of possible terms to discriminate. The individual variations are largely due to want of practice in the particular task set, but partly also to discrepancies in the psychic process. One gentleman said, for example, that in the experiments with three sounds, he kept the image of the middle one ready in his mind, and compared what he heard as either louder, lower, or the same. His discrimination among three possibilities became thus very similar to a discrimination between two.[29]

Mr. J. M. Cattell found he could get no results by this method,[30] and reverted to one used by observers previous [p. 525] to Wundt and which Wundt had rejected. This is the einfache Wahlmethode, as Wundt calls it. The reacter awaits the signal and reacts if it is of one sort, but omits to act if it is of another sort. The reaction thus occurs after discrimination; the motor impulse cannot be sent to the hand until the subject knows what the signal is. The nervous impulse, as Mr. Cattell says, must probably travel to the cortex and excite changes there, causing in consciousness the perception of the signal. These changes occupy the time of discrimination (or perception-time, as it is called by Mr. C.) But then a nervous impulse must descend from the cortex to the lower motor centre which stands primed and ready to discharge; and this, as Mr. C. says, gives a will-time as well. The total reaction-time thus includes both 'will-time' and 'discrimination-time.' But as the centrifugal and centripetal processes occupying these two times respectively are probably about the same, and the time used in the cortex is about equally divided between the perception of the signal and the preparation of the motor discharge, if we divide it equally between perception (discrimination) and volition, the error cannot be great.[31] We can moreover change the nature of the perception without altering the will-time, and thus investigate with considerable thoroughness the length of the perception-time.

Guided by these principles, Prof. Cattell found the time required for distinguishing a white signal from no signal to be, in two observers:

0.030 sec. and 0.050 sec.;

that for distinguishing one color from another was similarly:

0.100 and .110;

that for distinguishing a certain color from ten other colors:

0.105 and 0.117;

that for distinguishing the letter A in ordinary print from the letter Z:

0.142 and 0.137;

[p. 526] that for distinguishing a given letter from all the rest of the alphabet (not reacting until that letter appeared)

0.119 and 0.116;

that for distinguishing a word from any of twenty-five other words, from

0.118 sec. to 0.158 sec.

The difference depending on the length of the words and the familiarity of the language to which they belonged.

Prof. Cattell calls attention to the fact that the time for distinguishing a word is often but little more than that for distinguishing a letter:

"We do not, therefore, distinguish separately the letters of which a word is composed, but the word as a whole. The application of this in teaching children to read is evident."

He also finds a great difference in the time with which various letters are distinguished, E being particularly bad.[32]

I have, in describing these experiments, followed the example of previous writers and spoken as if the process by which the nature of the signal determines the reaction were identical with the ordinary conscious process of discriminative perception and volition. I am convinced, however, that this is not the case; and that although the results are the same, the form of consciousness is quite different. The reader will remember my contention (supra, p. 90 ff.) that the simple reaction-time (usually supposed to include a conscious process of perceiving) really measures nothing but a reflex act. Anyone who will perform reactions with discrimination will easily convince himself that the process here also is far more like a reflex, than like a deliberate, operation. I have made, with myself and students, a large number of measurements where the signal expected was in one series a touch somewhere on the skin of the back and head, and in another series a spark somewhere in the field of view. The hand had to move as quickly as possible towards the [p. 527] place of the touch or the spark. It did so infallibly, and sensibly instantly; whilst both place and movement seemed to be perceived only a moment later, in memory. These experiments were undertaken for the express purpose of ascertaining whether the movement at the sight of the spark was discharged immediately by the visual perception, or whether a 'motor-idea' had to intervene between the perception of the spark and the reaction.[33] The first thing that was manifest to introspection was that no perception or idea of any sort preceded the reaction. It jumped of itself, whenever the signal came; and perception was retrospective. We must suppose, then, that the state of eager expectancy of a certain definite range of possible discharges, innervates a whole set of paths in advance, so that when a particular sensation comes it is drafted into its appropriate motor outlet too quickly for the perspective process to be aroused. In the experiments I describe, the conditions were most favorable for rapidity, for the connection between the signals and their movements might almost be called innate. It is instinctive to move the hand towards a thing seen or a skin-spot touched. But where the movement is conventionally attached to the signal, there would be more chance for delay, and the amount of practice would then determine the speed. This is well shown in Tischer's results, quoted on p. 524, where the most practised observer, Tischer himself, reacted in one eighth of the time needed by one of the others.[34] But what all investigators have aimed to determine in these experiments is the minimum time. I trust I have said enough to convince the student that this minimum time by no means measures what we consciously know as discrimination. It only measures something which, under the experimental conditions, leads [p. 528] to a similar result. But it is the bane of psychology to suppose that where results are similar, processes must be the same. Psychologists are too apt to reason as geometers would, if the latter were to say that the diameter of a circle is the same thing as its semi-circumference, because, forsooth, they terminate in the same two points.[35]

The perception of likeness is practically very much bound up with that of difference. That  is to say, the only differences we note as differences, and estimate quantitatively, and arrange along a scale, are those comparatively limited differences which we find between members of a common genus. The force of gravity and the color of this ink are things it never occurred to me to compare until now that I am casting about for examples of the incomparable. Similarly the elastic quality of this india-rubber band, the comfort of last night's sleep, the good that can be done with a legacy, these are things too discrepant to have ever been compared ere now. Their relation to each other is less that of difference than of mere logical negativity. To be found different, things must as a rule have some commensurability, some aspect in common, which suggests the possibility of their being treated in the same way. This is of course not a theoretic necessity -- for any distinction may be called a 'difference,' if one likes -- but a practical and linguistic remark.

The same things, then, which arouse the perception of difference usually arouse that of resemblance also. And the analysis of them, so as to define wherein the difference and wherein the resemblance respectively consists, is called comparison. If we start to deal with the things as simply the same or alike, we are liable to be surprised by the difference. If we start to [p. 529] treat them as merely different, we are apt to discover how much they are alike. Difference, commonly so called, is thus between species of a genus. And the faculty by which we perceive the resemblance upon which the genus is based, is just as ultimate and inexplicable a mental endowment as that by which we perceive the differences upon which the species depend. There is a shock of likeness when we pass from one thing to another which in the first instance we merely discriminate numerically, but, at the moment of bringing our attention to bear, perceive to be similar to the first; just as there is a shock of difference when we pass between two dissimilars.[36] The objective extent of the likeness, just like that of the difference, determines the magnitude of the shock. The likeness may be so evanescent, or the basis of it so habitual and little liable to be attended to, that it will escape observation altogether. Where, however, we find it, there we make a genus of the things compared; and their discrepancies and incommensurabilities in other respects can then figure as the differentiœ of so many species. As 'thinkables' or 'existents' even the smoke of a cigarette and the worth of a dollar-bill are comparable -- still more so as 'perishables,' or as 'enjoyables.'
 
Much, then, of what I have said of difference in the course of this chapter will apply, with a simple change of language, to resemblance as well. We go through the world, carrying on the two functions abreast, discovering differences in the like, and likenesses in the different. To abstract the ground of either difference or likeness (where it is not ultimate) demands and analysis of the given objects into their parts. So that all that was said of the dependence of analysis upon a preliminary separate acquaintance with the character to be abstracted, and upon its having varied concomitants, finds a place in the psychology of resemblance as well as in that of difference.

But when all is said and done about the conditions which favor our perception of resemblance and our abstraction of its ground, the crude fact remains, that some [p. 530] people are far more sensitive to resemblances, and far more ready to point out wherein they consist, than others are. They are the wits, the poets, the inventors, the scientific men, the practical geniuses. A native talent for perceiving analogies is reckoned by Prof. Bain, and by others before and after him, as the leading fact in genius of every order. But as this chapter is already long, and as the question of genius had better wait till Chapter XXII, where its practical consequences can be discussed at the same time, I will say nothing more at present either about it or about the faculty of noting resemblances. If the reader feels that this faculty is having small justice done it at my hands, and that it ought to be wondered at and made much more of than has been done in these last few pages, he will perhaps find some compensation when that later chapter is reached. I think I emphasize it enough when I call it one of the ultimate foundation-pillars of the intellectual life, the others being Discrimination, Retentiveness, and Association.

On page 489 I spoke of differences being greater or less, and of certain groups of them being susceptible of a linear arrangement exhibiting serial increase. A series whose terms grow more and more different from the starting point is one whose terms grow less and less like it. They grow more and more like it if you read them the other way. So that likeness and unlikeness to the starting point are functions inverse to each other, of the position of any term in such a series.

Professor Stumpf introduces the word distance to denote the position of a term in any such series. The less like is the term, the more distant it is from the starting point. The ideally regular series of this sort would be one in which the distances -- the steps of resemblance or difference -- between all pairs of adjacent terms were equal. This would be an evenly gradated series. And it is an interesting fact in psychology that we are able, in many departments of our sensibility, to arrange the terms without difficulty in this evenly gradated way. Dif- [p. 531] ferences, in other words, between diverse pairs of terms, a and b, for example, on the one hand, and c and d on the other,[37] can be judged equal or diverse in amount. The distances from one term to another in the series are equal. Linear magnitudes and musical notes are perhaps the impressions which we easiest arrange in this way. Next come shades of light or color, which we have little difficulty in arranging by steps of difference of sensibly equal value. Messrs. Plateau and Delbœuf have found it fairly easy to determine what shade of gray will be judged by every one to hit the exact middle between a darker and a lighter shade.[38]

How now do we so readily recognize the equality of two differences between different pairs of terms? or, more briefly, how do we recognize the magnitude of a difference at all? Prof. Stumpf discusses this question in an interesting way;[39] and comes to the conclusion that our feeling for the size of a difference, and our perception that the terms of two diverse pairs are equally or unequally distant from each other, can be explained by no simpler mental process, but, like the shock of difference itself, must be regarded as for the present an unanalyzable endowment [p. 532] of the mind. This acute author rejects in particular the notion which would make our judgment of the distance between two sensations depend upon our mentally traversing the intermediary steps. We may of course do so, and may often find it useful to do so, as in musical intervals, or figured lines. But we need not do so; and nothing more is really required for a comparative judgment of the amount of a 'distance' than three or four impressions belonging to a common kind.

The vanishing of all perceptible difference between two numerically distinct things makes them qualitatively the same or equal. Equality, or qualitative (as distinguished from numerical) identity, is thus nothing but the extreme degree of likeness.[40]

We saw above (p. 492) that some persons consider that the difference between two objects is constituted of two things, viz., their absolute identity in certain respects, plus their absolute non-identity in others. We saw that this theory would not apply to all cases (p. 493). So here any theory which would base likeness on identity, and not rather identity on likeness, must fail. It is supposed perhaps, by most people, that two resembling things owe their resemblance to their absolute identity in respect of some attribute or attributes, combined with the absolute non-identity of the rest of their being. This, which may be true of compound things, breaks down when we come to simple impressions.

"When we compare a deep, middle, and a high note, e.g., C, f sharp, a'", we remark immediately that the first is less like the third than the second is. The same would be true of c d e in the same region of the scale. Our very calling one of the notes a 'middle' note is the expression of a judgment of this sort. But where here is the identical and where the non-identical part? We cannot think of the overtones; for the first-named three notes have none in common, at least not on musical instruments. Moreover, we might take simple tones, and still our judgment would be unhesitatingly the same, provided the tones were not chosen too close together. . . . Neither can it be said that the identity consists in their all being sounds, and not a sound, a smell, and a color, respectively. For this identical attribute comes to each of them in equal measure, whereas the first, being less like the third than the second is, ought, on the terms of the theory we are criticising, to have [p. 533] less of the identical quality. . . . It thus appears impracticable to define all possible cases of likeness as partial identity plus partial disparity; and it is vain to seek in all cases for identical elements."[41]

And as all compound resemblances are based on simple ones like these, it follows that likeness überhaupt must not be conceived as a special complication of identity, but rather that identity must be conceived as a special degree of likeness, according to the proposition expressed at the outset of the paragraph that precedes. Likeness and difference are ultimate relations perceived. As a matter of fact, no two sensations, no two objects of all those we know, are in scientific rigor identical. We call those of them identical whose difference is unperceived. Over and above this we have a conception of absolute sameness, it is true, but this, like so many of our conceptions (cf. p. 508), is an ideal construction got by following a certain direction of serial increase to its maximum supposable extreme. It plays an important part, among other permanent meanings possessed by us, in our ideal intellectual constructions. But it plays no part whatever in explaining psychologically how we perceive likenesses between simple things.

In 1860, Professor G. T. Fechner of Leipzig, a man of great learning and subtlety of mind, published two volumes entitled 'Psychophysik,' devoted to establishing and explaining a law called by him the psychophysic law, which [p. 534] he considered to express the deepest and most elementary relation between the mental and the physical worlds. It is a formula for the connection between the amount of our sensations and the amount of their outward causes. Its simplest expression is, that when we pass from one sensation to a stronger one of the same kind, the sensations increase proportionally to the logarithms of their exciting causes. Fechner's book was the starting point of a new department of literature, which it would be perhaps impossible to match for the qualities of thoroughness and subtlety, but of which, in the humble opinion of the present writer, the proper psychological outcome is just nothing. The psychophysic law controversy has prompted a good many series of observations on sense-discrimination, and has made discussion of them very rigorous. It has also cleared up our ideas about the best methods for getting average results, when particular observations vary; and beyond this it has done nothing; but as it is a chapter in the history of our science, some account of it is here due to the reader.

Fechner's train of thought has been popularly expounded a great many times. As I have nothing new to add, it is but just that I should quote an existing account. I choose the one given by Wundt in his Vorlesungen über Menschen und Thierseele, 1863, omitting a good deal:

"How much stronger or weaker one sensation is than another, we are never able to say. Whether the sun be a hundred or a thousand times brighter than the moon, a cannon a hundred or a thousand times louder than a pistol, is beyond our power to estimate. The natural measure of sensation which we possess enables us to judge of the equality, of the 'more' and of the 'less,' but not of 'how many times more or less.' This natural measure is, therefore, as good as no measure at all, whenever it becomes a question of accurately ascertaining intensities in the sensational sphere. Even though it may teach us in a general way that with the strength of the outward physical stimulus the strength of the concomitant sensation waxes or wanes, still it leaves us without the slightest knowledge of whether the sensation varies in exactly the same proportion as the stimulus itself, or at a slower or a more rapid rate. In a word, we know by our natural sensibility nothing of the law that connects the sensation and its outward cause together. To find this law we must first find an exact measure for the sensation itself; we must be able to say: A stimulus of strength one begets a sensation [p. 535] of strength one; a stimulus of strength two begets a sensation of strength two, or three, or four, etc. But to do this we must first know what a sensation two, three, or four times greater than another, signifies. . . .

"Space magnitudes we soon learn to determine exactly, because we only measure one space against another. The measure of mental magnitudes is far more difficult. . . . But the problem of measuring the magnitude of sensations is the first step in the bold enterprise of making mental magnitudes altogether subject to exact measurement. . . . Were our whole knowledge limited to the fact that the sensation rises when the stimulus rises, and falls when the latter falls, much would not be gained. But even immediate unaided observation teaches us certain facts which, at least in a general way, suggest the law according to which the sensations vary with their outward cause.

"Every one knows that in the stilly night we hear things unnoticed in the noise of day. The gentle ticking of the clock, the air circulating through the chimney, the cracking of the chairs in the room, and a thousand other slight noises, impress themselves upon our ear. It is equally well known that in the confused hubbub of the streets, or the clamor of a railway, we may lose not only what our neighbor says to us, but even not hear the sound of our own voice. The stars which are brightest at night are invisible by day; and although we see the moon then, she is far paler than at night. Everyone who has had to deal with weights knows that if to a pound in the hand a second pound be added, the difference is immediately felt; whilst if it be added to a hundredweight, we are not aware of the differences at all. . . .

"The sound of the clock, the light of the stars, the pressure of the pound, these are all stimuli to our senses, and stimuli whose outward amount remains the same. What then do these experiences teach? Evidently nothing but this, that one and the same stimulus, according to the circumstances under which it operates, will be felt either more or less intensely, or not felt at all. Of what sort now is the alteration in the circumstances, upon which this alteration in the feeling may depend? On considering the matter closely we see that it is everywhere of one and the same kind. The tick of the clock is a feeble stimulus for our auditory nerve, which we hear plainly when it is alone, but not when it is added to the strong stimulus of the carriage-wheels and other noises of the day. The light of the stars is a stimulus to the eye. But if the stimulation which this light exerts be added to the strong stimulus of daylight, we feel nothing of it, although we feel it distinctly when it unites itself with the feebler stimulation of the twilight. The pound-weight is a stimulus to our skin, which we feel when it joins itself to a preceding stimulus of equal strength, but which vanishes when it is combined with a stimulus a thousand times greater in amount.

"We may therefore lay it down as a general rule that a stimulus, in order to be felt, may be so much the smaller if the already pre-existing stimulation of the organ is small, but must be so much the larger, [p. 536] the greater the pre-existing stimulation is. From this in a general way we can perceive the connection between the stimulus and the feeling it excites. At least thus much appears, that the law of dependence is not as simple a one as might have been expected beforehand. The simplest relation would obviously be that the sensation should increase in identically the same ratio as the stimulus, thus that if a stimulus of strength one occasioned a sensation one, a stimulus of two should occasion sensation two, stimulus three, sensation three, etc. But if this simplest of all relations prevailed, a stimulus added to a pre-existing strong stimulus ought to provoke as great an increase of feeling as if it were added to a pre-existing weak stimulus; the light of the stars e.g., ought to make as great an addition to the daylight as it does to the darkness of the nocturnal sky. This we know not to be the case: the stars are invisible by day, the addition they make to our sensation then is unnoticable, whereas the same addition to our feeling of the twilight is very considerable indeed. So it is clear that the strength of the sensations does not increase in proportion to the amount of the stimuli, but more slowly. And now comes the question, in what proportion does the increase of the sensation grow less as the increase of the stimulus grows greater. To answer this question, every-day experiences do not suffice. We need exact measurements both of the amounts of the various stimuli, and of the intensity of the sensations themselves.

"How to execute these measurements, however, is something which daily experience suggests. To measure the strength of sensations is, as we saw, impossible; we can only measure the difference of sensations. Experience showed us what very unequal differences of sensation might come from equal differences of outward stimulus. But all these experiences expressed themselves in one kind of fact, that the same difference of stimulus could in one case be felt, and in another case not felt at all -- a pound felt if added to another pound, but not if added to a hundred-weight. . . . We can quickest reach a result with our observations if we start with an arbitrary strength of stimulus, notice what sensation it gives us, and then see how much we can increase the stimulus without making the sensation seem to change. If we carry out such observations with stimuli of varying absolute amounts, we shall be forced to choose in an equally varying way the amounts of addition to the stimulus which are capable of giving us a just barely perceptible feeling of more. A light, to be just perceptible in the twilight need not be near as bright as the starlight; it must be far brighter to be just perceived during the day. If now we institute such observations for all possible strengths of the various stimuli, and note for each strength the amount of addition of the latter required to produce a barely perceptible alteration of sensation, we shall have a series of figures in which is immediately expressed the law according to which the sensation alters when the stimulation is increased. . . ."

Observations according to this method are particularly [p. 537] easy to make in the spheres of light-, sound-, and pressure-sensation. . . . Beginning with the latter case,

"We find a surprisingly simple result. The barely sensible addition to the original weight must stand exactly in the same proportion to it, be the same fraction of it, no matter what the absolute value may be of the weights on which the experiment is made. . . . As the average of a number of experiments, this fraction is found to be about 1/3; that is, no matter what pressure there may already be made upon the skin, an increase or a diminution of the pressure will be felt, as soon as the added or subtracted weight amounts to one third of the weight originally there."

Wundt then describes how differences may be observed in the muscular feelings, in the feelings of heat, in those of light, and in those of sound; and he concludes his seventh lecture (from which our extracts have been made) thus:

"So we have found that all the senses whose stimuli we are enabled to measure accurately, obey a uniform law. However various may be their several delicacies of discrimination, this holds true of all, that the increase of the stimulus necessary to produce an increase of the sensation bears a constant ratio to the total stimulus. The figures which express this ratio in the several senses may be shown thus in tabular form:

"These figures are far from giving as accurate a measure as might be desired. But at least they are fit to convey a general notion of the relative discriminative susceptibility of the different senses. . . . The important law which gives in so simple a form the relation of the sensation to the stimulus that calls it forth was first discovered by the physiologist Ernst Heinrich Weber to obtain in special cases. Gustav Theodor Fechner first proved it to be a law for all departments of sensation. Psychology owes to him the first comprehensive investigation of sensations from a physical point of view, the first basis of an exact Theory of Sensibility."

So much for a general account of what Fechner calls Weber's law. The 'exactness' of the theory of sensibility to which it leads consists in the supposed fact that it gives the means of representing sensations by numbers. The unit of any kind of sensation will be that increment which, [p. 538] when the stimulus is increased, we can just barely perceive to be added. The total number of units which any given sensation contains will consist of the total number of such increments which may be perceived in passing from no sensation of the kind to a sensation of the present amount. We cannot get at this number directly, but we can, now that we know Weber's law, get at it by means of the physical stimulus of which it is a function. For if we know how much of the stimulus it will take to give a barely perceptible sensation, and then what percentage of addition to the stimulus will constantly give a barely perceptible increment to the sensation, it is at bottom only a question of compound interest to compute, out of the total amount of stimulus which we may be employing at any moment, the number of such increments, or, in other words, of sensational units to which it may give rise. This number bears the same relation to the total stimulus which the time elapsed bears to the capital plus the compound interest accrued.

To take an example: If stimulus A just falls short of producing a sensation, and if r be the percentage of itself which must be added to it to get a sensation which is barely perceptible -- call this sensation 1 -- then we should have the series of sensation-numbers corresponding to their several stimuli as follows:

The sensations here form an arithmetical series, and the stimuli a geometrical series, and the two series correspond term for term. Now, of two series corresponding in this way, the terms of the arithmetical one are called the logarithms of the terms corresponding in rank to them in the geometrical series. A conventional arithmetical series beginning with zero has been formed in the ordinary logarithmic tables, so that we may truly say (assuming our [p. 539] facts to be correct so far) that the sensations vary in the same proportion as the logarithms of their respective stimuli. And we can thereupon proceed to compute the number of units in any given sensation (considering the unit of sensation to be equal to the just perceptible increment above zero, and the unit of stimulus to be equal to the increment of stimulus r, which brings this about) by multiplying the logarithm of the stimulus by a constant factor which must vary with the particular kind of sensation in question. If we call the stimulus R, and the constant factor C, we get the formula

S = C log R,

which is what Fechner calls the psychophysischer Maasformel. This, in brief, is Fechner's reasoning, as I understand it.

The Maasformel admits of mathematical development in various directions, and has given rise to arduous discussions into which I am glad to be exempted from entering here, since their interest is mathematical and metaphysical and not primarily psychological at all.[42] I must say a word about them metaphysically a few pages later on. Meanwhile it should be understood that no human being, in any investigation into which sensations entered, has ever used the numbers computed in this or any other way in order to test a theory or to reach a new result. The whole notion of measuring sensations numerically, remains in short a mere mathematical speculation about possibilities, which has never been applied to practice. Incidentally to the discussion of it, however, a great many particular facts have been discovered about discrimination which merit a place in this chapter.

In the first place it is found, when the difference of two sensations approaches the limit of discernibility, that at one moment we discern it and at the next we do not. There are accidental fluctuations in our inner sensibility which make it impossible to tell just what the least discernable [p. 540] increment of the sensation is without taking the average of a large number of appreciations. These accidental errors are as likely to increase as to diminish our sensibility, and are eliminated in such an average, for those above and those below the line then neutralize each other in the sum, and the normal sensibility, if there be one (that is, the sensibility due to constant causes as distinguished from these accidental ones), stands revealed. The best way of getting at the average sensibility has been very minutely worked over. Fechner discussed three methods, as follows:

(1) The Method of just-discernible Differences. Take a standard sensation S, and add to it until you distinctly feel the addition d; then subtract from S + d until you distinctly feel the effect of the subtraction;[43] call the difference here d'. The least discernible difference sought is d + d' / 2; and the ratio of this quantity to the original S (or rather to S + d - d') is what Fechner calls the difference-threshold. This difference-threshold should be a constant fraction (no matter what is the size of S) if Weber's law holds universally true. The difficulty in applying this method is that we are so often in doubt whether anything has been added to S or not. Furthermore, if we simply take the smallest d about which we are never in doubt or in error, we certainly get our least discernible difference larger than it ought theoretically to be.[44]

Of course the sensibility is small when the least discernible is large, and vice versâ; in other words, it and the difference-threshold are inversely related to each other.

(2) The Method of True and False Cases. A sensation which is barely greater than another will, on account of accidental errors in a long series of experiments, sometimes be judged equal, and sometimes smaller; i.e., we shall make a certain number of false and a certain number of [p. 541] true judgments about the difference between the two sensations which we are comparing.

"But the larger this difference is, the more the number of the true judgments will increase at the expense of the false ones; or, otherwise expressed, the nearer to unity will be the fraction whose denominator represents the whole number of judgments, and whose numerator represents those which are true. If m is a ratio of this nature, obtained by comparison of two stimuli, A and B, we may seek another couple of stimuli, a and b, which when compared will give the same ratio of true to false cases."[45]

If this were done, and the ratio of a to b then proved to be equal to that of A to B, that would prove that pairs of small stimuli and pairs of large stimuli may affect our discriminative sensibility similarly so long as the ratio of the components to each other within each pair is the same. In other words, it would in so forth prove the Weberian law. Fechner made use of this method to ascertain his own power of discriminating differences of weight, recording no less than 24, 576 separate judgments, and computing as a result that his discrimination for the same relative increase of weight was less good in the neighborhood of 500 than of 300 grams, but that after 500 grams it improved up to 3000, which was the highest weight he experimented with.

(3) The Method of Average Errors consists in taking a standard stimulus and then trying to make another one of the same sort exactly equal to it. There will in general be an error whose amount is large when the discriminative sensibility called in play is small, and vice versâ. The sum of the errors, no matter whether they be positive or negative, divided by their number, gives the average error. This, when certain corrections are made, is assumed by Fechner to be the 'reciprocal' of the discriminative sensibility in question. It should bear a constant proportion to the stimulus, no matter what the absolute size of the latter may be, if Weber's law hold true.

These methods deal with just perceptible differences. Delboeuf and Wundt have experimented with larger differ- [p. 542] ences by means of what Wundt calls the Methode der mittleren Abstufungen, and what we may call

(4) The Method of Equal-appearing Intervals. This consists in so arranging three stimuli in a series that the intervals between the first and the second shall appear equal to that between the second and the third. At first sight there seems to be no direct logical connection between this method and the preceding ones. By them we compare equally perceptible increments of stimulus in different regions of the latter's scale; but by the fourth method we compare increments which strike us as equally big. But what we can but just notice as an increment need not appear always of the same bigness after it is noticed. On the contrary, it will appear much bigger when we are dealing with stimuli that are already large.

(5) The method of doubling the stimulus has been employed by Wundt's collaborator, Merkel, who tried to make one stimulus seem just double the other, and then measured the objective relation of the two. The remarks just made apply also to this case.

So much for the methods. The results differ in the hands of different observers. I will add a few of them, and will take first the discriminative sensibility to light.

By the first method, Volkmann, Aubert, Masson, Helmholtz, and Kräpelin find figures varying from 1/3 or 1/4 to 1/195 of the original stimulus. The smaller fractional increments are discriminated when the light is already fairly strong, the larger ones when it is weak or intense. That is, the discriminative sensibility is low when weak or overstrong lights are compared, and at its best with a certain medium illumination. It is thus a function of the light's intensity; but throughout a certain range of the latter it keeps constant, and in so far forth Weber's law is verified for light. Absolute figures cannot be given, but Merkel, by method 1, found that Weber's law held good for stimuli (measured by his arbitrary unit) between 96 and 4096, beyond which intensity no experiments were made.[46] König and Brodhun [p. 543] have given measurements by method 1 which cover the most extensive series, and moreover apply to six different colors of light. These experiments (performed in Helmholtz's laboratory, apparently,) ran from an intensity called 1 to one which was 100,000 times as great. From intensity 2000 to 20,000 Weber's law held good; below and above this range discriminative sensibility declined. The increment discriminated here was the same for all colors of light, and lay (according to the tables) between 1 and 2 per cent of the stimulus.[47] Delbœuf had verified Weber's law for a certain range of luminous intensities by method 4; that is, he had found that the objective intensity of a light which appeared midway between two others was really the geometrical mean of the latter's intensities. But A. Lehmann and afterwards Neiglick, in Wundt's laboratory, found that effects of contrast played so large a part in experiments performed in this way that Delbœuf's results could not be held conclusive. Merkel, repeating the experiments still later, found that the objective intensity of the light which we judge to stand midway between two others stands neither midway nor is a geometric mean. The discrepancy from both figures is enormous, but is least large from the midway figure or arithmetical mean of the two extreme intensities.[48] Finally, the stars have from time immemorial been arranged in 'magnitudes' supposed to differ by equal-seeming intervals. Lately their intensities have been gauged photometrically, and the comparison of the subjective with the objective series has been made. Prof. J. Jastrow is the latest worker in this field. He finds, taking Pickering's Harvard photometric tables as a basis, that the ratio of the average intensity of each 'magnitude' to that below it decreases as we pass from lower to higher magnitudes, showing a uniform departure from Weber's law, if the method of equal-appearing intervals be held to have any direct relevance to the latter.[49]

[p. 544] Sounds are less delicately discriminated in intensity than lights. A certain difficulty has come from disputes as to the measurement of the objective intensity of the stimulus. Earlier inquiries made the perceptible increase of the stimulus to be about 1/3 of the latter. Merkel's latest results of the method of just perceptible differences make it about 3/10 for that part of the scale of intensities during which Weber's law holds good, which is from 20 to 5000 of M.'s arbitrary unit.[50] Below this the fractional increment must be larger. Above it no measurements were made.

For pressure and muscular sense we have rather divergent results. Weber found by the method of just-perceptible differences that persons could distinguish an increase of weight of 1/40 when the two weights were successively lifted by the same hand. It took a much larger fraction to be discerned when the weights were laid on a hand which rested on the table. He seems to have verified his results for only two pairs of differing weights,[51] and on this founded his 'law.' Experiments in Hering's laboratory on lifting 11 weights, running from 250 to 2750 grams showed that the least perceptible increment varied from 1/21 for 250 grams to 1/114 for 2500. For 2750 it rose to 1/98 again. Merkel's recent and very careful experiments, in which the finger pressed down the beam of a balance counterweighted by from 25 to 8020 grams, showed that between 200 and 2000 grams a constant fractional increase of about 1/13 was felt when there was no movement of the finger, and of about 1/19 when there was movement. Above and below these limits the discriminative power grew less. It was greater when the pressure was upon one square millimeter of surface than when it was upon seven.[52]

Warmth and taste have been made the subject of similar investigations with the result of verifying something like Weber's law. The determination of the unit of stimulus is, however, so hard here that I will give no figures. The results may be found in Wundt's Physiologische Psychologie, 3d Ed. I. 370-2.

[p. 545] The discrimination of lengths by the eye has been found also to obey to a certain extent Weber's law. The figures will all be found in G. E. Müller, op. cit., part II, chap. X, to which the reader is referred. Professor Jastrow has published some experiments, made by what may be called a modification of the method of equal-appearing differences, on our estimation of the length of sticks, by which it would seem that the estimated intervals and the real ones are directly and not logarithmically proportionate to each other. This resembles Merkel's results by that method for weights, lights, and sounds, and differs from Jastrow's own finding about star-magnitudes.[53]

If we look back over these facts as a whole, we see that it is not any fixed amount added to an impression that makes us notice an increase in the latter, but that the amount depends on how large the impression already is. The amount is expressible as a certain fraction of the entire impression to which it is added; and it is found that the fraction is a well-nigh constant figure throughout an entire region of the scale of intensities of the impression in question. Above and below this region the fraction increases in value. This is Weber's law, which in so far forth expresses an empirical generalization of practical importance, without involving any theory whatever or seeking any absolute measure of the sensations themselves. It is in the

that Fechner's originality exclusively consists, in his assumptions, namely, 1) that the just-perceptible increment is the sensation-unit, and is in all parts of the scale the same (mathematically expressed,  Ds = const.); 2) that all our sensations consist of sums of these units; and finally, 3) that the reason why it takes a constant fractional increase of the stimulus to awaken this unit lies in an ultimate law of the connection of mind with matter, whereby the quantities of our feelings are related logarithmically to the quantities of their objects. Fechner seems to find something inscrutably sublime in the existence of an ultimate 'psychophysic' law of this form.

[p. 546] These assumptions are all peculiarly fragile. To begin with, the mental fact which in the experiments corresponds to the increase of the stimulus is not an enlarged sensation, but a judgment that the sensation is enlarged. What Fechner calls the 'sensation' is what appears to the mind as the objective phenomenon of light, warmth, weight, sound, impressed part of the body, etc. Fechner tacitly if not openly assumes that such a judgment of increase consists in the simple fact that an increased number of sensation-units are present to the mind; and that the judgment is thus itself a quantitatively bigger mental thing when it judges large differences, or differences between large terms, than when it judges small ones. But these ideas are really absurd. The hardest sort of judgment, the judgment which strains the attention most (if that be any criterion of the judgment's 'size'), is that about the smallest things and differences. But really it has no meaning to talk about one judgment being bigger than another. And even if we leave out judgments and talk of sensations only, we have already found ourselves (in Chapter VI) quite unable to read any clear meaning into the notion that they are masses of units combined. To introspection, our feeling of pink is surely not a portion of our feeling of scarlet; nor does the light of an electric arc seem to contain that of a tallow-candle in itself. Compound things contain parts; and one such thing may have twice or three times as many parts as another. But when we take a simple sensible quality like light or sound, and say that there is now twice or thrice as much of it present as there was a moment ago, although we seem to mean the same thing as if we are talking of compound objects, we really mean something different. We mean that if we were to arrange the various possible degrees of the quality in a scale of serial increase, the distance, interval, or difference between the stronger and the weaker specimen before us would seem about as great as that between the weaker one and the beginning of the scale. It is these RELATIONS, these DISTANCES, which we are measuring and not the composition of the qualities themselves, as Fechner thinks. Whilst if we turn to objects which are divisible, surely a big object may be known in a little thought. Introspection shows moreover [p. 547] that in most sensations a new kind of feeling invariably accompanies our judgment of an increased impression; and that is a fact which Fechner's formula disregards.[54]

But apart from these a priori difficulties, and even supposing that sensations did consist of added units, Fechner's assumption that all equally perceptible additions are equally great additions is entirely arbitrary. Why might not a small addition to a small sensation be as perceptible as a large addition to a large one? In this case Weber's law would apply not to the additions themselves, but only to their perceptibility. Our noticing of a difference of units in two sensations would depend on the latter being in a fixed ratio. But the difference itself would depend directly on that between their respective stimuli. So many units added to the stimulus, so many added to the sensation, and if the stimulus grew in a certain ratio, in exactly the same ratio would the sensation also grow, though its perceptibility grew according to the logarithmic law.[55]

If  Dstand for the smallest difference which we perceive, then we should have, instead of the formula  Ds = const., which is Fechner's, the formula  Ds / s = const., a formula which interprets all the facts of Weber's law, in an entirely different theoretic way from that adopted by Fechner.[56]

The entire superstructure which Fechner rears upon the [p. 548] facts is thus not only seen to be arbitrary and subjective, but in the highest degree improbable as well. The departures from Weber's law in regions where it does not obtain, he explains by the compounding with it of other unknown laws which mask its effects. As if any law could not be found in any set of phenomena, provided one have the wit to invent enough other coexisting laws to overlap and neutralize it! The whole outcome of the discussion, so far as Fechner's theories are concerned, is indeed nil. Weber's law alone remains true as an empirical generalization of fair extent: What we add to a large stimulus we notice less than what we add to a small one, unless it happen relatively to the stimulus to be as great.

Weber's law is probably purely physiological.

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.[57] 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,
[p. 549] 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 footnote. 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 the first formulating them and thereby turning psychology into an exact science (!).

[1] Human Understanding, II. xi. 1, 2.

[2] Analysis, vol. I. p. 71.

[3] The Senses and the Intellect, page 411.

[4] Essays Philosophical and Theological: First Series, pp. 268-273.

[5] Montgomery in 'Mind,' x. 527. Cf. also Lipps: Grundtatsachen des Seelenlebens, p. 579 ff., and see below, Chapter XIX.

[6] 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.

[7] 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.

[8] 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. 'Unterschiedsempfindüngs - 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.

[9] Cf. Stumpf, Tonpsychologie, I. 121, and James Ward, Mind, I. 464.

[10] 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.

[11] "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.)

[12] 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.

[13] Analysis, J. S. Mill's ed., II. 17. Cf. also pp. 12, 14.

[14] 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.

[15] 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 spiritualistic 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, can not you say 'knows it'? If there is anything our soul does not do to its past, it is to carry it with it.

[16] Sensations of Tone, 2d English Ed., p. 65.

[17] Psychology, I. 345.

[18] A Budget of Paradoxes, p. 380.

[19] 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.

[20] A. W. Volkmann: Ueber den Einfluss der Uebung, etc., Leipzig Berichte, Math-phys. Classe, x, 1858, p. 67.

[21] Ibid., Tabelle I, p. 43.

[22] 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.

[23] Sensations of Tone, 2d English Edition, p. 62.

[24] Compare as to this, however, what I said above, Chapter V, pp. 172-176.

[25] 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.

[26] 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 is 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, no 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 pepperment 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.

[27] Physiol. Psych., II. 248.

[28] Wundt's Philos. Studien, I. 527.

[29] Ibid. p. 530.

[30] 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.

[31] Mind, XI. 3.

[32] 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.

[33] 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.

[34] 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.)

[35] 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.

[36] Cf. Sully: Mind, X, 494-5; Bradley, ibid. XI. 83; Bosanquet: ibid. XI. 405.

[37] 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.

[38] 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. 206.

[39] Op. cit. p. 126 ff.

[40] Stumpf, pp. 111-121.

[41] 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 Xa, Xb, Xg, . . . etc. What is gained? The question immediately arises: How is a b g 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."

[42] 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.

[43] Reversing the order is for the sake of letting the opposite accidental errors due to 'contrast' neutralize each other.

[44] 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.

[45] J. Delbœuf Eléments de Psychophysique (1883), p. 9.

[46] Philos. Studien, IV. 588.

[47] Berlin Acad. Sitzungsberichte, 1888, p. 917. Other observers (Dobro. wolsky, Lamansky) found great differences in different colors.

[48] See Merkel's tables, loc. cit. p. 568.

[49] 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.

[50] Philosophische Studien, V. 514-5.

[51] Cf. G. E. Müller: Zur Grandlegung der Psychophysik, §§ 68-70.

[52] Philosophische Studien, V. 287 ff.

[53] American J. of Psychology, III. 44-7.

[54] 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 Vierteljahrschrift 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 Eléments de Psychophysique (1883), p. 134 ff.; J. Ward in Mind, I. 464: Lotze, Metaphysik, § 258.

[55] 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.

[56] This is the formula which Merkel thinks he has verified (if I understand him aright) by his experiments by method 4.

[57] Elsas: Ueber die Psychophysik (1886), 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.