on both sides, although we may pass from one to the other by sudden leaps, we do not know whether these leaps are magnitudes, still less whether they are equal magnitudes: above all it would be necessary to show that the intermedi aries which have helped us throughout our measurement could be found again inside the object which we have measured. If not, it is only by a metaphor that a sensation can be said to be an equal distance from two others.
Now, if the views which we have before enu merated with regard to luminous intensities are nu3i.j«tthe accepted, it will be recognized that the l different hues of grey which Delbceuf displays to us are strictly analogous, for our consciousness, to colours, and that if we declare that a grey tint is equi-distant from two other grey tints, it is in the same sense in which it might be said that orange, for example, is at an equal distance from green and red. But there is this difference, that in all our past experience the succession of grey tints has been produced in connexion with a progressive increase or decrease in illumination. Hence we do for the differences of brightness what we do not think of doing for the differences of colour: we promote the changes of quality into variations of magnitude. Indeed, there is no difficulty here about the measuring, because the successive shades of grey produced by a continuous decrease of illumination are discontinuous, as being CHAP, i SENSATION OF LIGHT 59 qualities, and because we can count approximately the principal intermediate shades which separate any two kinds of grey. The contrast A B will thus be declared equal to the contrast B C when our imagination, aided by our memory, inserts between A and B the same number of intermediate shades as between B and C. It is needless to say that this will necessarily be a very rough estimate. We may anticipate that it will vary considerably with different persons. Above all it is to be ex pected that the person will show more hesitation and that the estimates of different persons will differ more widely in proportion as the difference in brightness between the rings A and B is increased, for a more and more laborious effort will be required to estimate the number of intermediate hues. This is exactly what happens, as we shall easily perceive by glancing at the two tables drawn up by Delboeuf.1 In proportion as he increases the difference in brightness between the exterior ring and the middle ring, the difference between the numbers on which one and the same observer or different observers successively fix increases almost continuously from 3 degrees to 94, from 5 to 73, from 10 to 25, from 7 to 40. But let us leave these divergences on one side: let us assume that the observers are always consist ent and always agree with one another; will it then be established that the contrasts A B and B C are equal? It would first be necessary to 1 Elements de psychophysique, pp. 61, 69.
60 TIME AND FREE WILL CHAP. I prove that two successive elementary contrasts are equal quantities, whilst, in fact, we only know that they are successive. It would then be neces sary to prove that inside a given tint of grey we perceive the less intense shades which our imagina tion has run through in order to estimate the objective intensity of the source of light. In a word, Delbceuf's psychophysics assumes a the oretical postulate of the greatest importance, which is disguised under the cloak of an experi mental result, and which we should formulate as follows: ' When the objective quantity of light is continuously increased, the differences between the hues of grey successively obtained, each of which represents the smallest perceptible increase of physical stimulation, are quantities equal to one another. And besides, any one of the sensations obtained can be equated with the sum of the differences which separate from one another all previous sensations, going from zero upwards." Now, this is just the postulate of Fechner's psy chophysics, which we are going to examine.
Fechner took as his starting-point a law discovered by Weber, according to which, given Fechner's Psy- * certain stimulus which calls forth chophysics. a certain sensation, the amount by Weber i Law.. * which the stimulus must be increased for consciousness to become aware of any change bears a fixed relation to the original stimulus. Thus, if we denote by E the stimulus which corresponds to the sensation S, and by AE CHAP, i PSYCHOPHYSICS 6l the amount by which the original stimulus must be increased in order that a sensation of difference AT?
may be produced, we shall have -=-= const.
h, This formula has been much modified by the disciples of Fechner, and we prefer to take no part in the discussion; it is for experiment to decide between the relation established by Weber and its substitutes. Nor shall we raise any difficulty about granting the probable existence of a law of this nature. It is here really a question not of measuring a sensation but only of deter mining the exact moment at which an increase of stimulus produces a change in it. Now, if a definite amount of stimulus produces a definite shade of sensation, it is obvious that the minimum amount of stimulus required to produce a change in this shade is also definite; and since it is not constant, it must be a function of the original stimulus. But how are we to pass from a re lation between the stimulus and its minimum increase to an equation which connects the " amount of sensation " with the corresponding stimulus? The whole of psychophysics is Involved in this transition, which is therefore worthy of our closest consideration.
We shall distinguish several different artifices The underiy- in the process of transition from Wetions and the ber s experiments, or from any other which Fech- series ot similar observations, to a psy- ?eeache£aw " chophysical law like Fechner's. It is 62 TIME AND FREE WILL CHAP, l first of all agreed to consider our consciousness of an increase of stimulus as an increase of the sensation S: this is therefore called S. It is the n asserted that all the sensations AS, which corre spond to the smallest perceptible increase of stimu lus, are equal to one another. They are therefore treated as quantities, and while, on the one hand, these quantities are supposed to be always equal, and, on the other, experiment has given a certain relation AE = / (E) between the stimulus E and its minimum increase, the constancy of AS is expressed by writing AS = C -^-, C being a constant quantity. Finally it is agreed to replace the very small differences AS and AE by the infinitely small differences dS and dE, whence an equation which is, this time, a differential xTTT one: dS = C-=-. We shall now simply have to integrate on both sides to obtain the desired rela tion 1:S=C I --=-. And the transition will thus be JoE made from a proved law, which only concerned the occurrence of a sensation, to an unprovable law which gives its measure.
Without entering upon any thorough discussion 1 In the particular case where we admit without restriction A f* "C* Q Q being a constant. This is Fechner's " logarithmic law."
CHAP. I PSYCHOPHYSICS 63 of this ingenious operation, let us show in a few words how Fechner has grasped the real difficulty of the problem, how he has tried to overcome it, and where, as it seems to us, the flaw in his reason ing lies.
Fechner realized that measurement could not be introduced into psychology without first defining what is meant by the equality and Can two sen-,,.,.,.., sations be addition of two simple states, e.g. two equal without.. _,..,,.
being identi- sensations. But, unless they are identi cal, we do not at first see how two sensations can be equal. Undoubtedly in the physical world equality is not synonymous with identity. But the reason is that every phenomenon, every object, is there presented under two aspects, the one qualitative and the other extensive: nothing prevents us from putting the first one aside, and then there remains nothing but terms which can be directly or indirectly superposed on one another and consequently seen to be identical. Now, this qualitative element, which we begin by eliminating from external objects in order to measure them, is the very thing which psycho- physics retains and claims to measure. And it is no use trying to measure this quality Q by some physical quantity Q' which lies beneath it: for it would be necessary to have previously shown that Q is a function of Q', and this would not be possible unless the quality Q had first been measured with some fraction of itself. Thus nothing pre vents us from measuring the sensation of heat by 64 TIME AND FREE WILL CHAP, i the degree of temperature; but this is only a convention, and the whole point of psychophysics lies in rejecting this convention and seeking how the sensation of heat varies when you change the temperature. In a word, it seems, on the one hand, that two different sensations cannot be said to be equal unless some identical residuum remains after the elimination of their qualitative difference; but, on the other hand, this qualitative difference being all that we perceive, it does not appear what could remain once it was eliminated.
The novel feature in Fechner's treatment is that he did not consider this difficulty insur- mountable. Taking advantage of the ^c^ that sensation varies by sudden jumps while the stimulus increases con tinuously, he did not hesitate to call these differ ences of sensation by the same name: they are all, he says, minimum differences, since each cor responds to the smallest perceptible increase in the external stimulus. Therefore you can set aside the specific shade or quality of these suc cessive differences; a common residuum will remain in virtue of which they will be seen to be in a manner identical: they all have the common character of being minima. Such will be the defini tion of equality which we were seeking. Now, the definition of addition will follow naturally. For if we treat as a quantity the difference perceived by consciousness between two sensations which succeed one another in the course of a continuous increase CHAP. I PSYCHOPHYSICS 65 of stimulus, if we call the first sensation S, and the second S-f-AS, we shall have to consider every sensation S as a sum, obtained by the addition of the minimum differences through which we pass before reaching it. The only remaining step will then be to utilize this twofold definition in order to establish, first of all, a relation between the differences AS and AE, and then, through the substitution of the differentials, between the two variables. True, the mathematicians may here lodge a protest against the substitution of differential for difference; the psychologists may ask, too, whether the quantity AS, instead of being constant, does not vary as the sensation S itself; x finally, taking the psychophysical law for granted, we may all debate about its real meaning. But, by the mere fact that AS is re garded as a quantity and S as a sum, the funda mental postulate of the whole process is accepted. Now it is just this postulate which seems to us open to question, even if it can be understood. Break-down Assume that I experience a sensation SonheStUIthe s» and that> increasing the stimulus econtmuously» I perceive this increase after a certain time. I am now notified Quantities. of ^he increase of the cause: but why should I call this notification an arithmetical difference? No doubt the notification consists in the fact that the original state S has changed: 1 Latterly it has been assumed that AS is proportional to S.
66 TIME AND FREE WILL CHAP. I it has become S'; but the transition from S to S' could only be called an arithmetical difference if I were conscious, so to speak, of an interval between S and S', and if my sensation were felt to rise from S to S' by the addition of something. By giving this transition a name, by calling it AS, you make it first a reality and then a quantity. Now, not only are you unable to explain in what sense this transition is a quantity, but reflection will show you that it is not even a reality; the only realities are the states S and S' through which I pass. No doubt, if S and S' were numbers, I could assert the reality of the difference S' — S even though S and S7 alone were given; the reason is that the number S' — S, which is a certain sum of units, will then represent just the successive moments of the addition by which we pass from S to S'. But if S and S' are simple states, in what will the interval which separates them con sist? And what, then, can the transition from the first state to the second be, if not a mere act of your thought, which, arbitrarily and for the sake of the argument, assimilates a succession of two states to a differentiation of two magnitudes? Either you keep to what consciousness presents to you or you have recourse to a conventional we can speak rnode of representation. In the first tfcai' d£-me~ case you will find a difference between ancCoenve°nntionS S and S' like that between the shades of the rainbow, and not at all an interval of magnitude. In the second case you may intro- CHAP, i PSYCHOPHYSICS 67 duce the symbol AS if you like, but it is only in a conventional sense that you will speak here of an arithmetical difference, and in a conventional sense, also, that you will assimilate a sensation to a sum. The most acute of Fechner's critics, Jules Tannery, has made the latter point per fectly clear. "It will be said, for example, that a sensation of 50 degrees is expressed by the num ber of differential sensations which would succeed one another from the point where sensation is absent up to the sensation of 50 degrees...I do not see that this is anything but a definition, which is as legitimate as it is arbitrary." l We do not believe, in spite of all that has been said, that the method of mean gradations has DeiboBuf's re- se* psychophysics on a new path. The nun plausible, novel feature in Delbceuf's investi- aKchophy- gation was that he chose a particular £°3 Iev?icious case> ^n which consciousness seemed to decide in Fechner's favour, and in which common sense itself played the part of the psycho- physicist. He inquired whether certain sensa tions did not appear to us immediately as equal although different, and whether it would not be possible to draw up, by their help, a table of sensations which were double, triple or quadruple those which preceded them. The mistake which Fechner made, as we have just seen, was that he believed in an interval between two successive 1 Revue scicntifique, March 13 and April 24, 1875.
68 TIME AND FREE WILL CHAP, i sensations S and S', when there is simply a passing from one to the other and not a difference in the arithmetical sense of the word. But if the two terms between which the passing takes place could be given simultaneously, there would then be a contrast besides the transition; and al though the contrast is not yet an arithmetical difference, it resembles it in a certain respect; for the two terms which are compared stand here side by side as in a case of subtraction of two numbers. Suppose now that these sensations belong to the same genus and that in our past experience we have constantly been present at their march past, so to speak, while the physical stimulus increased continuously: it is extremely probable that we shall thrust the cause into the effect, and that the idea of contrast will thus melt into that of arithmetical difference. As we shall have noticed, moreover, that the sen sation changed abruptly while the stimulus rose continuously, we shall no doubt estimate the dis tance between two given sensations by a rough guess at the number of these sudden jumps, or at least of the intermediate sensations which usually serve us as landmarks. To sum up, the contrast will appear to us as a difference, the stimulus as a quantity, the sudden jump as an element of equality: combining these three fac tors, we shall reach the idea of equal quantitative differences. Now, these conditions are nowhere so well realized as when surfaces of the same CHAP, i PSYCHOPHYSICS 69 colour, more or less illuminated, are simultaneously presented to us. Not only is there here a con trast between similar sensations, but these sen sations correspond to a cause whose influence has always been felt by us to be closely connected with its distance; and, as this distance can vary continuously, we cannot have escaped noticing in our past experience a vast number of shades of sensation which succeeded one another along with the continuous increase in the cause. We are therefore able to say that the contrast between one shade of grey and another, for example, seems to us almost equal to the contrast between the latter and a third one; and if we define two equal sensations by saying that they are sensations which a more or less confused process of reasoning interprets as such, we shall in fact reach a law like that proposed by Delbceuf. But it must not be forgotten that consciousness has here passed through the same intermediate steps as the psychophysicist, and that its judgment is worth here just what psychophysics is worth; it is a symbolical interpretation of quality as quantity, a more or less rough estimate of the number of sensations which can come in between two given sensations. The difference is thus not as great as is believed between the method of least noticeable differences and that of mean gradations, between the psychophysics of Fechner and that of Delbceuf. The first led to a con ventional measurement of sensation; the second JQ TIME AND FREE WILL CHAP, i appeals to common sense in the particular cases where common sense adopts a similar convention. In a word, all psychophysics is condemned by its origin to revolve in a vicious circle, for the theoretical postulate on which it rests condemns it to experimental verification, and it cannot be experimentally verified unless its postulate is first granted. The fact is that there is no point of contact between the unextended and the extended, between quality and quantity. We can interpret the one by the other, set up the one as the equivalent of the other; but sooner or later, at the beginning or at the end, we shall have to recognize the conventional character of this assimilation.
In truth, psychophysics merely formulates with precision and pushes to its extreme consequences a conception familiar to common sense.
pushes to its As speech dominates over thought, quences the as external objects, which are common fundamental but natural to us all, are more important to us mistake of re-..
gardmg sensa- than the subjective states through tions as magnitudes. which each of us passes, we have every thing to gain by objectifying these states, by introducing into them, to the largest possible extent, the representation of their external cause. And the more our knowledge increases, the more we perceive the extensive behind the intensive, quantity behind quality, the more also we tend to thrust the former into the latter, and to treat our sensations as magnitudes. Physics, CHAP, i PSYCHOPHYSICS 71 whose particular function it is to calculate the external cause of our internal states, takes the least possible interest in these states themselves: constantly and deliberately it confuses them with their cause. It thus encourages and even exag gerates the mistake which common sense makes on the point. The moment was inevitably bound to come at which science, familiarized with this confusion between quality and quantity, between sensation and stimulus, should seek to measure the one as it measures the other: such was the object of psychophysics. In this bold attempt Fechner was encouraged by his adversaries them selves, by the philosophers who speak of intensive magnitudes while declaring that psychic states can not be submitted to measurement. For if we grant that one sensation can be stronger than another, and that this inequality is inherent in the sensa tions themselves, independently of all association of ideas, of all more or less conscious consideration of number and space, it is natural to ask by how much the first sensation exceeds the second, and to set up a quantitative relation between their intensities. Nor is it any use to reply, as the opponents of psychophysics sometimes do, that all measurement implies superposition, and that there is no occasion to seek for a numerical relation between intensities, which are not super- posable objects. For it will then be necessary to explain why one sensation is said to be more intense than another, and how the conceptions />; ro/ .-(LIBRARY 72 TIME AND FREE WILL CHAP, i of greater and smaller can be applied to things which, it has just been acknowledged, do not admit among themselves of the relations of con tainer to contained. If, in order to cut short any question of this kind, we distinguish two kinds of quantity, the one intensive, which admits only of a " more or less," the other extensive, which lends itself to measurement, we are not far from siding with Fechner and the psychophysicists. For, as soon as a thing is acknowledged to be capable of increase and decrease, it seems natural to ask by how much it decreases or by how much it increases. And, because a measurement of this kind does not appear to be possible directly, it does not follow that science cannot successfully accomplish it by some indirect process, either by an integration of infinitely small elements, as Fechner proposes, or by any other roundabout way. Either, then, sensation is pure quality, or, if it is a magnitude, we ought to try to measure it.
To sum up what precedes, we have found the notion of intensity to present itself under a double Thus inten- aspect, according as we study the states 5? iudfejre- °* consciousness which represent an external cause, or those which are self- 511™016111- In the former case the per- ception of intensity consists in a certain Sty ^f'piy- estimate of the magnitude of the cause c±»P£n°~ by means of a certain quality in the volvwL effect: it is, as the Scottish philoso- CHAP, i INTENSITY AND MULTIPLICITY 73