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the excessive amplitude that corresponds to sensation be confined to a particular set? A reason must exist. The unique agreement between the sensory hallucinations and the more general moral and intellectual disorder must have its particular physical counterpart; and for this “a strong downward escape of current” is at any rate a sufficiently comprehensible metaphor. *

7.- Veridical Hallucinations. There is one topic which I cannot altogether pass over here, as it has a distinct bearing on the centrifugal origin of hallucinations. There is a class of phenomena, not yet recognised by science, and for which the evidence has never yet been presented with anything like convincing fulness; but which–I do not think it rash to say—will be accepted as genuine by a large number of persons who quite realise the strength of the à priori presumption against it, whenever the quantity and quality of the evidence shall be adequately realised ; and which is accepted already by a considerable number of such persons as, at any rate, having a strong prima facie claim to attention. Readers of these Proceedings will hardly need to be told that I refer to the telepathic class—hallucinations of sight, sound or touch, which suggest the presence of an absent person, and which occur simultaneously with some exceptional crisis in that person's life or, most frequently of all, with his death. Visual and auditory phantasms occurring at such moments may be conveniently termed veridical hallucinations ; for while they are completely delusive as far as the percipient's senses are concerned-while they completely conform to our definition, "sensory percepts which lack the objective basis which

Kandinsky (in the Archio für Psychiatrie, 1881), agreeing with Meynert, denies this centrifugal influence, and regards the contribution of the higher (front) part of the cortex to hallucinations as something quite different–i.e., the remission of an inhibitory function normally exercised by this part on the specific sensory regions. But he fails to make out even a plausible case. His argument that the higher part cannot initiate hallucinations restson no better ground than his own inability, when suffering from hallucinations, to transform mental pictures into hallucinations at will ; and on the further experience-which was decidedly exceptional--that his hallucinations did not correspond in any marked way with his more general mental delusions. Again, if one asks in what the effect of the supposed inhibitory function would normally be shown, it must surely be in preventing ordinary mental images from taking on the more vivid characters of hallucinations. Now Kandinsky himself admits that in normal acts of imagination the cortical sensory region is stimulated from the higher part of the cortex; hence he seems involved in the difficulty of conceiving stimulation and inhibition to proceed at the same moment from the same quarter. Nor, again, does he make any attempt to show why the supposed inhibitory function, if it is normally operative, does not equally inhibit the normal stimulation derived from the periphery, i.e., normal perception of objects.

they suggest”-they nevertheless have a definite correspondence with certain objective facts, namely, the exceptional condition of the absent person. Such cases, if genuine, militate very strongly against M. Binet's theory that excitation from the external sensory apparatus is a sine quâ non of hallucinations. For here the occurrence of the hallucination depends on the distant event; that is what fixes it to take place at a particular time; and an occurrence thus conditioned cannot be supposed to be conditioned also by the accidental presence of real phenomena capable of supplying points de repère, or by an accidental morbid disturbance of the organ or the nerve. And if the brain be admitted to be the primary physical seat of the phenomena, there are, further, good reasons for supposing that its highest tracts are those first affected, and so that the hallucination is centrifugal. The chief reasons

are two. (1) The phantasm is often bodied forth with elements of a more or less fanciful kind-dream-imagery, so to speak, embroidered on a groundwork of fact; and these elements seem clearly to be the percipient's own contribution, and not part of what he receives. (2) Cases occur where actual intercourse between the two persons concerned has long ceased ; and where the supersensuous communication can only be supposed to be initiated by the quickening of long-buried memories and of dim tracts of emotional association. The hallucination in these cases would therefore be a complete example of the projection of an idea from within outwards; the sensorium reverberates to a tremor which must start in the inmost penetralia of cerebral process.

[NOTE.—I would specially point out that the argument in the last paragraph does not extend beyond the limits of the percipient's organism. It involves no physical expression of the fact of the transmission. If A is dying at a distance, and B sees his form, it is rarely that one can suppose any psychical event in A's mind to be identical with any psychical event provocative of the hallucination in B's mind. That being so, there will be no simple and immediate concordance of nervous vibration in the two brains ; and that being so, there is no very obvious means of translating into physical terms the causal connection between A's experience and B's. The case thus differs from “ thought-transference" of the ordinary experimental type, where the image actually present in the one mind is reproduced in the other ; where, therefore, a physical concordance does exist, and something of the nature of • brain-wave" can be conceived. This was quite rightly pointed out in the notice of the Proceedings of the Society for Psychical Research which appeared in Mind XXXVI. But it had also been pointed out by Mr. F. W. H. Myers and myself in the “ Theory of Apparitions" there criticised. In our rapprochement of veridical hallucinations to experimental thought-transference, we are confining ourselves to the psychical aspect; we connect the phenomena as being in both cases affections of one mind by another occurring otherwise than through the recognised channels of sense. The objector may urge that if we have not, we ought to have, a physical theory which will embrace all

a

the phenomena-that we ought not to talk about a rapport between A's mind and B's unless we can establish a bridge between their two brains. This seems rather to assume that the standing puzzle of the relation between cerebral and psychical events in the individual, B, can only be stated in one crude form-viz., that the former are prior and produce the latter. For ordinary purposes such an expression is convenient ; but the convenience has its dangers. Still, as the converse proposition would be equally dangerous,

crue remains which we cannot evade. Since we cannot doubt that B's unwonted experience has its appropriate cerebral correlate, we have to admit that the energy of B's brain is directed in a way in which it would not be directed but for something that has happened to A. In this physical effect it is impossible to assume that an external physical antecedent is not involved ; and the relation of the antecedent to the effect is, as I have pointed out, very hard to conceive, when the neural tremors in A's brain are so unlike the neural tremors in B's brain as they must be when A's mind is occupied with his immediate surroundings or with the idea of death, and B's mind is occupied with a sudden and unaccountable impression or vision of A. I can only suggest that the action of brain on brain is not bound to conform to the simplest type of two tuning-forks ; and that a considerable community of experience (especially in emotional relations) between two persons may involve nervous records sufficiently similar to retain for one another some sort of revivable affinity, even when the experience has lost its vividness for conscious memory.

But, however that may be on the physical plane, the facts of which we have presented and shall continue to present evidence are purely psychical facts; and on the psychical plane, we can give to a heterogeneous array of them a certain orderly coherence, and present them as a graduated series of natural phenomena. Will it be asserted that this treatment is illegitimate unless a concurrent physical theory can also be put forward ? It is surely allowable to do one thing at a time. There is an unsolved mystery in the background ; that we grant and reinember ; but it need not perpetually oppress us. After all, is there not that standing mystery of the cerebral and mental correlation in the individual -a mystery equally unsolved and perhaps more definitely and radically insoluble—at the background of every fact and doctrine of the recognised psychology ? The psychologists work on as if it did not exist, or rather as if it were the most natural thing in the world, and no one complains of them. May we not claim a similar freedom? ]

THE CALCULUS OF PROBABILITIES APPLIED TO

PSYCHICAL RESEARCH.

By F. Y. EDGEWORTH.

“Nous sommes si éloignés de connaître tous les agents de la nature qu'il serait peu philosophique de nier l'existence de phénomènes, uniquement parcequ'ils sont inexplicables dans l'état actuel de nos connaissances. Seulement nous devons les examiner avec une attention d'autant plus scrupuleuse, qu'il parâit plus difficile de les admettre ; et c'est ici que l'analyse des probabilités devient indispensable, pour determiner jusqu'à quel point il faut multiplier les observations ou les expériences, pour avoir, en faveur de l'existence des agents. qu'elles semblent indiquer, une probabilité supérieure à toutes les raisons que l'on peut avoir d'ailleurs, de la réjéter.”—LAPLACE.

It is proposed here to appreciate by means of the calculus of pro babilities the evidence in favour of some extraordinary agency which is afforded by experiences of the following type : One person chooses a suit of cards, or a letter of the alphabet. Another person makes a guess as to what the choice has been. This experiment—a choice by one party, a guess by another--is performed N times. The number of successful guesses exceeds the number which is the most probable on the supposition of mere chance, viz., m, where m=Nu (in the abovementioned cases respectively £ N and 24N), by a considerable number n, where n=Vv. There follow a second and a third similar series of trials in which the number of successes exceeds the number most probable on the hypothesis of mere chance, viz., N'u' N"u", by n' n" respectively. As the number of these series is increased, there occur some in which the number of successes falls below the most probable number. What probability in favour of the existence of some agency other than chance is afforded by (1) a single series such as the first, in which the successes are in excess ; (2) a set of series such as the first two or three, in all of which the successes are in excess ; (3) a chequered set of series in some of which the successes are in excess, in others in defect?

These problems may, for our purpose, be replaced by the following: Out of an urn known to contain an infinite number of white and black balls in the proportion u :1-u have been drawn N balls whereof N (u + 2) are white; and again N' balls whereof N' (u + v) are white; and so on.

v is sometimes negative. What is the probability in favour of agency other than chance deducible (1) from the first series ; (2) from a set of series in which v is positive; (3) from a chequered set of series?

The evaluation of such a posteriori probabilities involves three

operations which may be distinguished in analysis, though implicated in practice. The first (I.) is to determine what function the required probability is of two sets of variables; namely, à priori probabilities not given by (or deducible from) direct statistical experience, and “objective” probabilities (to use the phrase of Cournot), which are derived from statistical experience. The second operation (II.) is the treatment of the à priori probabilities; the discovery, assumption, or ignoration of those unknown quantities. The third operation (III.) is the evaluation of the objective probabilities. These three operations are taken as the principle of division for this study; as a principle of subdivision, the three problems above stated.

I. There is apt to appear something arbitrary in the form of the function expressing an à posteriori probability. When Donkin, for example, constructs a scheme expressing the probability that chessmen, found standing on a board in a certain position, or that neighbouring* stars, have not been so arranged by mere chance, one does not feel very confident that the formula, not merely a formula, is assigned by him. It should be observed, however, first that an identical value may be reached in different ways; very much as a multiple integral may be expressed in different forms. Secondly, and more importantly, there is a characteristic defectt of the calculus of probability, which leads us to expect a real discrepancy in the methods of performing our first operation. I allude to the fact that we are often unable to utilise all our datum, to calculate the relative probabilities (in favour of mere chance or some additional agency) for the particular event observed, but only for a class to which that event belongs. And there is something arbitrary in the selection of this class. An example of this peculiarity will presently appear.

(1) For the solution of our first problem two schemata present themselves, each recommended by high authority; the first perhaps more frequently employed in problems of the general sort to which ours belongs, the second, I think, more appropriate to our particular problem. According to the (a) first solution we regard the observed event—the drawing of N (u+v) white balls--as having resulted from some real constitution or proportion of the balls in the urn, some “possibility,” in the phrase of Laplace. By inverse probability, upon the principle of Bayes, we determine the probability that this constitution, or possibility, or cause of the observed event, was some ratio higher than u. Let $ (x) be the à priori probability that the sought ratio should have been the particular ratio ☺ Let f (x) be the objective probability that, if :(N—x) were the real distribution of the balls, then exactly

* Phil. Mag., series IV., Vol. I., pp. 463-466. † Cf. Venn, Logic of Chance, chap. viii., sections 17-23.

See p. 193.

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