(b.) Mathematics is the science of the presentations of Space and Time, as our thought forms, and cannot otherwise form them. Now, if we measure a real triangle, given not by thought, but by successive perceptions which may be too great for simultaneous intuition, and find in all similar attempts at measurement the same law confirmed which pure thought gave us, that the sum of the angles = 2 R; further, if we take note that the determinations of the perception are something necessarily imposed on the mind by the system of differences in the Non-Ego, thus have their causes in differences of the Non-Ego, it follows from the empirical confirmation of the mathematical laws, to which there is no exception, that the distinctions in the Non-Ego obey laws which certainly must correspond to the forms of the latter, but run so entirely parallel with the rational laws of Space and Time, that here again the assumption of a pre-established harmony is unavoidable, whilst an identity of the laws agreeing with the identity of the forms requires no such forced assumption.
(c.) The senses of Sight and Touch receive their impressions from qualities of body altogether different, by quite distinct media and quite different physiological processes; nevertheless we obtain from them spatial perceptions which exhibit as great an agreement as possible, and which confirm one another. Now, were the objects not themselves in Space, but existed in any other form of being, it would be in the highest degree wonderful that they should produce in the mind in such different ways such congruent spatial figures; thus, e.g., the seen ball never appears as felt die or anything else, but as felt ball. On the assumption of Space as real form of existence this puzzle vanishes.
(d.) Only sight and touch, but none of the other senses, are able to arouse in the mind the perception of Space. (For when we hear where a sound comes from, the comparison of the strength of the sound in the two ears is chiefly relied upon; comp. p.337.) Kant entirely overlooked this, otherwise he could not have set up his division of outer (Space-sense) and inner (Time-) sense. To subjective idealism this whim of the mind is absolutely incomprehensible, which nevertheless occurs with the appearance of external necessity; but it is just as incomprehensible if other corresponding forms are assigned to existence. Only the physiological consideration of the local construction of the different sense-organs can here afford a ready explanation; but if the body and the senses do not exist in Space, here, too, all possibility of comprehension is precluded.
These four considerations taken together render it highly probable that common sense is right in believing that Space and Time are just as much objective forms of existence as subjective forms of thought. This formal identity of thought and being is almost self-evident for one who assumes their essential identity (comp. C. Chap. xiv.)
Ad. II. As we do not intend to dispute but to assume the assertion of Kant placed at the head of this chapter, there is no reason to show here why the Kantian proof is no proof, and leaves the question quite open (comp. “The Thing in Itself,” viii. “Kritik der Transcendentalen Æsthetik”). We shall, however, offer other reasons in lieu thereof.
A naïve theory of immediate perception regarded the sense-impressions as images of the things, which perfectly correspond to them, as the reflected image to its object. When Locke and modern physical science had made the complete heterogeneity of the sensation and the quality of the object the common property of science, the retinal image which was perceived in the eyes of other beings was substituted for the thing, and the sensation in its content was now said to be identical with the retinal image as formerly with the thing,—a view which is still a common one. It was, however, thereby forgotten that it is something quite different to perceive an objective image within the extent of an eye in the eye of another with one’s own eyes, or even to have the visual sensation determinable only according to angular degrees without absolute superficial magnitude. It was forgotten that the mind does not sit as a second eye behind the retina and look at this image; it was not seen that one committed the same fault as before in the case of things, only in a more disguised fashion; for what appears to another eye as a retinal image is in this eye itself nothing but vibrating molecules, just as well as that which in things appears to the beholder as colour, brightness, &c., are in the objects only molecular vibrations. People accordingly allowed themselves to be duped by the pleasure of having discovered a camera obscura in the eye, and considered the former problem to be solved, whereas it had only been shelved for an external question. The physiology of the eye has since discovered that the eye is not a camera to exhibit diminutive images to the mind on the retinal ground, but a photographic apparatus, which so changes the molecular vibrations of the retina chemically-dynamically, that modes of vibration which have hardly any resemblance to the light vibrations in the ether are handed on to the optic nerve to be propagated farther, so that those modifications of light, e.g., which are felt as colour, are in the nerve combinations of variously strong functions of three different kinds of end-organs in the retina, whilst the corresponding modifications of the physical ray of light are only discriminated by the wave-lengths of the vibrations. Further, light has a velocity of about 200,000 miles in a second, the process in the optic nerve only one of about a hundred feet.
Thus much is established, that the qualitative conversion of light vibrations on their entrance into the retina is of the greatest importance, and would give the final death-blow to the view which assigns an importance to the image on the retina accidentally observable by other eyes, if the idea were not in itself absurd, that the optic nerve, like a second eye, looks at this image—and then? But perhaps the central organ of vision (the corpora quadrigemina), as a third eye, looks at the image of the optic nerve, and then the central organ of thought (the cerebral hemispheres), as fourth eye, the image of the corpora quadrigemina, and then, perhaps, a definite central cell or the cerebral centre of consciousness as fifth eye, the image of the cerebrum, not to push the matter directly to the sixth eye of a punctual central monad having its seat at some place or other in the brain! For this much is to be looked upon as physiologically established, that the sensation of sight can at the earliest take place in the central part into which the optic nerve runs in the corpora quadrigemina, but not in the course of the optic nerve itself. On the entrance of the nerve into the centre, however, we must assume another conversion of the modes of vibration, on account of the altered structure of the nervous matter, and because the importance of the central parts for perception would cease if the form of vibration remained unchanged, because then the sense must react with sensation on the vibrations of the optic nerve. In the corpora quadrigemina again, however, those extended thought-processes, in which the space-intuition is always found as an integral element, cannot take place. As such have their seat in the cerebral hemispheres, so also the visual sensations, which underlie the space-intuition, just as the sensations of touch, which again are developed at another spot in the brain, must be first conducted to the cerebrum, in order there, by help of thought, to acquire the extension of the space-intuition.
If, now, the object-image on the retina can be compared with a mosaic, which resembles the thing itself in its proportions, yet the isolated primitive nerve-fibres are far too much interlaced for an ideal section of the optic nerve on its entrance into the corpora quadrigemina to exhibit an order and position of the fibres corresponding to the retinal image; and even worse founded would be the assumption that in the central organ itself there occurs such a localised affection of cells, that between it and the retinal image a like proportionality of extensive relations obtains as between retinal affection and thing. But since these affected cells in the central organ itself would even then be still relatively dependent, and would communicate with one another only by fixed paths, even on such an unjustified assumption, it would still not be clear how the consciousness resulting as aggregate phenomenon from the plural cell-consciousness could come to order sensations in an extension, which should correspond to the relative positions of the affected cells. There is no bridge bet
ween the real spatial position of the material parts which produce sensations and the ideal spatial position of the conscious sensations ordered in extensive intuition; for space as real form of existence and space as conscious ideal form of intuition are as incommensurable as the real and the imaginary part of a complex number, although both are in themselves subject to the same formal laws. This is also the reason why even the physiologically untenable theories of a single ultimate central cell (how soon must it get fatigued!) or of a punctual central monad are altogether incapable of forming this bridge. If real and conscious ideal space are heterogeneous spheres, of which the one can have no part in the other, real space-relations of the sensation-forming material parts cannot have any influence on sensation at all; the position of the sensitive parts of the brain is indifferent, and only the mode of vibration, dependent partly on the nature of the central parts, partly on the intensity and quality of the conveyed motion, can influence the character of the resulting intuition.
This law, which must be self-evident a priori to every philosopher, for the rest, has already been formulated on the physiological side, and can hardly be seriously impugned. Lotze thus expresses it:—Identical vibrations of different central molecules call forth undistinguishable sensations, so that several simultaneously vibrating molecules of identical form of vibration produce a sensation, which qualitatively resembles the sensation excited by any one of these molecules, but quantitatively possesses the degree of strength of the sum of all the single sensations. If a person smells with one nostril, he has the same sensation, only more faintly, as if he smelt with two; and if the tactile nerves of the nose did not feel the stream of permeating air, the olfactory nerve alone would not in the normal state perceive the smell of the left and right nostril as different. The like holds good of taste, if it affects a smaller or larger part of the tongue and palate; only the simultaneous tactile feelings of contact, of the contraction of the skin, &c., distinguish the place touched; the taste itself becomes only stronger or weaker. Whether a sound reaches the left or right ear is only perceived by the feelings of tension excited simultaneously in the ear, partly directly, partly reflectorially. Here, too, it is not at all the auditory nerve, but tactile nerves, especially in the richly-supplied tympanum, which condition the feeling of localisation, as clearly follows from Ed. Weber’s diving experiments, which prove that this local feeling remains only so long as the auditory passages are filled with air, but is lost if the tympana are rendered inactive by the filling of the auditory passages with water. In vision we receive different impressions from the same point of light, it is true, if its image falls on differently situated places of one or both eyes; but the impressions are not to be distinguished when they fall on corresponding parts of both eyes. In a well-contrived arrangement of the experiment one is not at all whether one sees a light with the right or with the left, or with both eyes at once, if information on the point cannot be obtained by other expedients. The visual impressions of corresponding points of the two eyes are combined into a single strengthened impression.
According to Lotze’s theory we should not be able to distinguish whether a pain, feeling, touch, &c., affects the right or left half of the body, unless, owing to the want of symmetry, even in the smallest particular, of the two halves of the body, the accompanying sensations of tension, extension, pressure, &c., were not the same on the right half of the body as on the left, so that by this qualitative incongruence of the sensations, with the help of practice, we are enabled to distinguish right and left in our own body. In hearing, taste, and smell, also, as already mentioned, such attendant circumstances are present, making possible a certain discrimination of congruent sensations, according to the place acted on; but it is important, that here the nerve-trunks which mediate the specific sensation and those which report the accompanying differences are different, whence it follows, that if, by cutting off the latter, or by other well-contrived elimination of the accompanying differences, the pure sense-perceptions are excluded from the experiment, these are no longer able to afford the consciousness of local differences, and are thus altogether unable to produce space-intuitions. Otherwise is it with the senses of Touch and Sight. Every similar sensation of Touch at various parts of the skin is combined with characteristic accompanying differences, which are founded on the particular displacement, tension, extension, and participation of juxtaposed and underlying sensitive parts, when pressure is exerted on the skin, according to the softness or hardness, the special form of the limb, nature of the subjacent parts, thickness of the sensitive tactile corpuscles, &c., and which are almost all conducted to the brain through the same nerve-trunks. In the similar sensation of colour or light is associated with characteristic differences, according to the point of the retina that is affected, which are founded: (1) on the decreasing distinctness of the perception of similar impressions from the centre to the periphery; (2) on the currents induced in the neighbouring fibres, which again have a different issue, according to the position of the latter with respect to the point of the clearest vision; (3) on the reflex motor impulse to rotate the eye-ball, which upon every affection of a spot in the retina has for its consequence that the point of most distinct vision strives to occupy the place of the affected retinal point.
These three moments in conjunction give a different stamp to the similar sensations of every retinal fibre, to which Lotze, the author of this theory, gives the name of local sign. These differences also are partly conducted to the brain by the optic nerve, partly felt in the brain itself through the resistance, which the will must oppose to the reflex tendency to rotate the eye, in order to prevent it. It is now comprehensible how, in contrast to the sensations of smell, taste, and hearing, precisely the sensations of sight and touch can suggest to the mind the intuition of space, to wit, because with these the stimulus conveyed by every single primitive nerve-fibre has its qualitative definiteness through a well-organised system of accompanying differences, so that the vibrations excited in different nerve-fibres by similar external stimuli so far turn out different, that they can not blend in the mind into a single strengthened sensation, but yet so far resemble each other that the qualitatively similar portion can easily be perceived by the mind in the sensations produced through them. According to this we can only find the general law confirmed by the apparent exceptions, that identical vibrations of different parts of the brain blend into one sensation strengthened in degree; a law which both appears highly plausible a priori, and also empirically has not only no fact against it, but without it the phenomena of the lower senses already mentioned would be simply inexplicable. According to this law the vibrating molecule is perfectly indifferent to the mind, its mode of vibration alone has an influence on the mind; and when we see certain parts of the body (the nerves), certain parts of the nervous system (the grey matter), certain parts of the brain especially appropriated to higher influences of a definite kind, we can only ascribe this to the circumstance that these parts are adapted, by reason of their molecular constitution, either exclusively or chiefly, to the production of that kind of vibrations, which alone or chiefly are capable of exerting these influences on the mind.
If we now look upon this law as established, and Lotze’s theory of local signs (apart from the question whether those especially employed by him are exactly the right ones) as assured, we still do not get beyond the result, that, in sight or touch the mind receives from every primitive nerve-fibre, through the intervention of the brain, a special sensation, which is prevented by its individual character from blending with others, but yet is so like the others that it is an easy thing for the mind to perceive as such the similar foundation which they all possess. But we in no way get from this sum of simultaneous qualitatively similar and yet different sensations to their distribution in space, as presented in the field of vision and the cutaneous field of touch; we always stop short at the qualitative and intensive quantitative or graduated distinctions of the several sensations, and can in no way see
how it is possible for the extensively quantitative or locally extended to be imported into sensation from the vibrations of the brain molecules, since it is not the position of the single molecule in the brain, but only the duration, form, &c., of its vibrations which has influence on sensation, and these moments do not contain the elements of extensive quantity, which might stand in some relation or other to the extensive quantity of the retinal image. On the other hand, in virtue of the system of local signs, the extensive proximity and distance of the points of the retinal image from one another. or their actual contact, is changed into greater or less qualitative differences of the corresponding sensations, or least difference; and, accordingly, a material is presented to the mind, which, if the latter spontaneously reconverts this system of qualitative differences into a system of local relations, now compels the mind with necessity to assign such a place to every sensation in the space-image as corresponds to its qualitative determinateness; so that there is no room for caprice in regard to the space-determinations of a figure given by a sum of qualitatively distinct elements of sensation, but the mind is necessarily compelled to reconstruct the same in the relations in which the image on the retina appears to the eye of an onlooker, in conformity with experience.
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