Chapter IV (2)

In the professorial philosophy of our philosophy-professors we are still taught to this day, that perception of the outer world is a thing of the senses, and then there follows a long dissertation upon each of the five senses: whereas no mention whatever is made of the intellectual character of perception: that is to say, of the fact, that it is mainly the work of the Understanding, which, by means of its own peculiar form of Causality, together with the forms of pure sensibility, Time and Space, which are postulated by Causality, primarily creates and produces the objective, outer world out of the raw material of a few sensations. And yet in its principal features, I had stated this matter in the first edition of the present treatise[72] and soon after developed it more fully in my treatise "On Vision and Colours" (1816), of which Professor Rosas has shown his appreciation by allowing it to lead him into plagiarism.[73] But our professors of philosophy have not thought fit to take the slightest notice either of this, or indeed of any of the other great and important truths which it has been the aim and labour of my whole life to set forth, in order to secure them as a lasting possession to mankind. It does not suit their tastes, or fit into their notions; it leads to no Theology, nor is it even adapted to drill students for higher State purposes. In short, professional philosophers do not care to learn from me, nor do they even see how much they might learn from me: that is, all that their children and their children's children will learn from me. They prefer to sit down and spin a long metaphysical yarn, each out of his own thoughts, for the benefit of the public; and no doubt, if fingers are a sufficient qualification, they have it. How right was Macchiavelli when he said, as Hesiod[74] before him: "There are three sorts of heads: firstly, those which acquire knowledge of things and comprehend them by themselves; secondly, those which recognise the truth when it is shown them by others; and thirdly, those which can do neither the one nor the other."[75]--

[72] Anno 1813, pp. 53-55.

[73] For further details see my "Will in Nature," p. 19 of the
1st edition, and p. 14 of the 3rd. (P. 230 _et seqq._ of the
translation of the "Will in Nature," which follows the "Fourfold
Root" in the present volume.)

[74] Hesiod, ἔργα, 293.

[75] Macchiavelli, "Il principe," cap. 22.

One must indeed be forsaken by all the gods, to imagine that the outer, perceptible world, filling Space in its three dimensions and moving on in the inexorable flow of Time, governed at every step by the laws of Causality, which is without exception, and in all this merely obeying laws we can indicate before all experience of them--that such a world as this, we say, can have a real, objective existence outside us, without any agency of our own, and that it can then have found its way into our heads through bare sensation and thus have a second existence within us like the one outside. For what a miserably poor thing is mere sensation, after all! Even in the noblest of our organs it is nothing but a local, specific feeling, susceptible of some slight variation, still in itself always subjective and, as such therefore, incapable of containing anything objective, anything like perception. For sensation is and remains a process within the organism and is limited, as such, to the region within the skin; it cannot therefore contain anything which lies beyond that region, or, in other words, anything that is outside us. A sensation may be pleasant or unpleasant--which betokens a relation to the Will--but nothing objective can ever lie in any sensation. In the organs of the senses, sensation is heightened by the confluence of the nerve-extremities, and can easily be excited from without on account of their extensive distribution and the delicacy of the envelope which encloses them; it is besides specially susceptible to particular influences, such as light, sound, smell; notwithstanding which it is and remains mere sensation, like all others within our body, consequently something essentially subjective, of whose changes we only become immediately conscious in the form of the _inner_ sense, Time: that is, successively. It is only when the _Understanding_ begins to act--a function, not of single, delicate nerve-extremities, but of that mysterious, complicated structure weighing from five to ten pounds, called the brain--only when it begins to apply its sole form, _the causal law_, that a powerful transformation takes place, by which subjective sensation becomes objective perception. For, in virtue of its own peculiar form, therefore _à priori_, _i.e._ _before_ all experience (since there could have been none till then), the Understanding conceives the given corporeal sensation as an _effect_ (a word which the Understanding alone comprehends), which _effect_, as such, necessarily implies a _cause_. Simultaneously it summons to its assistance _Space_, the form of the _outer_ sense, lying likewise ready in the intellect (_i.e._ the brain), in order to remove that cause _beyond_ the organism; for it is by this that the external world first arises, Space alone rendering it possible, so that pure intuition _à priori_ has to supply the foundation for empirical perception. In this process, as I shall soon show more clearly, the Understanding avails itself of all the several data, even the minutest, which are presented to it by the given sensation, in order to construct the cause of it in Space in conformity with them. This intellectual operation (which is moreover explicitly denied both by Schelling[76] and by Fries[77]), does not however take place discursively or reflectively, _in abstracto_, by means of conceptions and words; it is, on the contrary, an intuitive and quite direct process. For by it alone, therefore exclusively _in_ the Understanding and _for_ the Understanding, does the real, objective, corporeal world, filling Space in its three dimensions, present itself and further proceed, according to the same law of causality, to change in Time, and to move in Space.--It is therefore the Understanding itself which has to create the objective world; for this world cannot walk into our brain from outside all ready cut and dried through the senses and the openings of their organs. In fact, the senses supply nothing but the raw materials which the Understanding at once proceeds to work up into the objective view of a corporeal world, subject to regular laws, by means of the simple forms we have indicated: Space, Time, and Causality. Accordingly our every-day _empirical perception_ is an _intellectual_ one and has a right to claim this predicate, which German pseudo-philosophers have given to a pretended intuition of dream-worlds, in which their beloved _Absolute_ is supposed to perform its evolutions. And now I will proceed to show how wide is the gulf which separates sensation from perception, by pointing out how raw is the material out of which the beautiful edifice is constructed.

[76] Schelling, "Philosophische Schriften" (1809), vol. i. pp. 237
and 238.

[77] Fries, "Kritik der Vernunft." vol. i. pp. 52-56 and p. 290 of
the 1st edition.

Objective perception makes use, properly speaking, of only two senses; touch and sight. These alone supply the data upon which, as its basis, the Understanding constructs the objective world by the process just described. The three other senses remain on the whole subjective; for their sensations, while pointing to an external cause, still contain no data by which its relations _in Space_ can be determined. Now _Space_ is the form of all perception, _i.e._ of _that_ apprehension, in which alone _objects_ can, properly speaking, present themselves. Therefore those other three senses can no doubt serve to announce the presence of objects we already know in some other way; but no construction in Space, consequently no objective perception, can possibly be founded on their data. A rose cannot be constructed from its perfume, and a blind man may hear music all his life without having the slightest objective representation either of the musicians, or of the instruments, or of the vibrations of the air. On the other hand, the sense of hearing is of great value as a medium for language, and through this it is the sense of _Reason_. It is also valuable as a medium for music, which is the only way in which we comprehend numerical relations not only _in abstracto_, but directly, _in concreto_. A musical sound or tone, however, gives no clue to spacial relations, therefore it never helps to bring the nature of its cause nearer to us; we stop short at it, so that it is no datum for the Understanding in its construction of the objective world. The sensations of touch and sight alone are such data; therefore a blind man without either hands or feet, while able to construct Space for himself _à priori_ in all its regularity, would nevertheless acquire but a very vague representation of the objective world. Yet what is supplied by touch and sight is not by any means perception, but merely the raw material for it. For perception is so far from being contained in the sensations of touch and sight, that these sensations have not even the faintest resemblance to the qualities of the things which present themselves to us through them, as I shall presently show. Only what really belongs to sensation must first be clearly distinguished from what is added to it by the intellect in perception. In the beginning this is not easy, because we are so accustomed to pass from the sensation at once to its cause, that the cause presents itself to us without our noticing the sensation apart from it, by which, as it were, the premisses are supplied to this conclusion drawn by the Understanding.

Thus touch and sight have each their own special advantages, to begin with; therefore they assist each other mutually. Sight needs no contact, nor even proximity; its field is unbounded and extends to the stars. It is moreover sensitive to the most delicate degrees of light, shade, colour, and transparency; so that it supplies the Understanding with a quantity of nicely defined data, out of which, by dint of practice, it becomes able to construct the shape, size, distance, and nature of bodies, and represents them at once perceptibly. On the other hand, touch certainly depends upon contact; still its data are so varied and so trustworthy, that it is the most searching of all the senses. Even perception by sight may, in the last resort, be referred to touch; nay, sight may be looked upon as an imperfect touch extending to a great distance, which uses the rays of light as long feelers; and it is just because it is limited to those qualities which have light for their medium and is therefore one-sided, that it is so liable to deception; whereas touch supplies the data for cognising size, shape, hardness, softness, roughness, temperature, &c. &c., quite immediately. In this it is assisted, partly by the shape and mobility of our arms, hands, and fingers, from whose position in feeling objects the Understanding derives its data for constructing bodies in Space, partly by muscular power, which enables it to know the weight, solidity, toughness, or brittleness of bodies: all this with the least possible liability to error.

These data nevertheless do not by any means yet give perception, which is always the work of the Understanding. The sensation I have in pressing against a table with my hand, contains no representation of a firm cohesion of parts in that object, nor indeed anything at all like it. It is only when my Understanding passes from that sensation to its cause, that the intellect constructs for itself a body having the properties of solidity, impenetrability, and hardness. If in the dark, I put my hand upon a flat surface, or lay hold of a ball of about three inches in diameter, the same parts of my hand feel the pressure in both cases; it is only by the different position which my hand takes that, in the one or in the other case, my Understanding constructs the shape of the body whose contact is the cause of the sensation, for which it receives confirmation from the changes of position which I make. The sensations in the hand of a man born blind, on feeling an object of cubic shape, are quite uniform and the same on all sides and in every direction: the edges, it is true, press upon a smaller portion of his hand, still nothing at all like a cube is contained in these sensations. His Understanding, however, draws the immediate and intuitive conclusion from the resistance felt, that this resistance must have a cause, which then presents itself through that conclusion as a hard body; and through the movements of his arms in feeling the object, while the hand's sensation remains unaltered, he constructs the cubic shape in Space, which is known to him _à priori_. If the representation of a cause and of Space, together with their laws, had not already existed within him, the image of a cube could never have proceeded from those successive sensations in his hand. If a rope be drawn through his hand, he will construct, as the cause of the friction he feels and of its duration, a long cylindrical body, moving uniformly in the same direction in that particular position of his hand. But the representation of movement, _i.e._ of change of place in Space by means of Time, never could arise for him out of the mere sensation in his hand; for that sensation can neither contain, nor can it ever by itself alone produce any such thing. It is his intellect which must, on the contrary, contain within itself, before all experience, the intuitions of Space, Time, and together with them that of the possibility of movement; and it must also contain the representation of Causality, in order to pass from sensation--which alone is given by experience--to a cause of that sensation, and to construct that cause as a body having this or that shape, moving in this or that direction. For how great is the difference between a mere sensation in my hand and the representations of causality, materiality, and mobility in Space by means of Time! The sensation in my hand, even if its position and its points of contact are altered, is a thing far too uniform and far too poor in data, to enable me to construct out of it the representation of Space, with its three dimensions, and of the influences of bodies one upon another, together with the properties of expansion, impenetrability, cohesion, shape, hardness, softness, rest, and motion: the basis, in short, of the objective world. This is, on the contrary, only possible by the intellect containing within itself, anterior to all experience, Space, as the form of perception; Time, as the form of change; and the law of Causality, as the regulator of the passing in and out of changes. Now it is precisely the pre-existence before all experience of all these forms, which constitutes the Intellect. Physiologically, it is a function of the brain, which the brain no more learns by experience than the stomach to digest, or the liver to secrete bile. Besides, no other explanation can be given of the fact, that many who were born blind, acquire a sufficiently complete knowledge of the relations of Space, to enable them to replace their want of eyesight by it to a considerable degree, and to perform astonishing feats. A hundred years ago Saunderson, for instance, who was blind from his birth, lectured on Optics, Mathematics, and Astronomy at Cambridge.[78] This, too, is the only way to explain the exactly opposite case of Eva Lauk, who was born without arms or legs, yet acquired an accurate perception of the outer world by means of sight alone as rapidly as other children.[79] All this therefore proves that Time, Space, and Causality are not conveyed into us by touch or by sight, or indeed at all from outside, but that they have an internal, consequently not empirical, but intellectual origin. From this again follows, that the perception of the bodily world is an essentially intellectual process, a work of the Understanding, to which sensation merely gives the opportunity and the data for application in individual cases.

[78] Diderot, in his "Lettre sur les Aveugles," gives a detailed
account of Saunderson.

[79] See "Die Welt a. W. u. V." vol. ii. chap. 4.

I shall now prove the same with regard to the sense of sight. Here the only immediate datum is the sensation experienced by the retina, which, though admitting of great variety, may still be reduced to the impression of light and dark with their intermediate gradations and to that of colours proper. This sensation is entirely subjective: that is to say, it only exists within the organism and under the skin. Without the Understanding, indeed, we should never even become conscious of these gradations, excepting as of peculiar, varied modifications of the feeling in our eye, which would bear no resemblance to the shape, situation, proximity, or distance of objects outside us. For _sensation_, in seeing, supplies nothing more than a varied affection of the retina, exactly like the spectacle of a painter's palette with divers splashes of colour. Nor would anything more remain over in our consciousness, were we suddenly deprived of all our Understanding--let us say by paralysis of the brain--at a moment when we were contemplating a rich and extensive landscape, while the sensation was left unchanged: for this was the raw material out of which our Understanding had just before been constructing that perception.

Now, that the Understanding should thus be able, from such limited material as light, shade and colour, to produce the visible world, inexhaustibly rich in all its different shapes, by means of the simple function of referring effects to causes assisted by the intuition of Space, depends before all things upon the assistance given by the sensation itself, which consists in this: first, that the retina, as a surface, admits of a juxtaposition of impressions; secondly, that light always acts in straight lines, and that its refraction in the eye itself is rectilinear; finally, that the retina possesses the faculty of immediately feeling from which direction the light comes that impinges upon it, and this can, perhaps, only be accounted for by the rays of light penetrating below the surface of the retina. But by this we gain, that the mere impression at once indicates the direction of its cause; that is, it points directly to the position of the object from which the light proceeds or is reflected. The passage to this object as a cause no doubt presupposes the knowledge of causal relations, as well as of the laws of Space; but this knowledge constitutes precisely the furniture of the _Intellect_, which, here also, has again to create perception out of mere sensation. Let us now examine its procedure in doing so more closely.

The first thing it does is to set right the impression of the object, which is produced on the retina upside down. That original inversion is, as we know, brought about in the following manner. As each point of the visible object sends forth its rays towards all sides in a rectilinear direction, the rays from its upper extremity cross those from its lower extremity in the narrow aperture of the pupil, by which the former impinge upon the bottom, the latter upon the top, those projected from the right side upon the left, and _vice versa_. The refracting apparatus of the eye, which consists of the _humor aqueus_, _lens_, _et corpus vitreum_, only serves to concentrate the rays of light proceeding from the object, so as to find room for them on the small space of the retina. Now, if seeing consisted in mere sensation, we should perceive the impression of the object turned upside down, because we receive it thus; but in that case we should perceive it as something within our eye, for we should stop short at the sensation. In reality, however, the Understanding steps in at once with its causal law, and as it has received from sensation the datum of the direction in which the ray impinged upon the retina, it pursues that direction retrogressively up to the cause on both lines; so that this time the crossing takes place in the opposite direction, and the cause presents itself upright as an external object in Space, _i.e._ in the position in which it originally sent forth its rays, not that in which they reached the retina (see fig. 1).--The purely intellectual nature of this process, to the exclusion of all other, more especially of physiological, explanations, may also be confirmed by the fact, that if we put our heads between our legs, or lie down on a hill head downwards, we nevertheless see objects in their right position, and not upside down; although the portion of the retina, which is usually met by the lower part of the object is then met by the upper: in fact, everything is topsy turvy excepting the Understanding.

The _second_ thing which the Understanding does in converting sensation into perception, is to make a single perception out of a double sensation; for each eye in fact receives its own separate impression from the object we are looking at; each even in a slightly different direction: nevertheless that object presents itself as a single one. This can only take place in the Understanding, and the process by which it is brought about is the following: Our eyes are never quite parallel, excepting when we look at a distant object, _i.e._ one which is more than 200 feet from us. At other times they are both directed towards the object we are viewing, whereby they converge, so as to make the lines proceeding from each eye to the exact point of the object on which it is fixed, form an _angle_, called the _optic angle_; the lines themselves are called _optic axes_. Now, when the object lies straight before us, these lines exactly impinge upon the centre of each retina, therefore in two points which correspond exactly to each other in each eye. The Understanding, whose only business it is to look for the _cause_ of all things, at once recognises the impression as coming from a _single_ outside point, although here the sensation is double, and attributes it to _one_ cause, which therefore presents itself as a single object. For all that is perceived by us, is perceived as a _cause_--that is to say, as the cause of an effect we have experienced, consequently _in the Understanding_. As, nevertheless, we take in not only a single point, but a considerable surface of the object with both eyes, and yet perceive it as a single object, it will be necessary to pursue this explanation still further. All those parts of the object which lie to one side of the vertex of the optic angle no longer send their rays straight into the centre, but to the side, of the retina in each eye; in both sides, however, to the same, let us say the left, side. The points therefore upon which these rays impinge, _correspond symmetrically to each other_, as well as the centres--in other words, they are _homonymous points_. The Understanding soon learns to know them, and accordingly extends the above-mentioned rule of its causal perception to them also; consequently it not only refers those rays which impinge upon the centre of each retina, but those also which impinge upon all the other symmetrically corresponding places in both retinas, to a single radiant point in the object viewed: that is, it sees all these points likewise as single, and the entire object also. Now, it should be well observed, that in this process it is not the outer side of one retina which corresponds to the outer side of the other, and the inner to the inner of each, but the right side of one retina which corresponds to the right side of the other, and so forth; so that this symmetrical correspondence must not be taken in a physiological, but in a geometrical sense. Numerous and very clear illustrations of this process, and of all the phenomena which are connected with it, are to be found in Robert Smith's "Optics," and partly also in Kästner's German translation (1755). I only give _one_ (fig. 2), which, properly speaking, represents a special case, mentioned further on, but which may also serve to illustrate the whole, if we leave the point R out of question. According to this illustration, we invariably direct both eyes equally towards the object, in order that the symmetrically corresponding places on both retinas may catch the rays projected from the same points. Now, when we move our eyes upwards and downwards, to the sides, and in all directions, the point in the object which first impinged upon the central point of each retina, strikes a different place every time, but in all cases one which, in each eye, corresponds to the place bearing the same name in the other eye. In examining (_perlustrare_) an object, we let our eyes glide backwards and forwards over it, in order to bring each point of it successively into contact with the centre of the retina, which sees most distinctly: we feel it all over with our eyes. It is therefore obvious that seeing singly with two eyes is in fact the same process as feeling a body with ten fingers, each of which receives a different impression, each moreover in a different direction: the totality of these impressions being nevertheless recognised by the Understanding as proceeding from _one_ object, whose shape and size it accordingly apprehends and constructs in Space. This is why it is possible for a blind man to become a sculptor, as was the case, for instance, with the famous Joseph Kleinhaus, who died in Tyrol, 1853, having been a sculptor from his fifth year.[80] For, no matter from what cause it may have derived its data, perception is invariably an operation of the Understanding.

[80] The Frankfort "Konversationsblatt," July 22, 1853, gives the
following account of this sculptor:--"The blind sculptor, Joseph
Kleinhaus, died at Nauders, in Tyrol, on the 10th inst. Having lost
his eyesight through small-pox when he was five years old, he began
to amuse himself with carving and modelling, as a pastime. Prugg
gave him some instructions, and supplied him with models, and at
the age of twelve he carved a Christ in life-size. During a short
stay in Nissl's workshop at Fügen, his progress was so rapid, that,
thanks to his good capacities and talents, his fame as the blind
sculptor soon spread far and wide. His works are numerous and of
various kinds. His Christs alone, of which there are about four
hundred, bear special witness to his proficiency, particularly if
his blindness is taken into consideration. He sculptured many other
objects besides, and, but two months ago, he modelled a bust of the
Emperor Franz Joseph of Austria which has been sent to Vienna."

But just as a single ball seems to me double, if I touch it with my fingers crossed--since my Understanding, at once reverting to the cause and constructing it according to the laws of Space, takes for granted that the fingers are in their normal position and of course cannot do otherwise than attribute two spherical surfaces, which come in contact with the outer sides of the first and middle fingers, to two different balls--just so also does an object seem double, if my eyes, instead of converging symmetrically and enclosing the optic angle at a single point of the object, each view it at a different inclination--in other words, if I squint. For the rays, which in this case emanate from one point of the object, no longer impinge upon those symmetrically corresponding points in both retinas with which my mind has grown familiar by long experience, but upon other, quite different ones which, in a symmetrical position of the eyes, could only be affected in this way by different bodies; I therefore now see _two_ objects, precisely because perception takes place by means of, and within, the Understanding.--The same thing happens without squinting when, for instance, I look fixedly at the furthest of two objects placed at unequal distances before me, and complete the optic angle at it; for then the rays emanating from the nearer object do not impinge upon symmetrically corresponding places in both retinas, wherefore my Understanding attributes them to two objects, _i.e._ I see the nearer object double (see fig. 2, page 70). If, on the contrary, I complete the optic angle at the nearer object, by looking steadily at it, the further object appears double. It is easy to test this by holding a pencil two feet from the eyes, and looking alternately at it and at some other more distant object behind it.

But the finest thing of all is, that this experiment may quite well be reversed: so that, with two real objects straight before and close to us, and with our eyes wide open, we nevertheless see but _one_. This is the most striking proof that perception is a work of the Understanding and by no means contained in sensation. Let two cardboard tubes, about 8 inches long and 1-1/2 inches in diameter, be fastened parallel to one another, like those of a binocular telescope, and fix a shilling at the end of each tube. On applying our eyes to the opposite extremity and looking through the tubes, we shall see only _one_ shilling surrounded by _one_ tube. For in this case the eyes being forced into a completely parallel position, the rays emanating from the coins impinge exactly upon the centres of the two retinas and those points which immediately surround them, therefore upon places which correspond symmetrically to each other; consequently the Understanding, taking for granted the usual convergent position of the optic axes when objects are near, admits but one object as the cause of the reflected rays. In other words, we see but one object; so direct is the act of causal apprehension in the Understanding.

We have not space enough here to refute one by one the physiological explanations of single vision which have been attempted; but their fallacy is shown by the following considerations:--

1^o. If seeing single were dependent upon an organic connection, the corresponding points in both retinas, on which this phenomenon is shown to depend, would correspond _organically_, whereas they do so in a merely _geometrical_ sense, as has already been said. For, organically speaking, the two inner and two outer corners of the eyes are those which correspond, and so it is with the other parts also; whereas for the purpose of single vision, it is the right side of the right retina which corresponds to the right side of the left retina, and so on, as the phenomena just described irrefutably show. It is also precisely on account of the intellectual character of the process, that only the most intelligent animals, such as the higher mammalia and birds of prey--more especially owls--have their eyes placed so as to enable them to direct both optic axes to the same point.

2^o. The hypothesis of a confluence or partial intersection of the optic nerves before entering the brain, originated by Newton,[81] is false, simply because it would then be impossible to see double by squinting. Vesalius and Cæsalpinus besides have already brought forward anatomical instances in which subjects saw single, although neither fusion nor even contact of the optic nerves had taken place. A final argument against the hypothesis of a mixed impression is supplied by the fact, that on closing our right eye firmly and looking at the sun with our left, the bright image which persists for a time is always in the left, never in the right, eye: and _vice versa_.

[81] Newton, "Optics." Query 15.

The _third_ process by which the Understanding converts sensation into perception, consists in constructing bodies out of the simple surfaces hitherto obtained--that is, in adding the third dimension. This it does by estimating the expansion of bodies in this third dimension in Space--which is known to the Understanding _à priori_--through Causality, according to the degree in which the eye is affected by the objects, and to the gradations of light and shade. In fact, although objects fill Space in all three dimensions, they can only produce an impression upon the eye with two; for the nature of that organ is such, that our sensation, in seeing, is merely planimetrical, not stereometrical. All that is stereometrical in our perception is added by the Understanding, which has for its sole data the direction whence the eye receives its impression, the limits of that impression, and the various gradations of light and dark: these data directly indicate their causes, and enable us to distinguish whether what we have before us is a disk or a ball. This mental process, like the preceding ones, takes place so immediately and with such rapidity, that we are conscious of nothing but the result. It is this which makes perspective drawing so difficult a problem, that it can only be solved by mathematics and has to be learnt; although all it has to do, is to represent the sensation of seeing as it presents itself to our Understanding as a datum for the third process: that is, visual sensation in its merely planimetrical extension, to the _two_ dimensions of which extension, together with the said data in them, the Understanding forthwith adds the _third_, in contemplating a drawing as well as in contemplating reality. Perspective drawing is, in fact, a sort of writing which can be read as easily as printed type, but which few are able to write; precisely because our intellect, in perceiving, only apprehends effects with a view to constructing their causes, immediately losing sight of the former as soon as it has discovered the latter. For instance, we instantly recognise a chair, whatever position it may be in; while drawing a chair in any position belongs to the art which abstracts from this third process of the Understanding, in order to present the data alone for the spectator himself to complete. In its narrowest acceptation, as we have already seen, this is the art of drawing in perspective; in a more comprehensive sense, it is the whole art of painting. A painting presents us with outlines drawn according to the rules of perspective; lighter and darker places proportioned to the effect of light and shade; finally patches of colouring, which are determined as to quality and intensity by the teaching of experience. This the spectator reads and interprets by referring similar effects to their accustomed causes. The painter's art consists in consciously retaining the data of visual sensation in the artist's memory, as they are _before_ this third intellectual process; while we, who are not artists, cast them aside without retaining them in our memory, as soon as we have made use of them for the purpose described above. We shall become still better acquainted with this third intellectual process by now passing on to a fourth, which, from its intimate connection with the third, serves to elucidate it.

This _fourth_ operation of the Understanding consists in acquiring knowledge of the distance of objects from us: it is this precisely which constitutes that third dimension of which we have been speaking. Visual sensation, as we have said, gives us the _direction_ in which objects lie, but not their _distance_ from us: that is, not their _position_. It is for the _Understanding_ therefore to find out this distance; or, in other words, the distance must be inferred from purely _causal_ determinations. Now the most important of these is the _visual angle_, which objects subtend; yet even this is quite ambiguous and unable to decide anything by itself. It is like a word of double meaning: the sense, in which it is to be understood, can only be gathered from its connection with the rest. An object subtending the same visual angle may in fact be small and near, or large and far off; and it is only when we have previously ascertained its size, that the visual angle enables us to recognise its distance: and conversely, its size, when its distance is known to us. Linear perspective is based upon the fact that the visual angle diminishes as the distance increases, and its principles may here be easily deduced. As our sight ranges equally in all directions, we see everything in reality as from the interior of a hollow sphere, of which our eye occupies the centre. Now in the first place, an infinite number of intersecting circles pass through the centre of this sphere in all directions, and the angles measured by the divisions of these circles are the possible angles of vision. In the second place, the sphere itself modifies its size according to the length of radius we give to it; therefore we may also imagine it as consisting of an infinity of concentric, transparent spheres. As all radii diverge, these concentric spheres augment in size in proportion to their distance from us, and the degrees of their sectional circles increase correspondingly: therefore the true size of the objects which occupy them likewise increases. Thus objects are larger or smaller according to the size of the spheres of which they occupy similar portions--say 10°--while their visual angle remains unchanged in both cases, leaving it therefore undecided, whether the 10° occupied by a given object belong to a sphere of 2 miles, or of 10 feet diameter. Conversely, if the size of the object has been ascertained, the number of degrees occupied by it will diminish in proportion to the distance and the size of the sphere to which we refer it, and all its outlines will contract in similar proportion. From this ensues the fundamental law of all perspective; for, as objects and the intervals between them must necessarily diminish in constant proportion to their distance from us, all their outlines thereby contracting, the result will be, that with increasing distance, what is above us will descend, what is below us will ascend, and all that lies at our sides will come nearer together. This progressive convergence, this linear perspective, no doubt enables us to estimate distances, so far as we have before us an uninterrupted succession of visibly connected objects; but we are not able to do this by means of the visual angle alone, for here the help of another datum is required by the Understanding, to act, in a sense, as commentary to the visual angle, by indicating more precisely the share we are to attribute to distance in that angle. Now there are four principal data of this kind, which I am about to specify. Thanks to these data, even where there is no linear perspective to guide us, if a man standing at a distance of 200 feet appears to me subtending a visual angle twenty-four times smaller than if he were only 2 feet off, I can nevertheless in most cases estimate his size correctly. All this proves once more that perception is not only a thing of the senses, but of the intellect also.--I will here add the following special and interesting fact in corroboration of what I have said about the basis of linear perspective as well as about the intellectual nature of all perception. When I have looked steadily at a coloured object with sharply defined outlines--say a red cross--long enough for the physiological image to form in my eye as a green cross, the further the surface on to which I project it, the larger it will appear to me: and _vice versa_. For the image itself occupies an unvarying portion of my retina, _i.e._ the portion originally affected by the red cross; therefore when referred outwards, or, in other words, recognised as the effect of an external object, it forms an unchanging visual angle, say of 2°. Now if, in this case, where all commentary to the visual angle is wanting, I remove it to a distant surface, with which I necessarily identify it as belonging to its effect, the cross will occupy 2° of a distant and therefore larger sphere, and is consequently large. If, on the other hand, I project the image on to a nearer object, it will occupy 2° of a smaller sphere, and is therefore small. The resulting perception is in both cases completely objective, quite like that of an external object; and as it proceeds from an entirely subjective reason (from the image having been excited in quite a different way), it thus confirms the intellectual character of all objective perception.--This phenomenon (which I distinctly remember to have been the first to notice, in 1815) forms the theme of an essay by Séguin, published in the "_Comptes rendus_" of the 2nd August, 1858, where it is served up as a new discovery, all sorts of absurd and distorted explanations of it being given. _Messieurs les illustres confrères_ let pass no opportunity for heaping experiment upon experiment, the more complicated the better. _Expérience!_ is their watchword; yet how rarely do we meet with any sound, genuine reflection upon the phenomena observed! _Expérience! expérience!_ followed by twaddle.

To return to the subsidiary data which act as commentaries to a given visual angle, we find foremost among them the _mutationes oculi internæ_, by means of which the eye adapts its refractory apparatus to various distances by increasing and diminishing the refraction. In what these modifications consist, has not yet been clearly ascertained. They have been sought in the increased convexity, now of the _cornea_, now of the crystalline _lens_; but the latest theory seems to me the most probable one, according to which the lens is moved backwards for distant vision and forwards for near vision, lateral pressure, in the latter case, giving it increased protuberance; so that the process would exactly resemble the mechanism of an opera-glass. Kepler, however, had, in the main, already expressed this theory, which may be found explained in A. Hueck's pamphlet, "Die Bewegung der Krystallinse," 1841. If we are not clearly conscious of these inner modifications of the eye, we have at any rate a certain feeling of them, and of this we immediately avail ourselves to estimate distances. As however these modifications are not available for the purposes of clear sight beyond the range of from about 7 inches to 16 feet, the Understanding is only able to apply this datum within those limits.

Beyond them, however, the second datum becomes available: that is to say, the _optic angle_, formed by the two optic axes, which we had occasion to explain when speaking of single vision. It is obvious that this optic angle becomes smaller, the further the object is removed: and _vice versa_. This different direction of the eyes, with respect to each other, does not take place without producing a slight sensation, of which we are nevertheless only in so far conscious as the Understanding makes use of it, as a datum, in estimating distances intuitively. By this datum we are not only enabled to cognize the distance, but the precise position of the object viewed, by means of the parallax of the eyes, which consists in each eye seeing the object in a slightly different direction; so that if we close one eye, the object seems to move. Thus it is not easy to snuff a candle with one eye shut, because this datum is then wanting. But as the direction of the eyes becomes parallel as soon as the distance of the object reaches or exceeds 200 feet, and as the optic angle consequently then ceases to exist, this datum only holds good within the said distance.

Beyond it, the Understanding has recourse to _atmospheric perspective_, which indicates a greater distance by means of the increasing dimness of all colours, of the appearance of physical blue in front of all dark objects (according to Göthe's perfectly correct and true theory of colours), and also of the growing indistinctness of all outlines. In Italy, where the atmosphere is very transparent, this datum loses its power and is apt to mislead: Tivoli, for instance, seems to be very near when seen from Frascati. On the other hand, all objects appear larger in a mist, which is an abnormal exaggeration of the datum; because our Understanding assumes them to be further from us.

Finally, there remains the estimation of distance by means of the size (known to us intuitively) of intervening objects, such as fields, woods, rivers, &c. &c. This mode of estimation is only applicable where there is uninterrupted succession: in other words, it can only be applied to terrestrial, not to celestial objects. Moreover, we have in general more practice in using it horizontally than vertically: a ball on the top of a tower 200 feet high appears much smaller to us than when lying on the ground 200 feet from us; because, in the latter case, we estimate the distance more accurately. When we see human beings in such a way, that what lies between them and ourselves is in a great measure hidden from our sight, they always appear strikingly small.

The fact that our Understanding assumes everything it perceives in a horizontal direction to be farther off, therefore larger, than what is seen in a vertical direction, must partly be attributed to this last mode of estimating distances, inasmuch as it only holds good when applied horizontally and to terrestrial objects; but partly also to our estimation of distances by atmospheric perspective, which is subject to similar conditions. This is why the moon seems so much larger on the horizon than at its zenith, although its visual angle accurately measured--that is, the image projected by it on to the eye--is not at all larger in one case than in the other; and this also accounts for the flattened appearance of the vault of the sky: that is to say, for its appearing to have greater horizontal than vertical extension. Both phenomena therefore are purely intellectual or cerebral, not optical. If it be objected, that even when at its zenith, the moon occasionally has a hazy appearance without seeming to be larger, we answer, that neither does it in that case appear red; for its haziness proceeds from a greater density of vapours, and is therefore of a different kind from that which proceeds from atmospheric perspective. To this may be added what I have already said: that we only apply this mode of estimating distances in a horizontal, not in a perpendicular, direction; besides, in this case, other correctives come into play. It is related of Saussure that, when on the Mont Blanc, he saw so enormous a moon rise, that, not recognising what it was, he fainted with terror.

The properties of the telescope and magnifying glass, on the other hand, depend upon a separate estimate according to the visual angle alone: _i.e._, that of size by distance, and of distance by size; because here the four other supplementary means of estimating distances are excluded. The telescope in reality magnifies objects, while it only seems to bring them nearer; because their size being known to us empirically, we here account for its apparent increase by a diminution of their distance from us. A house seen through a telescope, for instance, seems to be ten times nearer, not ten times larger, than seen with the naked eye. The magnifying glass, on the contrary, does not really magnify, but merely enables us to bring the object nearer to our eyes than would otherwise be possible; so that it only appears as large as it would at that distance even without the magnifying glass. In fact, we are prevented from seeing objects distinctly at less than from eight to ten inches' distance from our eyes, by the insufficient convexity of the ocular lens and cornea; but if we increase the refraction by substituting the convexity of the magnifying glass for that of the lens and cornea, we then obtain a clear image of objects even when they are as near as half an inch from our eyes. Objects thus seen in close proximity to us and in the size corresponding to that proximity, are transferred by our Understanding to the distance at which we naturally see distinctly, _i.e._ to about eight or ten inches from our eyes, and we then estimate their magnitude according to this distance and to the given visual angle.

I have entered thus fully into detail concerning all the different processes by which seeing is accomplished, in order to show clearly and irrefragably that the predominant factor in them is _the Understanding_, which, by conceiving each change as an _effect_ and referring that effect to its _cause_, produces the cerebral phenomenon of the objective world on the basis of the _à priori_ fundamental intuitions of Space and Time, for which it receives merely a few data from the senses. And moreover the Understanding effects this exclusively by means of its own peculiar form, the law of Causality; therefore quite directly and intuitively, without any assistance whatever from reflection--that is, from abstract knowledge by means of conceptions and of language, which are the materials of _secondary_ knowledge, _i.e._ of _thought_, therefore of _Reason_.

That this knowledge through the Understanding is independent of Reason's assistance, is shown even by the fact, that when, at any time, the Understanding attributes a given effect to a wrong cause, actually perceiving that cause, whereby _illusion_ arises, our Reason, however clearly it may recognise _in abstracto_ the true state of the matter, is nevertheless unable to assist the Understanding, and the illusion persists undisturbed in spite of that better knowledge. The above-mentioned phenomena of seeing and feeling double, which result from an abnormal position of the organs of touch and sight, are instances of such illusions; likewise the apparently increased size of the rising moon; the image which forms in the focus of a concave mirror and exactly resembles a solid body floating in space; the painted relievo which we take for real; the apparent motion of a shore or bridge on which we are standing, if a ship happens to pass along or beneath it; the seeming proximity of very lofty mountains, owing to the absence of atmospheric perspective, which is the result of the purity of the air round their summits. In these and in a multitude of similar cases, our Understanding takes for granted the existence of the usual cause with which it is conversant and forthwith perceives it, though our Reason has arrived at the truth by a different road; for, the knowledge of the Understanding being anterior to that of the Reason, the intellect remains inaccessible to the teaching of the Reason, and thus the _illusion_--that is, the deception of the Understanding--remains immovable; albeit _error_--that is, the deception of the Reason--is obviated.--That which is correctly known by the Understanding is _reality_: that which is correctly known by the Reason is _truth_, or in other terms, a judgment having a sufficient reason; _illusion_ (that which is wrongly perceived) we oppose to _reality_: _error_ (that which is wrongly thought) to _truth_.