Space, Time and Deity
3: The Order and Problems of Empirical Existence
Chapter 7: Appearances
Samuel Alexander
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Thing as synthesis of appearances, Problem III
CONSIDERED in itself, a thing is, we have seen, a portion of Space-Time with a certain contour of its own and a plan of configuration of the various motions which take place and are connected together within it. As a piece of Space-Time it has substance. As the whole within which the motions take place, it is the synthesis of them, and they are its changing and connected features or acts, or the accidents of its substance. This description applies equally to physical things and to minds, the whole and its details being in the case of mind enjoyed and not contemplated. The mind is the synthesis within its space and time of all the mind's acts or processes. The unifier which makes a thing a thing is its space-time. But considered as related to a mind and contemplated by it, a thing is seen, in the light of the general theory or hypothesis, to be a synthesis of sensa, percepta, images, memories, and thoughts or plans of configuration, whether of the whole or of parts of the whole. All these are partial objects which in their synthesis constitute the thing. The same result is arrived at from the deliverances of the mind itself. The thing as a whole is experienced as the synthesis of the various objects which in the course of the mind's experience of them (helped out by the experience of other minds) the mind finds integrated within the piece of Space-Time which is intuitively apprehended as that within which each partial object which belongs to the thing is found. Thus, for example, when a percept is identified with a memory, both the memory and the percept are discovered in the history of the mind to be
(184) unified within the space-time to which they both belong. Belonging as they do to different times, and unified by the same space, they are seen to belong to the one space-time of the thing. The mind in this experience enjoys correspondingly the unification of its acts of perceiving and remembering within its own space-time. Thus the synthesis characteristic of the thing is in no sense the work of the mind but discovered by it ; and the mind's own thinghood is the mind's own unity, which also it does not make, but is, or enjoys.
The kinds of appearances
But this synthesis of what really belongs to a thing is at the same time rejection of what does not belong to it. The thing is the synthesis or, if I may use without risk a simpler word; the sum or totality of its own parts. Considered as objects to a mind they may be called its real appearances, or its partial revelations to the mind. Moreover, they vary indefinitely according to the situation in time or place, or to the deficiencies, of the contemplating mind. It will be simplest to neglect for the moment these deficiencies of minds, such as we have in colour-blindness, for the objects selected by such defective minds are on the border between true or real appearances and illusory ones. Let us suppose standardised or normal minds. They will apprehend different real appearances of the thing in virtue of their position relatively to it in place and time ; and therefore it is all one whether we suppose different appearances presented to the same mind at different times in different places, or to several minds at the same time but at different places. The question of the unification of appearances to many minds comes later. These then are real appearances of the thing ; and whether sensa or images or thoughts, all alike are appearances, that is, partial revelations of the thing.
The appearances which do not belong to the thing itself are such as arise from the combination of the thing with other things, or from the intrusion of the mind of the observer into the observation. The first set of objects may be called mere appearances of the thing ; the second set, illusory appearances or illusions. Familiar
(185) examples of the first are the blue of a distant mountain, or the stick bent in water ; of the second, the colours seen by contrast, or the plane picture of a box seen solid. In the first case it is not the thing alone which we apprehend, but along with some other thing. Although in the widest sense there is only one 'thing' in the world, yet motions do cohere together in groups and form things, so that a plant is clearly a distinct thing from a stone ; and although what we shall call a thing is largely determined by our interest, so that a book is one thing from the bookseller's point of view and two or three hundred things or pages from a publisher's, yet also our interests are determined by the things, and we cannot help regarding the plant as a single thing. But it may be impossible to perceive a thing alone, and the foreign thing may distort the object and make it not a real appearance but a mere appearance. Illusory appearances always imply omission or addition or distortion owing to the abnormality of the percipient. Thus the thing itself accepts its real appearances and rejects mere appearances and illusory ones.
Now, it is the variability of the real appearances of a thing, such as, for instance, its varying hotness with the distance of the percipient, and the facts of mere appearance and illusory appearance which induce us to believe that appearances of physical things are mental and not non-mental objects. It is therefore of great importance to discriminate and discuss the different kinds of cases as briefly as is possible consistently with the great number of relevant data. I shall seek to show that in no case is the appearance mental. Even illusory appearances are non-mental. For they are prima facie on the same level as other physical appearances. The green we see on a grey patch by contrast with a red ground is as much non-mental and objective as the red. It is not an illusion that we see the green ; it is only an illusion that we perceive the grey paper green. An illusory appearance is illusory only in so far as it is supposed (whether instinctively in perception or by an act of judgment) to belong to the real thing of which it seems to be an appearance. In so far as it is
(186) illusory it is not a revelation of that thing at all but of something else. The illusion consists in the erroneous reference of it to where it does not in fact belong. But in itself the illusory appearance is as much object as the real appearance ; and only experience shows it to be misplaced. The difference between an illusory appearance and a mere appearance is that if it is wholly illusory it comes from the subject ; that is to say, whereas in the one case the distorting thing[1] is physical, in the other case it is the mind itself which produces the distortion.
It will, then, I think, appear that real appearances are indeed selected by the subject but are really contained in the thing ; that mere appearances arise from the failure to separate the thing from other) things with which it is combined as apprehended ; while illusory appearances arise from the introduction by the mind of new objects into the thing, or, what in certain cases comes under the same heading, the omission of objects which do belong to it. It should be premised that the distinction of illusory appearances from mere appearances is not always easy to carry out, and indeed in common usage the stick bent in water is spoken of as illusory, while I call it here a mere appearance. The real point of distinction is that a real appearance and a mere appearance really do belong to the things apprehended (though in the latter case not to the thing which seems alone to be apprehended) while an illusory appearance does not. It is introduced by the mind ; that is to say, there is some mental condition, not congenial to the true interpretation of the object, to which condition corresponds an object which is thus introduced into the true object and falsifies it. Illusions will consequently be conveniently treated along with the discussion of imagination, after the other kinds of variation. I shall begin with the simpler cases of sensations and pass from them to those of intuitions, which present much greater difficulty.
A simple example of variation of a real appearance is
Variations of real appearances: (1) due to position in place and time of percipient
(187) the change in the hotness of the fire as we move away from it, or in the brightness of a light. At the greater distance the illuminated thing affects the mind less according to a certain law. The mind, situated further off, selects a portion of the real brightness of the thing. The real bright colour of the thing is the quality and degree of the relevant movement which is in the thing. The quality does not change with the distance, other things remaining the same, but the brightness does. This selection, however, of the lower brightness from the real brightness does not mean that that real brightness is divisible into parts, as if intensities could be obtained by addition. It means simply that the distance of the eye (not the eye itself) secures that the larger intensity is apprehended as a lesser one. The larger intensity contains in this sense the lesser. The brightness contains all the degrees of brightness which are lower than itself on the scale. Or again the distance from a sound selects that amplitude of the same qualitative vibration which represents the diminished intensity produced by distance. For an ear at that distance the vibration has a diminished amplitude. We can therefore say the sounding body or the illuminated body contains these varying degrees of intensive quantity. The varying hotnesses of a hot body are less easy to understand. For heat is a 'localised ' sensation, and is not, like touch, both 'localised' and projected.' With eyes shut, we experience heat at our skin, and unless we also touch the object, in which case we project the heat also, we know nothing by heat of the hotness of the external body. So far as mere heat-sense goes, what we feel as our distance varies is merely changing degrees of hotness. It is when we are otherwise aware of the source of heat that we say the fire feels less hot at a distance ; as when for instance we first touch a hot brick and then feel it grow less hot as we retire. That we do select is verified by common speech, which does not say the fire is less hot when we move away, but less hot here. I am not able, therefore, to adopt, except with this reservation and with this interpretation, Mr. Nunn's statement that the fire possesses different hotness
(188) at different points,[2] as if the fire extended wherever we felt an impression of heat in our skins which we refer afterwards to the fire we see, or the candle flame we touch. The hotness of the fire resides in the fire itself. The hotness of the fire is in the fiery matter a real motion with its quality and intensity. When owing to the variation of our sensa we use instruments of measurement which are relatively independent of our senses, and at any rate independent of our sensation of heat, we measure the real hotness of the fire by the temperature.
These are the simplest illustrations of what is called the relativity of sensations, which is thought by some to mean that sensations are mental in character. In these cases, in fact, the mind in virtue of its position in space and time is affected by only a portion of the real characters of the thing revealed to it. The same explanation applies to other illustrations of the law, when we take into account that the selectiveness may be the result of the mind's organisation, or, what is the same thing, the organisation of the living organism which in a particular part is identical with the mind and wholly subserves it. Illusion is excluded at present, but it accounts for some cases which will be mentioned. The general statement is that because of the condition of the organism the real thing is apprehended only in part. Thus the familiar experience that if one hand has been in hot water and the other in cold, the same lukewarm water will seem cold to the one hand and hot to the other, arises from the previous alteration of the physiological zero of sensibility in the two hands. The degree of heat or cold felt depends on the difference between the real heat of the thing and the temperature of the hand itself. The water is really hotter than one hand and less hot than the other. The same thing happens when we change from winter to summer,
(189) and the body adapted to winter feels a slight warmth as if it were much greater. On the other hand, in the well-known paradox of sensation that, when a cold point of the skin, that is, a point specifically sensitive to cold, is touched by a hot metal point, we have the sensation of cold, we have illusory appearance. This is an illustration of the specific energy of the sensory nerves. When for any reason a certain part of the body is stimulated and a certain neural pattern of reaction ensues, that pattern of reaction is excited even by a disparate or inadequate stimulus. The mind then responds according to its normal method, and its object.is that which corresponds to such reaction. Here is a genuine illusory sensum due to the mind's own action. Such illusions are the price we pay for adaptation to our normal surroundings.
(2) due to varying sensitiveness
Some variations are due to the limits of the mind's susceptibility. Stimuli below the threshold of stimulation are not sensed at all. When two stimuli are apprehended together or in close succession their difference may not be sensed. Under these conditions the higher stimulus is not noticed to be different from the lower. The difference is there but not sensed, or at least not sensed as difference. In such cases the real thing, that is, the difference, does so far not reveal itself at all. This applies to all normal or standardised individuals. But sensitiveness varies in different individuals, whether it be sensitiveness to the intensity of a single stimulus or to difference of intensities of two stimuli. Or the defect of sensibility may be to quality of stimulus. A person may be tone-deaf and not distinguish the octave from its fundamental tone, or he may be colour-blind. Now in such cases of defect of sense for quality it is very difficult to say whether we are to attribute the variation to mere defect, so that what the person fails to sense is really present in the thing, only is not sensed, or are to set it down to illusion. It is impossible to say that the octave which is sensed not differently from the fundamental contains the fundamental, in the sense in which a higher intensity may contain the lower one. At most we can say that the real difference of quality is not sensed, and that so far as the note of
(190) higher pitch is taken to be of the same quality as the lower, the appearance is illusory, as in the case of the paradoxical sensation of cold from stimulation of a cold point by the hot rod. The two stimulations excite the same reaction, and correspondingly the sounds are heard identically.
The same difficulties arise in the case of colour-vision, and the discussion of them is more than ordinarily restricted for one who is not an expert in this department, because of the diversity of theories current in the 'subject. The extreme case is that of total colour-blindness where no colours are sensed but only brightness. Now, brightness is an ingredient of all colour-sensation, and such colour-blindness may be taken to be selection of a certain part of the real stimulus. The totally colour-blind person is in the position of a person the whole of whose retina is like the peripheral region of the normal person's, which also perceives only brightness. But here too there arise doubts, for the brightnesses which the abnormal person perceives in the various colours in full light are not in all respects agreeable to those of the normal man under the same conditions, but only when the colours are seen under a dim illumination which obliterates the colour for the normal eye also and leaves only greys. In ordinary red-green blindness, on one theory the patient simply confuses red and green because one of the substances,' the red and the green, in the retina is missing. This comes under the same head as tone-deafness, and is due to defect. On a different theory he sees neither red nor green but confuses the two because he really sees blue or yellow. The difficulty is especially strong on this second theory of supposing the confusion of quality to be other than a case of illusory appearance, due to the circumstance that the visual apparatus responds only in certain limited methods of response, whatever the quality of the stimulus. So in the normal person a colour seen as red when it falls on the centre of the retina changes to a brown in the middle zone of the retina, which is the appropriate response of vision to stimulation there.
Thus in many instances, and more particularly where
(191) variation of quality and not mere intensity is concerned, it may not be possible to attribute the variations to selection on the part of the mind from what actually is in the reality. There may be illusory appearance arising from the pre-adaptation of the mechanism which substitutes for the real sensum in the thing a sensum corresponding to the normal pattern of response. The real thing does not contain the substituted quality, but only it contains the foundation for thesubstituted quality. Thus defect may in such cases really act as illusion.
Mere appearances, Problem IV
Let us turn to mere appearances, of which illustrations have already been given. Here we do not sense the thing, of which we apprehend the mere appearance, taken by itself but in connection with some other thing which modifies it. What we sense or otherwise apprehend is not the thing by itself, but a new thing of which the thing forms a part ; and there is no reason to suppose that, illusion barred, the compound thing does not really possess what we sense. Thus the whistle of the express engine travelling away from us, to take Mr. Nunn's example, is die whistle of an engine in motion and has a different and lower note from a whistle at rest. The colour of the distant mountain is not the colour of the mountain alone but of the mountain and the atmosphere whose haze modifies the colour. Directly we know of the intervention of the modifying condition we cease to attribute the appearance to the thing itself. When we notice an opalescence in our glasses we know that the colours of things seen through them are not their own. Mr. Stout, who has rendered so great service to the discussion of these matters,[3] seems to treat all the sensible appearances of things, including their real appearances, as on the level of what I call mere appearances. For in real appearances one of the things which intervene between our apprehension and anything is our own body with its sense-organs. For us this position is unacceptable, because the action of the sense-organ is part of the process of sensing the
(192) sensum, not its object. The sense - organ cannot be treated merely as a thing which modifies the real thing in the way that motion added to a whistle modifies the pitch of its note, or as spectacles, them selves coloured, discolour objects around us. The distorting or qualifying thing must he either observed or observable in the sensible object. In truth, all appearances are prima facie real ones, and later are sorted out.
We conclude then, allowing for illusion, that the sensum in the thing itself is the qualitied configuration of real motion within the space-time itself of the thing, and that the real appearances of it are the whole or part of it as it is contained in the thing. It is only the selection which depends on the mind.
Variation in primary qualities. Real appearances
We come now to the variability of the shape, size, and position of things as they appear to the senses, that is to the varying appearances of the primary qualities of things which are not objects of sense at all but of intuition. By real shape I mean, in accordance with our hypothesis that things are complexes of space-time, the geometrical shape, and we have to account for its variation, in our experience of it. When a moment ago I spoke of sensa in the external thing as being real complexes of motion within it, I was speaking in the language of this hypothesis. The question of how we are aware of such motions did not arise, for in apprehending the quality and intensity of sensa we are not aware of their geometrical shape as extensive. But we have now to deal with the question direct, and as before we shall have to distinguish between real appearances of primary qualities and mere appearances and illusory ones. As an example of the first class let us take the familiar elliptic shape of the penny or the plate when seen sideways, or its varying size as the distance of the observer alters. As an example of the second, the stick bent in water, or the simpler instance of virtual images which we have in a looking-glass. I repeat an observation made before that from the point of view of knowledge it is indifferent whether we consider the contradictoriness of these appearances to various individuals
(193) at the same time or to one individual at different times.
As we move away from the plate at right angles to its centre the plate retains its circular shape but diminishes in size. Owing to the nature of the medium (and the illuminated plate does not exist without transmitting its light) the retinal image decreases and the coloured disc is seen in the corresponding size. It is seen as if it had the size of a smaller disc placed at normal distance for sight, which is, as James says, the distance at which it is conveniently touched ; which visual size we are in the habit of calling the real size as seen. The size of the visual object depends on the angle the thing subtends at the eye, because that determines the size of the retinal image. In saying that we see the plate as we should see a small plate situated at normal distance, I do not mean that we judge the size according to our usual experience. The size is not determined by any judgment but by what the actual size of a patch of colour at the actual distance of the plate is which corresponds to such and such a size of retinal excitation. The visual response in respect of the size, that is to say the intuitional response in respect of the extent of the thing which is called into play along with the colour excitement, has this seen size for its corresponding external object. It is not open to us to say, as may be thought natural, that we see the plate smaller at a distance because by experience we have learnt to connect the smaller retinal excitement with a smaller object. There is no precedent experience required, still less an act of judgment, comparable to that which enables us to interpret our sensations by ideas and so to fashion perceptions. The sight of the smaller visual object is immediate and sensory. To a smaller retinal excitement corresponds a smaller seen object, which is located where it is seen, namely, at the more distant place. We may if we choose call such a seen object an hallucination, but in that sense all sensation is equally hallucination. The large plate further off and the small plate near excite the same visual tract and are seen in equal size at their respective distances. The same plate when near and far
(194) excites different extents of retinal tract and is seen in different size. Custom may indeed produce illusion, and so may an inadequate stimulus, like that of the hot touch on a cold point, produce hallucination, but there is here no question either of custom or hallucination.
The distance of the eye then from the plate acts selectively as with the varying degrees of brightness. The size which we see is a portion of the real geometrical size of the plate (for I may leave out of account the enlargement of the plate when it is too near for accommodation and we see it with a halo round it), and the varying sizes are real appearances and contained within the real size.[4] The position of the eye, it might be thought, acts like the water in which a stick is seen bent, and the size is a mere appearance of the plate. But the position of the eye is not apprehended as the water is or the blue spectacles may be, and it merely acts, owing to the optical medium, as determining the mental selectiveness.
It may be urged, that the plate at a distance, when it looks small, is seen (not indeed in position as a whole but in its contour and extent) in a different place from its touch appearance ; and that this is accordingly contradictory to the proposition laid down as to intuition, that we do not apprehend different spaces of sight and touch and learn to co-ordinate them, but that we intuite the same space, and refer touches and colours to it as existing within it. But the apparent separateness of place does not in point of fact exist. We have only to hold the plate in our hands and move it away (which is the same thing as retiring from it) in order to assure ourselves that the touch and the colour of the plate are in the same place. The touch remains of the same felt extent ; the colour varies in size, but the seen contour of the plate coincides in place with the felt contour. I emphasise the words felt contour,' for it is not merely a case of seeing our hand shrink along with the plate, which of course it does to sight. This very simple experiment is of great
(195) importance for this and subsequent cases. For it shows that it is only in reference to Space as touched, and thought of in terms of touch, that the plate itself seems to shrink as it moves further off. Considered in themselves as purely visual objects (and they must be so regarded if we are to avoid confusion), the one patch of colour merely looks smaller than the other. If we know otherwise than by sight that they are appearances of the same thing we say that the thing shrinks to sight as it recedes. But if we do not know this, there is no thought of shrinkage. Now the experiment shows that the relative place of every part of the contour and of the interior of the contour remains the same place, and the extent is consequently the same. But if we suppose that touch conveys to us the real space, that is the relative place of every part of the thing, we naturally think that the eye misleads us. We might with equal right maintain that the touch in remaining constant is at fault. In fact neither is. There is a different vision of the one extent and shape under the different conditions, but it is still the same shape and size which is seen differently, that is the perspective is different.
The same considerations apply when the plate is seen obliquely. If it is turned round a vertical axis, the eye retaining its position, the horizontal axis shrinks and the circle becomes an ellipse with horizontal minor axis, for the horizontal diameter subtends a smaller angle at the eye than when seen from the front at the same distance. As the plate turns till it is end on, all the horizontal sections of the plate diminish and vanish and the plate is seen as a straight line. Thus, as before, the eye sees, owing to the selectiveness due to its position under the conditions of vision, only a portion of the geometrical horizontal sections of the plate. But though the space thus decreases for sight, the plate however elliptical it looks is still the same space as is touched ; a fact which is verified as before by holding the plate and turning it.
All perspectives, where the thing is seen without distortion by other conditions, follow the same plan. They are selected portions of the thing presented to
(196) sight, as in the instance of the plate. In this sense it is true to say that the real thing, in its intuitional character, is the totality of its perspectives, which are contained in it. It is not the " class of its perspectives " in the language of Mr. Russell, but it is that from which its perspectives are selected by the finite observer according to his position. It is the piece of real or geometrical space which synthesises all its perspectives. Perspectives(if no illusion or distortion creeps in) are not unreal because they are only perspectives ; they are partial, and the part need not falsify the whole from which it is taken, and if it is a spatial part it does not.[5]
Reason of the appearances
We have still to ask why it is that sight acts in this fashion, so as to apprehend a geometrical size at a greater distance as, in our language, a selection from the so-called real geometrical size which we touch, or which we see at a convenient touching distance. The above experiment, which shows that we see at a distance the whole 'extent which we touch at that distance, points the way. We have to go back to the fundamental character of any space that it is intrinsically temporal. What we see is an illuminated disc, whose various parts are at different dates because of the conditions of vision. The ends of the diameter are later than the centre. When the disc is moved off, its geometrical shape and size are unaltered, but its points as' illuminated alter their times with the distance. Simple geometry shows that at a greater distance the time-interval between the end and the centre is reduced, because the distance of the ends from the eye, the path which the light has to travel from them, is increased relatively less than the distance from the centre is. Consequently the ends are later than the centre by so much less when the disc is far off than when it is near. Thus while it is still the whole disc which is seen in its full geometrical extent, that extent looks smaller because it is filled with the qualitied events of illumination and is only apprehended through them. We see a smaller
(197) disc because the disc occupies less time under the conditions of vision. Were it not for these conditions there would be no such appearance.[6]
Mere spatial appearances
We come next to the mere appearances of spatial characters of things due to the presence along with the thing of another thing. In the looking-glass (which is supposed flawless) there is no distortion of the luminous point or thing in colour or brightness. The mirror is a contrivance for seeing things not visible directly by the eye, such as one's own face, and the object seen is called a virtual image because its position in touch-Space is that from which the rays of light would come if the real luminous point were there. But the seen image is a genuine sensum, seen under this arrangement.
It may be noted in passing that such virtual images, whether of oneself in a mirror or a stick in water, afford us an excellent commentary on the statement that a memory is the revelation of a past event as past. The optical image is not actual or, as is said, real,' but only virtual,' and is thus next door to an image in the psychological sense. The difference is that it is sensory, but it is still an actual revelation of the thing by the help of the mirror. Now in memory Time takes the place of the mirror, and it is a distorting memory to boot. There is no sensum present, only an image, but that image is the past object revealed, just as the virtual image in the mirror is the actual present object revealed. There is however a further difference which is vital. The mirror is separable from the thing it reflects. Time, however, is an essential part of the object remembered. Consequently the memories of a thing or event are its real and
(198) not its mere appearances, except so far as Time introduces foreign objects as well. Accordingly the memory is apprehended as past, as containing Time, whereas the mirror itself is no part of the face seen in it. This arraying of different facts in their likeness and unlikeness may be helpful to the understanding of all of them alike.
The mere appearance in this example belongs to the place of the image which seems, in reference to the Space which is touched, and also seen without the mirror, to be displaced to a point behind the mirror. We cannot say here that we see, as in the first set of examples, only a part of the real thing. We see the real thing exactly as it is, only it is displaced.[7] A baby may feel for the thing behind the mirror. In a well-known observation, a boy blind from a few days after birth but later at seven relieved of the cataract did the same thing. For visual Space is measured by the Space we touch. The displacement is due to the mirror, not to the selecting mind. Yet in spite of this displacement we have not two places, one visual, and one tactual, but one place which is seen luminous by the eye and may be felt by touch. Another metaphysical experiment, so simple that to call it an experiment seems ridiculous, demonstrates this. Stand before the mirror and touch your shoulder or anything which you do not see with the eye direct, but only see along with the finger in the mirror ; and then ask yourself whether the touch you feel and the colour you see are not in the same place, felt in the one case and seen in the other.[8] If you touch a thing like a pencil which is in front of you, so that you see it direct and also in the mirror, the judgment is troubled. For the virtual image is only seen with the help of the mirror, and the real pencil is seen as well as touched ; and there are thus two visions of Space at once. In the same way in the classical example of pushing one eye outwards and thus with the two eyes seeing a candlestick double, if you touch the candlestick and then observe alternately with
(199)either eye, you at once feel and see the candlestick in either case in the same place ; but with both eyes open there is the disturbing fact of two visual appearances of Space, and the feel is located with the object of the undisturbed eye. It is only when we have the normal visual intuition of Space, that is the bare intuition of it without an intervening apparatus, that we alise that the displacement in the mirror is a displacement at all and a mere appearance. In the Space of touch and normal sight the whole of the space in front of the mirror which is not seen direct by the eye is as it were swung round so as to seem behind the mirror. But it is the same space under this mere appearance. I imagine that if mirrors were organic to us and part of our visual apparatus we should have the same view of the world as we have now, and we should localise the touches of things and the colours of them precisely as we do at present. At any rate the displacement is a mere appearance of the primary characters of the thing seen, because we do not at present see the thing by itself but in its combination with a mirror. The displacement is a real character of that combination, and so when everything is treated equally no difficulty arises.
I cannot help confessing here how much simpler it would be and how much laborious explanation it would save, if only it were true that our intuitions and sensations were mental as is commonly supposed, and how easy it is compared with our procedure to refer all these variations in part to the mind or its body. The way of sin is always easy and that of virtue difficult. But in the end the easy road leads, it is said, to destruction ; and it is so here. We should be living in a world of sensations, which would be hallucinations, and of images ; some would be veridical and some not. But we could only discriminate the veridical ones by means of sensation, that is by other hallucinations. For it is of no use to urge that our appearances are partly determined by the thing and partly by our bodies. How shall we know what part is due to things except through observation, for which in turn we are dependent in part upon our bodies ? We are reduced to a world of consistent hallucination. But we
(200) cannot pass from it to a world of things independent of our individual selves except by recourse to such means as were adopted by Berkeley, of assuming a God who impressed these hallucinations upon us, an assumption necessary if things are to be independent of the single individual, but otherwise rather the statement of the problem than a solution of it. Or we may suppose that thought informs us of a world of things to which our appearances are the guide. But I do not know how that thought could have experience of its object or what sort of an object it could be ; and indeed the real world remains in this way an unknown. I cannot help adding that it deserves to remain so.
How there can be mistakes in space-perception
But we are faced with a grave problem of our own. We saw that we apprehend spatial characters by intuition, because the sensory stimulus excited places in our brains which as being attended by consciousness were aware of the space of the object. No local signs are needed because the place of our sensation in the mind is aware of the place of the object sensed. How then, it may be asked, can our intuitions ever vary as they do, whether there are distorting additions to the thing perceived or not ? The monad correlated with any point of the retina, that is the point-instant which is situated at the point of the visual region of the brain corresponding to that retinal point, is in communication with every point-instant in Space-Time, and it is aware of or knows ' the line of advance of the light from the real thing to the eye. Why then should the diminution of the retinal image as the eye recedes from the disc make any difference to the intuition of the disc's size or of its place in tactual Space, which is the same real Space as the visual one ? Or again, with the mirror, why does the monad stimulated in the brain by a point of light not follow the light and, knowing whence it came, see the thing reflected in the mirror where it is in reality, or geometrically ? The answer is got by considering the difference between the 'knowledge ' (in the extended or metaphorical sense of that term) which a point-instant or any complex of them
(201) possesses as being merely spatio-temporal, and the consciousness in the strict sense which only belongs to them in virtue of being thrown into action by a sensory or other stimulation. The monad as such, as a mere point-instant, is infallible and any complex of them infallible : that is, in reference to Space-Time and its elements and whatever complexities there may be in it of a purely spatio-temporal and non-qualitative character. But when a piece of Space-Time is awakened into consciousness, and this is of course not possible in fact to a single monad but only to a complex of them, the case is different. As having consciousness, that is as having that quality, they are limited by the conditions under which their consciousness is evoked, and in ourselves consciousness is evoked in the first instance through sensation, though intuition pure and simple is more elementary than sensation. Hence the consciousness belonging to a piece of neural (that is mental) space is limited to the object which is presented in sensation. Though it possesses perfect knowledge,' as spatiotemporal, of all parts of Space-Time, it is conscious only of the space and time of its object, and that object is a sensory one as well, and has secondary as well as primary qualities. Thus we have intuition in vision only of the primary qualities of the visual object, and we intuite, not place or shape or size in and for itself, but the place, shape, and size of a colour, that is which is occupied by colour. The parts of the optic centre affected by the coloured patch of my face seen in the mirror do not know the real place of the face but the place of the colour seen, and they suffer variation or distortion or displacement in accordance with that of the colour. When the colour of the disc shrinks in extent with the distance, it is that extent of which the intuition is conscious.
Thus our intuitions are affected by whatever conditions affect the perception by sense of a thing. Illusion being excluded, the sensa are determined by the thing itself taken along with the medium by which its sensa are transmitted and without which as in colour the sensa would not exist, for there are no colours in the absence of illumination ; or else they are determined by the
(202) participation of some other thing in the total which is contemplated. The body and mind of the percipient act only selectively and do not determine the nature of the sensum. The mirror then is a contrivance by which I can see my shoulder which is otherwise invisible. The rays from a luminous point are deflected from their course and the thing is seen where seen—not in its geometrical place, which is equivalent on the whole to the place of Space which is apprehended by the touch or undisturbed eye. The conditions of direct vision are such that rays of light proceed to the eye from the luminous point. By the mirror the rays of light which reach the eye produce the same effect on the eye as rays proceeding from a point behind the mirror in geometrical Space. For vision then the space in front of the mirror is displaced by the mirror. This is the consequence of a contrivance necessary for seeing the colour at all. Hence the intuition of the place follows the conditions which determine the sensing of the colour.
We are now in face of the solution of the problem. The senses are not adapted to perceive Space but to perceive the quality of their own specific secondary qualities. The eye is not an organ for apprehending Space but colour. The apprehension of Space is a concomitant incident and is not the work of vision but of the space of the nerve centres, or of the mind, provoked into consciousness through sensory stimulation. Now the price we pay for having our intuitions of Space aroused through sense is that they are subject to whatever variations may be necessary for the proper business of vision. The same thing is true of the other senses as well, but is operative in different degrees. The proper object of the skin is pressure, not form or size ; of the ears sound, and not the place of it. But the nature of the medium which renders the object at once what it is and sensible to our sense-organs affects our intuition of its primary qualities. In order that we may see the colours of a disc at a distance clearly the angle subtended at our eye according to the laws which the medium obeys grows smaller ; and the like. Sight is indeed a finely discrimin-
(203)-ative means of intuiting place and form, more so than touch, and while touch remains the standard sense, sight is used in optical instruments to help out touch. But the laws of the medium subject the intuition of Space to the conditions which affect the sensing of colour, and thus produce variability of appearance in a high degree. Hearing is notoriously uncertain in its deliverances as to locality. Touch on the other hand is in contact with the thing, so far as the contact is complete—and it never is. Hence relatively to sight, we attain by touch a closer approximation to real or geometrical space than by sight. For other reasons than his we can echo the poet Lucretius, who when he mentions touch becomes lyrical and appeals to Heaven. Tactus enim, tactus, pro divum numina sancta.
The superiority of touch
Hence it is, namely on account of its relative freedom from variation as compared with the other senses, that in respect of the apprehension of primary qualities which it does not indeed supply but mediates, touch is used as the standard sense. We call then the real shape of the object, as we see it, that which we see when the look of the thing coincides with its touched appearance. When the touch is circular the real visual shape is taken to be the circular one ; and in general it is the one we have of the object when seen from the front at about touching distance. Every visual shape belongs to the thing as well as this. But this particular shape is found to be the one whose possession accounts for the others as partial appearances of it, and is thus the foundation of them. If the disc were geometrically elliptic it would not be seen in the actual elliptic form it has when seen obliquely. But if it is really circular it would be. Moreover if it were seen circular from the side it could not be really circular. When once we have established a particular visual appearance as the closest approximation by sight to the geometrical character of the object, we can go on and draw inferences as to the geometrical character of the thing from its appearance under optical instruments like magnifying glasses or microscopes.
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Touch does but give us the closest approximation we can get through the naked senses to the real primary qualities of things.[9] It is itself by no means a perfect messenger of the outside world. It varies in discriminativeness for place at different parts of the skin. Thus outlines are more delicately apprehended by the lips than by the fingers, or by the fingers of a blind man, which are trained, than by the fingers of a normal person. On this varying discriminativeness are founded various illusory judgments, as when two compass points passing from the cheek so as to touch the two lips seem to move apart. Mistakes of judgment are mixed up in these phenomena as elsewhere, e.g. the familiar experience of seeming to touch two things and not a single one when two fingers are crossed, the so-called paradox of Aristotle. Even apart from all illusions whether of perception or judgment we have such variations as the one mentioned previously, that two touched points feel further apart than if the interval between them also contains touched points. Now the superiority of touch over sight, in general, is due to the nature of its object, which does not need like colour a medium but is conveyed to the body direct. Hence the variations in the case of touch appear to be due in the main to defect on the part of the sense-organ and not to any requirements like those of sight which produce alteration or distortion in the sense-object. Thus a polygon with a large number of sides may be indistinguishable to the feel from a circle. The polygon's contour has slightly projecting points, but the difference from the smooth circle is below the threshold of discrimination in respect of the intensity of the pressure, and the touch cannot discriminate their place either. That is, the point of the polygon and the point which corresponds to it on the circle fail when they are felt together or in close succession to evoke in the touch centres a consciousness which is aware of difference of locality. They may even fail to affect actually different places, owing to the arrangement of the nerve fibres to various places. Thus the circle and the polygon are
(205) confused much in the same way as two intensities of a quality of sense are confused. The case is one of defective receptivity for the external world and not of illusory appearance. That defectiveness is owing to the dependence of the places in the brain which apprehend locality upon the qualitative sense-excitements which let in the intuitions.
Correctives of defects of intuition
All our intuitions thus bear the defects of our senses. This is the disability under which we labour, which compensates the privilege of consciousness and the greater wealth of revelation which consciousness renders possible. We can sense the qualities of matter and life, but the price we pay is that we are denied the exact awareness of Space-Time which every monad has. This disability is not confined to the conscious order of existents but to every order above that of bare Space-Time. Complexity of space-time, when it carries with it in the empirical order of the world's development an empirical quality, means also that the being endowed with that quality is shut off from perfect apprehension of Space-Time. For he apprehends it, as we through consciousness, so he through his own acts with his distinctive character, and is limited by their conditions as we by sense-perception. It is only the bare point-instant, the element of motion or Space-Time, which is in sympathetic communion with the places and shapes and sizes of things. In this respect the mere monad or point-instant knows' Space-Time better than Newton or Laplace or Mr. Russell. Your monad is your only natural mathematician, who neither has nor needs the science of mathematics, but lives mathematically, and consorts so with his fellows. For point-instants are related to one another, so far as may be, as minds are with one another, and they know each other by sympathy. Yet this is not knowledge or intuition of Space-Time, for point-instants can no more contemplate each other than we can each other, and there is nothing below them for them to contemplate. They have no science. But what is perfect and exact communion for them is unattainable by us. We cannot
(206) contemplate primary qualities in their exact being, but we can have science of them and that science is mathematics. Thought in the form of mathematical science takes us back indirectly to what the monads or point-instants know directly. We in a manner get rid of our consciousness and go back to a more primitive condition.
Our remedy for the disabilities under which our intuitions labour is found in our capacity for reflection, for contemplating not merely the particular but the law of its configuration. This capacity helps us in two ways. Being aware of deviations of particular observations from real spatio-temporal fact, it invents instruments to make the observations more exact (both in respect of the primary and the secondary qualities) ; and though we are in the end always dependent on our senses for the observations, it devises methods, for controlling the instruments themselves and for cancelling errors of the observer, which as far as possible make us independent of our own defects. In the next place it invents science, and in particular in respect of intuition it makes mathematics. For the minute first-hand and perfect acquaintance which the monad has of the world, it substitutes spatiotemporal laws as contained in arithmetic and geometry, and their progeny. Exact intuitions of things being unattainable and also useless, it gives us something better and more valuable. Mathematics is thus engendered from the defects of our intuitions, as the other sciences from the defects of our senses. And it is the fundamental science because it deals with the fundamental material of which all qualities represent complexities. It does not as we have seen before differ from other sciences except in this simplicity of its material. Not in virtue of the hypothetical character of triangles or numbers ; for all science is conversant in like manner with such hypotheticals, and these hypotheticals are not inventions of the mind but, so far as valid, universals in things—realities therefore, so far as established, and not mere hypotheses. Not because of its alleged a priori character. For in fact it is experimental and deals with empirical determinations of Space-Time like triangles or integers or irrationals. It
(207)is only its material which is a priori and not its methods. The material is a priori because it is categorial ; and mathematics is unlike metaphysics in that it does not explain what Space and Time are but is concerned only with the discovery and inter-connection of its empirical determinations. So understood it remains the basal science ; and being unencumbered with regard for qualities it is concerned only with the laws of intuitional objects.
Nothing however can he further from the truth than the doctrine inherited from Locke that our ideas of primary qualities resemble their originals in things, while those of secondary qualities do not. The language of representation is not available for us and indeed is universally obsolete. For us ideas are things or partial selections from them (and, if we include imaginations and illusions, rearrangements of them), and we are at one with Berkeley except that whereas for him things were ideas and there are no things which were not ideas, for us reversely there are no ideas which are not, or do not belong to, things. But let us for a moment retain the Lockeian conception of copying. It is then untrue that our intuitions are exact copies of things any more than our ideas of secondary qualities are. We are not less bantered by our intuitions than by our senses, and we are so because we cannot rid ourselves of the defects of our senses. It is true that our intuitions never deceive us as to quality ; but that is because in the strict sense they have no quality, being merely spatio-temporal. But otherwise they are never copies just because they are provoked in our apprehension by the sensing of the sense-qualities. If we are to choose we must rather say that we are nearer to reality in our sensations of secondary qualities than in our intuitions of primary ones. For in respect of the one we are cheated at first hand and with respect to the others at second hand. In the one case we are cheated, when we are cheated, by the principal ; in respect of the other we are cheated by an innocent person who is compelled to be a confederate. Our senses only cheat us by their weakness and partiality
(208)of selection, but our intuitions cheat us because our senses are cheats.
I have thought it tedious to introduce into this discussion the variations of our intuitions of Time. There too we are restrained by the senses without the mediation of which time-intuitions would not be evoked. Very largely the variations in the appearances of Time are matters of illusion and the effect of past experience, as in the familiar illusions of the varying durations of our experiences in actual occurrence or in retrospect.
I end by repeating an observation with which I began ; that all these variations of sense or intuition are but illustrations of what arises out of the relation of finites of any kind to one another according to their position in space and time, and the limitations of their organisation which prescribe how much shall be revealed to them and how much not. The history of our experience of these variations of them verifies in the special case of minds a universal rule. This is the really important result for us of the inquiry.
