2. We must, therefore, face the question: If phenomenal space is `constructed', how is it constructed? As we do not directly apprehend space (and things in it), how can what we do directly apprehend `amount to' (for us) the perception of physical objects in space?

a. It should be useful here to consider three, plainly interrelated yet distinct, concepts: materialness, physicalness and spatialness -

i) We generally use the term ` matter' in a `mind and matter' kind of way to refer to that which is there to be perceived [Note the relevance of this to the other, extended, uses of `matter' as in `the matter in hand' or `Does it really matter?'] So matter is for us that which occupies space.

ii)Our use of `physical' is somewhat broader; to be physical it is sufficient that something occurs in space - so that we tend to think of physical events occurring to material objects. Parallel with our simplistic distinction between mind and matter, we have a, possibly less simplistic, distinction between the mental and the physical. To characterise something as physical is to assert that it is subject to the `laws of physics' - though this does not help since we define laws of physics in terms of physical events. We might say that, whilst material objects have dimensions, physical events involve dimensions.

iii) And the dimensions in question are spatial dimensions. To characterise X as spatial is to assert that it is related to Y in a spatial-dimensions way. What we are talking of then, as spatial, is a potential for physical occupancy by material objects.

i) If such conceptual extrapolation were possible for us, then we could have concepts of 4th, 5th, 6th dimensions - which we certainly have not. Indeed `4th dimension' has become a cliche for the mysterious, the necessarily unknowable.

ii) More importantly, we do not `build up'; we `break down'. Two dimensions (area) is intelligible to us only as the surface of a three-dimensional object. One dimension (distance) is intelligible only as the distance between three-dimensional objects. Until we can conceive three-dimensional-ness we cannot conceive dimensionalness at all. In the new-born infant experience nothing is above or below or left of or right of anything else any more than it is nearer or further away than anything else. Aboveness and rightness/leftness are intelligible only in terms of a three-dimensional world. Indeed, `What would be the top and what the bottom in a two-dimensional world?' is the same kind of non-question as `What colour does the blind man see everything as?'! So it is quite wrong to think of a visual (or any other kind of) appearance as two-dimensional; as appearance it is not dimensional at all.

Here anyone who likes `practical exercises' may try putting an arm behind his or her back and moving it, outstretched, from the shoulder until it bumps against a table or some such. We perceive that the arm moves through space - but there is nothing remotely spatial in the kinaesthetic and tactile appearances, in the experience per-se, from which we make this perceptual judgement. Unless we already had a concept of three-dimensionalness, such a judgement would not be possible; nothing can be a sign for anyone for a situation of which he has no concept.

d. We said people perceive that their arms move through space. It seems that the concepts of space and of motion are interdependent - or, should we claim only that the concept of motion is dependent upon the concept of space? Movement must be from one place to another; without the assumption of spatial relationships nothing could count as movement. Here refer back to Topic 10, 1. b. - changes within presented appearances do certainly occur, we could not perceive events if they did not, but such changes can count as movements only as and when we see the appearance as a state of affairs in a spatial (three-dimensional) world.

The recognition that there is certainly a logical relationship between the concepts of space and motion - whether it be an interdependence or merely a dependence - gives rise to two questions:

i) If we did have some direct acquaintance of a sensory kind with motion as such (as has been suggested many times), would this provide the concept (we have) of space? and -

ii) If we had no experience of motion, could we ever gain the concept (we have) of space, i.e.of three-dimensionalness?

It should be apparent that, in answering these questions, we will determine whether the relationship is indeed an inter-dependence or merely a dependence. We shall consider i) now and defer consideration of ii) until we have done a little more groundwork.

We need to ask: Does the idea of a sense of motion make sense? And, insofar as it could make sense, what (mode of) experience would it give us? It is certainly difficult to conceive; being in motion would have to be a sensible quality of things in the same way as being red, or noisy, or hard or smelly is a sensible quality of things and it just doesn't seem to be like that. We must acknowledge, of course, the problem about using perception words for sensory (per-se) experiences - and recognise also that for somebody born blind the notion of colour is just as mysterious and unattainable. But that blind man has no idea of colour - though he has of the objects which (he is told) are coloured - whereas we do have an idea of motion (as distinct from the idea of the objects which move) and one which just does not seem to be related to any given sense mode. The motion we see is not a different motion from the motion we feel.

Let us not be too cavalier about it; we have allowed that there could be any number of other senses. But only (here refer back to Topic 9 4. c)) insofar as such senses were characterised by that unique uniqueness - that data-presenting function. So that, if there were another sense, one which (with our language problem) we found ourselves calling a sense of motion (as we might say `a sense of seeing'), it could only give us the same kind of data as all other senses do - a structured diversity in yet another mode. We could, thereby, have enhanced access to the perception of changes (just as a blind man who regains his sight has enhanced access) - but this would not turn the changes perceived into motion; it would simply provide another way of perceiving motion (a new and different set of signs) - once a concept of motion had been developed.



3. So - having rejected the shortcut of a direct sensory perception of motion and accepted that the concept we have of space must, in some way, be constructed by us from the ordinary, familiar range of sense-experience, we must consider in what way, by what process, that concept can be gained from that experience. To attempt this, we should be as clear as possible about what the concept in question is.

a. It is a useful starting point to consider how we do in fact talk about space, how we commonly use the term `space' -

i) We have all seen billboards which announce `This space to let'. This, at the very least, implies that space is something worth paying money for - consider also parking- spaces. So it should be clear that we are talking about a something, not a nothing - an entity, not an absence of any entity.

ii) We often describe homes, shops, parks, even cities, as spacious. We mean by this that there is ample room to move about in them and to deposit the things we need to deposit.

iii) We talk of spacing (single or double) when we typewrite. Here we are concerned with how many entities (in this case typed words) are placed on a given quantity of paper.

iv) We ask: `Is there space in the refrigerator for a flagon of wine?' Will this physical object fit into that physical object?

The common feature of most common usages is very plainly `room to put something'. Nearly always when we speak of space we are speaking of a potential for occupancy - of a physical entity by a physical entity.

b. But, as established, a space is something, not nothing - and when it is occupied, it does not cease to exist; it simply becomes an occupied space as distinct from an unoccupied one. If you called up to the conductor `Is there any space on the bus?' and he replied `Yes, a lot - but it's full of people', you would probably be quite annoyed - but the conductor would in fact be right; his bus is a fully occupied space.

Now, an occupied space just is a physical object. Here refer back to Identity: any physical object (as such) is the particular physical object that it is by virtue of its space/time-track - i.e. the occupancy of contiguous volumes of space (spaces) through a continuity of time. So - our (phenomenal) external world - as a physical entity - consists of filled and empty spaces - and

i) It is only the filled spaces (the physical objects) that we perceive - or, more properly, that `have sensible qualities', enabling us to perceive that....(whatever).

ii) One of the things which we do, thereby, perceive is that there are empty spaces between the filled spaces - i.e. a potential for occupancy currently not realised (room to put something).

So, filled spaces are bounded by empty spaces, and empty spaces are bounded by filled spaces.

c. Now, you should have noticed that we have been talking about spaces, finite (bounded) entities, not about `Space'. This is why it has been possible to say simple, and fairly obvious, things in a quite intelligible way.

Unfortunately, when people try to talk (or to think) about Space (which seems to demand a capital letter!), they attempt to treat it both as an entity (an object of perception) and as an infinity - an endless progression. Since an infinite entity is plainly an absurdity, they inevitably end in confusion.

The very term `Space' is basically misleading - in much the same way as we found the terms `Truth' and `Knowledge' to be misleading. It somehow suggests a kind of `super-entity' which contains all physical objects yet is, itself, not contained at all. Yet the very concept of containment is intelligible only in terms of one finite entity contained by (i.e. limited to within) another finite entity. And if one of these entities is a physical object, then the other must also be a physical object (i.e. something perceivable through the interpretation of sensory experience). A finite object cannot be contained by an infinity!

Failure to recognise this can lead to the asking of some very silly (pseudo)- questions such as -

i) How vast is Space? - What are we comparing it with? A big flea is much smaller than a small elephant. If someone asks `How big is your car?' he will be told `Big', ` Small', `Medium' or whatever within the framework of the familiar range of car sizes. We can compare spaces with other spaces, but nothing could count as the size of `Space'.

ii) What is beyond Space? - Since `beyond' is here used as a spatial term, the only thing that could be `beyond space' is another space - but then, of course, it would not be beyond it - it would just be it.

iii) When do we reach Outer Space? - Outer to what? We can distinguish easily enough between the inner space and the outer space of a cupboard (what goes in behind the cupboard doors and what has to sit on top). By a slight extension of this we can, so long as we are thinking of this planet, the world, talk fairly intelligibly of those volumes beyond the world's normal orbit as `outer space'. But always there must be a reference-point for inner/outer-ness and an assumption of containment - the space between the earth's orbit and the sun or whatever.

iv) What if everything doubled in size overnight; how could we know? - We couldn't know because there would be nothing to know. Size (spatial magnitude) is intelligible only as the relative magnitude of filled and empty spaces.

These may seem childishly obvious points, yet all too often people fail to see the implication of them. Since space is (spaces are) measurable only in terms of occupants of space (physical objects), space exists only by virtue of its partial occupancy. There could be no such thing as totally empty space there would simply be nothing (or, more properly, not be anything) - and space is not nothing.

d. Let us be clear then, that when we talk of space we are talking of particular spaces, particular instances of spatialness - in just the same way as when we talk of fruit we are talking of particular instances of fruitness; ` infinite space' makes no more sense than `infinite fruit'. Just as we gain our concept of fruitness from our perceptual experience of (that which is common to) particular bananas, apples, oranges and so on, we gain our concept of spatialness from our perceptual experience of (that which is common to) particular filled and empty spaces. And - once again - the experienced states of affairs from which any (universal) concept is (or could have been) abstracted are then regarded as the instances of that universal kind.

There is no more need for a space of which all spaces are bits than for a cat of which all cats are bits. So - there is nothing mysterious about our having a concept (effectively equivalent concepts) of spatialness - provided only that we can and do perceive particular spaces as three-dimensional objects. Since spatialness is three-dimensional-ness, the experience we must have is of a structure, manifested to us within apperances per-se, which counts for us as three-dimensionalness.

As it is the filled spaces, not the empty ones, which `have sensible qualities', we should turn our attention to the perception of the physicality of physical objects.



4. Our problem is that, although we have got rid of the nonsenses about infinite space and such and settled for the quite manageable, inter-related, concepts of spatialness, physical- object-ness and three-dimensionalness, their very inter-relation presents us with what seems to be, prima-facie, a chicken-and-egg problem.

a. Once we have a concept of spatialness (or three- dimensionalness) there is no problem about identifying certain experiences as of physical objects - i.e. three-dimensional objects. Three-dimensionalness just is the characteristic of any space, filled or empty. And a physical object is an occupant of space. But, having dismissed any notion of `direct acquaintance' with space, we have found ourselves obliged to explain the concept of spatialness as abstracted from the physicality (the three-dimensionalness) of occupied (and, by extension, occupiable) spaces. Thus, unless we can somehow account for the perception of physical objects (as three-dimensional) without any reference to the occupancy of space, then we are looking at the same kind of circular reasoning as defining husbands in terms of wives and wives in terms of husbands without any reference to (or concept of) the institution of marriage. [We may well be reminded of the old song about the hole in the bucket - which could be repaired only if it didn't exist.]

b. We must, therefore, try - however difficult it may be - to think back to primitive experience and consider what, within that experience, could count as the perception of a physical (three-dimensional) object without the benefit of any prior concept of spatialness to `see this as an instance of'. Let us be quite clear about what the problem is: X cannot be a sign of Y for Z unless and until Z has a concept of Y-ness. Therefore, if the perception of X as such depended on its being recognised as a Y, the process could never get starteds. We must, therefore, be able to give some account of perceiving a physical object as three- dimensional - or,more properly, perceiving that an object is three-dimensional (i.e. a physical object) - in terms solely of presented appearances (per-se) and further predicted appearances (per-se).

c. A first attempt to do this might well involve the notion of solidity - solid-ness. How is this experienced?

i) We generally use the term `solid' to distinguish between different kinds of substances, to distinguish gases and liquids from those which are `hard all the way through'. [The once-popular term `impenetrable' doesn't really help much because, under sufficient pressure, any substance is penetrable]. But plainly this use is inappropriate; gases and liquids occupy space in just the same way as so-called solids do. So the only notion of solidness which is appropriate must be the notion of presenting a surface which is sensorily perceptible (not necessarily in visual sensing).

ii) But the notion of surface is intelligible only as the surface of a three-dimensional object. There must, as it were, be somethlng behlnd it. [Here it should be noted that, in these terms, even a vacuum (a genuinely unoccupied space) presents a surface - the `inner surface' of whatever (occupied space) contains the vacuum].

Think also of the `hard right through'. In discovering that anything is hard right through (as distinct from merely surmising this) what we are doing is experiencing a succession of different hard surfaces. The point is that we never could directly perceive (as `within the appearance') the `something behind it' because (of necessity) the surface would always get in the way. [Think about that `of necessity'; this is not something we discover to our chagrin, it is a matter of what counts as a surface.]

iii) We also use `solid' to distinguish from `hollow'. Here think about a golfball and a ping-pong ball; normally we would judge them to be solid and hollow respectively by their weight but, if we were asked to `prove' it (i.e. to persuade a sceptic that it were so - refer back to Topic 3), we would probably cut both balls in two to show their insides. This is fine, so long as we already have a concept of solidness. What we are now presented with are two new surfaces, one of which is flat and the other concave. But flatness and concaveness are spatial concepts - they are what we judge things to be when we are already thinking in spatial-relation terms. A (flat) photograph would present the same surfaces in the same way and enable us to make exactly the same judgement. There is nothing either flat or concave in the appearance per-se. And exactly the same applies to tactile access to the two surfaces; the experience, the appearing, just is how it is. Here it is pertinent to think about illusion - it is always possible to misjudge the physical shape presented without necessarily misjudging the structure of the appearance itself.

So, solidness does not provide any shortcut to the gaining of the concept (which we all do gain very quickly) of physical- object-ness. It is only when we have that concept that we can use `solid' to make useful distinctions between kinds of physical objects.

d. The problem arises because we have not considered carefully enough just what it is we are asserting in actual experience terms when we assert that X is a physical object; we have felt ourselves to be seeking an experience which, of necessity, we just could not have. The problem dissolves when we take absolutely seriously the point made in Topic 10 (4. b)) that, although we are talking (or thinking) about objective reality, all that ever can count for us as a particular state of affairs pertaining - at any level of complexity - is a succession of sensory experiences (some of which we are having and some of which we are anticipating) which we accept as the presented appearances of that state of affairs.

Thus simultaneously, and by the same process, sensory experience leads to the expectation of further sensory experience of a particular kind (appearings are signs for sequences of appearings) and states of affairs experienced lead to expectation of further states of affairs being experienced (situations perceived are signs for us of more complex situations pertaining). And the total anticipated sequence in experience-per-se terms is all that can count for us as the total state of affairs perceived.

So - all that we are asserting (in verifiability terms) when we assert that this pen is a physical object is that, when we have those experiences which count for us as perceiving it in various modes and from various angles, we shall be presented with (i.e. experience) sequences of appearances of a specifiable kind. And we call such sequences physicality, three-dimensionalness, solidity, in making the transition from experience per-se to experience of external reality.

This is, for most people, a difficult point - not to grasp, but to come to terms with. But, when we do come to terms with it, we realise that this `predictability of experience' (seen as presented by external reality) is not only all that we can have, it is all that we need, for the perception of the physicalness (the three-dimensionalness) of physical objects - and, thereby, the `construction' of spatialness.

e. Think back to sensing (Topic 9) and the two points made that

i) what is given by sensing is a structure of sensory diversity in each sense mode - and

ii) all sense modes are functioning simultaneously, and all reveal or display structures `according to the blueprint' - which is the nature of objective reality.

It is not surprising, therefore, that there is a certain graphability between the structures and sequences displayed in the various sense-modes. It is possible, for instance, for us to show in the visual mode (as marks on paper) variations in temperature or in sound or in pressure. We look at a barometer to observe what we would feel if we were sufficiently sensative. Beethoven actually composed some of his greatest music (on paper) when he was almost stone deaf. It is possible to `translate' the variation-patterns of one sense mode into another sense mode - almost as we might translate a particular message from one language to another. Irrespective of the mode, the structure is what we perceive, and what we predict, and when we are operating in presented appearance (i e external world) terms, it is that structure which is for us physical objects spatially related to each other.

Try the simple exercise of looking at a cluttered desk in front of you and, at the same kind, drawing a finger lightly across the surfaces presented, watching the point where the finger is touching. Although colour is totally and fundamentally different from `feel', the colour-changes will tend to correlate very closely with the feel-changes.

For this reason our predictions from experience had to experience expected are not only within sense-modes, they are across sense-modes; from how something looks we can tell how it will feel.

A philosophical teaser (its origins are lost in antiquity) concerns a man born blind who gains sight in adulthood. He is quite familiar, tactilely, with balls and cubes and a ball and a cube are within his sight-range (but beyond his grasp range) at the moment of his gaining sight. Could he tell, from his new visual experience, which was which?

No doubt the poor man would be somewhat confused to begin with but, if he were even moderately bright, he would fairly quickly correlate the `multiness' of the visual cube and the `oneness' of the visual ball with the familiar `multiness' of the tactile cube and `oneness' of the tactile ball - though he would need rather more experience to reconcile the sixness of the visual cube with the eightness of the tactile one - just as we all need experience (consider illusion again) to accept and expect such minor variations in `how/what' relationships as occur, for instance, when a stick is half submerged in water.

Consider examples of some oddities where the senses seem not to correlate - `invisible glass' has been the cause of some nasty accidents because it departs from the `general rule' that what can be perceived tactilely can equally be perceived visually. Macbeth's dagger, had it not been hallucinatory, would have been an experience of the reverse kind - and clouds of smoke and moonbeams are, of course, just that; to small children it is initially puzzling that they can't feel these.

We might say that (in general) physical objects are those things which are both seen and felt, but this would be misleading. It would create unnecessary mysteries about such oddities as those mentioned above and, more importantly, it would raise difficult questions about how congenitally blind people can still gain a concept of objects in space as, plainly, they can and do.

It is better, therefore, simply to accept that all sense modes which do operate correlate in a way which permits inter-sensory prediction - and that this correlation is for us the physicality of those objects (describable and specifiable in three-dimension terms), that what we refer to as a physical object is simply the provider, not simply of sense-experience in all modes, but of specific, familiar, predictable patterns and sequences of sense-experience in all modes in such a way that any part of those pattern/sequences is for us a symptom of the totality of (different sense) pattern/sequence in question. Once we realise what (the analysis of) the concept of physicalness must be, we realise that we gain it, autoresponsively as we gain any concept, without any prior concept of spatialness. We have already seen that, once we have that concept, the concept of spatialness, the characteristic of filled and empty spaces, follows automatically. We might say that, granted physicality, space `just comes with it'.



5. At this point it should be valuable - and consolidatory - to look again at the `stages of perception'.

a. The `first stage' must remain as previously defined. Without the apprehension of the given as the pattern of experience that it is, there can be no inference at all.

b. But it could now be said that the `first inference' is perceiving that pattern as the appearance of the surfaces of physical objects - for the external reality we are assuming (as causal to our experience) precisely is (for us) the independent existence of physical objects in space.

c. We then, as sophistication through experience increases, see these surfaces as of particular, classified kinds of objects (and assemblages of objects) which, in turn, are symptoms for us of more complex situations - etc as before.

d. Thus, to say that we all find that we just think spatially is merely to recognise that, for us, acceptance of external reality just is, as the first essential, acceptance of physical objects, spatially related, as the givers of our experience.



6. But this is for us - as we happen to be. We should now return to the question: If what we think of as spatialness and physicality are merely phenomenal, in what sense, if at all, do space and physical objectivity exist in objective reality?

a. To approach this, we shall pick up again the question that was left unanswered (2. d. above) - if we did not move, could we gain the concept of space that we have?

We have said that the physicalness of an object just is its presentation to us of a predictable pattern and sequence of appearances. But the experience-sequences we predict all involve if/thens - if I turn it over I shall see..., if I touch it I shall feel..., if I move in a particular direction I shall experience.... Now, these turnings and touchings and movings are themselves knowable to us only as particular sensory experiences - so that the predicted pattern of experience which, for us, counts as perceiving a physical object includes experiences both of it and of ourselves.

b. It is not surprising, therefore, that, for people, space is predominantly that which they move through. The physical object with which each of us is most familiar is his or her own body. But it is quite conceivable that a being could have all the sense capacities (except kinaesthetic if that be a separate sense) and the reasoning capacities that we have - but not move at all. This lack of movement would in no way change the range and nature of sensory experience per-se, nor would it preclude the being from making predictions (in a conditioned way, just as we make predictions) from sense experience to sense experience. But could those actual and predicted sequences of experience ever `add up to' what we think of as objects in space?

Try to imagine a small flower, rooted in the ground, which sees and hears and feels just as we do, and reasons as we do, but cannot move about as we do (for argument, let's allow that it is never even blown by the wind). Each day a bee approaches the flower from roughly the same direction, lands on it and extracts pollen and then flies back the way it came. The flower's experience, as a sequence of appearings, would be exactly the same as ours would be; inevitably it will find itself predicting what comes next, just as we do. Certain visual changes (an increasing coverage by a brown-yellow patch of the visual field) would correlate with certain auditory changes (increasing volume of a buzzing noise) and certain tactile changes (when the brown-yellow pattern practically covered the visual field the buzzing would cease and tactile sensings would occur) - and then the whole lot in reverse. Now, since this flower reasons as we do, it would `move from appearings to appearances', would postulate an external reality causal to the regularity, the predictability, of its sensory experience, a `giver' of the `given'. But how could that external reality be for that flower an external reality of physical objects in space as we think of physical objects in space? There is nothing spatial in its experience (nothing dimensional) notwithstanding that what it is experiencing is what would be, for us, the approach through space of a bee towards it etc.

Now take the fantasy a stage further. There are two such flowers and, not only do they communicate about their world between them, but you have learned their language and can communicate with them. Fantastic though this may be, it is not inconceivable because

i) each is communicating in terms of his or her own experience - and

ii) the communication is about the objective reality common to all of them.

So - with the advantage of height, you warn them of the bee's approach. `Look out,' you say `Here he comes; I think he's heading for you this time Daisy'. And though you are talking in the language of objects moving through space, and they are understanding (i.e. expecting appropriately) in terms of their phenomenal worlds, which simply do not include objects moving through space as we conceive these, their expectations in terms of objective reality (i.e. in terms of what is actually happening and about to happen) will be exactly equivalent with our own. What our symbols signify to them can only be in terms of their `customary complexes' of experience.

Now, do we want to describe this as their perceiving objects moving through space in their phenomenal mode - or as both you and them perceiving certain sequences in objective reality, you in terms of phenomenal space and movement, them in terms of whatever may be their own phenomenal experience? Once again, it doesn't really matter, so long as we understand the question. Either way we have established that there is that (structural element) in objective reality which manifests for us what we think of as the physicality and space of our phenomenal worlds.