Talk about Talk about Surfaces

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  • Talk about Talk about Surfaces

    by Avrum STROLL and Robert FOELBER

    Summary This paper contains a detailed investigation of the way ordinary persons talk

    about surfaces. Among the results achieved are: 1) No theory of perception can be correct which holds that it is a necessary condition for seeing an object that we must also see its surface; 2) Not all cases of visual perception can be analyzed in terms of seeing part (or even all) of some surface as a necessary condition for seeing the object which has that surface; 3) Not every physical object has a surface, and 4) sur- faces are sometimes identified with a particular medium, such as macadam, and some- times are considered as a kind of logical entity - not visible, without depth, having no mass, a mere outer aspect.

    RCsumC Cet article contient une investigation dCtaillCe de la manikre dont on parle habi-

    tuellement de u surface a. Parmi les rksultats obtenus, on note: 1) Aucune thCorie de la perception ne peut valablement affirmer quune condition nicessaire pour voir un objet, est quon voie aussi sa surface; 2) On ne peut pas anlayser tous les cas de per- ception visuelle en prktendant que voir une partie ou la totalit6 de sa surface est une condition nCcessaire pour quun objet soit vu; 3) I1 nest pas vrai que tout Iobjet phy- sique ait une surface et 4) Les surfaces sont quelquefois identifiCes avec une substance particulitre, comme le macadam, alors que dautres fois elles sont considkrCes comme une sorte dentitk logique, non visible, sans profondeur, privie de masse, un simple .x aspect extkrieur B.

    Zusammenfassung Diese Arbeit enthalt detaillierte Untersuchungen iiber die Art und Weise, wie

    in der Alltagssprache iiber Oberflachen gesprochen wird. Die wichtigsten Ergebnisse lauten: 1) Keine Wahrnehmungstheorie, die behauptet, dass das Sehen der Oberflache eines Gegenstandes eine notwendige Bedingung fur das Sehen des Gegenstandes selbst sei, kann richtig sein; 2) Nicht alle Falle von Gesichtswahrnehmungen konnen dadurch analysiert werden, dass man von der Wahrnehmung eines Teiles oder der ganzen Oberflache des Objektes spricht, das wahrgenommen wird; 3) Nicht jedes physikalische Objekt hat eine Oberflache; 4) Oberflachen werden gelegentlich mit einem besonderen Medium identifiziert, wie z. B. einem Teerbelag; manchmal werden sie aber als eine Art von logischer Entitat betrachtet, die unsichtbar ist, keine Tiefe oder Masse hat und bloss einen eausseren Aspekta darstellt.

    PART I

    How do we talk about surfaces? The question arises if we wish to become clear about the nature of surfaces - what they are, what sorts of objects have them. The answers we give will depend upon the sorts of objects about which we are speaking. It will also depend on what we have

    Dialectica Vol. 31, No 3 4 (1977)

  • 410 Avrum Stroll and Robert Foelber

    done, can do, or wish to do, to such objects; and thus how we talk about surfaces will also depend upon the specific features which differentiate particular objects of the same sort from one another. In what follows we shall describe a gamut of increasingly complex cases in order to indicate how variegated our talk about surfaces is. We shall then point out some of the implications which these findings have for philosophy

    Talk about marbles

    We start with marbles (i. e., the sorts of small, round balls used in the childrens game) because they represent the simplest kind of case. To begin with, it should be noted that a marble is par excellence the sort of object that has a surface. It is also a paradigm of the sort of thing philosophers have called a physical object. Despite what many philosophers have asserted or at least implied, not everything which is a physical object, in the sense in which they use that term, has a surface; but we shall defer consider- ation of these sorts of cases until later. We shall also wholly ignore in the paper the difficult question of what ijs, or might be, meant by physical object. We merely wish to state here that marbles are good examples of things which are normally said to have surfaces. The surfaces of marbles can be described as rough, smooth, slippery, chipped, sticky, blemished, pitted or damaged; we can speak about sanding, polishing, painting, or waxing the surface of a marble; and of light being reflected from its surface. There is also a gamut of prepositional phrases which can be used in such talk. We can speak about imperfections in, below, at, near, on, or towards the surface. Sometimes such prepositional phrases have a spatial sense and

    1 The subject of surfaces has not been dealt with directly in the philosophical literature. Interest has been limited primarily to the role surfaces play in a theory of perception. (See, e. g., G. E. Moore, A Defence of Common Sense, in Con- temporary British Philosophy [ed. by J. H. Muirhead; London, 19251, and his Visual Sense-Data, in British Philosophy in the Mid-Century [ed. by C.A. Mace; London, 19571; C. D. Broad, Mind and Its Place in Nature London, 19231, pp. 148-151; H. H. Price, Perception [London, 19321, pp. 106-111, 142-144; J. L. Austin, Sense and Sensibi- lia [Oxford, 19621, p. 100; Thompson Clarke, Seeing Surfaces and Physical Objects, in Philosophy in America [ed. by Max Black; Ithaca, 19651.) The psychological litera- ture is more extensive, in particular the work of J. J. Gibson (The Senses Considered as Perceptual Systems [Boston, 19661 and An Ecological Approach to Visual Perception [forthcoming], but its concerns are less directed toward clarifying the nature of the concept of a surface than toward resolving issues in the psychology of perception, as properly they should be. Brian OShaughnessy (in his Material Objects and Per- ceptual Standpoint, Aristotelian Society Proceedings, 65, [1964-651, pp. 77-98) does say a few things about surfaces but his main interest is in how to characterize the nature of a material object. We hope in this paper to make a start toward exploring the logic of surface and to illustrate the fertility and importance of this concept for epistemo- logy and for a theory of persons.

  • Talk about Talk about Surfaces 411

    sometimes not; to say that there are flaws in the surface may, on some occasions, be to say that the surface itself is imperfect, on other occasions to say that there is, say, a speck in an otherwise homogenous surface.

    Before going on to show how our talk about surfaces will vary depending upon the different sorts of objects we are speaking about, let us now indicate how complex such talk may be even with respect to particular objects of the same sort. Suppose, for example, we bave a group of marbles manufac- tured in an identical way, so that to the naked eye they are indistinguishable from one another. They are the same size, the same color (say blue), made of glass, solid (i. e., not hollow, or built up in layers, or containing steel inserts or cores), and they come to us pristine from the manufacturer; that is, they are not painted, polished, waxed or in any other way altered by human artifice.

    Then of those marbles we can say that their surfaces are smooth or rough, shiny or dull, blemished or unblemished. But we cannot say that they are thick or thin, transparent or opaque, heavy or light, hard or soft (or mushy, pulpy, spongy). If, however, we were to paint a marble from this set, then depending on the nature of the covering material we used, whether it was a heavy enamel or light stain, viscid or smooth, clear or opaque, we might be able to say some of these things.

    The operations we perform upon these objects will thus have important implications for how we talk about them. Once a marble has been painted, we can speak about its new surface, and about the properties that surface has; and speak also about exposing or looating the original surface, for example, by chipping away or sanding away the paint. Certain kinds of contrasts now become applicable that were not applicable to the original marble. Of a solid glass marble, of the sort described above, we cannot speak of exposing its original surface by sanding or chipping the surface it has. Even though those marbles, as they come to us from the manufacturer are blue, there may be some hesitation in speaking of their surfaces as blue.

    Furthermore, of such marbles we cannot say that any of them has an inner or an outer or an upper or a lower surface; and because that is so, certain other important kinds of contrasts will not be possible.

    We cannot, for example, speak of painting or sanding or polishing the inner surface of such a marble. In this respect, solid glass marbles will differ from hollow marbles; these latter can be cut open and their inner surfaces painted a different color from their outer surfaces. With hollow marbles the inner-outer contrast becomes applicable in a way it does not with solid marbles. Even, if we cut a solid glass marble in half with a fine diamond saw,

  • 412 Avrum Stroll and Robert Foelber

    we would not normally speak of the newly-exposed surfaces of the marble as its inner surfaces. With an imperfection (a bubble) that exists in a trans- parent hollow glass marble, we can say that the bubble lies on its inner surface or that it lies just below the outer surface. But we cannot say of a solid glass marble that a bubble-like imperfection lies on its inner surface or just below its outer surface. The inner-outer contrast makes no sense in this case. We could, of course, say that the imperfection lies below its surface or perhaps even just below its surface, depending on how deep within the marble it lies.

    Suppose our solid glass marbles were transparent, like a thick optical glass, rather than opaque, and not colored rather than blue. Being solid they cannot be described as having transparent surfaces, just as being blue they could not be described as having blue surfaces. Even if they are hollow and transparent, one could not say, in general, that their surfaces are trans- parent. But if they are hollow, and if their inner surfaces were painted while their outer surfaces were not, then one might say that their outer surfaces - or in some contexts that their surfaces - were transparent. The inner-outer distinction is not in general applicable with respect to such a feature as transparency; it becomes applicable depending upon how the objects we are speaking about are made.

    Assume now that one of our original marbles comes from the manufac- turer with a large chip in it. Where is the chip? One might say it is in the marble, or that the marble has a chip in it. One might say that the surface of the marble has a chip in it. We can also say that the chip itself has a surface; its surface may be rough or smooth, for example. Though the chip has a surface, and though the chip may be in the surface of the marble, with respect to some operations - such as feeling, examining, or touching the chip - it would be peculiar to say that we are carrying out those operations with respect to the surface of the marble. Compare this example with that of a giant quarry gouged out of the surface of the earth. Does the quarry have a surface? If so, in looking at it, are we looking at the surface of the earth? It is questionable that we can say so without a special story. If we are examining a deep well with a flashlight can we say that we see the sur- face of the well when we see its bottom; and can we say that the well is in the surface of the earth?

    Talk about the surfaces of solid marbles is complex in other ways. As we have seen, we do not speak of the inner or outer surfaces of such marbles. But in addition we do not speak of other surfaces such marbles have or might have. Rather, one is inclined to say that the surface of a solid marble

  • Talk about Talk about Surfaces 413

    is homogenous, or continuous, or uninterrupted, or perhaps even unbroken - though, no doubt, each of these idioms may have special employments that can be misleading with respect to the point in question. Perhaps this point can best be brought out by saying that such a marble has one and only one surface, and accordingly that talk about the surflace or its sur- face is talk about one and only one surface.

    Such talk will therefore be unambiguous in a way in which talk about the surface of a table or a hollow pipe may not be. Suppose we ask some- one to sand and then paint the surface of a solid glass marble. Generally speaking, we would expect him to carry out these operations with respect to all of its surface. But in general, asking someone to perform an operation 0 on the surface of such a marble is not necessarily asking him to do 0 to all of its surface. Thus asking someone to try to scratch the surface of a glass marble with a diamond stylus is not necessarily to ask h i d o scratch all (i. e., every portion) of its surface. What the request that he scratch the surface, and the request that he sand the surface, have in common is that each of these operations will be performed upon one and the same thing; or, to put it somewhat differently, in making either request we are implicitly excluding the possibility that the object has other surfaces upon which these operations can be performed.

    But not every request, with respect to some operation, will be unambigu- ous in the sense that there is one and only one surface upon which it can be be carried out. Suppose for instance that we ask someone to paint the surface of a solid, wooden table. Normally, we would not expect him to paint all of the surface of the table; that is, we would not expect him to paint the sides, legs, or underside of the table. What we would expect him to do is to paint the sur-face, or upper face, or top, of the table. Now sup- pose that he is asked to try to scratch the surface of the table; would it be peculiar if he tried to scratch one of its legs, or can he carry out the oper- ation correctly only if he tries to scratch its upper surface? With respect to this example it is less clear what we would say.

    The burden of these remarks is to establish that it will depend on the operation to be performed, as well as on the particular constitution or dis- position of the object upon which it is to be performed, as to what one will mean by the phrase the surface in the requests that person makes. In asking someone to paint the surface of a marble, we intend that he shall paint all of its surface; but in asking him to paint the surface of a table we do not normally intend that he paint all of its surface. In particular, we are not asking that he paint the undersurface of the table. Thus, in speaking

  • 414 A m Stroll and Robert Foelber

    about tables we may presuppose that a table has more than one surface. Yet we also sometimes speak in such a way as to presuppose that a table has only one surface. Which presupposition we make will depend upon the operation we have in mind. With respect to the operation of calculating the surface area of a table, we presuppose that the table has one and only one surface; and in calculating its area we would have to include the areas of its sides, legs, undersides, and so on. With respect to calculating the sur- face area of a marble we would make a similar assumption. But marbles are unlike tables in two ways: (1) talk about the surfaces of marbles is always talk about one and only one thing, and (2) it is always talk about the same thing.

    The tendency to speak as if tables have only one surface, and that talk about such a surface is always talk about the same thing, is well documented in the philosophical literature.

    Sense-datum theorists, such as Moore, Broad and Price spoke in this way. That is why Moore, for example, said that in acts of veridical percep- tion, even when we see the whole top of a table straight on and in good light, but when we do not see its backside or underside, we are seeing only part of its surface. Such talk clearly assumes that a table has one and only one surface, rather than that it may have many surfaces, its underside being one of them, and its upper surface another. Moores manner of speaking thus suggests that talk about the surface of a table is no different from talk about the surface of a marble. As a generalization this is clearly mistaken. And though the point is complicated, we are inclined to think that even with respect to the operation of seeing (the surface) of a table it is mistaken. But this is a matter we shall discuss later.

    hollow pipe is like talk about the surface of a table. It may be ambiguous in that we may presuppose both that a hollow pipe has one surface, and that it has more than one surface; and also that the phrase the surface refers to the same object and that it does not. If we ask someone to sand and paint the surface of a hollow pipe we would normally expect him to sand and paint only its outer surface. In such talk the surface means the same as outer surface. But if we ask him to try to scratch the surface of such a pipe he may comply with the request by scratching either the outer or the inner surface. In such talk the sur- face is being used to refer to the whole surface area, and is to be contrasted with talk about inner and outer surfaces which implies that there is more than one surface. Suppose, finally, that the outer surface of a hollow pipe has been painted a bright orange color. Can we know without a more elaborate

    Talk about the surface of

  • Talk about Talk about Surfaces 415

    scenario than has been presented here whether that person would be cor- rectly carrying out the operation of trying to scratch the surface of the pipe if he merely scratches the paint? Must he go beneath the paint? Or will it do only if he scratches its unpainted inner surface?

    As this latter case illustrates, it is clear that the operations we perform or intend to perform upon objects influence how we speak about their sur- faces. This comment also applies to the sorts of materials we use in car- rying out these operations. Not only do certain kinds of contrasts become operative in carrying out such operations, but the sorts of materials we use influence our talk about surfaces in two ways. This is particularly evident in talk about special coverings we apply to objects - i. e., in talk about finishes, paints, resins and so on. Suppose we have a set of marbles with glass centers, but now some of their outer layers are made of clay or wood or plastic or steel. Solid glass marbles, dice, unfinished tables, the sun, peeled appres and lakes do not have covering layers which are composed of different materials from those which compose the objects themselves. All of these can thus be contrasted with unpeeled apples, finished tables, covered marbles, surfaced roads and the earth. Accordingly, surface talk is different for these two types of cases. First of all, when there is an outer layer or covering to an object surface-talk often comes to be extended to the outer layer or covering itself. Our glass marbles can be said to have wooden or plastic or clay or painted surfaces. Secondly, what counts as the surface in such cases will be highly dependent on the context; if a finish is put on to protect the surface, then we sometimes speak of the surface lying beneath the finish. Other times we speak of the finish itself as a sur- face; we describe a table finished with a high gloss lacquer as having (now) a smooth surface, and so on.

    Though one could continue to elaborate on the complexity of surface talk with respect to marbles, we feel enough has been said to illustrate the point. It is now time to see if we can extract some logical principles, in some narrower sense of that term than we have been presupposing here, which can be used as a basis for getting clear about surfaces. We are still far from an understanding of the nature of surfaces; to achieve such we will need to move to examples of different kinds of objects to see whether all of them can be said to have surfaces; what the surfaces of objects can be said to be, depending on the kinds of objects they are. Up to now we have been speaking implicitly about the surface of a particular kind of object, a marble, and our main point is that such talk is applicable because a marble of the requisite sort (solid, glass, etc.) has one and only one surface.

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    PART I1

    Two kinds of logical principles may be elicited from talk about these kinds of objects. The first principle concerns operations that can be per- formed upon such marbles. One may state it as follows:

    (I) If you 0 (where 0 is an operation of some sort) X, (and where X is the surface of Y) and (Y is a marble of the sort described above) then

    Examples of (I) would be sanding, polishing, washing, painting, scratch- ing, touching, etching. That is, to sand or polish or paint (say) the surface of Y is to sand or polish or paint Y . This principle holds categorically of these operations; that is, there is no way of sanding, polishing, painting or scratching, etc. the surface of Y without sanding, polishing, painting or scratching Y. It should be noted that though Y has one and only one sur- face in the sense explained above, it does not follow that these operations are performed upon all of that surface. As we earlier indicated, to scratch X (where X is a surface) is not necessarily to scratch all of X; and accord- ingly, scratching X is not necessarily scratching all of Y . But, nevertheless, to scratch X is to scratch Y.

    Though we shall see this principle is of limited generality, some degree of generalization with respect to it is possible. I t not only applies to marbles of the above sort, but indeed to all solid, round objects with one continuous surface, such as billiard balls constructed in this fashion, steel ball-bearings and so forth. I t states that with respect to these objects, and with respect to the kinds of operations mentioned above. 0-thing the surface of those objects in 0-thing those objects.

    We have formulated this principle in the above way in order to show that generalizations of some kind are possible with respect to talk about the surfaces of certain kinds of objects. As (I) stands, however, it is too general, since it makes no effort to specify the particular kinds of operations for which the principle holds. Obviously, the principle does not hold of all operations (or activities) that might be performed upon the surfaces of such objects. The principle as formulated is thus subject to easy counter-exam- ples. Among these might be such operations as just penetrating beneath the surface (with a drill) or examining fulZy (with a magnifying glass) the sur- face. It is persuasive to claim that in such cases one is not just penetrating beneath the object or examining fully the object. One might go further and distinguish certain kinds of intensional activities from the kinds of oper- ations we have mentioned. Thus thinking of the surface is an intensional activity, distinct in character from the operational activity of sanding the

    you 0 Y.

  • Talk about Talk about Surfaces 417

    surface; and here again it is plausible to argue that one can think of the surface of a marble without, in some sense, thinking of the marble.

    Given the possibility of such counter-examples, why then speak of (I) as a logical principle at all? There are two answers to the question; the first is that the principle does hold categorically of certain operations in the sense that, for example, it is impossible to perform these operations upon the sur- face of Y without performing them upon Y. The second answer is that like many so-called logical principles, such as the principle of transitivity, its range of application is restricted. It is, as we have stressed, limited to objects of the kind described and to a restricted range of operations that can be performed upon such objects. We have given examples of operationls belong- ing to the range without attempting to determine how large the range might be, or what operations belonging to it might have common. One might have approached the matter differently by asking: Of what operations does the theorem hold? And the theorem then might be thought of as characterizing a class of operations having something in common. Our procedure has in fact been to begin with some particular operations and to arrive at the theorem inductively as it were; but the alternative approach is, from a con- ceptual standpoint, equally satisfactory.

    Two operations are of particular importance in this connection. These are what might be called the sense-operations of touching and seeing. The principle holds categorically with respect to these operations. Touching the surface of Y is touching Y; and seeing the surface of Y is seeing Y. There are no cases in which it would be true to say that we touch the surface of Y and yet deny that we touch Y, where Y is ,an object of the sort described above. It should also be emphasized that touching and seeing are the main or paradigm sense-operations which are involved in talk about the surfaces of such objects. Other sense operations - smelling, hearing, tasting - are mentioned rarely, if at all, in surface-talk about such objects; indeed, hardly mentioned at all in surface-talk about any sorts of physical objects. One does not normally talk about tasting or smelling or hearing the surface of a solid glass marble. No doubt scenarios could be devised in which such talk would have a role. If, for example, a clay finish were applied to a marble one might say of it that one can hear it crackle as it dries; or that after it had dried, if one presses it, one can hear it crack or hear it give. Yet there is something unsettling about saying that it is the surface we hear crack or hear give in such cases. We are not denying that these other sense-operations are never mentioned in connection with surface talk about marbles, but only that such talk would have application in exceptional or unusual circums- tances; and in such circumstances, it is not clear what we would say. And

  • 418 Avrum Stroll and Robert Foelber

    because that is so, it is not clear whether the above principle would apply at all to talk mentioning such sense-operations, or if it does, whether it would hold categorically with respect to them z.

    One must be careful in devising counter-cases to the foregoing prin- ciple. For instance, the operation of removing the surface of Y does not entail that one is removing Y. If one removes the painted surface of a table one does not remove the table, and so on. And this objection would hold of solid glass marbles which have been painted, or have been covered by some material. But it would not hold of the marbles in our original set. If one reflects upon the nature of the object - that it is solid, glass, etc. - then the notion of removing its surface can be seen not to be applicable in the straightforward way it would be if the object had been painted. In the sense, for example, that refinishing the surface of such a marble by sanding or polishing it would count as removing its surface, then sanding or polishing the surface would count as sanding or polishing the marble.

    There are, of course, many operations which can be performed upon marbles which are not performed upon their surfaces. Among such oper- ations would be weighing, throwing, slicing, buying, burying, squashing, running over, and shattering to pieces the marble. Throwing or weighing a marble is not throwing or weighing its surface; and accordingly, with respect to these operations the converse of the principle does not hold. Nevertheless, for most of the operations we have mentioned above, the principle does hold in the converse direction. We have seen that polishing the surface of a marble is to polish the marble; it is also the case that to polish a marble is to polish its surface; there is no way of doing the former without doing the lat- ter. With respect to such operations as sanding, washing, polishing, cleaning, etc. the principle thus holds categorically in both directions. It is noteworthy that it holds in the converse direction for the sense-operation of touching. There is no way of touching a solid glass marble without touching its sur- face. In all of these cases, it should be stressed that the principle holds in a converse direction only if the marble is intact: it does not hold if the marble is crushed, chopped to pieces, cut in half and so on. It is also worth emphasizing here, though the point will be elaborated on later, that the principle is limited in its application to solid, round objects of the sort men- tioned above. I t does not hold in its converse direction of all physical

    If we are speaking about other kinds of objects than solid glass marbles such talk may be somewhat more common. We might speak of tasting the surface of a particular wine, or perhaps tasting through the surface; or say that the interior of a grape smells all right, though the surface has an odd odor, and so on. But even in these cases surface-talk with respect to these sense-operations seems strained and not quite straightforward.

  • Talk about Talk about Surfaces 419

    objects. As we shall see, we can touch trees, persons, and animals, for example, without touching their surfaces, and one reason for this is that such objects do not have surfaces.

    Though the principle does hold in a converse direction for some of the operations for which it holds in its original direction, there are some oper- ations with respect to which the converse does not hold, and accordingly, it follows that the converse does not hold categorically even with respect to the objects mentioned above. The most interesting of these for philosoph- ical purposes is the sense-operation of seeing. Suppose we show an observer one of our original blue marbles. Removing it from his presence, we then paint it a bright yellow color. After it dries, we hold it between our fingers in such a way that, close up, the object is easily seen suspended between them. Suppose now that without the observer having seen the marble from close up after it has been painted we begin to walk toward him from a dis- tance which is sufficiently far away so that he cannot see that a pebble-like object is suspended between our fingers. As we move closer to him, there may come a point at which he can see that such an object is suspended be- tween our fingers and yet cannot truly say what the object is, and cannot truly say even what color it is. This would be an example in which one could be said to be seeing the object without seeing its surface; for in order to be said to be seeing the surface of this object, one must be in a position to see certain features of the surface, color, striations, blemishes, etc. By hypothesis, our observer cannot make these sorts of discriminations; yet he can see the object.

    We shall have more to say about the complexities of our talk about seeing the surface of objects later on; but it is worth pausing here momentar- ily to indicate why this case is of philosophical import. First, it runs counter to the views of such theorists as Moore and Broad who assert that in every act of what they call veridical perception, where one can be said to be seeing a physical object, one must be seeing (and for Moore seeing direct- ly) at least part of the surface of that physical object. In what follows we shall generate a range of counter-examples to show that this principle is false; but even here, in what might be called a favored case for the view, it can be seen to be dubious; for one can truly say that our observer is seeing the marble while also truly denying that he sees its surface.

    Secondly, Moore seriously entertained for much of his career a view about the relationship obtaining between sense-data and physical objects, which in his last paper Visual Sense-Data he finally decisively abandoned. According to that view, when an opaque object is seen, and only one sense- datum is directly seen in seeing it, the sense-datum in question is always

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    identical with the part of the objects surface which is being seen. Moore took it that the is in the sentence This sense-datum is a part of the surface of a physical object, always expresses identity; namely that the sense- datum just is the surface which is being seen. He ends his paper by saying that it now seems to me that it certainly does not. But I still think that no philosopher, so far as I know, has explained clearly what the relation R is, where it is not identity. We shall have more to say about this point later, but our results so far indicate that if Principle (I) holds categorically, as it does with respect to seeing, then it follows that if what we directly see when we look at a solid glass marble is part of its surface, then what we are directly seeing in such a case is the marble in question. For there is no way of seeing the surface without seeing the marble; to do the one is to do the other. It is not clear that one would wish to express this point by saying that the relationship involved is one of identity, but whatever term one chooses to use to describe the situation, it is clear that its use entails that it would be inconceivable that one could see the surface of an object and still not see the object. The relevance of these comments to the issue of scepticism is complicated; but insofar as a sceptic is willing to concede that we directly see part of the surface of Y, he cannot consistently argue that we do not thereby see Y.

    Before attempting any initial characterization of the nature of surfaces, let us state a principle - call it (11) - which is analogous to (I). This principle does not concern operations that can be performed upon the sur- face of Y, but rather concerns qualities or properties or features which sur- faces have. We state (11) as follows:

    If F is some property holding of X, where X is the surface of Y, and where Y is a round, solid, object of the sort described earlier, then F holds of Y. Some examples: if the surface of Y is pitted, polished, waxed, sticky, clean, dirty, wet, damp, etc. then Y is pitted, polished, waxed, sticky, clean, dirty, wet, damp, etc. The principle holds categorically, but clearly its con- verse does not. A marble may be light or heavy, made of glass or steel, hard or soft; but none of these properties holds of its surface.

    PART I11 It is now time to make an initial assessment of what the marble example

    has taught us about surfaces. We have seen that marbles are the sorts of things that have surfaces, and that depending on how they are made, what is done to them, and so forth, talk about their surfaces will vary. But what is such talk about? Is the surface of a marble a thing - is it the paint, or the clay, or the glass; or is the surface of a glass marble not itself glass,

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    or is the surface of a painted marble not itself paint, and so on? These are complicated questions. Before answering them we shall have to look at some examples of things other than marbles. But before doing so, let us ask: what do the marble examples tell us?

    It is clear that the surface of a marble is something which belongs to the marble. It is that part or portion of the marble which impinges upon some medium - such as air or water - which is not itself the marble. The psychologist Gibson defines a surface as the interface of an object and the medium; presumably, on this definition, the surface is the point of con- junction where marble and air meet. If Gibson is correct then the air would also have a surface, for there is a place where it meets a marble medium. But we do not speak of air as having a surface: and we do not speak of the point of conjunction between the air and the marble as the surface of the air. Why then should we speak of the point where marble and air conjoin as the surface of the marble?

    The dictionary defines a surface as the exterior or outside of an object or body. Is it because air is not an object or body that we do not speak of it as having a surface which impinges upon the marble? Or is it that the notion of an exterior or outside to air makes no sense in the way in which it does make sense when we speak about a marble? Does it not make sense when we speak about a marble? Does it not make sense to say that a return- ing space craft plunges into the air - that it meets the surface of the air before doing so? Is this not like a diver who hits the surface before plunging into the water beneath it? The question of whether air is an object or not is thus difficult to answer. But even if we say that air is an object this would not be a ground for saying that it has a surface; for some things we would clearly call objects, such as trees and persons, do not have surfaces either. More likely it has something to do with airs being amorphous, that is, not having a sharply defined outline at the point where it meets the marble.

    For the dictionary also defines a surface as the outermost or uppermost boundary of an object, and if air has nothing that could be called an outer- most or uppermost boundary then this may well be a reason for saying it has no surface. But if a surface is an outermost or uppermost boundary, what does that mean? The dictionary tells us, further, that a surface is some- thing without depth - as it tells us in an eye-stopping phrase, a surface is a mere outside. What part of a solid glass marble would be its mere outside? How deep into the marble would we have to cut before we cut beneath the mere outside? If the marble covered with paint or clay is covered with a medium that has depth or thickness is then the paint or the clay not the surface after all, even though it is the exterior or outside of the object?

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    According to the dictionary, we should say that the paint or clay is the surface, for the dictionary states that a surface is a boundary. We take it that a boundary is something that separates one thing from another thing; and surely the clay covering separates the marble from the air. We have here, then, a necessary condition for the definition of a surface: namely, that it is a boundary. But clearly this is not a sufficient condition. The equator is a boundary, yet it is not a surface. If we have a body of water contained in an open cube-shaped tank, the water impinges against the sides of the tank and against the air at its top. There are six boundaries here, yet we speak only of the water which impinges against the air as the surface. So if being a boundary is a necessary condition for being a surface, it is clearly not a sufficient condition.

    That being a boundary is a necessary condition seems clear enough. The marble examples help us see this. They explain why when we speak of the exterior of most points of a solid glass marble we use surface-talk; they explain why when we cover the surface of such a marble with some mate- rial, such as clay or paint, surface-talk shifts to these covering materials, because they now become the boundary between the marble and its imping- ing environment. They explain why when we remove these covering mate- rials we again uncover the surface.

    The question we want to raise now is whether it is possible to find a set of necessary and sufficient conditions that define the concept of being a sur- face. But in order to see whether this is possible we shall have to extend the range of examples in order to make sure that the definition, if it could be found, would accommodate all the cases. When we do this we find that our talk rises in an order of complexity that makes the marble examples seem simple by comparison. Obviously we cannot explore all of these cases fully here; but even touching lightly on some of them will illustrate the point that it is difficult to find a definition that fits all of the cases.

    PART IV

    Marbles resemble the earth, the sun, apples and oranges, and other objects in being round or nearly round; yet surface-talk differs with respect to these objects. Consider the sun, for example. We do use surface talk with respect to the sun. We say that the temperature at the surface is such and such; that giant flames leap up from the surface, and extend many miles above it. What else do we say about the surface of the sun? Is the surface red? It seems odd to say this; just as it seemed odd to say of a solid glass marble that is blue that its surface is blue. But unlike such a marble the

  • Talk about Talk about Surfaces 423

    sun is not solid. So what else can we say about its surface; is it pitted, blem- ished, hot, gaseous, smooth, rough, etc? It seems that none of these predi- cates apply. Why should this be so? Probably because the sun is a gaseous ball. Unlike a lake or other large liquid body, things do not break through the surface of the sun, nor do they float on the surface. It would seem that predicative surface-talk requires that objects be of a certain density before such talk becomes operative; in this respect, talk about the sun resembles talk about clouds.

    The earth differs from the sun in being a non-gaseous body; and it dif- fers from our original set of marbles in not being made of any single solid material, such as glass. It is more like a marble with a steel core, or one we have painted or covered with clay. Surface-talk about the earth is very rich. We can speak about somethings being at, below, above the surface; of drilling through, burrowing beneath, resting upon the surface, and so forth. Sometimes the surface is identified with the crust; and the crust has a certain thickness. Does this mean that the surface has a certain thickness? It is not clear that we would assert so. The surface of the earth is covered with bodies of water, forests, deserts, grassy plains. But to say that it is covered with these does not imply that we do not see the surface. If a forest completely covers an area of the earths crust, does this mean that the forest has become the surface? Or is the surface the surface of the forest? Such talk tends to diverge from talk about marbles. A still more striking dif- ference between them is the following: though the earth has an outer crust, just as a marble covered with clay has, we do not speak about uncovering the original surface when we dig a deep well - no matter how deeply we dig it. If we could strip the crust of the earth this would be like peeling an apple. What we would have left in both cases might be said to have a surface; but it wouldnt be the original surface. The earth, apples, oranges thus differ from covered marbles or painted tables in this respect.

    Surface-talk is still different with respect to bodies of water, such as lakes, seas, oceans. The surface of a lake is like the surface of a solid, glass marble. It has no finish, cannot be peeled off. Surfaces of such bodies of water have describable features; they may be calm, rough, choppy, glassy, covered with seaweed, dotted with boats, and so on. Things may be on, below, beneath, at, near, through, or just above the surface of a lake. Two interesting features of surface-talk about such bodies of water: (1) though they may have discernible outlines or boundaries as such, it is only the uppermost layer or boundary of water which is characterized as its surface - not the bottom, sides, and (2) it is in surface-talk about lakes that we find an analogy with talk about tables Sur-face, as the word indicates,

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    literally means the upper-face or t ~ p . When we talk about painting the surface of a table, we mean the top of the table. In this respect, surface-talk about marbles and the earth differs from surface-talk about tables and lakes; marbles do not have a top in the way in which a table does. The notion that a surface is a boundary thus becomes very complicated in such cases. Lakes do not have outermost boundaries in the way that marbles do; they have top boundaries in the way in which marbles do not. Is there some sense of boundary that captures both of these notions? If so, it is difficult to see what it might be.

    Though talk about the surfaces of lakes and tables is frequently talk about their uppermost boundaries, there are still differences within such talk. I do not speak about the top of a lake in the way I do about the top of the table. If swimming in a lake, I come to the surface, I do not come to the top of the lake; indeed, in the sense in which mountains have tops, and perhaps tables have tops, lakes do not have tops at all. I can, to be sure, speak of something as floating on top of the water, and in such con- texts, as floating on the surface of the water, but the idiom on top of the water must not be conflated with the idiom the top of the water. If I examine the surface of a lake, I am therefore not normally said to be examining the top of the lake *.

    But even in speaking of tables per se, the words surface and top are not always interchangeable. If I put a new surface on a table, I am not necessarily putting a new top on it; nor is it the case that if I remove the surface I am removing the top of the table. Talk about surfaces and tops of tables is in fact very subtle. The top of a table may be made of wood or marble; I may even say that the table has a wooden or marble surface; yet I might hesitate to say that the surface is made of wood or marble, even though not hesitating to say that the top is. How we speak in these situations will depend to a great extent upon the context; what object is directly under consideration with respect to what operation; and accordingly what we identify as the surface or the top of the table will depend upon the situations which require talk of one sort or the other.

    Among the multifarious definitions of surface which good dictionaries give us, one of the most interesting is the characterization of a surface as the part of something that is presented to a viewer, with little or no examin- ation; the outward appearance or characteristic of something; its external aspect. This sense of surface is something that Moore, Broad, Price and

    * We do speak about the bottom of the lake; but in such talk, the top ot the lake is not the contrast we intend.

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    other sense-datum theorists have been particularly attracted to. On the basis of it, they have tended to identify the external properties of a physical object with those that belong to the surface of it. That an apple is red, or mottled, or dirty, or sticky are all features which the surface of the apple presents. One thus might be tempted to say that all external properties are surface properties, while all (as it were) internal properties were non-surface properties of an object. But this would be incorrect. We can say, of course, that being sweet or sour, being rotten or wormy are internal properties of an apple, say, in the sense that if we bite into the apple these are features we may discover beneath the skin. We cannot say that the surface is sour or sweet, rotten or wormy, but rather that the apple is, and to the degree that we can say this, we can say that these are internal properties of the apple. But there are properties of an apple which are not internal in this sense (i. e., where we do not go beneath the surface to discover them), and yet which are not surface properties. The identification of surface properties with external properties is thus mistaken; among such external properties, for example, would be the property of weighing a certain amount, being so many inches high, being of a pear-like or perfectly round shape, being quartered or divided, and so on.

    PART V

    Mention of the foregoing examples was designed to reinforce the points that being a boundary or an external aspect or property of something is not a sufficient condition for being a surface of that something, and accordingly that surface-talk is not fully capturable in terms of conditions that are both necessary and sufficient - that such talk is open-textured in Waismanns sense of that term. The difficulties in trying to find a condition or set of conditions sufficient for determining something to be a surface are increased by reflecting upon a range of things which may have boundaries or external aspects, and yet which do not have surfaces at all. Among these are the following:

    1. Shadows, rainbows, lightning are, if not describable as physical ob- jects, then at least describable as physical phenomena. One can draw an out- line around a shadow, so that a shadow has a boundary; yet it would be odd to say that a shadow has a surface. No properties or features can be attri- buted to the surface of a shadow per se; it cannot be said to be dark or light, thick or thin, smooth or rough, wet or damp; nor can it be removed, sanded, polished, and so forth. One can speak about measuring the surface area of a shadow, but in such cases one usually means the surface (say of

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    the ground or earth) covered by the shadow; one is not measuring the sur- face of the shadow itself. With rainbows and lightning surface-talk seems wholly inapplicable; yet rainbows have boundaries; and in a certain sense, so does lightning (lines can be drawn around rainbows and lightning flashes in photographs, for example; yet surface-talk would be inapplicable in such cases). Obviously, non-visual or non-tactual physical phenomena qualify even less for surface-talk. We do not speak of the surface of a sour taste or the surface of a clap of thunder.

    Lightning, shadows, and rainbows are not three-dimensional objects; one might infer from this fact that it is a necessary condition for ascribing a surface to something that it be threedimensional. We do in fact think this condition holds for most things, but it clearly fails for cases described in geometry and topology. Whether these are specialized, technical uses and thus require special conditions for the applicability of surface-talk is not a question we wish to raise here.

    2. Some items clearly belonging to the class of what Moore, Broad and Price would call physical objects, do not have surfaces. Among these are clouds, mountains, trees and persons (this list is not even remotely exhaus- tive, of course). Let us briefly speak about each of the four items mentioned in this category.

    a. Clouds, for example, are constituted by layers of gas and moisture, and have a top layer. But a cloud doesnt have a surface. Unlike a sub- marine which can come to the surface of a body of water, an airplane does not rise to, or even above, the surface of a cloud. We see the tops of the clouds but not their surfaces. One explanation for the withholding of sur- face-talk here is that the objects that have surfaces must have a certain density or compactness before such talk is applicable; clouds are like most gas (argon, helium, etc.) in being insufficiently dense for surface-talk to

    b. It would be odd to speak of climbing to the surface of a mountain if what we are speaking about is climbing to the peak of the mountain or its top. Even if submerged in a tunnel, dug into the side of a mountain, one who emerged from the tunnel would not normally be described as emerging at the surface of the mountain, but rather at the surface of the earth. Like such astronomical bodies as the moon and Mercury, the earth can be said to have a mountainous surface, or its surface can be said to be mountainous, but surface-talk about mountains themselves is much more restricted, if it occurs at all. Normally we would not say that the surface of a mountain is covered with snow, but rather that the mountain is covered

    apply *

  • Talk about Talk about Surfaces 427

    with snow. What would it mean to say that the surface of a mountain is wet or slippery or treacherous? Insofar as these terms have application they are likely to be elliptical ways of speaking about the earth, the terrain, the soil, and so on. Similar remarks apply to canyons and gorges. It would be peculiar to say as we peer into the depths of the Grand Canyon that we see its surface; no doubt less peculiar to say as we peer from the bottom that we can see the surface - but surface of what? Most probably the surface of the earth, but in this case we might also say the surface of the canyon. But would we say that we see the surface of the canyon if we look at the canyon from above? Such talk is net like that about the surfaces of bodies of water.

    c. Trees do not have surfaces. What would it mean to say one sees the surface of a tree; what properties would the surface have? Do we ever say that the surface of a tree is slippery, wet, dry, pitted, blemished, etc.? What operations can be performed upon the surface of a tree? Can we polish, sand, paint, remove, dig into the surface? Such operations can be performed upon trees, but not upon their surfaces; in this respect trees differ from marbles. One interesting feature of trees - a feature they have in common with persons - is that though we do not normally speak about the surfaces of trees as such, we do speak about the surfaces of particular parts of trees. We can say that the surface of a leaf is smooth, or covered with dust, or waxy; and we can perform certain operations upon the surface, such as cleaning or waxing it. The logical principles involved here - doing 0 to the surface of Y is doing 0 to Y, where Y is the leaf itself - are much like those that apply to marbles; but we shall not speak about the respects in which they do and do not resemble those principles. It is probable that we do not speak of the surfaces of trees because trees as objects are too irre- gular to have firm outlines or boundaries; for similar reasons surface-talk may be strained when used of things that are too fuzzy, like shaggy rugs, Afro wigs, cotton candy and wild grasses.

    d. The case of persons - and indeed of most animals - is particularly interesting. We do not speak of the surface of a person; one who touches a girl may touch her skin or her hair, but in so doing is not touching her surface. Her skin can be said to have a surface; yet the logic of surface- talk with respect to the skin is complicated - we can pat the surface lightly with a cloth, but it is doubtful that in general we wash, oil, or paint the surface; instead we tend to speak of performing these operations on the skin itself. Moreover, it is not the surface of the skin that has blemishes, pustules, acne, or pores, but the skin itself. Still, surface-talk seems relevant here. We do not speak of the surfaces of most animals - cats, dogs, even snakes

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    - yet, oddly enough, if we make a statue of a person, or a cat or a dog, we can speak about the surface of the statue; it can be smooth or rough, pitted or unblemished; we can wax or wash it. Here we offer the conjecture that we do not speak about the surfaces of human beings, or animals, inso- far as we think of them as animate. As persons, human beings may lack the sorts of boundaries which some of their bodily parts possess. What may be involved here may be a form of Cartesianism in the language which pro- hibits the use of surface-talk with respect to things as amorphous as persons or other living creatures, but allows such talk with respect to inanimate representations of them, such as busts and statues.

    PART VI

    For philosophy, what is the import, if any, of the foregoing discussion? What we have to say here will of necessity be brief; hopefully the points

    to be made now can be fleshed out in terms of the preceding remarks. We list them seriatim:

    1. What are surfaces? Our answer is that they are roughly boundaries of things, but that no precise characterization of surfaces (in terms of neces- sary and sufficient conditions) can be provided. This can be put in an alter- native mode by saying that talk about surfaces is open-textured. What will be meant by surface will depend on the particular object being spoken about, what kind of an object it is, what features it can be described as having, and what operations can be done to it. In this sense, then, talk about surfaces is open-textured in Waismanns sense. We have seen how the phrase the surface can be be construed as referring to different things, depending on the context in which it is employed. When used of tables some- times it is used to refer to the top of the table; sometimes it is used to refer to the area of the table which abuts some medium, such as the air; sometimes it is used to refer to the finish applied to the table; sometimes it is used to refer to the outermost layer of such a finish, and so on.

    2. Are surfaces things or entities? Again the answer will depend on the context. Sometimes the surface of something will be taken to be identical with a certain thing (the crust of the earth, the macadam applied to a road newly surfaced, the heavy paint applied to the top of a table), and some- times it will not. When it is not, it will be considered as a kind of logical entity - not visible, without depth, having no mass, a mere outer aspect.

    This way of speaking about surfaces is thus ambiguous; and the detec- tion of this sort of ambiguity has important implications for modem theories of perception. It allows us to answer Moores question, for example. It will

  • Talk about Talk about Surfaces 429

    be recalled that Moore wishes to know what is the relationship between what is directly seen and part of the surface of a physical object that is seen. He rejects the position that this is always a relationship of identity. Moore is clearly correct that the relationship between what is directly seen and the surface of an object is not always that of identity. There is also no doubt that some of the time the relationship is that of identity. The difference be- tween the two cases can be brought out as follows.

    When I see in good light the top of an unfinished wooden table what I am directly seeing is not only part of the surface of the table but the whole surface. What I am directly seeing in such a case is identical with the sur- face of the table. If I look at a body of water whose surface I can encompass in one glance, then what I am directly seeing is identical with the surface of that body of water. Seeing Lake Victoria from its southern shore, as J. H. Speke did, is on the other hand a case of seeing only part of its surface (it is too large for the whole surface to be seen at the horizon). This would be a case in which what is directly seen is identical with part of the surface of Lake Victoria.

    But there are cases in which I can see a physical object without seeing any part of its surface. These are also cases in which I can be said to be seeing something directly. For instance, if I see, on a clear night and with- out the use of telescopic equipment, the planet Venus, I can be said to be seeing Venus directly, but I cannot be said to be seeing its surface (it is covered with clouds). If I fly over Lake Victoria at a sufficient height, I can be said to be seeing Lake Victoria, yet not be said to be seeing its surface (for I cannot discriminate any features of the surface).

    3. The significance of these findings for modern theories of perception can be brought out as follows:

    a. Not all cases of visual perception can be analyzed in terms of seeing part (or even all) of some surface as a necessary condition for seeing the object which has that surface. In order to say that we see the surfaces of physical objects, we must be close enough to them to discern certain features they possess; scratches in the surface, imperfections, various kinds of marks, etc. At a sufficient distance, talk of seeing the surface of an object thus becomes inapplicable. The philosophical literature on perception which has suggested otherwise has done so because it tends to concentrate on such items as tables, chairs, bells, inkwells, blackboards which are not only a curiously professorial collection, but which are also things we normally see at close range and usually in a small room. But no theory of perception can be adequate which employs parameters so limited in scope.

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    b. No theory of perception can be correct which holds that it is a neces- sary condition for seeing an object that we must also see its surface. A second reason in support of th is contention is one advanced earlier: there are physical objects - human beings, animals, trees, clouds - and certain sorts of physical phenomena - reflections, shadows, lightning, etc. - which by their very nature do not have surfaces. Of these it is true to say, on certain occasions, that we see them, but false to say that we see their surfaces.

    University of California, San Diego

    Dialectica

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