Perceptual and Motor Skills, 1977,44, 1191-1205. @ Perceptual and Motor Skills 1977
CONCEPT OF VISUAL SENSATION CLAUS BUNDESEN'
Copenhagen University, Denmark Summary.-A direct-realist account of visual sensation is outlined. The explanatory notion of elements in visual sensation (atomic sensations) is reinterpreted, and the suggested interpretation is formally justified by constructing a Boolean algebra for visual sensations. The related notion of sensory levels (visual field vs visual world) is discussed.
This paper is devoted to conceptual clarification of the nature of visual sensation. The explanatory notions of elements and levels in visual sensation are treated in some detail. A general pattern of explanation for visual sensation is thus discussed, but specific modes of physiological processing are not hypothesized. The suggested concept of visual sensation is introduced from a standpoint of direct realism. SENSATION AND ~ R C E P T I O NIN A FRAMEWORK OF REALISM Philosophers have argued that the attempt to make a general psychological theory of perception is doomed to failure (e.g., Hamlyn, 1957; Ryle, 1949). This was not meant to exclude the possibility of psychological inquiry into conditions of visual perception but a psychological theory stating sufficient conditions .for seeing something should be excluded. The sound basis of this thesis appears to be that perception, in ordinary language, is necessarily veridical : Consider a case of perfect visual illusion such as Ames' famous distorted room (Ittelson, 1952). The naive subject looking into the distorted room claims to see a normal rectangular room. In ordinary language the subject is wrong; he cannot see a normal room since rhe room is really distorted. Yet the psychological processes of the subject may, in principle, be exactly the same as they would have been if the room had not been distorted, in which case his daim would have been right. Thus whether a subject perceives something is not only a function of his psychological processes. If the fact that a subject sees something is not purely a psychological one, then psychology needs a term that corresponds to seeing (in the ordinary sense) but lacks the nonpsychological implications of this word. Expressions like visual experiefice can do the job. By definition, then, the visual experience of a subject is uniquely determined by his psychological processes. Further, when a subject sees a normal room, then he experiences that room as normal though the converse is not always the case. 'Thanks are due to Axel Larsen for helpful discussion. Requests for reprints should be sent to Claus Bundesen, Psychological Laboratory, Copenhagen Universirg, Njalsgade 94, DK-2300 Copenhagen S., Denmark.
1192
C.
BUNDESEN
What was the visual experience of Ames when he took the position of his naive subject? It differed significantly from the experience of the naive subject insofar as Ames identified the room as a distorted one. On the other hand, it was similar to the naive experience insofar as it looked to Ames as if the room had been a normal rectangular one. W e may say that his visual k z p ~ e s s i o nwas qualitatively the same as that of the naive subject though his visual identification of the room was different. In general terms a distinction is made between visual impressions and visual experiences, the former being components of the latter. A few examples may serve to further clarify the relations between seeing, visual experiences, and visual impressions: 1. If the timing is just right, two successive flashes of light at spatially separated points appear as continuous movement of a single light, optimal apparent movement (Wertheimer, 1912). More precisely the subject has a visual impression of a continuously moving light. The naive subject is deluded by his visual impression and thinks that a light is actually moving; he has a visual experience of a moving light though he does not really see one. The informed subject is not deluded; he has no visual experience of a moving light though his visual impression is the same. 2. When identifying the letter A visually, one will ordinarily not notice that it contains a triangle. One sees the letter without seeing the triangle, since one has no visual experience of this triangle. Yet, one has a visual impression of the triangle, as one has a visual impression of the A. Visual impressions are most readily characterized (Sellars, 1956) through description of that of which they are impressions (a rectangular room, a moving light, an A ) . In particular, the visual impressions of a subject are often implicitly characterized by statements of the form: It looked to the subject as though the stimulus situation were such and such,
implying that: Judging from the visual impression of the subject, such and such a stimulus situation should be expected,
which means that: The subject had a visual impression of such and such a stimulus situation.
For various reasons a subject may be unable to describe his visual impressions or to describe that of which they are impressions, that is, their content. Indeed, he may not know the content of his impressions because he lacks pertinent concepts. For instance the child who lacks the concept of a triangle cannot know whether he has a visual impression of a triangle. The
CONCEPT OF VISUAL SENSATION
1193
experience presupposes concepts which the impression does not. In this respect even lines and angles are on a par with letters. The suggested account is one of direct realism (cf. Armstrong, 1961) : What is seen is always present in the stimulus situation. Thus a subject does not construct what he perceives and the object is not produced by the perception. Specifically what is seen is not a visual representation of the real thing. When a subject sees a red square, he has a visual experience and, therefore, a visual impression of a red square. Visual experiences and impressions are representations but these are not the objects seen: These are neither red nor square. The framework resembles that of Reid (1764/1967), who apparently was the first to insist upon a distinction between sensation and perception (Boring, 1942). In Reid's ( 1785/1967) terminology, the external senses have a double province-to make us feel, and to make us perceive. They furnish us with a variety of sensations, some pleasant, others painful, and others indifferent; at the same time they give us a conception and an invincible belief of the existence of external objects. . . . This conception and belief which narure produces by means of the senses, we call perception. The feeling which goes along with the perception, we call sensution (p. 247 f ) .
Reid also demonstrated his concept of sensation paradigmatically by cases of illusion without delusion-such as in Example 1 above. Accordingly visual impressions may jusdy be termed visual sensations.
ELEMENTSIN VISUALSENSATION
A notion of simple sense-impressions, atomic sensations, was formed within the British tradition of empiricism and associationism as represented by Locke (1690/1961), Berkeley (1709/1910, 1710/1910), and Hume ( 1739/1896). The simple impressions were held to be immediately given in sensory perception, and these should be the basic elements of the mind. Complex impressions were considered to be compounds of simple ones. In fact any content of the mind, any experience, was assumed to be derived from simple impressions by operations like copying and compounding. It was the tradition of British empiricism "that made perception the primary problem in psychology and that indicated the fundamental line of attack" (Boring, 1950, p. 169). Reid's (1764/1967) categorical distinction between sensation and perception was soon assimilated to the systematic structure of empiricism and associationism. Perception was then considered to be an elaboration of sense-impressions by the addition of associated ideas whereas sensation was treated as the production of pure impressions. The idea that perceptual experience is derived from atomic sensations is still alive. Beginning with the works of Hubel and Wiesel (1959) and Lettvin, Maturana, McCdoch, and Pitts (1959), neurophysiological studies of eye
1194
C. BUNDESEN
and brain succeeded in finding different types of single cells which responded specifically to characteristic features of retinal stimulation-such as the presence of an edge oriented in a certain way within a specific part of the visual field. These cells seem to be organized hierarchically such that higher levels are concerned with more complex features (Hubel & Wiesel, 1962, 1965). In one interpretation the simple sensory features correspond to atomic sensations, whereas higher-order features represent steps in "perceptual generalization" (Hubel, 1963). Whether or not the atomistic approach to perception is tenable, however, some of the sensory features may possibly correspond to atomic sensations from which complex impressions are built by compounding. A formal reconstruction of the notion of atomic sensations will be developed, using the present concept of visual impressions. The first problem concerns the definition of relations by which the atomic organization can be implemented in the universe of visual impressions. Some definitions are suggested below: 1. One impression is a part of another, if the presence of the former is a necessary condition for the presence of the latter. For example, the impression of an angle is a part of the impression of a triangle, and the impression of redness is part of the impression of a red square. 2. One impression is the anion of some other impressions, if the presence of the former is a necessary and sufficient condition for the joint presence of the other ones. For example, the impression of a pair of lines is a union of two impressions of single lines. 3. One impression is the intersection of some other impressions, if it is the union of those parts which are common to these. For example, the impression of circularity is the intersection of all impressions of circular objects. It seems to follow from these definitions that the union of a subject's current visual impressions defines his total visual impression and, further, that any visual impression equals the intersection of those total impressions in which it takes part. Let E be a set of visual impressions such that any total impression is a union of members of E. If the sensory generation of each of the members of E were explained, then the sensory generation of any total impression could, in principle, be derived. Further the generation of any visual impression would be derivable, as the impression could be specified as an intersection of total impressions. In short, any visual impression could be reduced to E, as it would be an intersection of unions of members of E. If no proper subset of E could do the same job, E would qualify as a bare o f sensory elementr. The idea of a base of sensory elements is clearly related to the notion of a set of atomic sensations to which any impression is reducible. On the present account, however, there are many different bases of sensory elements. An obvious base is provided by the set of all total impressions, but this is
CONCEPT OF VISUAL SENSATION
1195
hardly the most simple one. The problem is, accordingly, to find a base of sensory elements which is optimal with respect to functional simplicity. TOa good first approximation any total impression can be uniquely specified by content in terms of moving, colored regions in three-dimensional space. Hence, it is reasonable to search for a functionally simple base of sensory elements, the contents of which are expressed in terms of color, shape, and movement. Existing data on sensory feature extraction suggest that some of these elements may be impressions of colored, moving line segments at specific spatial positions (McCullough, 1965; Stromeyer & Mansfield, 1970) or, possibly, impressions of specific spatial frequencies in the two dimensions of the visual field (Blakemore & Campbell, 1969; Campbell & Robson, 1968; Graham & Nachmias, 1971). The suggested interpretation involves the assumption that a given visual impression may be specified uniquely by each of several types of represented content. It should be noted how this assumption relates to the fundamental distinction between sensing and knowing: Given that the visual identification of an object is based on a visual impression of that object, sensation and percepcual identification ate not discriminable by the types of their content. The difference between sensing and knowing, however, is expressed by the ways in which these relate to their content. An act of visual identification involves a specific conceptual interpretation on the p a t of the subject, and the content of the act is the meaning of that interpretation; a full desuiption of the act should therefore exhaust its content. The content of a visual impression, on the other hand, is indicated to the subject rather than conceived by the subject. As suggested in Formula 2, such indications may be grounded in a multitude of contingent correlations. A full description should specify the impression uniquely in terms of indicated content. Selection among unique specifications should be a matter of convenience, however, and exhaustive description of indicated content should be pointless. The difference between perceptual interpretation and sensory indication is thus reflected in the fact that, unlike an act of visual perception, a given visual impression may equally well be specified in terms of each of several types of represented content. BOOLEANALGEBRA OF VISUALSENSATIONS The previous account of the notion of sensory elements in vision was based on a few definitions of important relations between visual impressionsthe relations of patt, union, and intersection. Any atomistic approach to sensation necessarily presupposes relations like these. It may still be questioned, however, whether the suggested definitions ate formally adequate, that is, whether the defined relations do have the required formal properties. For example, it is easy to see that the defined "patt" relation has the required prop-
1196
C . BUNDESEN
erty of transitivity, but it is not at all obvious that the principles of disuibution are valid for the defined relations of "union" and "intersection." The present section demonstrates that the set of visual impressions can, in fact, be organized by Boolean relations along the lines previously suggested. Thus, a Boolean algebra is formed from the set of visual impressions (which is augmented by two purely formal entities: a universal element and a null element). Further the concept of total visual impressions is formally defined, and it is established that any visual impression is the intersection of those total impressions of which it is a part. The construction is founded on three existential postulates. First, if impressions y and z may coexist, then there is an impression x which is defined by the joint presence of y and z. Second, for any impression y, there is an impression x which is defined by the absence of y. Third, there is an impression x such that x is never present. The third postulate has no material content but serves a technical function in providing the system with universal and null elements. In the following presentation, p and q are variables for persons at temporal points, and x, y, z, w , and x,, y,, z,, w, ( n = 1, 2, 3, . . .) are variables for visual impressions. S is a binary predicate which is true of a p (left field) and an x (right field) such that p has x. The three postulates above are summarized in Axioms 1 and 2 below: A x i o m 1.
A x i o m 2.
Expbmtion. In the suggested formalization, the first postulate states that ( Y )(z){(Ep) (pSy & pSz) + (Ex) ( p ) b S x @ (PSy & pSz)l), which follows from Axiom 1. The second postulate is expressed as Axiom 2. The third postulate states that
which follows from Axioms 1 and 2, since the larter implies the existence of elements y and z such that ( p ) [ H (pSy & ~ S Z ) ] . The formalized postulates thus follow from the axioms. To prove the converse, it will suffice to derive Axiom 1 from the first and third postulates. Assuming that (Ep) (pSy & pSz), then (Ex) (p) b S x t, (pSy & p S z ) ] , according to the first postulate; assuming (Ep) (pSy & ~ S Z )then , (Ex) ( 9 ) PSx t, (pSy & pSz)] by virtue of that the third postulate. W e condude that the axioms are logically equivalent to the formalized postulates. N
CONCEPT OF VISUAL SENSATION
Definition 1. Definition 2. ( x )( y ) { ( x = y )
Definitions 1 and 2 entail
* ( P ) (PSY
-
( x )( Y ) [ ( x C Y )
+
PSX)l
[ ( xC y) & ( y
cx)])
and ( x ) ( Y ) { [ ( x= Y )
[GI As the formal properties of the identity relation are reducible to reflexivity and substitutability (Rosser, 1953), Formulas 5 and 6 show the formal adequacy of Definition 2.
Definition 3. ( x )( Y ) ( z ) { U ( x , Y , z )
PSXI
+
- ( P I [Psx
PSY).
(PSY Q' pSz)l)
From Axiom 1 and Definition 3 it follows that ( y ) ( z ) ( E x ) [ U ( x , y, z ) ] , and from Definitions 2 and 3 it follows that ( x ) ( y ) ( z ) ( w ){ [ U ( x , y, z ) & U ( w , y, z ) ] + ( x = w ) ) . Consequently, U is a composition on the set of visual impressions,
[71
which justifies the next definition.
Definition 4. ( Y ) ( z ) { ( YU z )
= (7%)[ U (x,Y, z)I)
Definitions 3 and 4 imply that
-
( x )( Y ) [ ( x U Y )
Definition S. (x) (Y) (z)
tn
( x , Y ,Z )
* ( P ) [PS
=
%)I-
(Y U
(w) ((w
c Y BL w c z ) + P S W ) ~ )
By virtue of Definition 2, it follows from Definition 5 that ( x ) ( Y ) ( z ) ( w ) { [ n( x , Y ,
2)
t~
n ( w , YI
Z)I
-)
(X
= w)).
191
To show that ( y ) (z) (Ex) [fl ( x , y, z ) ] , the first step is to prove that
Proof. According to Axiom 2, for any elements y, z , there are elements y , z , such that ( 9 ) ( p S y l o w p S y ) and ( p ) ( p S z l o ~ p S z ) . From Axiom 1, there is an element xl such that ( p ) b S x l o ( P S y l & ~ S Z I ) ] .From Axiom 2 , accordingly, an element x exists such that ( 9 ) ( p S x o - ~ S X I ) , whence ( p ) b S x t, ( p S y = & ~ S Z I ) ]and , therefore ( p ) b S x t, ( p S y v p S z ) ] , which
-
was to be proved.
The next step is to prove that ( x ) ( Y ) ( z ) { ( P ) [ P s ~o (PSY v P S Z ) I
-,
n (x, Y, .)I.
~111
Proof. Assume that ( p ) b S x o ( p S y v pSz)]. By virtue of Definition 5, it will suffice to derive that ( p ) {pSx o ( w )[ ( w c y & w C z ) + pSw]). Suppose that pSx. Then either pSy or pSz, each of which implies that ( w )[ ( w C y & w C z ) + pSw]. Conversely, suppose that ( w )[ ( w C y & w C z ) + pSw]. As the initial assumption implies that x C y and x C z, it follows that pSx. Hence Formula 11 is established. Formulas 10 and 11 show that ( y ) ( z ) ( E x )[n ( x , y, z ) ] . Thus, considering Formula 9, we have that
n
- -
is a composition on the set of visual impressions
[I21
Note that Formula 11 can be strengthened to
n ( x , Y , z)). [I31 Proof. It is sufficient to derive ( p ) PSx t, ( 9 S y v p S z ) ] from n ( x , y, z) (XI (Y) (z)((P)[Psx
(PSY v P S Z ) I
for arbitrary x, y, z. Assume that n ( x , y, z ) . According to Formula 10, there is an element xl such that ( p ) b S x l o ( p S y v pSz)]. Formula 11 implies that n (x,, y, z ) . From Formula 9 we infer that x = xl, whence ( p ) [pSx o ( p S y v pSz)], which was to be derived. Defiltkio.n 6. (Y) (z){(Y
n Z) = (
4 [ n ( x , Y, z ) I I
Definition 6 is justified by Formula 12. Definitions 5 and 6 imply that (x)(Y)[(x
n Y) = (Y n % ) I .
It follows from Axiom 2 that ( E y ) ( E x )( p ) (pSx o - p S y ) , (b) (EY) ( x # Y ) .
[I41
whence [I51
Two special elements, V and A, will now be considered in turn. From Formula 4, there is an element x such that ( 9 ) ( - ~ S X ) , whereas from Definitions 1 and 2, there is at most one such x. This justifies the following definition. Definition 7 .
v = ( . 7 x ) [ ( P )(-PSx)l W e shall prove that ( y ) [ ( y n V ) = y] and ( x ) { ( y )[ ( y fl x ) = y] + x =V). Proof. From ( p ) ( - p S V ) , we infer that ( y ) ( P )b S y o ( p S y v pSV)], which from Formula 13 implies that ( y ) [ n(y, y, V ) ] . Consequently, ( y ) [ ( y n V ) = y], according to Definition 6. Further, suppose that ( y ) [ ( y n x )
1199
CONCEPT OF VISUAL SENSATION
= y]. It follows that (V fl x ) = V, as well as ( x V, which condudes the proof. We have thus established that (k) ( Y )[ ( Y
n
X)
n V ) = x.
Hence x
=
= YI
and specifically
v =
n
( IX){(Y)[(Y
=
x)
[I71
YII.
From Formula 4 and Axiom 2, there is an element x such that ( p ) p S x , and from Definitions 1 and 2, there is at most one such x :
Definition 8. A
= ( 7%) [ ( P ) P S ~ I
W e shall prove that ( Y ) [ ( YU A ) = y] and ( x ) { ( ~ ) [ (Uy x ) = y] -+ x = A ) . Proof. From ( p ) p S A , we infer that ( y ) ( p ) FSy t, (pSy 8r p s ~ ) ] , which from Definitions 3 and 4 implies that ( y ) [ ( y U A ) = y]. Further, assume that ( y ) [ ( y U x ) = y]. Through ( A U x ) = A and ( x U A ) = x, we get x = A, which concludes the proof. Thus we have that ( f i ) ( Y ) [ ( Y U x ) = Yl
and specifically A
Definition 9.
=
( 7 x ) { ( r ) [ ( yU x )
= YII.
-
y = ( t x ) [ ( P )(PSx e= --.PSY)l Definition 9 is justified by Axiom 2 and Definitions 1 and 2. W e show that ( x ) { [ ( x U = V] & [ ( x r l x ) = A ] ) : Proof. According to Definition 9, ( x ) ( p ) ( p ~ ; t, - p S x ) , whence ( x ) ( p ) [- ( P S X & 9s;) & (pSx v P S ; ) ] , and therefore ( x ) { [ ( x U = V] & [(x n = A]}, q.e.d. Thus it is established that
-
x)
x)
x)
u
(EY){[(~ Y)
= VI ~c
[(x
n
Y)
=~
and specifically
Two principles of distribution will be proved, namely,
1 )
Pol
C . BUNDESEN
u
( x ) ( Y ) (z){[x n (Y Z)I [(x n Y) ( x n z)I).
u
= [231
Pr0of.r. Formula 22 is expanded into ( x ) ( y ) ( z ) ( p ) { p S [ x U ( y n z ) ] o p S [ ( x U y ) n ( X U z ) ] ) . By repeated use of Definitions 3, 4, and G and Formula 13, this is reduced to ( x ) ( y ) ( z ) ( p ) { ~ S & X (PSy v ~ S Z ) H ] [ ( p S x & p S y ) v ( p S x & p S z ) ] } , which is clearly true. The proof of Formula 23 is quite sirnilat. Finally, it should be noted that " C " is definable in terms of " U": (XI
(Y){(x
c
Y)
- [(x
u
Y)
= YI).
t241
Proof. By Definitions 1, 3, and 4, Formula 24 is transformed into ( x ) ( y ) { ( P ) ( P S y -+ p S x ) o ( p ) [ ( p S x & P S Y ) pSyl1, which is readily established. Formulas 7, 8, 12, 14, 15, 16, 18, 20, 22, and 23 correspond to a well known set of postulates for a Boolean algebra (Huntington, 1904, pp. 292 f ) . By virtue of Formulas 17, 19, and 21, we have thus established that the set ofvisual impressions augmented by V and A is organized by U , n, and as a Boolean algebra, in which V and A are the universal and null elements, respectively. Hence, from Formulas 5, 6, and 24, it follows that Axioms 1 and 2 and Definitions 1 through 9 are formally adequate. The relations between visual impressions defined by these axioms and definitions do have those formal properties which ate implicit in the terminology of "parts," "unions," and so on. It is convenient to assume the set of visual impressions to be denumerable. It is difficult to ascertain whether this assumption is true. However, if it is false, it will still work as an approximation. Axiom 3. The set of visual impressions is denumerable. To obtain a practical notation for the treatment of total impressions, a pair of recursive definitions is introduced: Definition 10.
and
for n = 1, 2, 3, . . . Definition 11.
1201
CONCEPT OF V I S U A L SENSATION ( X I ) . . . ( x +~I ) [II{xI, . . . , Xn , xn) n Xn + 1) 1,
( II{xI,
. ..
+
I} =
for n = 1, 2, 3, . . . If (Ex)Fx, then expressions "S{x: Fx)" and "n{x: Fx)" are defined through Definitions 10 and 11 by virtue of Axiom 3. It is easily proved that (xl ) . . . (x,) ( 9 ) hSS{xl, . . . , x,) C ) ( ~ S X & I . . . & ~SX,)],from which it follows that
[=I (pSxl v . . . v
( p ) [ p S Z { x : Fx) o ( x ) ( F x + p S x ) ] , provided that ( E x ) F x .
Similarly, we have that (xl) . . . (x,) ( p ) bSn[{xl, . . . , x,) pSx,)], whence ( p ) [PSII{x: Fx)
++ (Ex)( F x & p S x ) ] , provided
c*
that ( E x ) Fx.
[261
At any time, the union of a subject's visual impressions defines his total visual impression: Definition 12. (PI [tote(p) = Z{x: ~ S x l l
As pSh, for any p, {x: pSx) is never empty. Hence Definition 12 needs no restrictions. From Definition 12 and Formula 25 we have ( f ~b S) t o t e ( ~ ) I .
Further, it is provable that
Proof. From Formula 27 and Definition 1, it follows that pSx, if x C tote (p). The remainder of the proof consists in showing that ( p ) (x) {pSx + [x C tote(p)]). Suppose that qStote(p), that is, qSS{x: pSx). It follows from Formula 25 that (x) (pSx -+ @x). Thus we have that ( 9 ) ( q ) [@tote ( p ) + (x) (pSx + qSx)], which is to say that ( p ) ( x ) {pSx + ( q ) [qStote(p) + qSx] ), whence ( p ) (x) {pSx + [x c tote ( p ) ] ), which was to be proved. Let us say that x is a total visual impression, if there is a p such that x is the total visual impression of p: Definition 13. (x){TotaLc
=tote(#)])
It is easy to prove, then, that any proper visual impression equals the intersection of those total impressions of which it is a part: For any x such that x # V , x
= n(y:
( x C y ) & Totaly).
1291
Proof. The following conditions are equivalent: x # V; (Ep)pSx; (Ep) (Ey) { ( x C y) & Ly = tote ( p ) ] ); and (Ey) [(x C y ) & Totaly]. Hence,
1202
C. BUNDESEN
expression "n{y: ( x C y ) & Totaly)" is defined for any x such that x # V. It will now suffice to prove that ( p ) {pSx t, (Ey) [ ( x C y) & Totaly & pSy]) on the assumption that x # V (see Formula 26). First, that ( 9 ) {pSx c (Ey) [ ( x C y ) & Totaly & pSy]) follows from the fact that pSx is implied by ( x C y) & pSy. Second, suppose that pSx. It is implied that x C tote(#), that is, ( E y ) [ ( x C y) gr Totaly gr pSy]. Thus, (p){pSx + ( E y ) [ ( x C y) & Totaly & pSy]), which concludes the proof. It is time to take stock. In the previous section, a reinterpretation of the old notion of elements in visual sensation was proposed. A set of atomic sensations to which any visual impression is reducible was interpreted as a base of sensory elements such that any impression is an intersection of unions of members of that base. The proposal relied on (a) a few definitions of important relations between visual impressions-the relations of part, union, and intersection-and ( b ) the thesis that any visual impression is the intersection of those total impressions of which it is a part. The present section has demonstrated in some detail that the set of visual impressions can, in fact, be organized along the lines previously assumed. The suggested definitions of part, union, and intersection were thus shown to be formally adequate by constructing a Boolean algebra from the set of visual impressions augmented by a universal and a null element. From a formal definition of total visual impressions, it was also established that any visual impression is the intersection of those total impressions in which it takes part. The formal justification for the suggested concept of sensory elements is, of course, no proof that a functionally simple base of elements will ultimately be established. Existing data on sensory feature extraction are suggestive, but the empirical evidence for any particular base of elements is still ambiguous. It appears likely, however, that the search for elements in visual sensation was impeded by the traditional assumption that the content of atomic sensations should be particularly simple, conceptually and introspectively. That assumption was based on the empiricist thesis that atomic sensations ate the germs of concepts; without this thesis, the assumption seems unwarranted. Thus, on the present account of visual sensation, impressions of specific spatial frequencies are formally as suited for the status of sensory elements as are impressions of colored points.
LEVELS IN VISUAL SENSATION From the concept of sensory elements, we turn to the concept of sensory levels. Consider, first, the classical "visual phenomena" (Boring, 1942) such as color mixture, sensitivity, afterimages, and contrast. In past or present terms, these belong to the field of visual sensation. The special theories of these phenomena are sensory ones which cannot-and should not-explain the visual
CONCEPT OF VISUAL SENSATION
1203
identification of such things as color and brightness. Otherwise, the theory of Mach bands (Ratliff, 1965) was disproved by the simple fact that a subject may easily fail to notice these bands. Next, consider the so-called phenomenal constancies, such as the constancies of size, shape, brightness, and color. The traditional theories-from Berkeley (1709/1910) to Helmholtz (1867), and from Woodworth (1938) to distinguish these from true sensory phenomena. to Gibson ( 1966)-used They were commonly treated under the heading of perception. Still, by the present account, the constancies belong to the field of sensation as do the visual phenomena mentioned above. Size conscancy may serve as a paradigm: When a man walks away from you, his apparent size normally remains constant, though his projective size gets progressively smaller. That is, it looks as though the man is getting farther away, and as though his real size remains constant. As you have a visual impression of a man of constant size (see Formulas 1 through 3 ) , this exemplifies perfect size constancy. On the other hand, if you watch a man from a tower, it may well occur that he looks unrealistically small and, perhaps, quite near to you. So your visual impression is one of an unrealistically small man. Even i f you recognize that the man is perfectly normal, this is a case of imperfect size conscancy. Hence, phenomenal size constancy concerns visual impressions as distinct from visual experien;es.* As both the phenomena of the visual field and the constancies of the visual world are captured by the present concept of visual sensation, a distinction between two levels of sensation may be required. A sensory-level distinction would imply that, though the sensation of the visual world is not a matter of conceptual interpretation of the sensations of the visual field, it is functionally based on field sensations rather than directly on retinal stimulation. Such an assumption was suggested by the classical investigations of the effect of reducing the conditions of viewing (see, e.g., Holway & Boring, 1941; Katz, 1911). In reduced conditions where constancy breaks down, different visual world impressions may apparently be formed (derived) with the constraints imposed by a given (primitive) visual field impression. It should be noted how far the problem of the relation between visual field and visual world impressions is really a conceptual one. In a very influential account Gibson (1950) argued that field and world impressions are produced by different modes of visual processing. The world mode should not include the field mode; the two modes should rather exclude each other as should be evidenced by the fact that it seems impossible to examine the visual field while keeping attention to the visual world. In connection with the present concept of visual sensation, however, this argument from introspection 'In contrast, the phenomena of transposition (Ehrenfels, 1890) do not belong to the topic of visual sensation. Imperfect transposition of size is shown i f visual recognition is impaired as a result of a change in size w e n though the visual impressions may be the same as in the case of perfect transposition.
1204
C. BUNDESEN
looses its force: A visual field impression can be specified as an impression of a certain pattern of retinal stimulation. Though a subject will usually not attend to the way the projections of things are reflected in his visual impressions, it is implied (see Formulas 2 and 3) that he has a field impression if he has a visual impression at all. With a visual impression of textured surfaces, for instance, Gibsonian texture gradients are always represented in a field impression. Thus, given the present concept of visual sensation, a sensory-level distinction between visual field and visual world sensation is wholly reasonable.
CONCLUSION The immediate objects of perception are always present in the stimulus situation, but perception requires mental representation. Visual sensation is one type of representation required for visual perception. Sensation implies neither knowledge, nor any kind of conceptual interpretation. Unlike an act of visual perception, a given visual sensation (sense-impression) may equally well be specified in terms of each of several types of represented content. A systematic account of visual sensation may be based on the notion of sensory elements (atomic sensations). A specification of this notion was proposed, and the proposal was formally justified by constructing a Boolean algebra for visual sensations. In considering the idea of sensory levels, however, it was suggested that the sensation of the visual world is functionally based on field sensations. If so, the atomistic pattern of explanation should be restricted to the sensation of the visual field. In consequence, the theory of visual sensation should be an account of the generation of each of the impressions contained in a base of field elements, supplemented by an account of the principles of generation of total visual impressions from total visual field impressions. REFERENCES ARMSTRONG, D . M. Percepiion and the physical world. London: Routledge
& Kegan Paul. 1961. BERKELEY, G. An essay towards a new theory of vision. In A. D . Lindsay ( E d . ) , A neu, theory of vision and oiher wriiings. London: J. M. Dent, 1910. Pp. 1-86. (Originally published 1709) BERKELEY. G. A treatise concernine the ~ r i n c i ~ l eofs human knowledee. In A. D . ~ i d d s a(Ed.), ~ A new theory>f vision an2 other writings. ~ o n d & : J. M Dent, 1710) 1910. Pp. 87-195. (Originally . published BLAKEMORE, C., & CAMPBELL, F. W. On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images. Journal of Physiology, 1969, 203, 237-260.
BORING,E. G. Sensation m d perception in the history of experimental psychology. New York: Appleton-Century, 1942.
BORING, E. G. A history of experimental psychology.
(2nd ed.) New York: Appleton-Century, 1950. CAMPBELL, F. W., & ROBSON, J. G. Application of Fourier analysis to the visibility of gratings. Iournal of Physiology, 1968, 197, 55 1-566. EHF~NPBLS, C. vON. Uber Gestaltqualitaten. Vierteljahrsschrift fur wissenschaftftliche Philosophie, 1890, 14, 249-292. GIBSON,J. J. T h e perception of the visual world. Boston: Houghton, 1950.
CONCEPT OF VISUAL SENSATION
1205
GIBSON, J. J. The senses considered UJ perceptual systems. Boston: Houghton, 1966. GRAHAM, N., & NACHMIAS,J. Detection of grating paaerns containing two spatial frequencies: a comparison of single-channel snd multiple-channels models. Vision Research, 1971, 11, 251-259. HAMLYN, D. W. T h e psychology of perception. London: Routledge & Kegan Paul, 1957. HELMHOLTZ,H . VON. Handbuch der physiologischen Optik. Leipzig: Leopold Voss, 1867. HOLWAY,A. H., & BORING, E. G. Determinants of apparent visual size with distance variant. American Jortrnd of Psychology, 1941, 54, 21-37. HUBEL, D. H. The visual cortex of the brain. Scientific American, 1963, 209(5), 54-62. HUBEL, D. H., & WIESEL,T. N. Receptive fields of single neurones in the cat's striate cortex. Journal of Physiology, 1959, 148, 574-591. HUBEL, D. H., & WIESEL, T. N. Receptive fields, binocular interaction, and functional architecture in the cat's visual cortex. Journal o f Physiology, 1962, 160, 106-154. HUBEL, D. H., & WIESEL. T. N. Receptive fields and functional architecture in rwo nonstriate visual areas (18 and 19) of the cat. Journal of Neurophysiology, 1965, 28. 229-289. H ~ E D., A treatise of human nature. In L. A. Selby-Bigge (Ed.), Hume's treatise. Oxford: Clarendon Press, 1896. (Originally published 1739) HUNTINGTON, E. V. Sets of independent srulates for the algebra of logic. Trans~, 5, 288-309. actions of the Avmican ~ a t h e m a t i c f ~ o c i e t 1904, IITELSON, W . H. The Ames demonstrations in perception. Princeton: Princeton Univer. Press, 1952. KATZ, D Die Erscheinungsweisen der Farben und ihre Beeinflussung durch die individuelle Erfahrung. Zeirschrift fir Psychologie Esganzungsband, 1911, 7 , 1-425. LETWIN, J. Y.,MATURANA,H. R., MCCULLOCH,W. S., & PITIS, W . H. What the frog's eye tells the frog's brain. Proceedings of the Institute of Radio Engineers, 1959, 47, 1940-1951. LOCm, J. An essay concerning human understanding. (I. W . Yolton, Ed.) London: J. M. Dent, 1961. (Originally published 1690) MCCULLOUGH,C. Color adaptation of edge detectors in the human visual system. Science, 1965, 149, 1115-1116. RATLIFF, F. Mach bands: quanlitative studies on neural networks in the retina. San Francisco: Holden-Day, 1965. REID, T. An inquiry into the human mind on the principles of common sense. In W . Hamilton (Ed.), Philosophical works. Vol. 1. Hildesheim: Georg Olms, 1967. Pp. 93-211. (Originally published 1764) REID,T. Essays on the intellectual powers of man. In W. Hamilton (Ed.), Philosophical works. Vol. 1. Hildesheim: Georg Olms, 1967. Pp. 213-508. (Originally published 1785) RossaR, J. B. Logic for mathematicians. New York: McGraw-Hill, 1953. RYLE, G. T h e concept of mind. London: Hutchinson, 1949. SELLARS,W. Empiricism and the philosophy of mind. In H. Feigl & M. Scriven ( M s . ) , Minnesota studies in the philosophy of science. Vol. 1. The foundations of science and the concepts of psychology and psychoanalysis. Minneapolis: Univer. of Minnesota Press, 1956. Pp. 253-329. STROMEYER,C. F., 111, & MANSFIELD,R. J. W. Colored aftereffects produced with moving edges. Perception and Psychophysics, 1970, 7. 108-114. WERTHEIMER,M. Experimentelle Studien iiber das Sehen von Bewegung. Zeitschrift f i r Psychologie, 1912, 61, 161-265. WOODWORTH,R. S. Experimental psychology. New York: Holt, 1938.
Accepted April 20, 1977.
CONCEPT OF VISUAL SENSATION CLAUS BUNDESEN'
Copenhagen University, Denmark Summary.-A direct-realist account of visual sensation is outlined. The explanatory notion of elements in visual sensation (atomic sensations) is reinterpreted, and the suggested interpretation is formally justified by constructing a Boolean algebra for visual sensations. The related notion of sensory levels (visual field vs visual world) is discussed.
This paper is devoted to conceptual clarification of the nature of visual sensation. The explanatory notions of elements and levels in visual sensation are treated in some detail. A general pattern of explanation for visual sensation is thus discussed, but specific modes of physiological processing are not hypothesized. The suggested concept of visual sensation is introduced from a standpoint of direct realism. SENSATION AND ~ R C E P T I O NIN A FRAMEWORK OF REALISM Philosophers have argued that the attempt to make a general psychological theory of perception is doomed to failure (e.g., Hamlyn, 1957; Ryle, 1949). This was not meant to exclude the possibility of psychological inquiry into conditions of visual perception but a psychological theory stating sufficient conditions .for seeing something should be excluded. The sound basis of this thesis appears to be that perception, in ordinary language, is necessarily veridical : Consider a case of perfect visual illusion such as Ames' famous distorted room (Ittelson, 1952). The naive subject looking into the distorted room claims to see a normal rectangular room. In ordinary language the subject is wrong; he cannot see a normal room since rhe room is really distorted. Yet the psychological processes of the subject may, in principle, be exactly the same as they would have been if the room had not been distorted, in which case his daim would have been right. Thus whether a subject perceives something is not only a function of his psychological processes. If the fact that a subject sees something is not purely a psychological one, then psychology needs a term that corresponds to seeing (in the ordinary sense) but lacks the nonpsychological implications of this word. Expressions like visual experiefice can do the job. By definition, then, the visual experience of a subject is uniquely determined by his psychological processes. Further, when a subject sees a normal room, then he experiences that room as normal though the converse is not always the case. 'Thanks are due to Axel Larsen for helpful discussion. Requests for reprints should be sent to Claus Bundesen, Psychological Laboratory, Copenhagen Universirg, Njalsgade 94, DK-2300 Copenhagen S., Denmark.
1192
C.
BUNDESEN
What was the visual experience of Ames when he took the position of his naive subject? It differed significantly from the experience of the naive subject insofar as Ames identified the room as a distorted one. On the other hand, it was similar to the naive experience insofar as it looked to Ames as if the room had been a normal rectangular one. W e may say that his visual k z p ~ e s s i o nwas qualitatively the same as that of the naive subject though his visual identification of the room was different. In general terms a distinction is made between visual impressions and visual experiences, the former being components of the latter. A few examples may serve to further clarify the relations between seeing, visual experiences, and visual impressions: 1. If the timing is just right, two successive flashes of light at spatially separated points appear as continuous movement of a single light, optimal apparent movement (Wertheimer, 1912). More precisely the subject has a visual impression of a continuously moving light. The naive subject is deluded by his visual impression and thinks that a light is actually moving; he has a visual experience of a moving light though he does not really see one. The informed subject is not deluded; he has no visual experience of a moving light though his visual impression is the same. 2. When identifying the letter A visually, one will ordinarily not notice that it contains a triangle. One sees the letter without seeing the triangle, since one has no visual experience of this triangle. Yet, one has a visual impression of the triangle, as one has a visual impression of the A. Visual impressions are most readily characterized (Sellars, 1956) through description of that of which they are impressions (a rectangular room, a moving light, an A ) . In particular, the visual impressions of a subject are often implicitly characterized by statements of the form: It looked to the subject as though the stimulus situation were such and such,
implying that: Judging from the visual impression of the subject, such and such a stimulus situation should be expected,
which means that: The subject had a visual impression of such and such a stimulus situation.
For various reasons a subject may be unable to describe his visual impressions or to describe that of which they are impressions, that is, their content. Indeed, he may not know the content of his impressions because he lacks pertinent concepts. For instance the child who lacks the concept of a triangle cannot know whether he has a visual impression of a triangle. The
CONCEPT OF VISUAL SENSATION
1193
experience presupposes concepts which the impression does not. In this respect even lines and angles are on a par with letters. The suggested account is one of direct realism (cf. Armstrong, 1961) : What is seen is always present in the stimulus situation. Thus a subject does not construct what he perceives and the object is not produced by the perception. Specifically what is seen is not a visual representation of the real thing. When a subject sees a red square, he has a visual experience and, therefore, a visual impression of a red square. Visual experiences and impressions are representations but these are not the objects seen: These are neither red nor square. The framework resembles that of Reid (1764/1967), who apparently was the first to insist upon a distinction between sensation and perception (Boring, 1942). In Reid's ( 1785/1967) terminology, the external senses have a double province-to make us feel, and to make us perceive. They furnish us with a variety of sensations, some pleasant, others painful, and others indifferent; at the same time they give us a conception and an invincible belief of the existence of external objects. . . . This conception and belief which narure produces by means of the senses, we call perception. The feeling which goes along with the perception, we call sensution (p. 247 f ) .
Reid also demonstrated his concept of sensation paradigmatically by cases of illusion without delusion-such as in Example 1 above. Accordingly visual impressions may jusdy be termed visual sensations.
ELEMENTSIN VISUALSENSATION
A notion of simple sense-impressions, atomic sensations, was formed within the British tradition of empiricism and associationism as represented by Locke (1690/1961), Berkeley (1709/1910, 1710/1910), and Hume ( 1739/1896). The simple impressions were held to be immediately given in sensory perception, and these should be the basic elements of the mind. Complex impressions were considered to be compounds of simple ones. In fact any content of the mind, any experience, was assumed to be derived from simple impressions by operations like copying and compounding. It was the tradition of British empiricism "that made perception the primary problem in psychology and that indicated the fundamental line of attack" (Boring, 1950, p. 169). Reid's (1764/1967) categorical distinction between sensation and perception was soon assimilated to the systematic structure of empiricism and associationism. Perception was then considered to be an elaboration of sense-impressions by the addition of associated ideas whereas sensation was treated as the production of pure impressions. The idea that perceptual experience is derived from atomic sensations is still alive. Beginning with the works of Hubel and Wiesel (1959) and Lettvin, Maturana, McCdoch, and Pitts (1959), neurophysiological studies of eye
1194
C. BUNDESEN
and brain succeeded in finding different types of single cells which responded specifically to characteristic features of retinal stimulation-such as the presence of an edge oriented in a certain way within a specific part of the visual field. These cells seem to be organized hierarchically such that higher levels are concerned with more complex features (Hubel & Wiesel, 1962, 1965). In one interpretation the simple sensory features correspond to atomic sensations, whereas higher-order features represent steps in "perceptual generalization" (Hubel, 1963). Whether or not the atomistic approach to perception is tenable, however, some of the sensory features may possibly correspond to atomic sensations from which complex impressions are built by compounding. A formal reconstruction of the notion of atomic sensations will be developed, using the present concept of visual impressions. The first problem concerns the definition of relations by which the atomic organization can be implemented in the universe of visual impressions. Some definitions are suggested below: 1. One impression is a part of another, if the presence of the former is a necessary condition for the presence of the latter. For example, the impression of an angle is a part of the impression of a triangle, and the impression of redness is part of the impression of a red square. 2. One impression is the anion of some other impressions, if the presence of the former is a necessary and sufficient condition for the joint presence of the other ones. For example, the impression of a pair of lines is a union of two impressions of single lines. 3. One impression is the intersection of some other impressions, if it is the union of those parts which are common to these. For example, the impression of circularity is the intersection of all impressions of circular objects. It seems to follow from these definitions that the union of a subject's current visual impressions defines his total visual impression and, further, that any visual impression equals the intersection of those total impressions in which it takes part. Let E be a set of visual impressions such that any total impression is a union of members of E. If the sensory generation of each of the members of E were explained, then the sensory generation of any total impression could, in principle, be derived. Further the generation of any visual impression would be derivable, as the impression could be specified as an intersection of total impressions. In short, any visual impression could be reduced to E, as it would be an intersection of unions of members of E. If no proper subset of E could do the same job, E would qualify as a bare o f sensory elementr. The idea of a base of sensory elements is clearly related to the notion of a set of atomic sensations to which any impression is reducible. On the present account, however, there are many different bases of sensory elements. An obvious base is provided by the set of all total impressions, but this is
CONCEPT OF VISUAL SENSATION
1195
hardly the most simple one. The problem is, accordingly, to find a base of sensory elements which is optimal with respect to functional simplicity. TOa good first approximation any total impression can be uniquely specified by content in terms of moving, colored regions in three-dimensional space. Hence, it is reasonable to search for a functionally simple base of sensory elements, the contents of which are expressed in terms of color, shape, and movement. Existing data on sensory feature extraction suggest that some of these elements may be impressions of colored, moving line segments at specific spatial positions (McCullough, 1965; Stromeyer & Mansfield, 1970) or, possibly, impressions of specific spatial frequencies in the two dimensions of the visual field (Blakemore & Campbell, 1969; Campbell & Robson, 1968; Graham & Nachmias, 1971). The suggested interpretation involves the assumption that a given visual impression may be specified uniquely by each of several types of represented content. It should be noted how this assumption relates to the fundamental distinction between sensing and knowing: Given that the visual identification of an object is based on a visual impression of that object, sensation and percepcual identification ate not discriminable by the types of their content. The difference between sensing and knowing, however, is expressed by the ways in which these relate to their content. An act of visual identification involves a specific conceptual interpretation on the p a t of the subject, and the content of the act is the meaning of that interpretation; a full desuiption of the act should therefore exhaust its content. The content of a visual impression, on the other hand, is indicated to the subject rather than conceived by the subject. As suggested in Formula 2, such indications may be grounded in a multitude of contingent correlations. A full description should specify the impression uniquely in terms of indicated content. Selection among unique specifications should be a matter of convenience, however, and exhaustive description of indicated content should be pointless. The difference between perceptual interpretation and sensory indication is thus reflected in the fact that, unlike an act of visual perception, a given visual impression may equally well be specified in terms of each of several types of represented content. BOOLEANALGEBRA OF VISUALSENSATIONS The previous account of the notion of sensory elements in vision was based on a few definitions of important relations between visual impressionsthe relations of patt, union, and intersection. Any atomistic approach to sensation necessarily presupposes relations like these. It may still be questioned, however, whether the suggested definitions ate formally adequate, that is, whether the defined relations do have the required formal properties. For example, it is easy to see that the defined "patt" relation has the required prop-
1196
C . BUNDESEN
erty of transitivity, but it is not at all obvious that the principles of disuibution are valid for the defined relations of "union" and "intersection." The present section demonstrates that the set of visual impressions can, in fact, be organized by Boolean relations along the lines previously suggested. Thus, a Boolean algebra is formed from the set of visual impressions (which is augmented by two purely formal entities: a universal element and a null element). Further the concept of total visual impressions is formally defined, and it is established that any visual impression is the intersection of those total impressions of which it is a part. The construction is founded on three existential postulates. First, if impressions y and z may coexist, then there is an impression x which is defined by the joint presence of y and z. Second, for any impression y, there is an impression x which is defined by the absence of y. Third, there is an impression x such that x is never present. The third postulate has no material content but serves a technical function in providing the system with universal and null elements. In the following presentation, p and q are variables for persons at temporal points, and x, y, z, w , and x,, y,, z,, w, ( n = 1, 2, 3, . . .) are variables for visual impressions. S is a binary predicate which is true of a p (left field) and an x (right field) such that p has x. The three postulates above are summarized in Axioms 1 and 2 below: A x i o m 1.
A x i o m 2.
Expbmtion. In the suggested formalization, the first postulate states that ( Y )(z){(Ep) (pSy & pSz) + (Ex) ( p ) b S x @ (PSy & pSz)l), which follows from Axiom 1. The second postulate is expressed as Axiom 2. The third postulate states that
which follows from Axioms 1 and 2, since the larter implies the existence of elements y and z such that ( p ) [ H (pSy & ~ S Z ) ] . The formalized postulates thus follow from the axioms. To prove the converse, it will suffice to derive Axiom 1 from the first and third postulates. Assuming that (Ep) (pSy & pSz), then (Ex) (p) b S x t, (pSy & p S z ) ] , according to the first postulate; assuming (Ep) (pSy & ~ S Z )then , (Ex) ( 9 ) PSx t, (pSy & pSz)] by virtue of that the third postulate. W e condude that the axioms are logically equivalent to the formalized postulates. N
CONCEPT OF VISUAL SENSATION
Definition 1. Definition 2. ( x )( y ) { ( x = y )
Definitions 1 and 2 entail
* ( P ) (PSY
-
( x )( Y ) [ ( x C Y )
+
PSX)l
[ ( xC y) & ( y
cx)])
and ( x ) ( Y ) { [ ( x= Y )
[GI As the formal properties of the identity relation are reducible to reflexivity and substitutability (Rosser, 1953), Formulas 5 and 6 show the formal adequacy of Definition 2.
Definition 3. ( x )( Y ) ( z ) { U ( x , Y , z )
PSXI
+
- ( P I [Psx
PSY).
(PSY Q' pSz)l)
From Axiom 1 and Definition 3 it follows that ( y ) ( z ) ( E x ) [ U ( x , y, z ) ] , and from Definitions 2 and 3 it follows that ( x ) ( y ) ( z ) ( w ){ [ U ( x , y, z ) & U ( w , y, z ) ] + ( x = w ) ) . Consequently, U is a composition on the set of visual impressions,
[71
which justifies the next definition.
Definition 4. ( Y ) ( z ) { ( YU z )
= (7%)[ U (x,Y, z)I)
Definitions 3 and 4 imply that
-
( x )( Y ) [ ( x U Y )
Definition S. (x) (Y) (z)
tn
( x , Y ,Z )
* ( P ) [PS
=
%)I-
(Y U
(w) ((w
c Y BL w c z ) + P S W ) ~ )
By virtue of Definition 2, it follows from Definition 5 that ( x ) ( Y ) ( z ) ( w ) { [ n( x , Y ,
2)
t~
n ( w , YI
Z)I
-)
(X
= w)).
191
To show that ( y ) (z) (Ex) [fl ( x , y, z ) ] , the first step is to prove that
Proof. According to Axiom 2, for any elements y, z , there are elements y , z , such that ( 9 ) ( p S y l o w p S y ) and ( p ) ( p S z l o ~ p S z ) . From Axiom 1, there is an element xl such that ( p ) b S x l o ( P S y l & ~ S Z I ) ] .From Axiom 2 , accordingly, an element x exists such that ( 9 ) ( p S x o - ~ S X I ) , whence ( p ) b S x t, ( p S y = & ~ S Z I ) ]and , therefore ( p ) b S x t, ( p S y v p S z ) ] , which
-
was to be proved.
The next step is to prove that ( x ) ( Y ) ( z ) { ( P ) [ P s ~o (PSY v P S Z ) I
-,
n (x, Y, .)I.
~111
Proof. Assume that ( p ) b S x o ( p S y v pSz)]. By virtue of Definition 5, it will suffice to derive that ( p ) {pSx o ( w )[ ( w c y & w C z ) + pSw]). Suppose that pSx. Then either pSy or pSz, each of which implies that ( w )[ ( w C y & w C z ) + pSw]. Conversely, suppose that ( w )[ ( w C y & w C z ) + pSw]. As the initial assumption implies that x C y and x C z, it follows that pSx. Hence Formula 11 is established. Formulas 10 and 11 show that ( y ) ( z ) ( E x )[n ( x , y, z ) ] . Thus, considering Formula 9, we have that
n
- -
is a composition on the set of visual impressions
[I21
Note that Formula 11 can be strengthened to
n ( x , Y , z)). [I31 Proof. It is sufficient to derive ( p ) PSx t, ( 9 S y v p S z ) ] from n ( x , y, z) (XI (Y) (z)((P)[Psx
(PSY v P S Z ) I
for arbitrary x, y, z. Assume that n ( x , y, z ) . According to Formula 10, there is an element xl such that ( p ) b S x l o ( p S y v pSz)]. Formula 11 implies that n (x,, y, z ) . From Formula 9 we infer that x = xl, whence ( p ) [pSx o ( p S y v pSz)], which was to be derived. Defiltkio.n 6. (Y) (z){(Y
n Z) = (
4 [ n ( x , Y, z ) I I
Definition 6 is justified by Formula 12. Definitions 5 and 6 imply that (x)(Y)[(x
n Y) = (Y n % ) I .
It follows from Axiom 2 that ( E y ) ( E x )( p ) (pSx o - p S y ) , (b) (EY) ( x # Y ) .
[I41
whence [I51
Two special elements, V and A, will now be considered in turn. From Formula 4, there is an element x such that ( 9 ) ( - ~ S X ) , whereas from Definitions 1 and 2, there is at most one such x. This justifies the following definition. Definition 7 .
v = ( . 7 x ) [ ( P )(-PSx)l W e shall prove that ( y ) [ ( y n V ) = y] and ( x ) { ( y )[ ( y fl x ) = y] + x =V). Proof. From ( p ) ( - p S V ) , we infer that ( y ) ( P )b S y o ( p S y v pSV)], which from Formula 13 implies that ( y ) [ n(y, y, V ) ] . Consequently, ( y ) [ ( y n V ) = y], according to Definition 6. Further, suppose that ( y ) [ ( y n x )
1199
CONCEPT OF VISUAL SENSATION
= y]. It follows that (V fl x ) = V, as well as ( x V, which condudes the proof. We have thus established that (k) ( Y )[ ( Y
n
X)
n V ) = x.
Hence x
=
= YI
and specifically
v =
n
( IX){(Y)[(Y
=
x)
[I71
YII.
From Formula 4 and Axiom 2, there is an element x such that ( p ) p S x , and from Definitions 1 and 2, there is at most one such x :
Definition 8. A
= ( 7%) [ ( P ) P S ~ I
W e shall prove that ( Y ) [ ( YU A ) = y] and ( x ) { ( ~ ) [ (Uy x ) = y] -+ x = A ) . Proof. From ( p ) p S A , we infer that ( y ) ( p ) FSy t, (pSy 8r p s ~ ) ] , which from Definitions 3 and 4 implies that ( y ) [ ( y U A ) = y]. Further, assume that ( y ) [ ( y U x ) = y]. Through ( A U x ) = A and ( x U A ) = x, we get x = A, which concludes the proof. Thus we have that ( f i ) ( Y ) [ ( Y U x ) = Yl
and specifically A
Definition 9.
=
( 7 x ) { ( r ) [ ( yU x )
= YII.
-
y = ( t x ) [ ( P )(PSx e= --.PSY)l Definition 9 is justified by Axiom 2 and Definitions 1 and 2. W e show that ( x ) { [ ( x U = V] & [ ( x r l x ) = A ] ) : Proof. According to Definition 9, ( x ) ( p ) ( p ~ ; t, - p S x ) , whence ( x ) ( p ) [- ( P S X & 9s;) & (pSx v P S ; ) ] , and therefore ( x ) { [ ( x U = V] & [(x n = A]}, q.e.d. Thus it is established that
-
x)
x)
x)
u
(EY){[(~ Y)
= VI ~c
[(x
n
Y)
=~
and specifically
Two principles of distribution will be proved, namely,
1 )
Pol
C . BUNDESEN
u
( x ) ( Y ) (z){[x n (Y Z)I [(x n Y) ( x n z)I).
u
= [231
Pr0of.r. Formula 22 is expanded into ( x ) ( y ) ( z ) ( p ) { p S [ x U ( y n z ) ] o p S [ ( x U y ) n ( X U z ) ] ) . By repeated use of Definitions 3, 4, and G and Formula 13, this is reduced to ( x ) ( y ) ( z ) ( p ) { ~ S & X (PSy v ~ S Z ) H ] [ ( p S x & p S y ) v ( p S x & p S z ) ] } , which is clearly true. The proof of Formula 23 is quite sirnilat. Finally, it should be noted that " C " is definable in terms of " U": (XI
(Y){(x
c
Y)
- [(x
u
Y)
= YI).
t241
Proof. By Definitions 1, 3, and 4, Formula 24 is transformed into ( x ) ( y ) { ( P ) ( P S y -+ p S x ) o ( p ) [ ( p S x & P S Y ) pSyl1, which is readily established. Formulas 7, 8, 12, 14, 15, 16, 18, 20, 22, and 23 correspond to a well known set of postulates for a Boolean algebra (Huntington, 1904, pp. 292 f ) . By virtue of Formulas 17, 19, and 21, we have thus established that the set ofvisual impressions augmented by V and A is organized by U , n, and as a Boolean algebra, in which V and A are the universal and null elements, respectively. Hence, from Formulas 5, 6, and 24, it follows that Axioms 1 and 2 and Definitions 1 through 9 are formally adequate. The relations between visual impressions defined by these axioms and definitions do have those formal properties which ate implicit in the terminology of "parts," "unions," and so on. It is convenient to assume the set of visual impressions to be denumerable. It is difficult to ascertain whether this assumption is true. However, if it is false, it will still work as an approximation. Axiom 3. The set of visual impressions is denumerable. To obtain a practical notation for the treatment of total impressions, a pair of recursive definitions is introduced: Definition 10.
and
for n = 1, 2, 3, . . . Definition 11.
1201
CONCEPT OF V I S U A L SENSATION ( X I ) . . . ( x +~I ) [II{xI, . . . , Xn , xn) n Xn + 1) 1,
( II{xI,
. ..
+
I} =
for n = 1, 2, 3, . . . If (Ex)Fx, then expressions "S{x: Fx)" and "n{x: Fx)" are defined through Definitions 10 and 11 by virtue of Axiom 3. It is easily proved that (xl ) . . . (x,) ( 9 ) hSS{xl, . . . , x,) C ) ( ~ S X & I . . . & ~SX,)],from which it follows that
[=I (pSxl v . . . v
( p ) [ p S Z { x : Fx) o ( x ) ( F x + p S x ) ] , provided that ( E x ) F x .
Similarly, we have that (xl) . . . (x,) ( p ) bSn[{xl, . . . , x,) pSx,)], whence ( p ) [PSII{x: Fx)
++ (Ex)( F x & p S x ) ] , provided
c*
that ( E x ) Fx.
[261
At any time, the union of a subject's visual impressions defines his total visual impression: Definition 12. (PI [tote(p) = Z{x: ~ S x l l
As pSh, for any p, {x: pSx) is never empty. Hence Definition 12 needs no restrictions. From Definition 12 and Formula 25 we have ( f ~b S) t o t e ( ~ ) I .
Further, it is provable that
Proof. From Formula 27 and Definition 1, it follows that pSx, if x C tote (p). The remainder of the proof consists in showing that ( p ) (x) {pSx + [x C tote(p)]). Suppose that qStote(p), that is, qSS{x: pSx). It follows from Formula 25 that (x) (pSx -+ @x). Thus we have that ( 9 ) ( q ) [@tote ( p ) + (x) (pSx + qSx)], which is to say that ( p ) ( x ) {pSx + ( q ) [qStote(p) + qSx] ), whence ( p ) (x) {pSx + [x c tote ( p ) ] ), which was to be proved. Let us say that x is a total visual impression, if there is a p such that x is the total visual impression of p: Definition 13. (x){TotaLc
=tote(#)])
It is easy to prove, then, that any proper visual impression equals the intersection of those total impressions of which it is a part: For any x such that x # V , x
= n(y:
( x C y ) & Totaly).
1291
Proof. The following conditions are equivalent: x # V; (Ep)pSx; (Ep) (Ey) { ( x C y) & Ly = tote ( p ) ] ); and (Ey) [(x C y ) & Totaly]. Hence,
1202
C. BUNDESEN
expression "n{y: ( x C y ) & Totaly)" is defined for any x such that x # V. It will now suffice to prove that ( p ) {pSx t, (Ey) [ ( x C y) & Totaly & pSy]) on the assumption that x # V (see Formula 26). First, that ( 9 ) {pSx c (Ey) [ ( x C y ) & Totaly & pSy]) follows from the fact that pSx is implied by ( x C y) & pSy. Second, suppose that pSx. It is implied that x C tote(#), that is, ( E y ) [ ( x C y) gr Totaly gr pSy]. Thus, (p){pSx + ( E y ) [ ( x C y) & Totaly & pSy]), which concludes the proof. It is time to take stock. In the previous section, a reinterpretation of the old notion of elements in visual sensation was proposed. A set of atomic sensations to which any visual impression is reducible was interpreted as a base of sensory elements such that any impression is an intersection of unions of members of that base. The proposal relied on (a) a few definitions of important relations between visual impressions-the relations of part, union, and intersection-and ( b ) the thesis that any visual impression is the intersection of those total impressions of which it is a part. The present section has demonstrated in some detail that the set of visual impressions can, in fact, be organized along the lines previously assumed. The suggested definitions of part, union, and intersection were thus shown to be formally adequate by constructing a Boolean algebra from the set of visual impressions augmented by a universal and a null element. From a formal definition of total visual impressions, it was also established that any visual impression is the intersection of those total impressions in which it takes part. The formal justification for the suggested concept of sensory elements is, of course, no proof that a functionally simple base of elements will ultimately be established. Existing data on sensory feature extraction are suggestive, but the empirical evidence for any particular base of elements is still ambiguous. It appears likely, however, that the search for elements in visual sensation was impeded by the traditional assumption that the content of atomic sensations should be particularly simple, conceptually and introspectively. That assumption was based on the empiricist thesis that atomic sensations ate the germs of concepts; without this thesis, the assumption seems unwarranted. Thus, on the present account of visual sensation, impressions of specific spatial frequencies are formally as suited for the status of sensory elements as are impressions of colored points.
LEVELS IN VISUAL SENSATION From the concept of sensory elements, we turn to the concept of sensory levels. Consider, first, the classical "visual phenomena" (Boring, 1942) such as color mixture, sensitivity, afterimages, and contrast. In past or present terms, these belong to the field of visual sensation. The special theories of these phenomena are sensory ones which cannot-and should not-explain the visual
CONCEPT OF VISUAL SENSATION
1203
identification of such things as color and brightness. Otherwise, the theory of Mach bands (Ratliff, 1965) was disproved by the simple fact that a subject may easily fail to notice these bands. Next, consider the so-called phenomenal constancies, such as the constancies of size, shape, brightness, and color. The traditional theories-from Berkeley (1709/1910) to Helmholtz (1867), and from Woodworth (1938) to distinguish these from true sensory phenomena. to Gibson ( 1966)-used They were commonly treated under the heading of perception. Still, by the present account, the constancies belong to the field of sensation as do the visual phenomena mentioned above. Size conscancy may serve as a paradigm: When a man walks away from you, his apparent size normally remains constant, though his projective size gets progressively smaller. That is, it looks as though the man is getting farther away, and as though his real size remains constant. As you have a visual impression of a man of constant size (see Formulas 1 through 3 ) , this exemplifies perfect size constancy. On the other hand, if you watch a man from a tower, it may well occur that he looks unrealistically small and, perhaps, quite near to you. So your visual impression is one of an unrealistically small man. Even i f you recognize that the man is perfectly normal, this is a case of imperfect size conscancy. Hence, phenomenal size constancy concerns visual impressions as distinct from visual experien;es.* As both the phenomena of the visual field and the constancies of the visual world are captured by the present concept of visual sensation, a distinction between two levels of sensation may be required. A sensory-level distinction would imply that, though the sensation of the visual world is not a matter of conceptual interpretation of the sensations of the visual field, it is functionally based on field sensations rather than directly on retinal stimulation. Such an assumption was suggested by the classical investigations of the effect of reducing the conditions of viewing (see, e.g., Holway & Boring, 1941; Katz, 1911). In reduced conditions where constancy breaks down, different visual world impressions may apparently be formed (derived) with the constraints imposed by a given (primitive) visual field impression. It should be noted how far the problem of the relation between visual field and visual world impressions is really a conceptual one. In a very influential account Gibson (1950) argued that field and world impressions are produced by different modes of visual processing. The world mode should not include the field mode; the two modes should rather exclude each other as should be evidenced by the fact that it seems impossible to examine the visual field while keeping attention to the visual world. In connection with the present concept of visual sensation, however, this argument from introspection 'In contrast, the phenomena of transposition (Ehrenfels, 1890) do not belong to the topic of visual sensation. Imperfect transposition of size is shown i f visual recognition is impaired as a result of a change in size w e n though the visual impressions may be the same as in the case of perfect transposition.
1204
C. BUNDESEN
looses its force: A visual field impression can be specified as an impression of a certain pattern of retinal stimulation. Though a subject will usually not attend to the way the projections of things are reflected in his visual impressions, it is implied (see Formulas 2 and 3) that he has a field impression if he has a visual impression at all. With a visual impression of textured surfaces, for instance, Gibsonian texture gradients are always represented in a field impression. Thus, given the present concept of visual sensation, a sensory-level distinction between visual field and visual world sensation is wholly reasonable.
CONCLUSION The immediate objects of perception are always present in the stimulus situation, but perception requires mental representation. Visual sensation is one type of representation required for visual perception. Sensation implies neither knowledge, nor any kind of conceptual interpretation. Unlike an act of visual perception, a given visual sensation (sense-impression) may equally well be specified in terms of each of several types of represented content. A systematic account of visual sensation may be based on the notion of sensory elements (atomic sensations). A specification of this notion was proposed, and the proposal was formally justified by constructing a Boolean algebra for visual sensations. In considering the idea of sensory levels, however, it was suggested that the sensation of the visual world is functionally based on field sensations. If so, the atomistic pattern of explanation should be restricted to the sensation of the visual field. In consequence, the theory of visual sensation should be an account of the generation of each of the impressions contained in a base of field elements, supplemented by an account of the principles of generation of total visual impressions from total visual field impressions. REFERENCES ARMSTRONG, D . M. Percepiion and the physical world. London: Routledge
& Kegan Paul. 1961. BERKELEY, G. An essay towards a new theory of vision. In A. D . Lindsay ( E d . ) , A neu, theory of vision and oiher wriiings. London: J. M. Dent, 1910. Pp. 1-86. (Originally published 1709) BERKELEY. G. A treatise concernine the ~ r i n c i ~ l eofs human knowledee. In A. D . ~ i d d s a(Ed.), ~ A new theory>f vision an2 other writings. ~ o n d & : J. M Dent, 1710) 1910. Pp. 87-195. (Originally . published BLAKEMORE, C., & CAMPBELL, F. W. On the existence of neurons in the human visual system selectively sensitive to the orientation and size of retinal images. Journal of Physiology, 1969, 203, 237-260.
BORING,E. G. Sensation m d perception in the history of experimental psychology. New York: Appleton-Century, 1942.
BORING, E. G. A history of experimental psychology.
(2nd ed.) New York: Appleton-Century, 1950. CAMPBELL, F. W., & ROBSON, J. G. Application of Fourier analysis to the visibility of gratings. Iournal of Physiology, 1968, 197, 55 1-566. EHF~NPBLS, C. vON. Uber Gestaltqualitaten. Vierteljahrsschrift fur wissenschaftftliche Philosophie, 1890, 14, 249-292. GIBSON,J. J. T h e perception of the visual world. Boston: Houghton, 1950.
CONCEPT OF VISUAL SENSATION
1205
GIBSON, J. J. The senses considered UJ perceptual systems. Boston: Houghton, 1966. GRAHAM, N., & NACHMIAS,J. Detection of grating paaerns containing two spatial frequencies: a comparison of single-channel snd multiple-channels models. Vision Research, 1971, 11, 251-259. HAMLYN, D. W. T h e psychology of perception. London: Routledge & Kegan Paul, 1957. HELMHOLTZ,H . VON. Handbuch der physiologischen Optik. Leipzig: Leopold Voss, 1867. HOLWAY,A. H., & BORING, E. G. Determinants of apparent visual size with distance variant. American Jortrnd of Psychology, 1941, 54, 21-37. HUBEL, D. H. The visual cortex of the brain. Scientific American, 1963, 209(5), 54-62. HUBEL, D. H., & WIESEL,T. N. Receptive fields of single neurones in the cat's striate cortex. Journal of Physiology, 1959, 148, 574-591. HUBEL, D. H., & WIESEL, T. N. Receptive fields, binocular interaction, and functional architecture in the cat's visual cortex. Journal o f Physiology, 1962, 160, 106-154. HUBEL, D. H., & WIESEL. T. N. Receptive fields and functional architecture in rwo nonstriate visual areas (18 and 19) of the cat. Journal of Neurophysiology, 1965, 28. 229-289. H ~ E D., A treatise of human nature. In L. A. Selby-Bigge (Ed.), Hume's treatise. Oxford: Clarendon Press, 1896. (Originally published 1739) HUNTINGTON, E. V. Sets of independent srulates for the algebra of logic. Trans~, 5, 288-309. actions of the Avmican ~ a t h e m a t i c f ~ o c i e t 1904, IITELSON, W . H. The Ames demonstrations in perception. Princeton: Princeton Univer. Press, 1952. KATZ, D Die Erscheinungsweisen der Farben und ihre Beeinflussung durch die individuelle Erfahrung. Zeirschrift fir Psychologie Esganzungsband, 1911, 7 , 1-425. LETWIN, J. Y.,MATURANA,H. R., MCCULLOCH,W. S., & PITIS, W . H. What the frog's eye tells the frog's brain. Proceedings of the Institute of Radio Engineers, 1959, 47, 1940-1951. LOCm, J. An essay concerning human understanding. (I. W . Yolton, Ed.) London: J. M. Dent, 1961. (Originally published 1690) MCCULLOUGH,C. Color adaptation of edge detectors in the human visual system. Science, 1965, 149, 1115-1116. RATLIFF, F. Mach bands: quanlitative studies on neural networks in the retina. San Francisco: Holden-Day, 1965. REID, T. An inquiry into the human mind on the principles of common sense. In W . Hamilton (Ed.), Philosophical works. Vol. 1. Hildesheim: Georg Olms, 1967. Pp. 93-211. (Originally published 1764) REID,T. Essays on the intellectual powers of man. In W. Hamilton (Ed.), Philosophical works. Vol. 1. Hildesheim: Georg Olms, 1967. Pp. 213-508. (Originally published 1785) RossaR, J. B. Logic for mathematicians. New York: McGraw-Hill, 1953. RYLE, G. T h e concept of mind. London: Hutchinson, 1949. SELLARS,W. Empiricism and the philosophy of mind. In H. Feigl & M. Scriven ( M s . ) , Minnesota studies in the philosophy of science. Vol. 1. The foundations of science and the concepts of psychology and psychoanalysis. Minneapolis: Univer. of Minnesota Press, 1956. Pp. 253-329. STROMEYER,C. F., 111, & MANSFIELD,R. J. W. Colored aftereffects produced with moving edges. Perception and Psychophysics, 1970, 7. 108-114. WERTHEIMER,M. Experimentelle Studien iiber das Sehen von Bewegung. Zeitschrift f i r Psychologie, 1912, 61, 161-265. WOODWORTH,R. S. Experimental psychology. New York: Holt, 1938.
Accepted April 20, 1977.
