In-1
Introduction
     The elements of perception may be identified by their simplicity. They are
simple in the sense that they cannot be in any way transformed; they are proper
elements because they genuinely provide the foundations of empirical claims.
     The development of the analysis of perception leads to the recognition
first of unbridgeable differences in sensory experience, and thence to the
limits which sense imposes on theory. Subsequently some contemporary puzzles
are recast in a less misleading or more promising form and solutions are
proposed.
     It is possible to identify sensory information about the world and so
distinguish this information from any theories in which it may figure. A clear
division can be drawn between observation statements which are comparatively
complex assertions about what is perceived or what, in principle, could be
perceived, and the literally sensed information which at the present moment can
simply be reported by a perceiver. Both simple reports and observation
statements are distinguished in their turn from the systematic statements of
the empirical sciences and from the informal empirical claims reflected by
ordinary usage.
     Historically the elements of perception can be traced to those ideas which
Berkeley introduced to the world in his Principles in 1710. Among the rules
governing ideas was his assertion that an idea must be perceived in order to be
an idea at all; that is, 'esse is percipi'.1 This fundamental condition was
developed partly in his MS notebooks2 and later in his published works, with
the result that the Berkeleyan idea emerged as a quite distinctive
philosophical concept, and strikingly unlike any 'idea' as understood either by
Locke or later by Hume.
     Berkeley did not fully exploit the implications of his theory of ideas,
largely no doubt because he was a serious working cleric who gave only a part
of his study to philosophy. It is well-known too that the Principles which we
read today is only Part I of a four-part work. The other Parts appear as traces
in the notebooks, or sometimes provide the subject matter of other volumes
which he published at intervals throughout his life.3 It is also true that
Berkeley held several views about the external world which were incompatible
with one another, and which he in fact did not even attempt to resolve. I have
shown elsewhere that the sources of these conflicts were his scientific
assumptions, not the specific features of his account of ideas.4
failed to develop the implications of Berkeley's ideas. This fact is apparent
to any inquirer, and the reason is not far to seek. With few exceptions,
scholars have not recognized the role of the theory of notions which Berkeley
introduced in order to balance his theory of ideas.5 Consequently the concept
of the Berkeleyan idea has remained rather more bland than is justified by the
records. As I shall argue in what follows, the most fruitful account of ideas
identifies them as the elements of perception, and in markedly restrictive
terms.
     This approach requires the explicit recognition that notions provide a
counter-poise for ideas and always have done so.1 For Berkeley, notions include
both relations and minds. They are those things that can be known, but cannot
be perceived. Among them is found, of course, the celebrated rule that, for an
idea, 'to be is to be perceived'. In any event, the Berkeleyan ideas were not
given the development which brings out their peculiar merits, and which so
clearly separates them from all other ideas and comparable concepts.
     The essential points made by Berkeley can be stated briefly. Each idea is,
by definition, that which is perceived by the sense appropriate to it. For our
purposes, the most interesting ideas are those pertaining to sight, touch and
hearing, which are, respectively, a particular color or combination of colors;
a continuous or discontinuous surface; and a particular pitch, whether definite
or indefinite. According to Berkeley, an idea may be sensed, imagined or
remembered. It may also be either simple, as is a perceived yellow; or complex,
                                                               In-2
as is a perceived yellow lemon. Some of the more telling features of his theory
of ideas follow from these few explicit rules.
     An idea is either a specific sensation, or it is an image or mental
picture derived from whichever sense one pleases. A test by which some supposed
idea may be identified as an idea is whether one can form an image of it.
     Each idea is clear, complete at the moment it is perceived, and cannot
recur. An idea is clear in the sense that it is that particular idea and no
other. If it is indistinct, it is clearly an indistinct idea. At the moment it
is perceived an idea is complete because it has no hidden parts, nor can it
possess a distant side or be perceived from an alternative perspective. No idea
can recur because, by definition, each idea exists at the moment it is
perceived. An idea may be succeeded by a qualitatively identical idea, but the
perception of an identical idea marks a new moment, not the recurrence of a
previous moment together with the idea which then signaled it. Strictly
speaking too, the moment at which each idea is perceived is properly attributed
to the perceiver, not to the idea. Thus, an idea is perceived at a given
moment, and a new idea indicates a successive moment. But the successive
moments, like the ideas, belong to the personal history of the perceiver in
which each idea occurs only once.
     Most important is the recognition that every idea is logically independent
of every other idea. This follows readily enough from Berkeley's having
assigned relations to his theory of notions, but some of the remoter
consequences have passed unnoticed. For one thing Berkeley insisted that
nothing can be like an idea but an idea.1 The likeness exhibited by
qualitatively identical ideas is not therefore itself an idea. Likeness, as
distinct from the ideas which are alike, is not perceptible. What indeed is the
image of likeness?
     It is worth noticing too that a putative absent idea is not an idea at
all. The phrase 'absent idea' is a contradiction in terms; or at best it may be
interpreted as an imprecise way of referring to some sensory experience other
than those presently occurring.1 In either case, an absent idea is not to be
understood as some especially obscure kind of idea which is now veiled and only
awaits perception.
     This excursion into Berkeleyan theory presents the historical case for
identifying the elements of perception with ideas as found in the literature.
It is acknowledged that Berkeley did not emphasize the same points which I
shall develop, nor is it likely that he would altogether have approved of some
of the conclusions. Still the ancestry of this leading concept is not in
dispute; hence the choice of the words 'perception' and 'idea' as terms which
distinguish sensory experience from the claims that we make about it.
     In the teeth of much customary usage I shall take the words 'perception'
and 'sensation' to be equivalent. This is done not from the sheer love of
opposition, but in order to signal a departure from the usual tracks of
discussion. Historical precedent can again be found in Berkeley, but the
important consideration is that some necessary distinctions are best drawn by
eliminating the psychological overtones attaching to these two terms.
     From this sketch of the background it is apparent that strictly
interpreted ideas introduce a slant on sense experience that is notably
different from other accounts. The explanatory value of these special ideas
springs from a re-division of the information which no one pretends is not
available to any ordinary perceiver. It is not disputed that the perceiver's
beliefs and habitual use of language must figure in any account of ideas, but
beliefs and language cannot replace the perceived idea, and they are
distinguishable from it. The enterprise is to discover in which respects ideas
determine evidence by showing first, how they support observation claims; and
ultimately, how they come to limit the redescription of physical objects.
     To sum up, Berkeley was right to insist on the rigid distinction between
ideas and everything else that can be thought, although ideas may be stranger
than even he supposed. At any rate some of the special features of ideas lend
                                                              In-3
themselves to the solution of problems that have arisen from fairly commonplace
empirical descriptions. With sufficient application, the less obvious terms of
some well-known puzzles also can be isolated and examined, as we shall see. Our
first task however is to attend to some details.
                                           fnIn-1
Footnotes for the Introduction
In-2 n.1  The Works of George Berkeley in 9 Volumes, eds. A.A. Luce and T.E.
          Jessop, London, 1948-1957, Vol.II, p.42. All references to Berkeley's
          works will be to this edition.
     n.2  Works, Vol.I, p.53 and Add.MS 39305 fol.8r.
     n.3  See my Complementary Notions: A Critical Study of Berkeley's Theory
          of Concepts, The Hague, 1972, pp.57-64.
     n.4  Ibid., pp.89-96, 127-35.
     n.5  The late T.E. Jessop is the outstanding exception. See his Editor's
          Introduction in Vol.II of the Works, and his edition of Berkeley in
          the series Nelson Philosophical Texts.
In-3 n.1  This is the thesis of Complementary Notions.
In-4 n.1  Works, Vol.I, p.102.
In-5 n.1  See my Persons: Theories and Perceptions, The Hague, 1973, pp.12-13.
                                                               I-1
Chapter I - Identifying the Elements of Perception
     Ordinary discourse about the world and its furniture accurately reflects
our interests in these things, and commonly conceals some major joins with
customary descriptions. The sensory evidence which is covered over by words is
apt to be forgotten for that reason, until some obviously odd consequences
intrude themselves in our arrangements of the scene. It is well therefore to
begin with the original joins, first by examining the special role of ideas,
and then by focussing on some of their more noteworthy limitations.
     So far it is clear that ideas have no potential; they cannot be other than
they are. Now is the one and only moment pertaining to any idea, but it does
not follow from this that an idea is to be taken to be some comparatively
unstable sort of object. On the contrary, ideas are not objects at all; at
least, as ideas, they do not belong to any system of concepts as objects do.
This difference between ideas and objects is of some moment. Valid inferences
can be made about objects of different kinds because such objects are held to
be part of some single scheme. Moreover, a particular kind of object may be
related to all others simply by logical fiat, with the consequence that the
totality of things can be encompassed by the cats and non-cats.
     Ideas are less tractable. Any scheme in which they may figure is
inherently transient. Furthermore it cannot be stressed too much that ideas are
logically independent. Not only is each idea wholly independent of every other
idea; but ideas are also asymmetrically related to non-ideas.1 This curiosity
is manifested in several ways, and the account begins when an idea is
perceived.
     A particular idea, say green, can be noticed or registered in that one
attends to it, even though it is not named 'green' or anything else at the
time. A second idea, green, may similarly be registered and given a name of its
own, or simply noted as 'same', or not given any name at all. So far it is
claimed that ideas must be perceived, but need not be named. The usefulness of
naming is simply to enable the perceiver to recall the idea more readily: It is
a commonplace experience that information which is labelled accurately is more
easily recalled. Consider, for example, the revelation to the beginning logic
student that fallacious arguments have specific, identifiable causes, and that
fallacies themselves actually have names.
     Both activities of the perceiver so far have been concerned with one
specific idea, or its successor; and of these he could say, either 'green' or
'same' and mean simply to report the color he perceives now. He is not, either
implicitly or explicitly, making any claim about his perception beyond what he
takes it to be at the moment he perceives it. Moreover he has no possibility of
checking his registration with a second look, because a second look is, by
definition, a second idea. Of the second idea he could say that it seems to him
like its predecessor, and there is no way to dispute the comparison with him.
As the analysis requires, for ideas, 'esse is percipi.'
     When the question arises as to whether a particular kind of idea would be
appropriate in a given setting; for example, whether the dining room would look
best if it were painted 'Williamsburg blue', then the relations which hold
among objects become important. Decisions about the mixing of paints, their
appearances wet and dry, the lighting of the room, its size and use and the
texture of the walls, all must be considered; and because paints and walls and
rooms are plainly objects, the rules of objects apply. But between the
acknowledged object and the reported idea, there is an imbalance in description
and inference that is best displayed by comparing the uses of words denoting
ideas, and then contrasting ideas with objects.
     If one uses the word 'green' in order to mention the color green, it is
not unreasonable to suppose that the color meant is the middle color of the
visible spectrum. It is, after all, true that green is the middle color of the
visible spectrum. It is equally plausible to assume that if, in response to the
question, 'What do you see?' the reply given is, 'Green,' then the green meant
is very like the green mentioned before, and that in fact one is talking about
                                                               I-2
the same color. Confusion occurs because ordinary usage tends to disguise the
fact that in these two instances two different kinds of greens are being
mentioned.
     The reported green, in the second instance, essentially is named when the
word 'green' is used. The name 'green', like all names, picks out its bearer,
but does not define it. This mentioned green is an individual idea which is
perceived at that moment and which cannot be repeated for reasons already
given.
     The use of the word 'green' to refer to the middle color of the visible
spectrum is a way of classifying a color that may or may not be perceived at
that moment. This condition immediately signals that this use of 'green' does
not refer to any green understood to be an idea. For the record, Berkeley
called this sort of green a relation or concept, and designated it a notion so
as to distinguish it from his necessarily perceived ideas. In any event, the
difference between the one green and the other is important, not least because
an idea is momentary and quite unrelated to any other idea, whereas a concept
is timeless and essentially related to other concepts in the system to which it
belongs.
     It is therefore a conflation of uses which allows us to say, grammatically
if rather ponderously, 'I see the middle color of the visible spectrum,' when
no spectrum is seen at all.* It would be accurate to state instead, 'I see
green, and I classify this green as being the color which is the middle color
of the visible spectrum.' This is awkward but informative, because it
faithfully distinguishes the report of a color from one way in which it can be
described.
     To sum up, a reported x is not green because it is the middle color of the
visible spectrum, but it may be called the middle color of the visible spectrum
because it is green; that is, because it is perceived to be green. When
describing colors within a spectrum, one can say that the color y which is
between yellow and blue is green. When so described, y is green because it is
the color located between yellow and blue, whether any green is perceived or
not. True to its function of naming, one can always say of the reported green,
'this green' or 'this x'. Of the described green, its characteristic function
is reflected by the phrase, 'any green' or 'any y'. Accordingly though x and y
may both be called 'green', x   y; which is all the same as noticing that an
idea is not a description.
     The difference between a perceived color, or idea, and a physical object
can be shown in a different way. The continuity which is habitually and
reasonably attributed to a particular color, such as yellow, conceals a
mistaken inference.1 On close examination this supposed continuity proves to be
correctly ascribed to some physical object which is held to display the color
yellow, or simply to 'be yellow'. Now obviously no one supposes that this
uncritical usage converts a momentary color into a continuous object;
nevertheless it is still worth remarking that the non-recurring idea and the
comparatively permanent object are defined as having these distinctive and
incompatible features.
     There is no serious dispute about the definition of physical objects, in
so far as a physical object is generally held to be both visible and tangible,
at least in principle. It has been argued however, notably by A.J. Ayer, that
statements about objects 'go beyond' the information that can be strictly
derived from sensory observation.2 This is a major part of Ayer's theory of
sense qualia, without which he has argued there can be no sensory claims made
at all. I think that Ayer's account of the individual's progress from sensory
evidence to statements about the external world, as presented in The Central
Questions of Philosophy, is largely true.1 My reservations are about his choice
of the elementary conditions of perception, and these are taken up later when
the differences between sense qualia and ideas are discussed.2
     It is clearly a virtue of the Ayerian sense qualia to provide grounds for
insisting on the severely limited foundations of empirical claims. In doing so,
sense qualia promote the collapse of the gratuitous distinction between 'the
                                                               I-3
actual character of one's sense experience' and 'the character one b li     i
to have'.3 It is true that Ayer admits one kind of exception which still
requires this distinction, but the problem is founded on the sort of special
information one possesses in a limited number of cases. The example discussed
most recently is the Muller-Lyer illusion, and its chief interest is in showing
the close relationship between sense qualia and significant information.4
     Apart from such a special case, it is held that where the actual character
of one's experience is sensory, in the first instance the experience in
question can only be registered. Ayer's argument here, against David Pears, is
that the sole way of being mistaken about one's experience in any ordinary case
is to make a purely verbal error, in the literal sense of saying 'red' when one
meant to say 'blue'; or even 'leaf' when one meant 'petal'. This latter,
apparently more elaborate report is possible for Ayer because his sense qualia
and consequent concept of one's experience is more complex than are strictly
interpreted ideas.
     Some few further comparisons of sense qualia and ideas are instructive
here and can be presented briefly. There is first the point that different
inferences are justified by the same kind of registration.
     A sense quale x may be registered in the form, 'I see x.' This does not
entail the proposition, 'There is an x, and I see it,' but it does entail,
'There is an x that I see.'
     An idea y may be registered in the form, 'I see y.' Similarly, this does
not entail the proposition, 'There is a y, and I see it,' but it does entail,
'There is a y when I see it.' This follows because an idea by definition exists
only as and when it is perceived, and to be seen is one way of being perceived.
     On the other hand, the account of likeness appropriate to sense qualia and
ideas follows the same path. Of a sense quale x and of an idea y, one can say:
This x or y I judge to be like a w (or unlike a z) which I formerly saw (and
called 'a') and which I now recall.
     The chief differences between ideas and sense qualia will be apparent when
the role of the perceiver and the continuity of sensory information is treated
in some detail. Even then however the point about one's making purely verbal
errors will continue to hold good; always for ideas and, with the exception
noted, also for sense qualia. This general claim follows because the
registration of either sense qualia or ideas is neither true nor false from the
point of view of the perceiver. Only the classification of experiences
introduces a truth value. For it is their being related to future experiences,
including the succeeding moment, which casts qualia and ideas in a form that
may agree or disagree with the state of affairs they are used to describe. So
long as the registration is of the present experience and places no bets on its
successors, it is quite beyond the reach of contrary observations.1 It is not
especially interesting of course, but it is indubitably, because necessarily,
secure.
     All of the peculiarities noted so far about ideas would perhaps have only
a certain nuisance value if ideas could be avoided by changing the terms of
discussion. If it were possible to give another, nicely interlocking account of
the world in which every element in the description filled just the place
alloted to it, then we should be well-advised to abandon these recalcitrant
elements of perception. This has been tried on some few occasions, but only at
the cost of ignoring the sensory facts. The problem is that ideas, as
understood here, cannot be entirely ignored because their absence has
identifiable repercussions. Indeed, where entire kinds of ideas are confined to
early infancy, or are never perceived at all, as pitches are not perceived by
the wholly deaf, a sizable and very complex part of the ordinary world simply
does not exist for that perceiver.1 The facts reveal that ideas, like sense
qualia, are and always have been essential to human existence as we commonly
know it, because they are essential to ordinary human knowledge. They do not
however form a straightforward part of discursive knowledge, although they
evidently provide the foundations for a portion of it. Yet a foundation is not
here a bridge, and it remains true that to register an idea is not to make an
                                                               I-4
assertion about anything' A first conclusion is therefore that the analysis of
ideas reveals a logical gap between strictly sensory evidence and the empirical
claims it is supposed to justify' The failure to appreciate this aspect of
things is, as further discussion will show, the source of some well-known
puzzles.
Ideas and their Spaces:
     The heterogeneity of ideas is a commonplace. Usually it has been noticed
with reference to propositions about physical objects in which the truth values
of statements expressing tactual and visual observations are found to vary
independently. Manifestly a change of color does not affect the tangible shape
of a physical cube, and that is all that is required to make the point.
     There is also a longer tradition of noticing the heterogeneous features of
ideas which have to do with sight and touch, and this is given its most
dramatic expression in philosophical literature in the 'Problem' originally set
out by William Molyneux in a letter to John Locke headed "Dublin July.7.88."
This letter, which differs in one important respect from the one that Locke
later published, includes the well-known query about the relation between
information derived from sight and from touch. If, asks Molyneux,
     A Man, being born blind, and having a Globe and a Cube, nigh of the same
bignes sic, Committed into his Hands, and being taught or Told, which is Called
the Globe, and which the Cube, so as easily to distinguish them by his Touch or
Feeling; Then both being taken from Him, and Laid on a Table, Let us Suppose
his Sight Restored to Him; Whether he could, by his sight, and before he touch
them, know which is the Globe and which the Cube? Or Whether he could know by
his sight, before he stretched out his Hand, whether he could not Reach them,
tho they were Removed 20 or 1000 feet from Him?
                       (Bodleian Library: MS Locke c.16, fol.92r)1
Molyneux, Locke and Berkeley all replied, "No," to the first question, although
the reasons that could be given by Locke and Berkeley are mutually
exclusive.2 In any event, the negative response to the 'Molyneux Problem'
introduces a good many further questions about observations. Both Molyneux's
claim and those of his successors point to the fact that visible and tangible
ideas are quite unrelated, as ideas; that colors and evens or unevens may be
described as parts of one thing, but that it is only the description which
relates them. This is the case, even though ordinary usage does not ordinarily
distinguish between the two kinds of spaces, and the several figures, sizes and
distances of things.
Visible Ideas:
     A word here about color will avoid confusion. By a color is meant that
type of idea detectable by sight, and whose contrasts provide visible shapes.
Colors include the spectral and non-spectral colors, as well as black and white
and all of the grays such as could be registered by those whose sight has been
diminished to the level of noticing different shadows, as in the case of
cataract patients. In general, and for greater ease of exposition, it will be
assumed when a color is discussed that strictly speaking it is a particular hue
which is meant, and that all such hues are understood to be as bright as they
can be and fully saturated, unless an explicit exception is made. Thus the word
'color' will refer in most cases to just the sort of sense perception one would
have on viewing the visible yellow produced by dividing a white light with a
prism in the ideal conditions described by Newton.
Tangible Ideas:
     An idea is said to be even when it is tangibly continuous; an uneven idea
is tangibly discontinuous. A smooth marble slab is sensibly even in the way
meant; the surface of terrycloth is uneven. Similarly a circular table has an
even or continuous perimeter, whereas the corners of a rectangular table are
tangibly discontinuous with the straight edges, and therefore are uneven. For
our purposes tangibly detectable differences in motion and temperature are
                                                               I-5
uninteresting and hence will be excluded.
Audible Ideas:
     Pitch is taken to be the elementary aural idea, instead of the more usual
sound. The reason for this choice is that any audible perception is of some
pitch or other, whether definite, like middle C; or indefinite, like the peal
of a churchbell. Among other indefinite pitches are the audible emanations of
kettle drums and sirens.
     The analytic superiority of pitch to sound is revealed by the fact that
any intelligible discussion of sounds must sooner or later include, at least
implicitly, references to definite or indefinite pitches.
     Pitch is moreover translatable into a coherent theory, as sound is not.
Thus the exact pitch of any audible idea or perception is describable in terms
of the numbers of vibrations per second of a wave of a definite length, and
subsequent perceptions can be predicted by the production of a wave of such and
such a type. In the case of indefinite pitches, which include more than one
note, the audible pattern can similarly be described and subsequently
produced. Builders of musical instruments and bell founders have exploited
these relationships for centuries of course, even though they could not measure
vibrations very accurately in their workshops. Of necessity the ear reigned
unchallenged, as it did and does for musicians. But again, there is no problem
here, since the essential musical concepts include pitch, volume and interval.
It is obvious then that further analysis of audible perceptions is best served
by developing the explanatory resources of the concept of pitch. For whenever
one hears, it is a pitch that is heard. By contrast, claiming to hear a sound
is of the same order as claiming to see a sight.1
     These three kinds of ideas; colors, evens and unevens, and pitches, bring
into focus some other aspects of sensory experience which have received very
little attention. If an object and the space which it occupies are defined
reciprocally, then one of the more promising ways of inquiring into ideas is to
consider their several relations to their respective perceived spaces. The
concept of a perceived space that is meant here is one in which the appropriate
kind of idea, say blue, can be succeeded by another idea of the same kind, such
as violet, but not by F#. Perceived space is thus identified by the kinds of
changes it exhibits. It may therefore be said that if there is a perceived
space, then selected changes can take place in it, or with reference to it.
     It may be added here that this account of perceived space is modelled on
that given about direction by Edwin Abbott in Flatland. There he wrote that
direction is related to motion in such a way that; if there is a direction,
then one can move in it. This allowed him to assert that the inhabitants of the
two-dimensional Flatland could actually possess height, as well as length and
breadth, without realizing that height is a dimension. This, he argued, follows
because dimension means direction, and where there is direction, there must be
the possibility of motion; whereas for the Flatlanders, 'upward' meant only
'northward'.1 The question arose from the consideration that Flatlanders, while
being shaped like geometrical figures, are nevertheless perceptible to one
another as lines having 'brightness'. The sides of the figures, or the lines of
which they are composed, must therefore be broad as well as long, even though
the dimension that we should call height is quite unknown to Abbott's creations
and experientially forever unknowable to them.
     However one may judge the special convictions of Flatland's inhabitants,
the inclusion of Abbott's account of their limitations is not quite frivolous.
In what follows, we shall find that the concept of direction is a key relation
which we perceivers habitually employ in organizing the world. The immediate
point however is that distinctive spaces, like distinctive motions, are to be
recognized because they signal real and inevitable differences in sensory
experience.
Spaces and Orders:
     Visual space is never empty. In this respect it is unique among
sensorily-defined space' The ground for this claim is that the space which
presents colors to the eye does not exhibit change by the alternation of empty
and occupied, as do both auditory and tangible space. In other words visual
space has no threshold of perception for its elements. Hence under conditions
in which the attentive perceiver can see, he will see at least one color. 'If I
open my eyes at noonday, I cannot choose but see,' is, when suitably qualified,
a familiar truth. The special features of visual space which follow from this
state of things have not been fully explored. The first comparison is with the
other two most important senses, hearing and touch.
     In contrast with visual space, auditory space is said to be empty when one
listens and does not hear any pitch at all, whether definite or indefinite.
'There is nothing there,' we say; meaning 'nothing is heard,' even though one
is poised to hear. Silence intervenes, and pervades conscious auditory
experience. This is not of course to claim that the world is ordinarily silent;
indeed it is not. Nevertheless patterns of silence are an integral part of
speech, as they are of music. And although we usually exploit only a
comparative silence, this does not alter the fact that auditory space can be
empty in the required meaning of the word. It still makes sense to assert, for
example, 'I hear nothing, although I am listening.'
     Tactual space is said to be empty when, even though one is moving, no
resistance to the motion is felt. When one is walking, obviously the ground or
floor provides a tangible base; nevertheless the walking is sensibly
unrestricted as to direction, duration and speed. Motion of the body is not
only possible, but no obstruction is apparent, nor is any medium through which
one moves noticeable. As in the case of hearing, tactual space is alternately
filled and empty. And here too one can reasonably assert, 'I feel nothing,'
although I am moving, or perhaps simply waving my hand.
     Two features of those ideas found in auditory space and in tactual space
should be noted. First, the occurrence of each kind of idea is essentially
sequential. Second, each kind of idea may be absent from its appropriate space
in the above-described sense of leaving the space perceptibly quite empty.
     The fact that visual space is never empty means that under suitable
conditions, whenever one looks, then one inevitably sees some color or other.
Closing one's eyes does not empty visual space; rather visual space is
eliminated altogether. Similarly the closing off of one's ears does not
reproduce the silences of patterned speech, but eliminates silence and pitch
together. It follows immediately from there being filled visual space that no
one who possesses normal vision can reasonably assert, 'I see nothing, although
I am looking.' A further result is that the space of visual perception, unlike
that of hearing and touch, is essentially static. The colors necessary to any
visual information are seen simultaneously, or they are at any rate judged to
be seen simultaneously. The consequence is that our habitual picture of a
stable external reality is anchored in visual space.
     The physical-object theory embedded in our language promotes the
acceptance of a constant object which either is unchanging or which changes
only very slowly and, above all, predictably. On either view of change, the
bias of language is towards a continuous physical object. All this is
well-known, as is the fact that most of our judgments about physical objects
are based on sight rather than on touch, for obvious practical reasons. Theory
too favors sight, except when survival is at issue.1 It is rare indeed to find
questions about physical objects whose answers are confined to the strictly
tangible arena.
     The evidence given so far makes it obvious that there are two competing
kinds of spaces which underlie physical objects. The continuous tangible object
is, on analysis, a continuous visible object in that it can literally be kept
in view, or at least part of it can. Perceptually it will not vanish in the
face of a closely kept watch. The same is not true of the traditionally solid,
tangible object which is in fact perceived by a sequence of tangibly unrelated
touches, or by a tangibly continuous passage along what is said to be the same
object. A hamster might be identified in one grasp or in easily related ones by
being inclosed in the hands; a horse presents a problem of a different order.
More important, the sequential perception of inherently sequential tangible
ideas does not obviously justify claims about continuous tangible objects. It
is not at all clear where the object has gone when it is not felt.
     The convention of claiming to see the whole object, or a goodish part of
it, and of touching some rather small part of the allegedly same object
produces the continuous physical object of a stable world. There is no quarrel
with this strategy and its results; it has the indisputable virtue of working
for most purposes, but it is still well to know what we are about. In
particular it is worth noticing that continuity is largely dependent on the
properties of visual space, because tangible information, like auditory
information, is essentially sequential.
     There is another and quite different element of continuity that supports
our customary assertions about physical objects. This is the perceptual
constant, a concept which silently figures in each kind of perception so far
reviewed, and which will be examined later. For now it is enough only to
mention this constant, and to identify it as the perspective from which any
sensory information is acquired or recognized.1
     Another way of addressing the question of the several spaces of
perceptions or ideas is to consider the possible uses of each space. Is the
perceived space one that is filled, or is it alternately filled and empty? Are
the ideas which may be perceived in it found together with other ideas of the
same type, or must they each file past in review? For a particular enterprise,
there is a right kind of perceptual space, and there is a right use of the
perceptual elements.
     If one undertakes to produce a naturalistic painting of a wisteria vine,
it is necessary to see both the wisteria to be depicted and the canvas, or
other surface, on which the vine is to appear. The elements to be noted and
transferred in their correct spatial relationships are the colors apparent in
the wisteria. Consequently this activity may be described as one of seeing and
seeing; the elements seen occur simultaneously in their respective spaces; and
the painted vine, like its original, is a stable one.
     Speaking a rich and flexible language, like English or French, is a very
different kind of activity involving radically different perceptual elements.
Again the demands of ideas and their peculiar space introduce the terms on
which one can hope to succeed in using such languages. The pitches heard and
the intervals of silence incorporated in a natural language belong to the
characteristic features of auditory space. Any normal perceiver who learns such
a language will first be able to hear it spoken, and then be able to speak it
himself and to hear his own words. Each of these perceptions, whether spoken or
heard, is sequential, with the result that the auditory world is always passing
away. This fact is well known to composers who frequently repeat phrases. They
thereby introduce a familiar pattern whose familiarity is known to be pleasing
to listeners, and whose recognition is guaranteed by its recent occurrence in
the composition.
     When a native speaker comes to read his own language, he first sees the
words and then hears what the script says. He need not indeed pronounce every
word to himself, but he could do so; and if he were to read a text aloud, he
would not need to alter the order of the words for an ordinary listener. No
special knowledge of grammar is needed, because the written language conforms
to the sequential requirements of the spoken language and its auditory space.
     Writing one's own language reverses the perceptions employed by a reader.
Whereas one reads by first seeing and then hearing, one writes by first hearing
and then seeing. The habitual alternation of these two kinds of perceiving is
made clear whenever it is necessary to read what one has written. Again the
point to be noticed is that these uses of a natural language preserve the
sequence of speech, which itself reflects the transient conditions of auditory
space' Words talk, and natural languages whether written or read maintain the
strict linear sequence of speech because that is the unique form which can be
heard.
     An artificial language, by contrast, frequently cannot be pronounced
because even though it possesses the necessary words, it deviates from a clear
sequential presentation. A good and familiar example is found in propositional
logic in those instances which provide as many as four sets of brackets. There
is no denying that these forms can be written clearly and read accurately, but
many of them cannot be read aloud because they literally cannot be
articulated. 0ne can sympathize with various attempts to pronounce a
proposition like:
Still, it is well to have seen it written somewhere before hearing it read,
say, in a seminar. A pictorial or verbal memory of this sort of proposition is
necessary because its perceived elements are presented out of order. The reason
for this is that the forms in which propositional logic is written exploit the
static conditions of vigual space rather than the transient conditions of
auditory space. The strict linear sequence so essential to the ear is ignored,
with the result that many hundreds of catholic propositions are literally mute.
Observation Statements and James' Squirrel:
     If ideas and their respective kinds of spaces are defined reciprocally,
then the heterogeneity of ideas reflects a state of things rather more profound
than a simple taste for empiricism. It is apparent to any serious inquirer that
a color and a pitch, or better, an idea blue and an idea F#, may both belong to
a perceiver, but that no relationship independent of their thus being perceived
is to be found between them. Again, all temporal references are properly
ascribable to the perceiver, not to the idea. But if ideas are heterogeneous as
they have been found to be, whence physical objects and what, precisely, are
the rules governing observations? The vexed question of observation statements
has not, I believe, received sufficient attention, partly because it is not at
all clear that ordinary observations have been accurately distinguished from
literally given perceptions, or ideas.
     The apparent permanence of the visible world has played its part in
encouraging ambiguity about observations in principle, and observations in
fact. When it is recognized that visual space is never empty and that physical
objects are defined as being visible, tangible and continuous, it is not
difficult to appreciate how visibly perceived shapes come to be thought of as
permanent features of a reliable landscape. A distant oak tree in a meadow
never seems to be absent from the meadow; and so it is held that, like the
meadow itself, the tree is a continuous physical object as the definition of
such objects requires. In fact as an observed object, the meadow shares the
problems of the oak tree, but it is easier to concentrate for now on the tree.
     Two assumptions obscure some gaps in our more innocuous observations of
things. There is the customary belief that if an object like a tree is observed
when one takes a second look, after ranging elsewhere, then the object has been
there all along. Certainly this interpretation conforms with the prescribed
scheme for a physical object; but it is rather more remote from the perceived
ideas which provide the evidence for there being any perceived object at all.
The tree in our example is not continuously perceived; at best, it can be
counted on to recur when sought out under suitable conditions.
     The informal background for this confidence is the conventional opinion
that the oak tree is a tree, whether or not it happens to be seen. Unobserved
trees are quite secure. Nevertheless the reliability of an unobserved tree is
to be sharply distinguished from the incoherence of an allegedly unperceived
idea. Unperceived ideas are impossible because self-contradictory; hence one is
not entitled to make the casual assumption that there are some unperceived
elements by which the tree might be detected which are like the perceived
ones. Since there are no unperceived ideas at all, there can be no question of
attaching them in some obscure way to the unperceived physical tree. The
intermittent perceived ideas which signal the presence of ordinary physical
objects must therefore be recognized as elements of perception, and not simply
be assimilated as parts of objects. This is especially important when one is
making statements about observations in which ordinary usage invites the
blending of ideas with objects.
     In order to examine statements about observations it is necessary to
attend to the literal grounds of the claims that are being made. Where
something is seen, a color or colors will be found; and where there is no
color, there is no visual information to our purpose. These straightforward
conditions have the advantage of insisting on some telling details. The gaps
between ideas and objects are not altogether forgotten, with the result that a
given theory and the evidence for it are more readily discriminated.
     William James' celebrated example of the squirrel and the tree illustrates
some limits which govern observations. In the second paper of a series of
popular lectures delivered in 1906-07, James describes settling an argument
which arose among members of a camping party. He continues:
The corpus of the dispute was a squirrel - a live squirrel supposed to be
clinging to one side of a tree-trunk; while over against the tree's opposite
side a human being was imagined to stand. This human witness tries to get sight
of the squirrel by moving rapidly round the tree, but no matter how fast he
goes, the squirrel moves as fast in the opposite direction,* and always keeps
the tree between himself and the man, so that never a glimpse of him is
caught. The resultant metaphysical problem now is this: Does the man go round
the squirrel or not? He goes round the tree, sure enough, and the squirrel is
on the tree; but does he go round the squirrel? (p.43) ...'Which party is
right,' I said, 'depends on what you practically mean by 'going round' the
squirrel. If you mean passing from the north of him to the east, then to the
south, then to the west, and then to the north of him again, obviously the man
does go round him, for he occupies these successive positions. But if on the
contrary you mean being first in front of him, then on the right of him, then
behind him, then on his left, and finally in front again, it is quite obvious
that the man fails to go round him, for by the compensating movements the
squirrel makes, he keeps his belly towards the man all the time, and his back
turned away. Make the distinction, and there is no occasion for any farther
dispute. You are both right and both wrong according as you conceive the verb
'to go round' in one practical fashion or the other.'(p'44)1
     Ayer recounts this example in his Origins of Pragmatism and ends by
remarking:
     It can hardly be denied, I think, that James gives the right answer to
this conundrum. What is more questionable is his taking it as a model for
metaphysical disputes. Admittedly such disputes do arise, in many instances,
because the different criteria for the application of some concepts yield
conflicting results, but I doubt if they ever turn on quite such simple
ambiguities as James's story would suggest.1
     While sharing the doubts that Ayer expresses about the force of James'
example of a supposed metaphysical dispute, I am not so confident about James'
answer to the conundrum. No one of course pretends that James' purpose in
introducing the squirrel example was to discuss the special problem of
observation statements. Nevertheless the assumptions that underlie some of the
claims made about the squirrel and tree, and indeed about observations, are
instructive. To begin, we shall take as our subject an American gray squirrel,
a large oak tree, surrounding grass and a blue sky.
     It is common ground that anyone who startles a wild squirrel that is near
a largeish tree has seen the last of the squirrel. With a flourish of tail the
animal slips around to the far side of the tree and stays there. By keeping the
tree between himself and his would-be perceiver, deemed hunter, the squirrel
becomes perceptible in principle, though not in fact. As a physical object, the
squirrel like the tree is commonly said to be continuous though unperceived.
     The suspicions that the squirrel harbors about mankind makes him an
awkward physical object since, as a nearby object, he ought to be perceptible
in fact. As an object, he is most readily compared with the tree, but unlike
the tree there is no further sensory evidence for his presence. Consequently,
when James asserts that one could 'go round' the squirrel even though the
squirrel is not observed at all, it is worth noticing the details.
     There is a quite good sense, given the squirrel's habits, in which it is
possible to walk around the squirrel's tree while failing to walk around the
squirrel. As the quoted passage shows, James' response to this familiar problem
is to assert that by 'going round' can be meant to pass sequentially to the
north, east, south and west and back to the north of some one object. If the
squirrel is on the tree and James, say, occupies successively places north,
east, south, west and then north of the tree, then he must have occupied
similar places in relation to the squirrel and therefore must have gone around
the squirrel, even though the squirrel resolutely remained unseen.
     Now clearly this will not do, at least not in support of an observation
claim about the squirrel. First and ex hypothesi, the squirrel has not been
observed since he was first spotted and retreated to the tree. Second, if
successively occupying places at each of the major points of the compass in
relation to some one object constitutes going around it, then equally the
squirrel has gone around James. Third, so far as observations are concerned,
there are good grounds for supposing that the squirrel has actually watched
James all along. Having prominent eyes on the sides of one's head is very
useful for seeing just over edges without being seen. Fourth, it is clear that
in this example, James' working assumption is not merely about compass
directions and the invisible squirrel, but about the continuous tree and the
physical space in which it is located. These latter concepts enable him to find
the squirrel, but only by an indirect pursuit.
     The role of the tree is here crucial in providing a plausible account of
an observation. Something after all must actually be observed. Consider the
ways of going around which distinguish the tree from the squirrel. If 'going
round' means;
(i) going around the outside of the perimeter of an object, then one can
readily go around the tree; or if it means,
(ii) seeing every visible side of the object when it rests, say, on its
vertical axis, then again the tree presents no problems.
But it is plain that the squirrel has not been seen as prescribed by (ii) since
it is conceded that, once on the tree he has not been seen at all. It is agreed
too that the prospective observer has never in fact passed behind the
squirrel's back which would be visible, and so cannot have gone around him in
this respect. This agreement tends to mask a further important issue. If the
observer had passed behind the squirrel's back and seen it, then he would be
able to say when this occurred and report the color of the squirrel's coat at
the time.
     The scene that I have elaborated from James' original squirrel and tree is
odd, not because of its description, but because the scene itself is a dynamic
one. Our customary belief about visual space and most of the things in it is
that they stay put. Animals are admitted to move around in their several
fashions, but it is generally supposed that they really are somewhere out
there, even if for the moment not observed by anyone at all. They do not, in
short, have to be part of someone's perceptual experience in order to continue
to exist. And so it comes about that physical objects ordinarily are said to
endure unperceived by anyone, and Berkeley, exceptionally, said that physical
objects need be perceived only by the Berkeleyan God.1
     Critics who have ridiculed Berkeley's opinions nevertheless are inclined
to seek to give stability to perceptibles unperceived by man. This enterprise
has its roots in the suspicion that the way things seem to be might not be
related to the other ways that they are in any very obvious manner.And so the
most diverse partisans  as well as most of the
adopting a God's-eye view of continuous physical objects.2
     If James' claim to go around the squirrel by going around the tree is
about observation in fact, then clearly he needs at some moment to observe the
squirrel, or at least see a flash of color that will count as having observed
him. If the claim is about observation in principle, then James needs to
introduce a theory of continuous physical objects which includes at a minimum
the squirrel, the tree, surrounding grass and the sky. For even a sketchy
account of the problem makes use of all of these objects, or similar ones,
though without calling attention to them.
     Consider the concept of 'going round' as consisting in standing in the
successive relationships of north, east, south, west and then north of some
other physical object. Not only is it true on this interpretation that the
squirrel is just as much going around James as James is going around the
squirrel, but the tree is going around them both, and in opposite directions at
the same time! This follows because when James is north of the squirrel, and
the squirrel is therefore south of James; the tree is correspondingly north of
the squirrel and south of James. If subsequently James is west of the squirrel
and the squirrel east of James, the tree is found east of James and west of the
squirrel. And so this pattern of change continues (see Figure 1).
     Since it is granted that the tree cannot, as a standard physical object,
move in opposite directions simultaneously, it is not unreasonable to introduce
the rule that any such object that is said to be going around any other such
object must antecedently be admitted to be in motion. The tree is thereby
eliminated, but not without introducing the unstated condition that the world
of physical objects, and especially their setting, is stable, even when
unobserved and therefore sensibly unknown.
     The squirrel, who undoubtedly is moving, is not so easily vanquished. If
one introduces the rule that whoever describes the greater circle in passing
from north to east to south to west to north again, is going around anyone
describing a lesser circle which has the same center point, then different
issues come to the fore.
     It is not always obvious which circle is the greater one. A man who places
his hand on a tree trunk and walks around the tree while continuously touching
it, might well describe a circle smaller than a squirrel would describe by
jumping around the tree along its upper branches.
     More important is the consideration that unless a center point is
explicitly fixed, it is not at all certain what 'going around' can mean. We
have noticed that circumambulation by compass directions requires a stable and
visible setting. But the fact is that what is stable and what is visible are
different. The need for a fixed point immediately introduces the question as to
what kind of fixed point. Is it to be observed or directly related to the
observation of the squirrel, or is it to be the ideal center of some motion
that relates James and the squirrel? If it is the latter, notice the results.
     James and the squirrel are necessarily equidistant from each other; hence
if James is only a moderate distance from the tree, a circle which relates the
two positions of man and squirrel can have a center outside the perimeter of
the tree (see Figure 2). James could see through this theoretical center to the
tree, but the squirrel, whose actual position determines part of the
circumference of the theoretical circle, is not observed. He is, as noted,
always to be found on the far side of the tree, illustrating its character of
being a physical object and therefore possessed of a presently unseen dimension
(see Figure 3).
     If the center of the circle that relates James and the squirrel is taken
to be the center of the tree, then for reasons already given it is quite
possible that the squirrel is going around James, though at a greater altitude.
     To sum up so far: Either the tree is the center of the circles described
by James and the squirrel, and then it is uncertain who describes the greater
circle and therefore 'goes round' the other; Or, the center of the tree is not
the center of the circles described, and the rules relating James and the
squirrel place them on the circumference of a circle whose center is not
governed by the tree, but only by the necessary condition that they are
equidistant from each other. But then it is implausible to hold that James goes
                                                               I-12
around a squirrel that he never sees.
     The latter alternative, even though it includes a circle with a
theoretical center, more nearly reflects the state of affairs. The fact is that
a part of the tree, indeed the part occupied by the much sought after squirrel,
is a far side and therefore is not seen. The same theory that anchors the tree
firmly to the stable ground and surrounding scenery, is the theory that
guarantees that a part of the tree will be invisible in any observation that
can be made. In this particular case, the far side is always on the perimeter
of the circle used to relate James and the squirrel, and this leaves the circle
visibly incomplete; one cannot say where its edge is. The circle cannot simply
be scanned, nor can this crucial part of its circumference be pointed at. The
squirrel as a physical object is widely supposed to be observable, but it
cannot be said at any given moment just where he is, or in what manner he is
disporting himself in the tree. Whatever else the squirrel is in this example,
he is not a simple subject for casual observation claims.
     The issues which James' original discussion introduced are only relatively
more complex because he has provided the would-be observer with a moving
target. The especially elusive qualities of the squirrel merely underscore a
fact that is too often ignored in making claims about observations, and this is
that physical objects have far sides, and that visual perceptions do not. This
has led positively to the development of perspective drawing,1 and negatively
to a good many misapprehensions about the grounds on which we are justified in
making observation claims and in predicting subsequent observations.
     As James' squirrel has shown, it is all too easy to overlook some
important details when one is engaged in tracking a diverting object. Thanks
partly to the development of natural languages, we have some entrenched
attitudes about the chief questions, and these lead us to take a God's-eye view
of physical objects without noticing that this is what we are doing. James is
right, of course, to exploit some of the practical advantages of this view; it
is the uncritical combination of theory and evidence which is the source of the
dispute.
     The most secure grounds for claiming to have gone around the squirrel
without at the same time being circumambulated oneself, is to select the tree
and call its circumference 'the innermost circle'. The path described by the
squirrel on the tree is designated 'the middle circle', and a path described
around the perimeter of the tree at some twenty yards or more from its base is
'the outermost circle' (see Figure 4). To include the squirrel with greater
certainty, the circles could be thought of instead as hollow cylinders or
tubes; each larger tube would then inclose every smaller tube. In either case,
the claim would be that to describe the greatest perimeter is to go around
everything it incloses. And since the squirrel is somewhere on the innermost
circle, in going around the outermost circle, one would perforce go around the
squirrel too.
     It is not claimed of course that adopting this proposal is the same thing
as making an observation. It is however a step towards making an observation
claim about the squirrel. And it clearly separates the plan or description of
an observation from what is observed. The colors said to belong to the squirrel
are yet to be seen.
     The justification for this tactic of pursuing the squirrel with circles is
that one can say where the squirrel is, because one knows where the tree is. It
is because the tree is actually seen that the squirrel can be located in
principle. Moreover, if the squirrel were to remain at rest, a partial
description could be given of his position on the observed tree. But he could
not be seen, or approached, until some account is taken of the observer's
perspective.1 A straightforward observation of the squirrel is, in fact,
frustrated by his reaction; but he is locatable in principle together with the
observed tree. This is so because squirrel and tree are deemed to be physical
objects which belong to the same kind of spatial system; that is, the
macroscopic visual system.
     Membership of this spatial system immediately signals that any evidence
for the objects which figure in it must begin with perceived colors. This
condition has the further advantage of calling attention to the difference
between being a gray squirrel and simply being gray. James' special difficulty
was that he excluded any subsequent sighting of the squirrel, hence any genuine
evidence of his presence, by the limited terms of the example. It was intended
to place the squirrel on the tree and having done so, to go around the squirrel
by going around the tree. But this was not possible because James was still
unable to indicate quite where the squirrel was, to point to him. Yet this is
what the stable observed world ought to provide. The fact that James' suggested
solution includes a world of places instead of pathways illustrates his beliefs
and preferences about observations.
     The concept of a pathway to the squirrel is easily described. If I were by
fiat to arrest the squirrel at some point on the tree, a point now invisible to
me, then I could come to observe him by going around the tree to the side that
I now call the far side. This undertaking does not require a constant,
unperceived squirrel or unperceived part of the tree that in any way resembles
the tree I now perceive and the squirrel I shall perceive. What is required to
exhibit such a pathway is a predictable sequence of observations, in this case
the brownish grays that I now call the three subsequently obseved with the
several grays that I shall call the squirrel. This ordered, literal noticing of
colors is a basic technique that we all use anyway when we are not deceived by
our own words.
     It is not disputed that for the purposes of James' example the squirrel is
a physical object and therefore continuous. Like the tree, grass and sky, the
squirrel is held to be a part of the furniture of the world in which we all
have an undeniable interest. Nevertheless it is worth distinguishing this
object from the evidence for him. In doing so we can more readily notice just
how the confusion of ideas with inferences produces anomalies.
     Because the squirrel is a physical object, it is in principle safe to
blink when observing him. Unlike an idea, a squirrel is presumed to be able to
succeed himself in one's sensory experience. Yet while it is true that the
squirrel by definition can continue his way on the far side of James' tree,
there is no empirical evidence for his duration, and empirical evidence is the
only evidence that there can be. After the first glimpse, there just are no
visible ideas which suggest the presence of the squirrel at all.1 No gray is
seen, and no non-gray can be seen, since a non-gray is not the name of some
other perceived color, but the notification of the absence of a color.
     The gray squirrel provides a telling contrast with the gray evidence for
his presence. In particular it is informative to be told that a part of the
tree is not occupied by the squirrel. Because squirrels and trees belong to the
same system of objects, one can validly infer that if some part of the tree is
not occupied by the squirrel, then that part is non-squirrel- occupied.
Moreover, and given the terms of the example, it is reasonable to conclude too
that the squirrel is somewhere else on the tree. Squirrels and trees endure
unperceived, although the evidence for them does not. Thus the squirrel is a
genuine non-tree and the tree a genuine non-squirrel; but the gray is not a
non-brown nor is the non-brown a gray at the same level of discourse. This is
brought out by the fact that unperceived non-brown gives no information, even
in principle, about perceived gray, although it is true that one can say of a
perceived gray, that it may be called as well non-brown. The converse is not
however possible because of the logical independence of ideas, and the
consequence that any inferences about ideas must always begin with the
perceived idea. The tendency to overlook this difference between objects and
ideas has bedevilled observation claims for some time, and given some puzzles a
longer run than they have deserved.1
     To sum up, the God's-eye view is based on the convention that in going
around something or other, one goes around a fixed point which is usually
identified with the object itself. We have noticed in James' example that this
is by no means a straightforward enterprise. The complications introduced by
observation claims and evidence for such claims serve to illustrate some of the
gaps concealed by our ordinary usage about ordinary things. In particular the
elusiveness of the squirrel underscores the dissimilarities separating physical
objects from the observer and his perceptions, and incidentally introduces the
frequently unnoticed role of perspective in conditions in which it cannot be
ignored.
     I have suggested that we have a bias toward stable objects, and a
God's-eye view of the world as a great container of those objects, largely
because of the continuously filled character of visual space. Since the
conditions of visual perception are unlikely to change much, we should do well
to recognize the remoteness of the evidence from the theory that it is intended
to support. To pass from perceived colors to continuous and inevitably
partially unperceived objects requires some carefully planned intervening
steps. Still, along the way we shall find that the oddities produced by our
theories can usually be resolved, provided that the terms of the claimed
observations are given careful scrutiny.
                      Footnotes for Chapter I
I-2  n.1  See below, ravens puzzle, Chapter II.
I-5  n'1  As in the example of the color continuum; see below, Chapter III.
     n.2  The most recent instance appears in Ayer's reply to the contributors
          in Perception and Identity: Essays presented to A.J. Ayer with his
          replies to them, Ed. G.F. Macdonald, London, 1979, pp.280-93.
I-6  n.1  A.J. Ayer, The Central questions of Philosophy, London, 1973, Chapter
          V, 'Construction of the Physical World'. An earlier, similar version
          appeared in The Origins of Pragmatism, Studies in the Philosophy of
          Charles Sanders Peirce and William James, London, 1968.
     n.2  See below, Chapter III.
     n.3  Perception and Identity, p.288.
     n.4  See below, Chapter III.
I-8  n.1  Perception and Identity, p.287.
I-9  n.1  One of the best witnesses about sight and hearing and their
          contribution to our interpretation of things, is Helen Keller. See
          her account in The Story of My Life, London, 1959. A recent witness
          about the role of sight, its early loss and restoration is Sheila
          Hocken. See her Emma and I, London, 1977, and Emma V.I.P., London,
          1980.
I-10 n.1  See de Beer, The Correspondence of John Locke, Oxford, 198x, vol.y,
          p.z.
     n.2  For a detailed discussion, see my article, "Locke and Berkeley on
          'The Molyneux Problem", Journal of the History of Ideas, No.2, 1969
          and Errata, No.4, 1969.
I-13 n.1  For a discussion of some relationships between sight and hearing, see
          Persons:, Chapter II; Not Sights and Not Sounds, pp.32-61.
I-14 n.1  Edwin Abbott, Flatland, Oxford, 1978, pp.6; 68ff.
I-17 n.1  See Persons:, pp.62-63; 66ff.
I-18 n.1  See below, Chapter III.
I-24 n.1  William James, Pragmatism: A New Name for Some Old Ways of Thinking,
          London, 1907, pp.43-44.
I-25 n.1  Origins of Pragmatism, p.200.
I-28 n.1  That is, the philosophical God, not the Church of Ireland one. For
          the difference, see Berkeley, Vol. V, p.140.
     n.2  There is a curious fascination about the Berkeleyan cast of the ideal
          case entertained by both Ayer and Michael Dummett. See Perception and
          Identity, pp.30-31; 33-35; 296-98.
I-32 n.1  See below, Chapter IV.
                                                             fnI-2
I-34 n.1  See below, Chapters III and IV.
I-35 n.1  Following the original example I disregard auditory information,
          though that may be promising. It may also be misleading since other
          tree dwellers could produce apparently the same effects.
I-36 n.1  See below, Chapter II.
                                                            textfnI-1
*    This qualification eliminates the ambiguity which might not otherwise
exclude a reported rainbow, or a white light divided by a prism.
*    Obviously James is here using fixed compass points rather than imagining
the witness pursuing the squirrel, for in the latter case, the man would be
moving around the tree in the same direction as the squirrel. See discussion
below on James' concept of the scene.
                                                              II-1
Chapter II - The Dissolution of Hempel's Ravens paradox
Observations and Inferences:
     The difference between informal observation statements that cause no
trouble and those that produce odd consequences is easily disguised by ordinary
usage. This indeed is the chief source of the problem. The statement that,
'Tigers are warm-blooded,' seems innocuous enough, and it is widely believed to
be true. Similarly the statement that, 'Tigers are usually orange and black,'
looks equally reasonable, and both assertions are at least informally thought
to be based on genuine observations.1 It is supposed that the reasons for
assenting to the two statements are that some tigers have actually been
observed; that their warm-bloodedness and coloring have been duly noted and
reported; and that the observers were neither lying nor suffering from
hallucinations. All goes well with this attitude toward evidence, until the
valid inferences which are supposed to be derived from it are questioned. At
this point the difference, even for a tiger, between being striped orange and
black and being warm-blooded begins to matter. Habitual intuitions falter, and
the reason is that being non-orange or non-black is remarkably less informative
than being non-warm-blooded. Yet these are the terms that will figure in a
validly inferred contra-positive.
Hempel's Ravens:
               Selten wir gesehen haben
               Swarze swanen und wize raben.
     When Hugo von Trimberg made this remark in the 13th century, both coloring
variants were of course unknown, and generally thought to be fantastic. The
subsequent recognition of black swans proved that the color of their feathers
was a non-essential genuinely empirical element in their description, and so
one may assume the same is true of ravens. The puzzle about ravens rather is
about the correct inferences to be drawn from Hempel's proposition, "All ravens
are black."
     If this statement is taken to be an empirical generalization, and no one
has supposed that it is a definition, then the way seems to have been opened
for a great deal of superfluous supporting evidence. The proposition, "All
ravens are black," may be rendered as well, "All non-black things are
non-ravens," or "For any x, if x is a raven, then x is black." It follows that
the blackness of all ravens is compatible with the existence of members of any
of the three classes; black ravens, black non-ravens and non-black non-ravens.
We accordingly arrive at the conclusion that observations of a black raven, a
black fountain pen or a white handkerchief all are equally good evidence for
the claim that all ravens are black.1
     Confronted with this result one might well ask if any observation can fail
to count either for or against Hempel's original assertion. It is my view that
the evidence can be selected and irrelevant claims identified and excluded,
once it is recognized that the apparent paradox suppresses important
differences between two kinds of generalizations.
     The immediate consequences of the ravens case are odd at any rate, though,
as Ayer remarks in his account of the problem, not paradoxical in the strict
sense.1 Instead Hempel's example belongs to the class of those
counter-intuitive consequences which can be deduced from selected empirical
descriptions.
Counter-intuitive Consequences:
     Counter-intuitive empirical accounts must have an explanation. Intuitions
about observations are, after all, derived from previous observations; hence it
can hardly be satisfactory simply to accept counter-intuitive results as an
occasional curiosity of empirical descriptions. The question then is how do
these skewed accounts of things come about, and by what means do they produce
their surprising relationships.
                                                         II-2
Essentially a counter-intuitive empirical description is an account of
sensory evidence which leads systematically to a conclusion that sorts oddly
with the original evidence. In each such case, the account owes its effect, as
I shall argue, to the fact that it trades on misdescriptions of the evidence.
These are of several identifiable kinds and include in one form or another the
misrepresentation of the relationships which hold among logically independent
observations founded on ideas.
     There would appear to be two main sources of counter-intuitive
consequences. The first is the simple misdescription of the empirical
evidence. This can occur when the various types of evidence on which the
account rests are conflated. A case in point, and one which has recurred not
infrequently, is the practice of combining colors and visible shapes in a
single description and treating them as if there were no grounds for
distinguishing between them. Accounts of the color continuum depend on this
confusion, partly no doubt for historical reasons.1
     Conversely, there is the mistake of drawing distinctions in empirical
descriptions where there is no sensory difference to be noted. Here the ravens
example is ready to hand. With its easy transition from empirical evidence to
its negation, Hempel's account of the ravens provides a clear instance of a
system of descriptions being uncritically applied to a fundamentally different
system of inferences. The problem here, as we shall have occasion to notice, is
that the relationship between non-black and say, orange, is a good deal less
straightforward than Hempel and his critics have suggested.
     Apart from the misdescription of evidence in individual and identified
cases, counter-intuitive results equally can follow from intuitions which have
long been admitted to the realm of assured facts. The history of scientific
discovery provides a familiar gallery of entrenched misdescriptions which were
systematically reinforced by language. Those wrong theories which were long in
fashion were so hedged about by customary usage and habits of mind that their
preeminence is no matter for surprise. We should now say that our predecessors
erred in the teeth of the evidence, but the fact is that the plainest evidence
was as good as invisible to those whose range of expectations had been formed
on principles different from our own, including even different principles of
observation. The world was given phlogiston and denied bacteria for a very long
time for reasons such as these.
     To conclude these preliminary remarks, it is no accident that Hempel's
ravens paradox has prospered in conditions where the essential, empirical
features which produce the tension in his account have been allowed to pass
unchallenged. It is all very well to take A as any given subject and B as some
appropriate predicate, and then to pronounce that for one's present purposes,
it shall be held that, "For any x, if x is A, then x is B." Under the same
general rules, being a non-A or a non-B are obvious ways of failing to be an A
or a B, respectively, and all goes swimmingly so long as only these most
general rules are allowed to count. By contrast however, any genuine
observation must include an observed element, or idea, in its correct
description, and the denial of this feature is more complex than simple
negation. I shall argue therefore that the problem of evidence and confirmation
touching Hempel's ravens repays closer attention.
The Logic of Observation Statements:
     It is the peculiar logic of observation statements which unravels the
ravens problem. Hempel's assertions are supposed to be about observation
statements, but in fact disregard the ideas on which observations must be
founded. The first step is to look again at Hempel's account and the way it
addresses the elements of perception.
     Put briefly, the perceptual element or idea which is essential to any
observation statement is more restricted than Hempel has noticed. The report of
an observed black raven must include, for instance, visually perceived black of
a shape judged to be the shape of a raven. The foundation of the claimed
                                                              II-3
observation statement is therefore the perceived idea, black; the particular
raven-shape is derivative, as is the background from which the shape is
distinguished.
     Given that a color can be predicated of a physical object, like a raven,
color still is a predicate of a special type, and this has some interesting
consequences which have been largely ignored. For one thing, a perceived color
such as black is logically independent of every other perceived color. Whereas
a color is immediately perceived, any visible shape, like a raven-shape, is
derived from the colors of its figure and ground. There is also the fact that,
in its original form, Hempel has alighted on a proposition that has a strictly
interpreted idea as one of its terms. In some ways this makes his example a
comparatively simple one, but the original proposition is not fundamentally
different from any other purported empirical generalization. This follows
because all observation statements finally rest on equally restricted ideas. It
is therefore no objection to argue that empirical claims which are more remote
from the ordinary range of sense experience are exempt from the restrictions
following from our analysis of ideas. Those comparatively complex claims, for
their part, are limited by the description of the sorts of observations, and
hence ideas, which will be allowed to count. This point is discussed
subsequently. It is now enough to be reminded that all visual observations,
including the reading of dials and the distinguishing of inked characters on
paper, depend on the literal perception of colors. It is for this reason that
the noticing of an idea like black cannot be assumed to be just one more way of
picking out physical objects like ravens.
     The first objection is then that Hempel's ravens example introduces a
predicate that does not fit easily into empirical generalizations. This is a
serious result, because the resistance of ideas undermines the technique that
Hempel must use in order to produce the puzzling effects of his exercise.
Ultimately, as we shall see, Hempel cannot have pointed out a genuine
shortcoming in confirmation theory because his claims are founded on a
misrepresentation of the terms which he is entitled to use. The argument begins
with noticing the consequences of negating that fundamental observation, the
essentially perceived idea.
     In order to dissolve Hempel's ravens paradox, the customary use of
entailment must be challenged. I shall argue that it can be challenged
successfully because it does not fit the observed facts when they are correctly
described; and ex hypothesi, these facts matter.
     The problem is stated so as to suggest to us those observations which
illustrate the original proposition; that is, "All ravens are black," the
counter-example of the original proposition, and those observations which are
compatible with the original proposition, but which are not instances of it. It
follows that, apart from the counter-example, all other observations are
compatible with the original proposition, and so they tend to confirm it.
     Tension results from our observing individuals which apparently do not
count either for or against the blackness of ravens, but logically tend to
confirm the original proposition, thanks to the powers of entailment.
     There are several questions now to be considered.
     First, how are logically equivalent propositions related to genuine
observations? Taking up Hempel's own example of the ravens, what is literally
seen? Second, what special features does the ravens example exhibit? A propos
of this question it is well to list some points which have not been much
noticed.
(i) The ravens case owes its dramatic effect to the apparent simplicity of its
terms. In fact, as we shall see, they overlap in a way that is not perfectly
obvious.
(ii) One of the terms of the example; that is, black, is a color and therefore
is fundamental to visually based claims. Yet this is untypical of the terms of
most deliberate observations which are not so simple as the ravens example, and
consequently are also less startling in their effects.
(iii) The fact that any observation can be decided instantly either for or
against the ravens example obscures the sequence of prescribed observations
which characterize empirical investigation. This last point will be taken up
after the ravens case is examined.
1. Ravens:
     The idea black is one of the terms in the fundamental observation
statement, "This raven is black." We have noted that ideas must be perceived,
and that they are logically independent of one another. It follows that no idea
such as a color has a color as its complement, and therefore that to say of a
visually perceived figure that it is 'non-black' is not to make a report either
of the color literally seen or indeed of any color at all. There is accordingly
a quite good sense in which entailment is observationally meaningless in
fundamental observation statements.
     Hempel's arguments assume that this is not the case, and that is the
source of a major problem. The issue turns on the relationship between a
perceived color and the term which names it; and the complement of a color and
the term which names the complement. The fact is that these terms name
different kinds of things; the color, an idea, being essentially perceived, the
complement being inevitably imperceptible.
     The term non-black on which Hempel relies is ambiguous. When it is
correctly interpreted, it does not sustain his puzzle. There is first black and
its complement non-black. These terms exclude each other and also exhaust the
possibilities of attribution. They are therefore contradictories, and for this
reason non-black can provide Hempel with one of the terms of his
contra-positive.
     Second, there are the colors black and orange. These exclude each other as
well, but the terms and their relationship are quite different. In this case,
black and orange are said to name perceived colors. Now a perceived black
excludes any prospective perceived orange because these colors are sensory
rivals. For example, a perceived black square is perceived now and so occupies
this perceived space now. At the next moment, a perceived orange square may
succeed the black square. There is however no logical relationship between the
prior black and successor orange as perceived; the temporal succession belongs
to the perceiver, not to the colors. Perceived black and perceived orange are
therefore contraries, since any two such colors are incompatible under this
description, but evidently not exhaustive of the colors which may be
perceived. The point to emphasize is that the non-black which excludes black as
its complement, and hence stands in a necessary relationship to black, is
imperceptible. The non-black which is a perceived orange is properly given a
different account. This non-black, which also excludes black, does so because
orange and black are both held to be ideas. As ideas, they are perceptual
rivals, and their relationship as essentially perceived colors is contingent on
their being perceived at all.
     To sum up so far, a perceived color is logically independent of every
other perceived color; and its complement, to which it is necessarily related,
is imperceptible. Hence a term which names the complement of a color does not
name anything that is perceptible, and perforce does not name a color. It
follows that a negative color term, like non-black, does not name what one
sees. But it does name what one infers.
     It is not denied that an orange square is validly inferred to be also a
non-black square. Indeed if x is perceived orange, it follows that x is
non-black, non-purple, non-blue and so on, save only non-orange itself. This is
so because every color term can be said to form part of the complement of every
other color term. Still, from a valid inference which gives such a negative
color term, nothing follows about any other perceived color. The reason for
this conclusion is that there is a basic asymmetry between perceptions and
inferences when the object of perception is an idea such as a color.
     Inferences about observations require prior perceptions, but once again
                                                              II-5
the perceptions are the logically independent colors. Consequently, if x is
perceived orange, then x is inferred non- black. The inference is valid; it is
irreversible; and no proposition about any other perceived color follows from
it because a perceived color cannot be given an identifying description. A
color is, in this respect, quite unlike a geometrical figure, which can be
described both as a rectangle and as a figure possessing four equal angles. In
this case, either term may be used for picking out such a figure, whereas
non-black is hardly so related to orange. We may therefore conclude that the
valid inference from a color term produces a strictly useless complement, if
one pretends that the complement names anything that is literally seen. To
repeat, this is not to deny the validity of the inference, but it is to insist
that this admission does not transform the color complement into an observation
of the required, basic type.
     To report non-black is not to report a color; hence the contra-positive of
the ravens example in fact substitutes an inference for a color term. But if
this is the case, the contra- positive is not a generalized observation
statement, and consequently is not equivalent to the original proposition, as
Hempel's puzzle requires. In any case, the simple substitution of the
contra-positive for the original proposition cannot be sustained.
     The impossibility of identifying the non-black of the contra-positive with
any perceived color undermines the supposed equivalence of the original
proposition and the contra-positive. We need not look out for non-black items
of any sort because we can be assured that they are not to be seen. However the
non- ravens might be represented as another issue.
     As it happens, the non-ravens form part of the same question in this
case. I have said that the terms of Hempel's ravens example overlap, and this
is readily noticed when one comes to a discussion of the sort of observation
which would count in favor of or against the blackness of all ravens. Obviously
color is noted only by sight; somewhat less obviously, colored ravens too are
noted only by sight. That is, in so far as a raven is reported to be one color
rather than another, the report is literally the report of a visible figure
judged to be a raven- shape of the color perceived. The inspection of ravens
must therefore be conducted in terms of reported raven-shapes. Not only is
there no need to include the whole range of those properties of ravens which
Hempel implicitly invites us to add to the account, but to do so is to
misrepresent the visual evidence of which he has made so much. We must assume,
of course, that there is a range of standard raven-shapes, but this is hardly a
case of special pleading. If we were not to make such an assumption, we should
not be able to detect any raven by sight as the generalization requires.
     The empirical generalization, "All ravens are black," is about the color
of raven-shapes if it is about anything at all. Its alleged empirical character
gives grounds for supposing that it is founded on an observation such as, "This
raven is black," which is the report of the color of a raven-shape. One can
assume too that there has not been perceived until now a raven-shape of a color
other than black. Still, it is raven-shapes which matter, and they matter
precisely because only they can provide empirical evidence in favor of the
generalization, or evidence to contradict it.
     We have noted before that it is not possible to pick out a perceived color
when provided only with an imperceptible color complement. This asymmetry
applies also to shapes when they are identified by their color, as this example
requires them to be. Consequently black non-ravens may be inferred, but like
non-black non-ravens, they are not literally seen. The shape, like the color,
must be noticed because it is a colored shape. It need not however be named,
any more than a color need be.
     The relationships of the several classes to Hempel's generalization, and
the evidence they provide for it, can be stated briefly.
1. Black ravens. A member of this class is more accurately reported as
this-black-raven-shape. It is an instance of the generalization, and is
immediately perceived.
                                                              II-6
2. Non-black ravens. A member of this class may be described as a raven-shape
other than black. An example of a report would be this-lilac-raven-shape. Lilac
is said to be a color other than black, and so it is non-black. The perceived
lilac-raven-shape is therefore inferred to be a non-black-raven-shape, and as
such it is a counter-example of the generalization.
3. Non-black non-ravens. This is a peculiarly elusive class because it is quite
imperceptible under this name. An example might be reported as
this-green-blotter-shape. Green is a color other than black, and so it is
non-black. This inference about the color is combined with a further inference
about a perceived blotter-shape which is that this perceived shape is a shape
other than a raven-shape. The perceived green-blotter-shape is therefore
inferred to be a non-black-non-raven-shape, and from this imperceptible figure
nothing follows about any perceived colored shape whatever. It is therefore
quite unrelated to any perceived evidence about the color of raven shapes.
4. Black non-ravens. A member of this class may be described as a black-shape
other than a raven-shape. An example of a report would be
this-black-lamb-shape. The perceived black-lamb-shape is therefore inferred to
be a black-non-raven-shape. Again, from this inferred and indeterminate black
figure nothing follows about any definite shape. This conclusion is quite apart
from the question whether any allegedly perceived non-raven can be both a
figure and indeterminate, though a color need not have outlines. In any case,
nothing that is an inferred black-non-raven-shape is related to any question
about a perceived color which is the color of raven-shapes.
     To conclude this section, it is held that if Hempel's original proposition
is supposed to be an empirical generalization, then it must be about the color
of raven-shapes. Consequently the only observations which can count in the
inquiry must at least be observations that are raven-shaped, since from an
observation which is essentially a perceived colored-shape, it is not possible
to infer anything about another perception. Non- ravens are therefore as firmly
excluded from this empirical claim as are non-colors. It follows that the
non-ravens which are spawned by the consequences of entailment are logically
irrelevant to empirical observations, and are therefore to be dismissed. Both
terms of the contra-positive are now manifestly unlike those of the original,
empirical generalization. Hempel's ravens paradox accordingly dissolves. Q.E.D.
2. Empirical generalizations:
     The awkwardness of Hempel's ravens example is partly a result of the fact
that a perceived color, and its equally perceived shape, is decided in a
moment. Strictly speaking, another look signals another moment, one which may
well provide a perceptibly different successor color. It is true that our usual
talk about ravens suggests more continuity than momentary raven- shapes can
offer, but I have pointed out that any easy transition from Hempel's ravens to
ordinary physical objects is inconsistent with the use which he makes of
logical equivalences. Hempel relies on immediate judgments. Moreover, the
possibility of our spotting a counter-example in passing also depends on the
momentary raven-shape.
     In contrast with Hempel, the sober empiricist requires more evidence. To
be plain, no one who assumes that a raven is a physical object, with a full
range of descriptions suitable to the family of corvines, would be at all
concerned with an acknowledged non-raven. Prior descriptions of ravens would
include the sorts of ideas to be expected were a raven observed. The class of
non-ravens would then obviously be quite irrelevant to any empirical
investigation.
     It might be said, of course, that scientific inquiry is not Hempel's
enterprise, and this is certainly conceded. Still it can hardly be denied that
an empirical generalization must be founded on a consistent account of its
supporting evidence. For this reason Hempel's term ravens has been rendered as
raven-shapes, since the sole evidence for his generalization is based on our
observations of colors.
                                                         II-7
While Hempel's choice of terms may be a curious one for a generalization,
the analysis does have the advantage of bringing out the role of colors and
colored-shapes in observation statements. In systematic, visual observations,
the indispensable information will always be some perceived color or colors and
the shapes in which they are first noticed. This is so, no matter how many
other interpretations may be given as well. An exercise such as using a
microscope to search for a single cell on a glass slide readily illustrates the
irreplacable information provided by contrasting colors.1 There is one respect
therefore in which the ravens case leads to a generally interesting conclusion:
Where the question is genuinely about a colored-shape, such as literally a
colored E-shape, the strictures on Hempel's ravens example apply, and
non-E-shapes are as irretrievably unrelated to E-shapes as color complements
are unrelated to perceived colors. In both cases the proposed inference from
the unperceived to the perceived fails to overcome the logical independence of
ideas.
     If the ravens example is instructive because of the analysis it requires,
its career spent in masquerading as an ordinary empirical generalization has
been notably misleading. In particular, the ordered sequence of observations
which underlies any empirical inquiry has been obscured in two respects. The
first was seen in the tendency to treat colors, or ideas, as if they enjoyed
the full complement of inferences that characterize descriptions. This error
emerged most uncompromisingly when one was invited to infer which idea was
meant by a reported non- black.
     The second obscurity that can be attributed to Hempel's ravens example is
to be found in the assumption that ravens are both physical objects and readily
detected by sight. The latter alternative was dealt with in our examination of
colors and colored shapes. We now turn to ravens when they are taken to be
standard physical objects. Once again the details are worth bringing to light,
for when the evidence for an empirical generalization is carefully described,
irrelevant reports can be identified as such, and dismissed from further
discussion. The following examples are designed both to illustrate the
legitimate use of valid inferences in observation claims, and to show how these
inferences are governed by the identifying description of the object in
question.
Invertebrates:
     Consider the well-known example of kidneyless invertebrates. In this case
the property sought is not, like color, so obvious that it is overlooked, but
instead is so obscure that in practice it is given a substitute. If we follow
for the moment the divisions set out in Hempel's example, Scheffler's
proposition, 'All invertebrates lack kidneys,' clearly is compatible with the
class mentioned, with non-invertebrates which possess kidneys and with
non-invertebrates which lack kidneys.1 Beginning with the invertebrates, we may
take as examples the starfish, the goldfish and the ordinary desk blotter,
respectively.
     The assertion that the property of either possessing or lacking kidneys is
too obscure to employ in unsystematic observation is literally true. Neither
kidneys nor vertebrae are unfailingly obvious in ordinary conditions, although
their working substitutes are readily noticed. Our question is which sequence
of observations leads from the information which is apparent, to the empirical
relationship here asserted to hold between invertebrates and the lack of
kidneys.
     Unlike colors, kidneys are not usually noticed unless some trouble is
taken to make the inspection. Invertebrates are more easily seen, though again
not because one readily sees the lack of vertebrae any more than one sees the
lack of kidneys. If it is not proposed to dissect every individual in order to
determine whether or not it possesses kidneys, obviously some quite noticeable
external feature which will pick out invertebrates is needed.
     It is a fundamental principle of comparative anatomy that members of the
animal kingdom will tend to have much the same major internal arrangements so
long as they continue to have much the same external appearance. Indeed the
original claim that "All invertebrates lack kidneys," is a generalization which
depends on this principle, since no one supposes that all invertebrates have
been examined. Our practice shows therefore that it is thought reasonable to
apply this rule to some striking external feature of known types of
invertebrates which then readily distinguishes them from vertebrates. The
feature chosen in this case is the vertebrate skeleton and its observed
relation to a well-defined head and spinal column.
     Briefly, the existence of an endoskeleton is evidence for a central mass
of nerves some of which are protected by a spinal column with its complement of
vertebrae. For all ordinary purposes, the animal kingdom is divided between the
vertebrates and the invertebrates. The vertebrates can be picked out by their
skeletal structure, leaving all the other animals as identified invertebrates.
It is true that being an invertebrate is not an infallible sign of lacking
kidneys; this assumption relies on previous dissections of other specimens of
the same type and the anatomical principle mentioned. It might be noted too
that the relationship between being kidneyless and being an invertebrate is
undoubtedly a highly integrated empirical generalization and not a simple
definition, since any kidney-possessing starfish would not cease to be an
invertebrate on that account, but would instead be given a sub-class of its own
while remaining among the invertebrates.
     In summary, the pattern of observations which tends to confirm the claim
that "All invertebrates lack kidneys," is as follows: One seeks first animals.
The animals which do not have an endoskeleton are then selected because
previous dissection has shown that the members of their class do not have a
spinal column and the accompanying vertebrae. These animals are the
invertebrates, and it is also known that every one of their class so far
examined has been found to lack kidneys. Given therefore the discovered
relationship between external appearance and internal structure, no rational
inquirer would habitually undertake a separation of kidney-possessors from
non-kidney-possessors scalpel in hand. The assumption is always of course that
the searcher after invertebrates can tell the animals from the non-animals. On
this view then we can conclude as well that the serious, not to say sane,
inquirer will ignore in his searches both the manifestly vertebrate goldfish
and the apparently inanimate desk blotter.
Molluscs:
     The proposition that "All bi-valvular molluscs are cold- blooded," avoids
the conflated observations and concealed inferences that bedevilled the issue
in the discussion of the properties of ravens and invertebrates. In this
example it is impossible even to pretend that one can decide a given instance
by a single look, as in the case of ravens. It is equally obvious that the
unforthcoming mollusc is not going to provide any behavioral clues or an
obvious alternative description that picks him out just as well as being called
a mollusc. The only readily identifiable features of the bi-valvular mollusc
consist in its being composed of a pair of hinged shells fitted more or less
tightly together and inclosing a comparatively soft interior which usually is
not visible in the living animal. This structure gives no information about
blood temperature, and so the careful observer seeks bi-valvular animals. He
omits, as the single- minded pursuer of logical equivalences would not, both
non- mollusc and cold-blooded frogs, and non-mollusc and non-cold- blooded
tigers. He then either warms or cools to a noticeable degree the immediate
environment of the mollusc, presumably water, and notes whether the mollusc
has, as the original proposition requires of its type, changed to the
temperature of its medium. If so, the animal has been shown to be cold-blooded
and a standard mollusc; if not, it may have been cooked or frozen, or be a
wholly new type of mollusc requiring a sub-class of its own.
                                                         II-9
The case of the bi-valvular mollusc is instructive because it is clear
from the outset that any such mollusc must be distinguished from its
surroundings with no appreciable help from its activity; and then be tested for
cold-bloodedness, a test which requires at least two separate and related
observations. The emphasis consequently falls on the observations which will be
used for selecting molluscs in the first instance, and the further observations
which are required to determine the characteristic of being a cold-blooded
animal. Casual glances will not do.
     To conclude this section, real empirical claims rely on an ordered
sequence of observations. Disputed points about such claims require therefore
that any observations which come to be made either must count or be
discounted. Puzzles occur where there is apparent neutrality; where seemingly
innocuous observations obviously are not logically incompatible with some given
proposition. The solution consequently is to show that the supposedly neutral
reports are genuinely irrelevant to the sequence of observations being
considered, and are to be discounted on these grounds.
Conclusion:
     It is generally agreed that the concept of logical compatibility is
inadequate for drawing the distinction between informative and irrelevant
observation statements. I have argued that this consequence is not a
shortcoming of observation statements, but of a wrong analysis of them. The
reasons may be briefly recounted.
     Any observation statement, sooner or later, is founded on some real
observation or perceived idea. This condition applies to the complex
experimental results of the physical sciences just as much as to the working
observations of ordinary life. The meaning of our language demands that there
should be some sensory evidence for an empirical claim, and this evidence
ultimately is an idea of the required type. In the case of more complex
generalizations, useless inferences are eliminated early on because of the
pattern of evidence which serious research imposes. In principle therefore the
limits of any empirical inquiry can be made explicit, with the result that
irrelevant observations can be identified and excluded.
     The ravens example has amply shown that irrelevancies cannot be excluded
if ideas and their complements are judged to be the same kinds of things. In
one respect this is no more than to point out that some essential features of
observation statements, specifically ideas, are left out of account in the
classic model which Hempel has employed. The argument is however that this
model is the wrong one to use in the analysis of genuinely empirical
propositions. Hempel indicated the problem by devising the puzzle, but we have
noted that the effect he produces depends on inconsistencies in the description
of what is perceived. The evidence shows that we can neither infer colors nor
see color complements, and Hempel's conclusions require us to perform both of
these feats. The correct response to the ravens problem, and all its fellows,
consists therefore in recognizing first, that strictly interpreted ideas do
matter; and second, that theirasymmetrical relationship with valid inferences
inevitably limits the range of empirical generalizations.
     Finally, there may never in fact be a non-black raven, but the history of
the black swans points to the solution which we should choose on the day. And
we shall know the day by the observation; that is, by someone's reported
sighting of the familiar raven-shape in an unfamiliar color.




















                                              fnII-1
Footnotes for Chapter II
II-1 n.1  For the record, there are also white tigers that are not albinos.
          Their coloring is white with beige stripes, and they have blue eyes.
II-2 n.1  A.J. Ayer, Probability and Evidence, London, 1972, p.68.
II-3 n.1  Ibid., pp.67-8.
II-4 n.1  See below, Chapter III.
II-18 n.1 See below, Chapter III.
II-19 n.1 Israel Scheffler, The Anatomy of Inquiry, London, 1964, p.284.
          Scheffler uses this example in a different context, but the                analysis
          I have given would in any case eliminate 'the family cat' which            he
          mentions.
                                              III-1
CHAPTER III - Qualia, Percepts and Ideas
A good many theories of sense data have become entangled with ideas since
the beginning of the century. Moore's widely-read paper of 1903 introduced one
knot in the skein by associating a naive account of idealism with Berkeley,
among others.1 Russell's views on Berkeley recorded in Problems of Philosophy
further complicated the state of ideas by giving them a novel, and fatal,
redescription.2 As I have argued elsewhere, these two admittedly influential
accounts can now safely be disregarded as attacks on Berkeleyan ideas because
both Moore and Russell failed to identify their target.3
     Later candidates in the field have enjoyed a long season, not because they
have replaced ideas proper, but because they have seemed to make ideas
obsolete. The two most important theories, produced by Ayer and Goodman, cut
across the specific claims made for ideas. In the case of Goodman, the qualia
on which he builds would supersede ideas, if his descriptions could be
sustained. However, the fact that they include ambiguous accounts of
appearances ensures that ideas are not seriously challenged, even by his chosen
qualia of color which we shall examine. Ayer's qualia and percepts openly seize
a different level of the contested ground, but not one wholly unrelated to
ideas. For this reason it is both more interesting and more important to
delineate the areas where there is no conflict, as well as to show where
percepts and ideas inevitably exclude each other. We begin with Goodman.
Goodman and Qualia:
     In The Structure of Appearance Goodman introduces qualia as constituents
of what he calls 'a complete visual concretum'. Each concretum may be analyzed
into a 'color-spot-moment', but no single quale whether of color, place or time
can be found apart from the other two. In the discussion that follows it is
Goodman's analysis of color that is the most instructive, because he oscillates
between simply describing how things usually look, and giving an elaborate
account of how their looks must be composed. Yet both looks are identified as
qualia of color. Accordingly I shall argue that Goodman's account of color is
ambiguous beyond rescue.
     Goodman states in a section entitled 'Properties':
     Roughly, then, to say that a thing looks green is to make a statement
concerning a presented quality, a color quality of some presentation of the
thing, while to say that a thing is green is to make a more complex statement
concerning the color qualities exhibited by various presentations of the
thing. Obviously, the color names are thus used in two different ways in
ordinary language: in the one case for presented characters, which I shall
hereafter call qualia;3 in the other, for properties of things.1
And so it is clear first that qualia are about how things may look. A second
point is that, for Goodman, observations count; and a green quale is named in
accordance with its appearance, not its wavelength.
     Later Goodman tries to forestall some likely misapprehensions about qualia
in a section entitled, 'Qualia as atoms':
     In the first place, to say that qualia are phenomenal individuals
discoverable within experience is not to say that any quale is literally
separable from the rest of experience. A color quale cannot, indeed, be
actually lifted out of the stream of experience, but neither can a complete
visual concretum (a color-spot-moment) or a patch consisting of several of
these.
                      [omitted sentences]
If it be argued that nevertheless a color-spot- moment could exist by itself
while a color could not, I shall have to look at the evidence for this
statement before I understand what is meant. The sort of evidence usually
claimed for it is that we can get an image of a concrete individual but not of
                                                         III-2
a quale; but obviously we cannot get an image of a color-spot-moment
unaccompanied by others that surround it any more than we can get an image of a
color unaccompanied by a place and a time. Analysis, indeed, requires that the
elements in question, whether concrete or qualitative, be found within the
whole in question, and be distinguished from one another, but not that each or
any of them can somehow be enthroned in splendid isolation. (pp.135-6)
     The phrase 'get an image of' here can and does refer either to 'a concrete
individual' or to 'a color'. There nevertheless is some uncertainty about what
is meant. For example, to get an image of a color might mean to have an idea;
to perceive a color; to report 'green'. Or it might mean to form a picture of
some perceptible figure, say a blue pentagon or 'patch' on a yellow ground.
     Goodman continues:
     In the second place, division of a concretum into qualia is of course not
a spatial division. A visual concretum is already a spatially smallest
discernible particle of phenomena, and the further analysis into its three
component qualia leaves its space undivided. This analysis consists simply of
distinguishing the place from both the time and color that, together with the
place, make up the concretum. (p.136)
     Here the 'visual concretum' mentioned by Goodman is very like a minimum
sensibile, and this I believe introduces a serious ambiguity in his account of
color. We are no longer concerned with the look of things, but with the
elements which compose that look. Yet these are very different functions to be
assigned to colors which, all agree, are literally seen.
     The statement that a color-spot-moment 'is already a spatially smallest
discernible particle of phenomena' captures the identifying dimensions of the
venerable minimum visibile. True to his purpose Goodman focuses on the
structure of appearance to the exclusion of the elementary perceptions which
confront the observer. Having spoken of qualia as atoms it is not surprising to
find him describing a visual concretum as exhibiting a least discernible
color. It is worth noting however that an individual, smallest color is not
obviously like any color that may be perceived. In particular, a colored
expanse is not literally seen to be a summation of a collection of minimum
visibles. Goodman indeed affirms that the color-spot-moment belongs to
analysis, yet he holds too that qualia of color are concerned with the look of
things.
     The fact is that, for Goodman, the look of things is secondary to their
structure. This leads him to speak of qualia as atoms, and the
color-spot-moment becomes a building block of appearances. Unhappily this
choice of elements increases the dissimilarity between Goodman's description
and his stated interest in how things genuinely look. A perceived green is
first green, and only subsequently may it also be found to be a green of the
least discernible expanse.
     There is a separate, historical point that illuminates the issues. The
utility of the minimum visible is to distinguish ideas that literally are
perceived from descriptions of units that may be perceived. It signals
retrospectively the threshold of visual perception, in that if an expanse of
blue color, on being further diminished, then vanishes, the blue expanse last
perceived was a minimum visible. Strictly speaking, one never judges a
perceived blue dot to be a minimum visible, only a predecessor blue dot to have
been a minimum visible. Obviously then, more than one moment is required to
make this sort of judgment about the look of a thing. Perceptibly the colors of
color-spot-moments are identified in pairs.
     Visual concreta must perform the double function of being perceptibly
available as both the least colored expanse and the components of larger
patches of color. But when are these two expanses to be perceived? The addition
of visual concreta or of color-spot-moments to produce a larger colored area
obviously requires more time than a single moment. Even in the most favorable
case of a uniformly colored expanse, one can still ask how long a particular
                                                         III-3
color can be presumed to endure. Goodman's reply to this question underscores
his preference for structure over appearance, and also reveals the gulf between
his qualia of color and the perceived color, or idea.
     Goodman's interest in structure is reflected in his description of a color
quale as '...a presented quality, a color quality of some presentation of the
thing'. He is careful to distinguish this presented quality from 'properties of
things', but he nevertheless needs to preserve some kind of predictable
relationships among presented qualities. For instance, under the same
conditions, the presented qualities ought to be like their predecessors, and so
make appearances reliable. One telling question, as we shall see, can be
directed to the source of this likeness.
     Repetition and likeness are not difficult to locate in the analysis of
appearances founded on ideas. If it is asked how long a particular color can be
presumed to endure, the answer is however long that color is perceived. Color
and moment occur together and belong to the perceiver. Subsequent comparisons
and perceptible continuity are perforce equally related to the perceiver.
     It may be argued that Goodman's choice of the color- spot-moment has
certain advantages over ideas, such as delaying the introduction of a
perceiver. The usefulness of perceivers is examined in the following sections;
for now it is sufficient to point out that Goodman's chosen color-spot- moment
leaves him quite unable to solve the problem of the color continuum.
     Goodman's version of the puzzle is given in a section entitled 'Choice of
a Basic Predicate' in which he notes that the color continuum bids fair to
cause some trouble.
Although two qualia q and r exactly match, there may be a third quale s that
matches one but not the other. Thus matching qualia are not always identical.
Now this is somewhat paradoxical; for since qualia are phenomenal individuals
we can hardly say that apparently identical qualia can be objectively
distinct. Offhand, it seems that color qualia, for example, that look the same
must be the same. Yet if we say that q is identical with r because the two
match, then we shall have to say that q does and does not match s. Must we then
deny after all that the appearance of identity is a sufficient condition for
the identity of appearances, and try to explain how a difference between
phenomena can be nonphenomenal? Actually, the fact that some matching qualia
are distinct can be accounted for without going beyond appearance; we need only
recognize that two qualia are identical if and only if they match all the same
qualia. Although distinct qualia must indeed be phenomenally distinct, to say
they are phenomenally distinct is to say not that they fail to match but that
there is some quale that is matched by one but not by the other. Thus the
matching of nonidentical qualia does not force us into a contradiction. The
principle that two qualia are identical if and only if they match all the same
qualia is not a definition in our system; for identity has already been defined
in terms of our general apparatus (D2.044). (p.196)1
     By following this program one could never tell whether any two qualia are
identical, since they could never be matched with every other quale.2 A second
and related problem is that unless some qualia are known to be identical, it is
not at all clear that any appearances can be said to recur, and any information
be derived from experience. It may well be the case that identical qualia are
very rare indeed, and that their literal recurrence is not required for
significant sequences to be noticed. But then, the identity of significant
sequences and their proper range of variation must still be known. Slackening
the requirements from identity to some more vague type of resemblance does not
remove the need for some limits to be established and knowable. Moreover, those
cases in which something less than identity would suffice are only plausible
where there is more than one feature to be judged, and the look of a color
offers no alternative.
     It is characteristic of Goodman's interests that after following the above
quotation with two symbolized versions of 'identity', he opens the next
                                                         III-4
paragraph with:
     A quale, then, not only matches itself but may also match some other
qualia' Now may we not, perhaps, have here the basic predicate we want for
order construction? (pp.196-7)
He continues, remarking that 'matches' has been construed as 'a 2-place
symmetric predicate of qualia.'3 This introduces a third difficulty posed by
Goodman's approach to the puzzle of the color continuum, q, r and s. In the
context of the problem, it is clear that matching is based on how two color
qualia actually look, yet Goodman provides no room for a perceiver or judge of
such color qualia. On the contrary his emphasis on structure is intended to
dispense with perceivers and the elements of perception, for which I have
argued. But then it may be asked how, and indeed when, the matching is to be
done. For instance, it is not sufficient to describe how matching '...assigns a
distinct position to each quale in a category...'1 when the sequence of
discrimination and assigning is left unexamined.
     To sum up, Goodman's remarks on the problem of the color continuum show
that he is quite unable; (1) to pick out identical color qualia; and (2) to
justify the use of matching color qualia, as an alternative to the hopeless
pursuit of establishing the identity of two qualia. There is no dispute that
Goodman is primarily interested in providing categories for qualia and mapping
them. Yet a link is still needed between qualia and the properties of things.
For if none is available, then there is no reason to suppose that matching
color qualia can reveal recurring patterns. In that case, appearances cease to
be informative about anything beyond the fact of their occasional resemblances.
     As a technique for deciding the identity of two colors, it is obvious that
Goodman's proposed matching exercise will not do, because it can never be
done. If appearances are admitted to count, then it is they which must be
addressed. It is worth restating the terms of the problem so as to bring out
its undefended reliance on the ubiquitous philosophical 'color patch'. If the
color of a color patch-A is to be identified by sight, then the identical
colors of two patches, A and B, also are to be detected by sight. And since
identity is transitive, then any color patch which is identical in color with
our sample patch-B, must be identical with the other sample patch-A. However,
it is well-known that whereas patches A and B might appear to be identical when
examined, and similarly patches B and C might also appear to be identical; the
patches A and C might appear different. This is notoriously the case when
patches A, B and C have been selected from a surface which exhibits a color
continuum of a sufficient spread.
     Various responses to this result have been made. Among them is Goodman's
proposal to abandon the implicit assumption that patches which are
indistinguishable in color are identical in color. This device rescues the
transitivity of identity, but leaves indistinguishability adrift. What is more
serious is that, as a general practice, it is indistinguishability which is the
perceiver's guide to color discrimination, hence to the foundations of his
knowledge derived from vision. It may be questioned therefore whether such a
loss is worthwhile, even for those whose chief interest is to preserve the
coherent use of color predicates.1
     In fact the whole problem turns on a misapprehension about its terms, and
the culprit is the 'color patch'. The condition that a color recurs depends on
the continuity of the patch, which must therefore be presumed to have the
stability of a physical object. Moreover, the puzzle requires the inclusion of
such recurring patches as the patches A, B and C mentioned above. But if one
considers not the recurring object, but the momentary, perceived color, then it
is obvious that any two colors perceived together either are indistinguishable
or they are not. If indistinguishable, then they are identical; that is, they
exhibit the perfect qualitative likeness of like ideas.
     What is shown is the difference between the perceived colors which are
                                                         III-5
exclusively momentary ideas, and perceived colored shapes which are here called
'color patches'. In fine, the shape may properly be thought of as continuous;
the color is non-recurring and unique. The difference therefore is between
related ideas which are colors interpreted as a continuous figure and ground;
and an idea which is a color simpliciter. When this distinction is recognized,
then the special features of ideas dissolve this aspect of the puzzle.
     Transitivity is preserved by stipulating that, under essentially the same
conditions, like colors or like colored shapes will recur. The green band of
the visible spectrum may therefore be expected to look the same on a second
viewing, provided that the light source is of the same intensity as before, and
all of the other necessary conditions for producing the spectrum are repeated.
If there is a mismatch, then one seeks out the alteration in the conditions
prevailing during the second viewing. Similarly, the color of the dining room
wall will appear the same as before, provided the surface has not been altered
and the areas which are seen are lighted in the same way.1
     To conclude this section, Goodman chose his qualia in order to provide a
foundation for his analysis of appearance. The problem is that his choice led
him to emphasize the structure of appearance to the neglect of discernible
differences in appearances. Where the literal look of things is the chief
issue, it is not therefore quite unexpected to find that Goodman's qualia of
color lack precision. The penalty for such ambiguity is not long delayed, as
the color continuum puzzle reveals. The fact is that qualia cannot eliminate
inconsistent judgments about the colors composing a color continuum.
     When the analysis of appearances begins with ideas, the issues are
transformed. For when any particular color, or idea, is interpreted as an
element of perception, it can then be held that a given color is essentially
registered by the perceiver. Accordingly it follows that the perceiver's
decision about the likeness of such a color to any other color is immediate and
final.
Ayerian Qualia and Percepts:
     The Ayerian percepts are very like ideas, some of the time. The Ayerian
qualia are explicitly universals and therefore notably unlike ideas. The
relationship that Ayer establishes between these two concepts in the following
account illustrates their challenge to the role claimed for ideas.
     To begin, Ayer states that one of his chief interests in appearances is
"...to show how they are capable of sustaining the interpretations which we put
upon them." A second feature of his account requires that "...for anything to
be an appearance that it be something of which the observer at least implicitly
takes notice..."1 In developing his theme he shows how perceptual information
can be noted, organized and corrected, and thence provide for all the familiar
distinctions between real and illusory objects, dreaming and waking states, and
private impressions and publicly observable objects. The private/public
distinction appears very late in the discussion. The reason for this is that
the distinction requires the prior establishment of complex objects such as
individual human beings, and they not unnaturally are rather far removed from
the initial objects of perception.
     The current Ayerian qualia are available to the senses just as the earlier
sense-data have always been. There are the perceptions or qualia among which
can be noticed certain patterns. For example, one not only sees colors, but can
also see a collection of colors called a 'cat-pattern'. By tacitly exploiting
the descriptive features of these perceived patterns, one can come to recognize
objects which may subsequently be given descriptions. Such objects can then be
distinguished as publicly observable in principle, or be deemed private to the
individual as occasion might require.
     We are told first:
     There are two reasons why I shall follow a different procedure [from that
followed by Goodman in The Structure of Appearance]' In the first place, I am
                                                         III-6
mainly concerned not to organize appearances into a system but rather to snow
how they are capable of sustaining the interpretations which we put upon them.
Secondly, I propose to make it necessary for anything to be an appearance that
it be something of which the observer at least implicitly takes notice, and
this induces me to treat as primitive a number of concepts which, from a purely
logical point of view, it might be thought preferable to construct. Beginning
also with the visual field, I add to the qualia of colour, not only qualia of
size and shape, but also a set of patterns of which the description may be
borrowed from that of the physical objects with which they come to be
identified. Thus I shall speak of a visual chair-pattern, a visual
leaf-pattern, a visual cat-pattern, and so forth, and I shall construe these
terms as applying to any members of the range of visual patterns which would
typically lead the observer to think that he was seeing the corresponding
physical object. This is not to say that the character of the visual pattern is
wholly determined by the identity of the physical object which it actually
presents. If the object is camouflaged the pattern may be one that is
associated with a different object: in the case of a puzzle-picture one and the
same object may be responsible for patterns of different types; if the observer
is undergoing an hallucination there may be no object which the pattern
presents. Neither is it to say that the observer characterizes these patterns
as patterns. He notices them implicitly, in the sense that it is his
registering of them that governs his identification of the physical objects
which he thinks he sees. They provide the main visual clues on which our
everyday judgements of perception are based.
     Both spatial and temporal relations hold between these patterns and
between them and qualia of other sorts. Thus, a face-pattern encloses a
nose-pattern; a cat-pattern may be spatially coincident with a quale of black;
a bird-pattern may appear at successive moments at different points in a visual
field. Spatial relations hold only between data of the same sense which are
partners in the same sense-field, but temporal relations may hold between data
of different senses. For instance, a visual bird-pattern may precede or follow
an occurrence of a bird-note. It must be made clear that these descriptions are
intended to be purely qualitative. The reference to a bird-note should not be
understood as implying that the sound is caused by a bird. It serves only to
characterize a sound of a distinctive type. (pp.91-2)1
As to qualia and percepts, we subsequently read:
     When qualia are turned into particulars, whether by being located
demonstratively or descriptively, I shall usually refer to them as percepts. In
this I follow Russell... There is, however, one important point in which I
differ from Russell. Unlike him, I do not characterize percepts from the outset
as private entities. It is obvious that qualia are not private entities, since
they are universals which can be exemplified in anyone's experience. It might,
however, be thought that privacy accrued to them when they were turned into
percepts, in as much as their particularization had been made to depend on
their location in sense-fields which are presented to a single observer. But
the answer to this is that while the reference to a particular observer may
occur in our explanation of the way that percepts come into being, it does not,
and indeed cannot, occur in the primitive designation of percepts themselves.
As I have tried to make clear, this is simply a matter of recording the
presence of a set of patterns. Since persons do not yet come into the picture,
there is no implication that the patterns occur in the experience of any
particular observer, nor, therefore, that their concretion into percepts gives
any one person a monopoly of them. (pp'93-4)
Finally the contrast between Ayer's percipients or observers and any perceiver
of strictly interpreted ideas is made clear beyond a peradventure in the
following passage:
These difficulties [arising from the assumption that percepts require a
percipient to whom the percepts are exclusively attributed] are avoided by
                                                         III-7
making percepts neutral, which is not to be confused with making them common. I
shall, indeed, represent the theory out of which the physical world is
constituted as being developed by a single observer. This Robinson Crusoe
approach is not meant to be historical, but only to do justice to the fact that
any knowledge of the world which anyone acquires is bound to be based upon his
own experiences. It might seem, at first sight, as if this is to take the
idealist position which I have just been condemning, but there are two vital
points of difference. The first and most important is that the observer is not
permitted to conceive of the data with which he works as private to himself. We
shall see that this is eventually possible, but only when the theory has been
developed and is allowed to transform its own origins. The second is that the
observer is not identified either with myself or with any other person. If I am
asked who is then supposed to carry out the construction, my answer is that we
can think of it as being carried out by anyone who disposes of the necessary
percepts. (pp.98-9)
There then follows a detailed outline of the way in which a theory of the
physical world can be constructed from qualia, and the public/private
distinction justifiably be made.1
1. Some Problems about Qualia.
     One way of examining the Ayerian qualia and percepts is to set out one of
their virtues together with a related defect which has already been mentioned.
We noted that the distinction between how things are and how they look to be,
was collapsed by insisting on the fact that claims about qualia are about
perceptions and therefore are not to be confused with claims about physical
objects. It was however admitted at the same time that the Muller-Lyer illusion
provided an exception to the general rule.
     Ayer recounts the essential features of the problem as follows:
Suppose that two lines of approximately the same length are drawn so that they
both come within my field of vision and I am then asked to say whether either
of them looks to me to be the longer, and if so which. I think I might well be
uncertain how to answer. But it seems very strange to say that what, in such a
case, I should be uncertain about would be the meaning of the English
expression 'looks longer than'... I know quite well how the words 'looks longer
than' are used in English. It is just that in the present instance I am not
sure whether, as a matter of fact, either of the lines does look to me to be
longer than the other.2
I should argue that it is the Humean ancestry of percepts that promotes
indecision here. This hard case has in fact been brought before the wrong
court. For whereas it is true that percepts cannot offer grounds for deciding
about the look of these lines, ideas certainly can do so.
     If the two lines were held to be non-repeatable, as ideas are, then there
would be no difficulty in pronouncing on their apparent measures. Hesitation
about the comparative lengths of the two lines can be traced to their
pattern-like character and possible subsequent appearances. Added to Ayer's
working definitions and inferences is, of course, the well-known psychological
fact that lines drawn like the Muller-Lyer lines tend to deceive the observer
about their respective lengths. It is important therefore to undercut this
familiar source of misjudgment by reviewing some commonly ignored details which
affect the question.
     First, what must be seen are the colors of the figures and ground. It does
not matter whether they are named or not, but any seeing of the lines requires
one antecedently to have seen some difference between the colors. Second, one
is looking at two colored lines which, as these two colored lines, will never
be seen again. Lines that may be judged to be very like these lines can be seen
subsequently, but the lines that are literally seen are ideas, and for this
reason they are seen once and once only.
     Percepts, by contrast, cannot decide the issue because they are vulnerable
                                                         III-8
to a second viewing. The covert assumption which leads Ayer to acknowledge this
example as exceptional is that the same two lines can be measured on different
occasions. A first opinion about them consequently can be challenged, and be
corrected.
     Now this, I submit, is quite a different exercise from pronouncing on how
the comparative lengths of the two lines look to be at the moment. The Ayerian
percepts can destroy the first judgment by admitting an incompatible second
opinion; ideas permit no appeal. I should argue therefore that ideas are to be
preferred because they provide the correct restrictions on how the
indispensable colors look at the only moment they can be judged; that is, the
single occasion on which they are perceived.
     It might be replied here that there is a further objection. It does not
matter whether the Muller-Lyer lines are seen a second time, for it could still
be held that it is not possible to decide, when simply looking at them, whether
one line looks longer than the other.
     This objection focuses the dispute on a genuine difference between Ayerian
qualia and ideas. The qualia are not simply colors in this case, but colored
shapes that have a measurable dimension whether it is measured or not. Now we
are accustomed to believe that measured lengths give decisive information, at
least so far as ordinary perceived measurements are concerned. The grounds for
Ayer's professed hesitation might therefore be the unspoken conviction that the
lines could be measured, and the result of that exercise would give the true
answer. Moreover any judgment based on the look of the lines as the simple
colors they are is comparatively uncertain, and in tricky cases like this one,
such judgments are not to be trusted. Were the question whether the lines are
of the same color, it might be supposed that Ayer would give an opinion without
demur. For where the question is explicitly about perceived colors, the look of
them is the only information that could be available.
     I suggest therefore that the Muller-Lyer lines are not wholly unrelated to
the problem of the color continuum. Colored shapes, even very attenuated shapes
like lines, admit of a second opinion, or offer the observer an alternative way
of judging their length. Not to measure what is measurable is to refuse the
most reliable technique for deciding the question. It is therefore because the
Ayerian qualia can easily accommodate the lines as continuous shapes, that it
seems irrational to judge them solely by their present look. Ayer hesitates
because he knows there is a better way to decide doubtful cases. And so in this
instance, ideas and qualia produce different and incompatible replies to the
same question.
     The problem of the color continuum reveals further differences. In this
case Ayer provides a solution, but again the special features of qualia are
unhelpful rather than otherwise.
     Ayer takes up the problem, first noticing the contradictory results and
the consequent incoherence of 'our reports of the colours that objects look to
be'.1 He then queries the necessity of this conclusion remarking:
The whole argument rests on the assumption that, if I cannot discern any
difference in colour between A and B, I am bound in consistency to judge that
they look to me to be of the same colour. But what is to count here as
discerning a difference? No doubt if A and B are presented to me in isolation
from other objects I must judge that their colour looks the same. But, suppose
that they are presented to me in conjunction with C, which B looks to me to
match in colour but A does not. Why should I not say, just for this reason,
that A and B do not look to me to be of the same colour under this condition?
They would still look the same if C were removed from the field of vision, but
that is irrelevant. The very fact that the relation of looking the same in
colour, when objects are taken in pairs, is known not to be transitive can
count as a reason against making the question whether objects are discernible
in colour depend on our taking them exclusively in pairs.2
So far then, the reported colors of objects can be made consistent, provided
                                                         III-9
one is careful about the context. There remains however the question of how one
is to use color predicates informatively even to oneself. Ayer continues:
Evidently the rule [for the use of a word like 'yellow'] must depend on actual
or possible comparisons, so the question is whether its application must be
inconsistent. I think that it need not be. Let us return to our old example,
but now take A, B and C to be sense data*, and assume that the difference
between A and C is such that, being concerned with shades of colour, I apply
different colour predicates to them. Then, if B is presented with A alone I may
apply the same colour predicate to it as to A. If B, or another sense datum,
B', which is equivalent to B, in the sense that I should judge them to be of
the same colour in all contexts, is presented with C alone, I may apply the
same colour predicate to it as to C. If A, B and C, or their equivalents, are
presented together, I may apply a different predicate to B from that which I
apply to either A or C. There is no inconsistency here, since there is no
reason why two sense data which are equivalent in the sense defined should not
each satisfy different colour predicates in different visual contexts. But what
if B is presented alone? In that case the rule allows us to follow whichever of
the three options we choose. This makes it flexible but not incoherent, since
it does not commit us to conjoining them in any given case. (p.285)
     Ayer's use of contexts here is both promising and worrying. It is
promising because it focuses attention on the moment of comparison of any two
colors; worrying because it is not entirely clear that he has not commandeered
recurring colors in the guise of qualia. If qualia do recur, then they ought to
be recognized and given the same name, else how can they be said to have
recurred. If they do not strictly recur because whatever is actually perceived
is an Ayerian percept, then presumably there may be any number of percepts all
of a single quale of color, like yellow. Yet one still can be uneasy about what
is being compared, and what is recurring and how they are related.
     It seems to me that equivalent shades of color, especially B and B', are
introduced with insufficient ceremony. We are told that sense datum B may have
an equivalent sense datum B', '...in the sense that I should judge them to be
of the same colour in all contexts...' But how, it may be asked, are these
contexts known to be exhausted? It cannot be done by looking at all cases of B
and B' to check that they appear to be the same. If they are said to have the
same wavelength, they are no longer being judged by their ordinary appearances
as colors. In short, I do not believe that there is a meaning of equivalence
that can link the ruled equivalence of B and B' with the apparent sameness of A
and B when they are viewed alone. The latter case is important because the
viewing and judging are performed together. But this is done by a perceiver and
judge for whom I have claimed perceptual omniscience, but whom Ayer rejects on
other grounds.
     The objection to Ayer's solution is the somewhat curious one of claiming
that he is not entitled to it. He cannot have apparent equivalence without
admitting a judge, who is at least a covert perceiver. Then too, 'visual
contexts' and rules for comparing colors sort oddly with unowned percepts. I
suspect therefore that the judge who is so selectively employed in the pages of
Perception and Identity is the perceiver of ideas, thinly disguised for the
occasion.
     The chief shortcoming of percepts and qualia that has emerged so far is
their failure to restrict sensory information in several important respects.
This leads to the acceptance of oddities such as the Muller-Lyer case, or to
the introduction of a decidedly ad hoc solution to the problem of the color
continuum. The advantage offered by ideas is that of imposing fruitful limits
on the sensory evidence. By separating the evidence accurately, it is then
possible to provide a consistent approach to the solution of puzzles which
obviously give trouble to an analysis founded on qualia.
     It is admitted that the concepts which Ayer treats as primitive are
                                                        III-10
specifically designed, as he says, to set out the terms by which we relate
sensory information to empirical judgments. Still there are good reasons for
holding that the sense-contents and sense-data of his earlier writings have
been converted into qualia, and that together with percepts, these latest terms
function so as to overlap and sometimes conflict with the specific role
assigned to ideas. Hence qualia and ideas cannot co-exist without further
adjustment.
     Patterns and the neutrality of percepts are two of the concepts in
dispute, and others lurk in the background. For example, there is some room for
doubt about Ayer's use of 'presence' in 'the primitive designation of percepts
themselves'.1 There is also the account of privacy which serves Ayer well in
his development of a theory about appearances and the physical world. Still,
reservations remain when these concepts are quietly enlisted against a
skepticism which follows from the unalterability of ideas.
     Briefly, it is clear that patterns are introduced in order to enlarge the
scope of qualia in a familiar way. These patterns are very close indeed to
Hume's use of objects, especially when he wished to move easily between sensory
perception and description. Not inappropriately Ayer takes full advantage of
this flexibility. We consequently are given patterns and qualia that are
perceptible, like an orange patch of color. When required, we are also provided
with patterns that are more obviously descriptive; e.g. cat- like patterns, or
colors distributed in the shape of a cat. So long as we adhere to these terms,
it is plain that no perceiver is required for such patterned qualia to be said
to figure in the perceptible world; and it follows that the question as to
whether these patterned qualia are public or private is, as Ayer states, at
this juncture misconceived. There is a public/private distinction, but it is
not inevitably and immediately attached to any presumed percipient.
     Properly speaking, the Ayerian percepts are neutral because Ayer says that
they are. The question is whether a similar ruling can have a similar effect on
the concept of presence. We have been told that "reference to a particular
observer... does not, and indeed cannot, occur in the primitive designation of
percepts themselves. As I have tried to make clear, this is simply a matter of
recording the presence of a set of patterns."1
     It seems to me highly implausible to talk about the presence of some
appearance without conceding that the occurrence must take place now from some
percipient's point of view.2 The fact that Ayer insists on this condition not
only suggests strongly that his percepts differ sharply from ideas in this
respect, but that the Ayerian percepts share many features with described
colors, as distinct from perceived ones.
     On the evidence it is correct to say of an orange percept that it is the
color between red and yellow in the visible spectrum. Having secured this
option, Ayer obviously does not need any percipient actually to see the orange
color of the example. The difficulty arises when some percipient does see an
orange color. At this point I should argue that the orange color which is seen
is unlike the one just indicated by its position in the visible spectrum.
Although the seen orange color and the described one are obviously related by
usage, they are still to be distinguished, because the seen orange is an idea,
and an idea is not a description. In short, the two colors mentioned are
different, as were the two greens discussed in the first chapter.
     Of course Ayer does not claim to have a theory of ideas, but he does
provide descriptions of sensory evidence. The objection is that his percepts
and qualia do not discriminate accurately between a sensation and a minimal
description of it. It is true that this ambiguity allows Ayer to discuss
neutral percepts and even to argue that presence need not include any implicit
reference to a percipient. But then it can be replied that it is necessary to
distinguish between the kinds of presence that can be meant when one speaks of
the presence, say, of balanced stresses in an arch, and the presence of this
green blotter on my desk.
                                                   III-11
To sum up so far, either the concept of presence is ambiguous, and
therefore cannot distinguish between theoretical descriptions and observation
statements; or there are at least two kinds of presence, and the Ayerian
percepts may be associated with the one or the other as required. I think that
the latter alternative is the one intended, and that it is this choice of
percepts which leads to hesitation when one is confronted with a puzzling
description of sensory evidence. Percepts give away advantages because an
alternative and less decisive reply is available. The lines in the Muller-Lyer
case, when considered as percepts, are seen qualia; but the qualia may also be
seen again, or be deemed a continuous shape that could be measured accurately.
In either case, it is supposed that a perceived color may be judged different
on a second view. Language encourages us to believe there is a second view, but
it is nonetheless a mistake.
     Ayer's treatment of questions about privacy, and implicitly about
skepticism, deserve further attention.1 Here too it is evident that the
concepts of qualia and percepts paper over distinctions which are properly
drawn between these concepts and ideas. An idea literally is that which is
perceived by some sense; a quale may or may not come to be perceived, but when
it is perceived, it is a percept. No percept however is necessarily related to
any percipient, by definition. And percepts are stated not to be private, any
more than they are public, at the level of description which Ayer calls their
'primitive designation'.
     The contrast with ideas could hardly be more fundamental. Ideas are
private because by definition they belong to a perceiver; and on analysis, any
searching description of them is found to be inseparable from the perceiver's
history and perspective.2 Moreover, because ideas are the elements of
perception and logically independent, no description of perception can ignore
the restraints imposed by ideas. For these reasons, although percepts may be
made neutral as Ayer requires, the same type of innocuousness is not possible
for ideas. There is consequently no counterpart of ideas to be found among the
percepts, qualia and patterns with which we may come to describe the external
world.
     The way is now opened to the skeptic, but in order to make his case, he
must insist on retaining ideas. This can be done on the grounds given earlier,
that it is only ideas which capture some recalcitrant and important differences
between sensory experience and our descriptions of it. The plain fact is that
ideas undermine puzzling consequences by attending to the right kinds of
details. On the evidence then ideas are hardly dispensable; hence the skeptic
must be conceded this inherently private information.
     Changing the terms of one's perceptual evidence does not provide an escape
from ideas either. Because ideas cannot be captured in a description, they
cannot be redescribed into extinction. It is true that they may be ignored for
a very long time, but they will not go away.1 There is consequently a residual
privacy which cannot be entirely eliminated from empirical propositions.
should conclude therefore that the bounds of privacy are determined by
genuinely perceived ideas and that, given these unavoidable ideas, a studied
skepticism about the external world is only rational.
2. In Favor of Qualia.
     Even if the Ayerian qualia and percepts reveal selective weaknesses
arising from their ambiguous character, they also enjoy a corresponding
strength. The real and undeniable virtues of these qualia are that they
delineate and hold the middle ground of perceptual claims, and that this is
done in intelligible units. Qualia bridge gaps between essentially perceived
ideas and theories about enduring physical objects. Indeed the very patterns
which obscure the proper limits of ideas in puzzling cases are the same kinds
of patterns which open the high road to generalization. For patterned qualia
can recur, and they can be judged 'same' or 'different' without recourse to any
                                                        III-12
publicly known system of usage.
     Theories which include the simpler qualia and ideas draw several of the
same distinctions. There is first the primacy of sensory evidence, and the
consequent separation of such evidence from those descriptions in which it may
figure. Both qualia and ideas identify information that is held to be
detachable from physical object theory. They also both employ a private
language. In the case of ideas, further analysis leads to the recognition of
privacy in sensory experience, of perspective in empirical observations, and
thence to a studied skepticism about the external world.
     The Ayerian qualia introduce a different set of consequences. Private and
public information are defined reciprocally and enter our descriptions of the
world together. Accordingly there is no insuperable barrier for the lone
percipient to overcome in his fully articulated account of himself, the
external world and its other inhabitants.
     There is the further point that qualia enter the lists of empirical
descriptions just as ideas cease to be informative. Sensations and mental
images may be indispensable as the foundations of empiricism; as a matter of
record, common humanity requires that 'all men begin with sensations'. Yet
ideas, whether of sensation, imagination or memory obviously are themselves
insufficient for the development of empirical knowledge. And so at this
juncture the Ayerian qualia rightly take up their descriptive function.
     The texts quoted from Perception and Identity show clearly that Ayer has
not by any means abandoned the concept of a private language. Earlier claims
about ideas also support the use of a private language which takes note of or
names the simplest ideas. Qualia and ideas both require this to be a
possibility, notably in those cases in which the essence of the judgment made
is whether one asserts of a given sensation, 'same' or 'different'. On this
point it seems to me that Ayer must be right. The elements of perception under
any name one chooses must be genuinely sensed in order to be noticed at all;
hence no description of how words are used can be substituted for the
recognition of similarities and differences among observations founded on the
senses. There is no dispute that standard descriptions and usage can be taught,
and that it is necessary for ordinary human existence that they should be
taught. Still there is no evidence for supposing that sensory information can
be redesigned as part of any language game whatever. On this level, sensations
do not play.
     Some confusion about this point appears in a note by Wittgenstein in his
Remarks on Colour where we are told:
88. If the psychologist teaches us, 'There are people who see', we can then ask
him: 'And what do you call  people who see ?' The answer to that would have to
be: People who behave so-and-so under such-and-such circumstances.1
If the psychologist holds this view, then he is simply wrong. The short answer
is that people who see are people who are acquainted with colors tout court.
When possessed of this knowledge, they may be found behaving in the predictable
ways indicated, but the behavior is a consequence of the knowledge and not
identical with it. Because we can see, we have expectations which we habitually
judge by sight, but we do not watch ourselves making the judgments in order to
decide whether we can see. 0n the contrary, doubtful cases are resolved by
searching for predictable colors or differences of color, and opinions about
one's sight are founded on this sensory information.1
     In presenting the role of sense qualia, Ayer's theme is the exposition of
articulate sensory experience. The intelligible units introduced by patterned
qualia conform not only with the evidence presented to the senses, but also
exploit the significant divisions of information enshrined in ordinary usage.
It is known that the scanning actions of the functioning eye find some parts of
a given scene much more informative than others. It is not so widely
appreciated that patterned qualia of the type Ayer favors are found in ordinary
printed texts. Once again, it is the privately significant, but as yet unnamed
                                                        III-13
element which is recognized; in short the patterned qualia of a private
language.2
     Consider the following line of black marks on white paper, which shall be
called line A.
A.                                                          1
Line A is the lower half of a line whose upper half is line B, which is:
B.
Unlike line A, line B is intelligible; for when only the upper half of this
type-face is seen, sufficient information is still given to enable the reader
to see these marks as letters that form words. Both halves together appear
as:1
     Line B is a significant, though unnamed pattern; in fact an instance of
Ayerian qualia. As the reader's experience will have shown, on first
confronting line B it is necessary to pick out those marks which are same and
different, or to perform some similar exercise. The comparisons can be made
either between presently perceived marks, or between remembered and perceived
marks. In any case, at this level of noticing, the language of inquiry is
private because; (1) it is used to register the as yet uninterpreted sensory
evidence, and then, (2) it is notably abandoned for English when the
familiarity of line B is recognized.
     An illustration of this sort requires that several points should be made
quite clear. First, no one denies that by using different type-faces different
results could be produced; for example, by dividing the line of letters
horizontally as here, or perhaps by halving each letter diagonally. Still, this
present result cannot be dismissed, and it too could be produced with
variations indefinitely.
     Second, when looking at line B, one is not given more information than is
provided by line A; at least not in the sense that appreciably more of each
letter is visible. Neither the volume of ink nor the surface employed is here
an issue.
     Third, as the example reveals, it is manifestly the case that the pattern
exhibited by line B, but not at first named, is significant. For it is
precisely this visible pattern that is familiar, and that leads to a
recognition of the incompletely printed letters. Having recognized the separate
letters, it is then possible either to use their conventional names, or to see
them as assembled into words. But all of these activities are subsequent to
perceiving the sharply contrasting colors which are given.
     Fourth, the black and white ideas which compose the figure and ground of
both lines A and B are not themselves patterns of course, but their simplest
sensory foundations. When considered as patterned shapes, each instance is
properly an Ayerian percept.
     I should argue therefore that anyone who consciously sees the black marks
on white, and then registers the letters or the printed words of the sample
sentence, has employed the Ayerian qualia whether he approves of them or not.
In this instance they are shown to have a definite and identifiable function.
For here qualia are seen to relate the simplest sensory information; that is
colors, to the private discrimination and recognition of significant shapes;
and thence to printed statements in a known and natural language.
     A similar case occurs when watermarks are compared. Again a significant
pattern is noticed, but has no conventional name, or name of any type. Anyone
who doubts this assertion is invited to state briefly the precise ways in which
Figure 1 differs from Figure 2.1
                                                   III-14
The dating of paper by watermarks makes this sort of comparison
necessary. Hence anyone who would match a given watermark with the correct
example in the catalogues soon discovers that some informal names are
required. In the hunt for same or different features, there are no
straightforward linguistic conventions which fit these cases. It is hardly
surprising therefore that visual memory counts for a good deal in this
exercise. To hold the image of some detail of the pattern in mind, whether one
tags it with a name or not, is necessary for comparing the sample with what can
well be hundreds of candidates which differ very little from one another.
     To sum up, the function of patterned qualia in our recognition of sensory
objects is easy to overlook. This occurs because ordinarily we pass
inattentively from recognized qualia to conventional names for them, or to the
name of some more complex unit, such as an ordinary object, in which we have a
greater interest. Our descriptive talk about the world is, after all, largely
about the objects in it which are held to be publicly observable.
     The two cases which we have reviewed focus attention on the point at which
patterned qualia are introduced in our recognition of printed words and of
watermarked paper. The acknowledged oddity of these examples is enlisted in
order to reveal an activity on which we do not usually dwell. Indeed if it were
customary to discuss such cases, we should soon devise conventional names for
the features which currently lack them and so require other illustrations. The
point is that the supply of illustrations is inexhaustible. Finally, if as I
have asserted, all empirical claims ultimately are founded on ideas, then the
passage from sensations to organized information requires either the patterned
qualia which Ayer describes, or some similar concept which performs the same
functions under another name.
Ideas and Perspective:
1. The Perceiver.
     In many respects the Ayerian qualia can be aligned with a scheme of things
which includes ideas. Apart from the advantages exhibited in clarifying
physical-object theory, qualia have been shown to link many features of sensory
experience in a way that is informative about the world. There are still
however serious points of conflict between theories of qualia and of ideas
whenever attention is directed to the activities of a perceiver and his
inevitable perspective on sensory information.
     It is the perceiver who introduces into the account of ideas that privacy
which Ayer systematically excludes from his description of percepts and
qualia. Similarly, it is the perceiver who denies universality to any strictly
interpreted idea by attaching it irrevocably to his personal history. Again,
the perceiver is the herald of a rational skepticism that follows from the
privacy of his ideas. To deny these consequences or nullify their effects, it
would be necessary to reason away ideas, a feat not yet managed by their
critics.
     There has long been in the literature a marked distaste for skeptical
conclusions though this frame of mind can hardly be expected to enjoy much
influence outside the circle of the orthodox. Historically this bias has been
associated too with a dislike of sense-data, and with the denial of the
possibility of there being a private language. The arguments presented so far
have presumably raised new doubts about the opposition to a private language
and to sense-data, not least when the latter are recast as Ayerian qualia or as
ideas. If physical objects are thereby placed at one remove from the peculiar
certainty enjoyed by either percepts or by ideas, then that is how things are.
It is important to notice elementary barriers when confronted with them;
genuine differences cannot be collapsed in the ways that distinctions can be
obscured.
     The advantages of acknowledging the fact that an idea requires a perceiver
                                                        III-15
are, some of them, fairly obvious. The perceiver's point of view is the most
interesting concept for our purposes, especially when it is developed as the
sensible perspective from which any putative observation must be made.
Observation statements or claims, in their turn, gain a place in the
arrangement of information, and a good many of our customary assumptions make
rather more sense.
     First, the sensible perspective is emphatically to be distinguished from
any perceived ideas. It does not itself form a part of any observed scenes
whatever, not least because it is imperceptible.
     In a typical visual observation we notice some color or colors deemed to
be an object, from some perspective and at some time. The fact that colors
differ from perspectives and moments in ways that are obvious on analysis does
not remove these latter features from a careful description of the
observation. Certainly if one were to make a life-like visual representation of
an object noted by sight, all three of these observational conditions would be
carefully studied.1
     Second, the elusive gray squirrel made his literary career, it will be
recalled, by exploiting the perspectival limitations of his pursuer. By
remaining on the far side of his oak tree, wherever the far side proved to be
at the moment, he illustrated at least one difference between the wholly
perceived idea and the partially concealed physical object.
     Third, the conditions required in order to view the squirrel introduced
the concept of sequences of observations. Simple viewing was frankly abandoned,
and one supposed the squirrel to remain at rest while his pursuer walked around
to the occupied side of the tree. En route the perceiver would notice other,
formerly obscured parts of the tree, and see familiar ones from a different
perspective, finally viewing the squirrel as a gray figure of suitable
dimensions.
     The general features of this rather protracted squirrel hunt may be stated
briefly. These are the concepts of perspective and of the sequence of
observations required for detecting the object sought. As before, the
perceiver's ideas are his alone, and therefore they can figure in a description
of a visible scene only from his perspective.
     Visual observations are made sequentially of course, but their particular
order may be attributed either to the change of place of the perceiver, or
simply to the motion of a scanning eye. The ubiquitous perspective and the
sequence of contiguous views remain characteristic features of our noticing
visible objects.
     Thus when we come to act on our visual information, we may accurately be
described as selecting from among our ideas those which we require, and then
using them to arrive at the place which we intend. This method of ordering our
ideas applies both to macroscopic and to microscopic objects, although the
latter require some further distinctions to be made.
2. Heterogeneity of scale.
     It is by carefully attending to perspective and sequence that we can get
from here to there in predictable ways. This is true also of our dealings with
observations that differ so greatly in scale as to be quite heterogeneous.
     I understand any two observations belonging to the same sense to be
heterogeneous if the space appropriate to the one observation is such that the
other observation cannot be made in a space of the same scale.1 Perhaps the
clearest example is provided by microscopic and macroscopic visual
observations, but the same type of analysis could be shown to apply to human
auditory limitations.
     Anyone who seriously uses a reflecting microscope is a traveller moving
through at least two worlds. Each observation that he makes occurs at a moment,
is of a place and from a perspective according to the rules of the scale of
perceptions to be noted. Colors may reveal either the figure of a supposed
                                                        III-16
squirrel or a microscopic amoeba, but the two figures will not be found
together in any informative descriptive sense of the word. It is not just that
the one animal is very much larger than the other, and therefore that they are
incommensurable, as finite and infinite minds are said to be.1 They are
incommensurable figures because they are antecedently heterogeneous; that is,
no observation of the one can forthwith provide any observable information
about the other. Any link between these figures is produced and governed solely
by the observer, or perceiver, and inevitably from his perspective. By using
this approach the two worlds may be linked systematically, but this
relationship is never simply given.
     Once again examining the details can be rewarding. Let it be supposed that
a drop of ditch water, which is placed on a rectangular glass slide and covered
with a smaller square glass plate, or cover slip, contains at least one
microscopic amoeba. The slide is then placed under a microscope of say 100-X
power and suitably illuminated (see Figure). If the subject is then sought by
beginning observations at the left hand edge of the cover slip and moving
rightwards, the microscopic world will literally begin at a grayish vertical
band (the edge mentioned) and then be filled with grayish, brown and black dots
and slightly larger pieces apparently floating free in the water. The amoeba
when found will display a thin gray line which is an outer edge, inclosing (as
one moves towards the interior), some gray dots and larger bits, and appear
also to surround some closed fine gray-line figures (the vacuoles), if it is in
the most favorable position for viewing. If moving, say leftwards, the amoeba
will exhibit a procession of gray bits leftwards as if the interior of the
animal is flowing in the direction of motion, thereby noticeably advancing a
part of its outer edge. This is the gray line that was first noted in detecting
the amoeba. If this motion continues for a short period, the characteristically
indeterminate shape of the amoeba becomes somewhat more predictable than is
usually the case.
     So far it is clear that these microscopic observations have depended
entirely on noticing colors. The more convenient talk about the amoeba as an
animal was introduced only after its color had been sighted so to speak. One
naturally notices first the ideas, and subsequently incorporates them into a
description of the visible features of a putative physical object. The object,
having been established according to custom, can then be said to be moving
about in its environment. This environment is said to have three spatial
dimensions, rather than the two justified by sight, for the reason that the
amoeba is judged to be a physical object. In turn, the reason for forming this
judgment is that the observations which one can here make are best explained by
comparing them with similar observations of a macroscopic physical object in a
liquid medium. Hence despite the fact that we are acquainted with our
microscopic subject only in terms of grays and browns and occasional black
dots, it is convenient to say 'amoeba', with all the features of physical
objects that this implies.
     To bestow on an amoeba the tangibility in principle of an ordinary
physical object is not very extravagant for the present. Equally for the
moment, the amoeba can be given a place in external reality by making the
informal assumption that microscopic animals are contained in the larger world
inhabited by larger animals. It is not rash to suppose that the amoeba is still
to be found somewhere under the cover slip on the slide and, if it were sought
out, could be observed again. It could not exhibit precisely the same ideas,
but it could meet the ordinary definition of an amoeba, and we have the
advantage in our example of knowing where this one is likely to be.
     Several features are worth noticing here. At the same time that the amoeba
is judged to be moving leftwards; macroscopically, all is still. To the unaided
eye, there is no movement to be seen under the cover slip on the slide. One
question then is whether we are observing contradictory motions. Is there
motion leftwards or is there rest?
                                                   III-17
Manifestly there is no observation that includes at once both macroscopic
and microscopic ideas. Even the original edge of the cover slip presents two
incompatible ideas, as indeed were noted in passing. The one exhibited an
extremely thin, straight grayish line; the other showed a wavy grayish band
wide enough to accommodate a good many of the black and brown dots floating
free in the drop of ditch water.
     There is also the consideration that any animal, macroscopic or
microscopic, is observable only because of the ideas it presents to a
perceiver. In order to be visible it must display some color different from its
ground, and in the absence of such contrasting ideas, there are no observations
about which we can assert 'animal', or indeed 'figure'. The amoeba consequently
requires its microscopic ground in order to be observed at all, let alone to be
observed moving leftwards.
     The problem of motion is properly transferred to the problem of its arena,
and we are reminded of the reciprocal relation between space and the objects
which occupy it. The habit of thought which leads us to suppose that a drop of
water is observed from no perspective and without qualification also obscures
differences of scale which cannot be altered by the use of a common name.
Descriptively and hence for the purposes of any informative observations, there
are two areas of water, the one a drop and the other a lake.
     In a quite strong sense the amoeba does not inhabit the drop of ditch
water described macroscopically. It is more accurate to say instead that by
examining the drop under a microscope there is revealed an animal of the sort
commonly judged to be an amoeba, and moreover that it is engaged in a process
equally commonly said to be that of moving in a leftwards direction. If now, on
glancing up from the eyepiece of the microscope, one asks oneself whether the
amoeba is moving leftwards in the ditch water that is macroscopically available
to sight, the reply is that the question is misconceived. The amoeba and the
macroscopic water are never observed together. Hence any question about their
observed relationship can be discounted.
     Habitual usage makes it tempting to say that the amoeba must be contained
in the ditch water because the ditch water is contained in even larger
macroscopic units such as the glass slide, the room where the microscope
stands, the building containing the room, and so on. But this is to suppose
that the predictable observations about supposed physical objects rely on a
concept of space such that macroscopic spaces are held to contain microscopic
spaces just as one larger mixing bowl contains another. The differences however
are instructive.
     In the case of the bowls, the visual ideas by which they may be noted are
available all at once, and in the same perception. Observation claims about the
bowls can therefore be given the same points of reference in a single
descriptive system. The amoeba and the ditch water are not perceptible
together. They are approached differently, and any alleged common point of
reference; for example, the edge of the cover slip, has quite a different
description as a part of the microscopic world from the one it has as a part of
the macroscopic world.
     To sum up, the ordinary macroscopic world need not accommodate the motions
of the amoeba. This follows not because this animal operates secretly, or in
very small places, but because the only descriptive systems in which it can
figure are incommensurable with the scale of unassisted perception. The
amoeba's system of spatial references is quite simply closed to casual
observation, and cannot be annexed by being surrounded.
3. Relating the systems: the observer.
     Microscopic and macroscopic spaces and their respective objects are
perceptually exclusive. No description of either the object observed or its
observed surroundings in the one case can pick out an object on the other
scale. Even the edge of a single, undisputed macroscopic object like a cover
                                                        III-18
slip has two quite different descriptions when viewed directly and then through
the lenses of the microscope. Not only does the description change from thin
gray line to wide gray and wavy stripe, but there is no means of locating the
former edge simply by observing the latter. In short, no microscopic
observation will pick out the place of a macroscopic figure, or even identify
it solely on the evidence of what is literally seen through the microscope.
Informative observations require organization, and the observer's function in
this enterprise is essential.
     The passage from one space and its objects to a heterogeneous space and
its objects can be systematically described. This is possible because the
perspective of the observer gives continuity to the observations made.1 These
observations are literally ideas perceived successively; and the succession,
like the ideas themselves, is properly ascribed to the perceiver or observer.
It follows that systematic observations are transparently the work of the
traveller between these two worlds of different scales.
     Microsurgery illustrates the essential features of this undertaking.2 The
microsurgeon evidently must be able to recognize through his microscope the
organic structures on which he is operating, together with the microscopic view
of the instruments which he employs. The chief mechanical problem which arises
is that of providing him with a means of making sensibly significant movements
that are not inappropriate to the scale on which he is working. Historically,
gearing was a way of managing great differences of scale in movement, all
admittedly macroscopic. An analogous reduction in scale is required for the
microsurgeon.
     Part of the microsurgeon's work is similar to that of anyone who must
manipulate microscopic objects, although it is obviously more dramatic. Still,
once the manufacturing problems have been solved in producing the instruments,
the principle to be applied is clear. Systematic experiment and the perfection
of manual technique give the surgeon the required visual information and
appropriate range of sensory responses. The microsurgeon does not so much
'reach through' from one world to another, as devise experientially noticeable
macroscopic movements which he observes to produce identifiable microscopic
movements, and then learns these patterned sequences. He therefore does not
simply observe objects and forthwith plot their perceptible spatial
relationships. This is impossible because his hands and his smallest
instruments belong to heterogeneous spatial systems.
     The solution is to relate the two systems of spaces by organizing their
respective sequences of observations. Significant patterns of sight and touch
are noted and rehearsed using ideas perceived on both scales. This is the task
of the microsurgeon, or of any other skilled observer. And this is what is
done.
     The relationship between macroscopic and microscopic observations is
instructive because it brings to the fore the active role of the observer, or
perceiver. Observations genuinely are anchored in ideas, and the perspective of
the observer, the sensible perspective, provides the grounds for moving from
ideas to various kinds of informal and scientific explanations. As I have
argued previously, if the hypothesis of one's own body is introduced to give
order to ideas whose presence cannot be willed away; perspective, then, is
introduced to give order to other bodies, at least in so far as those bodies
are claimed to be observed.1 The 'far side' of a body, such as the squirrel's
tree, reminds us of the value of this perspective in justifying habitual
attitudes and usage.
     To conclude, the assembled evidence has shown that ideas, so notable for
their resilience in the face of redescription, have a fair claim to be the
acknowledged elements of perception. In passing, the necessities of observation
have also revealed some of the operations of a sensible perspective from which
ideas are encountered. The virtues of this exercise are the straightforward
ones of first, making clear the limits of sensory evidence; and second, of
                                                        III-19
stating some of the principles by which such evidence may be organized  This
analysis has addressed too some classic puzzles, and dealt with them chiefly by
showing that their perceptual elements were initially misdescribed. Finally,
observation claims, with their covert perceiver, have been found to be
considerably more complex and more interesting than our habitual use of
language would suggest. The systematic observer is now revealed to be a
traveller whose tale is one of pathways, of how to proceed among one's ideas in
good order on a subsequent occasion. Even when there is no special advantage in
plotting the course very accurately, still it is worth recalling that the ideas
along the way are every one perceived from a sensible perspective. This is the
traveller's inevitable vantage point, and like ideas, it resists being
altogether discounted.
                                       fnIII-1
Footnotes for Chapter III
III-1 n.1 G.E. Moore, 'The Refutation of Idealism', Mind, NS Vol.xii, 1903.
          Reprinted since 1922 in Philosophical Studies, London, 1970, pp.1-30.
     n.2  Bertrand Russell, Problems of Philosophy, London, 1912. Reprinted
          frequently, including New York, 1959, p.12ff.
     n.3  Complementary Notions, pp.19; 45-47 and 47-8; 108-11.
III-2 n.1 Nelson Goodman, The Structure of Appearance, Dordrecht, 1977, p.95.
          '3': Goodman here adds that: 'My usage of the terms "quale" and
          "property", along with much else in this and the following section,
          is taken from C.I. Lewis's Mind and the World Order (New York...,
          1929).'
III-8 n.1 Structure of Appearance, p.196.
     n.2  A point made by Ayer in Perception and Identity, p.283.
     n.3  Structure of Appearance, pp'197'
III-9 n.1 Ibid., p.197.
III-11 n.1  C. Wright, 'Language-Mastery and the Sorites Paradox', in Truth and
Meaning: Essays in Semantics, eds. Gareth Evans and John McDowell, Oxford,
1976, pp.223-47.
III-12 n.1  For a detailed discussion of the puzzle, see my paper, 'On taking
Ideas Seriously', delivered to the International Berkeley Society in 1979, to
appear in Berkeley: Critical and Interpretive Essays, ed. Colin M. Turbayne,
University of Minnesota Studies, Minneapolis, 1982, pp.35-47.
III-13 n.1  Central Questions, p.91. (Pelican edition.)
III-17 n.1  Ibid., pp.99-106.
     n.2  A.J. Ayer, The Problem of Knowledge, Harmondsworth, (Pelican
          edition,) 1956, p.65, and quoted by David Pears in Perception and
          Identity, p.75.
III-21 n.1  Perception and Identity, p.284.
     n.2  Ibid.
III-24 n.1  See above, (p. III-16).
III-26 n.1  See above, (p. III-16).
     n.2  On perspective, see below.
III-28 n.1   This is of some moment because The Problem of Knowledge is a
sustained attack on skeptical arguments, systematically fortified by
sense-data.
     n.2  See above, Chapter I.
III-29 n.1  In this respect ideas have a curious resemblance to the moral
questions which underlie concepts in jurisprudence. See J.W. Harris, Legal
                                                            fnIII-2
Philosophies, Oxford, 1980, especially pp.3-5; 128-38; 209-17.
III-32 n.1  Ludwig Wittgenstein, Remarks on Colour, ed. G.E.M. Anscombe,
Oxford, 1977, Part I, Entry 88, p.14e. The German text runs: "88. Wenn der
Psychologe uns lehrt 'Es gibt Menschen, welche sehen', so konnen wir ihn
fragen: "Und was nennst Du  Menschen, welche sehen ?' Darauf musste die Antwort
sein: Menschen, die unter den und den Umstanden sich so und so benehmen."
(p.14).
III-33 n.1  For an account of sight and colors, see Persons:, pp.12-13; 35-37;
51.
     n.2  The examples given in Perception and Identity of a sentence of spoken
          German, and of a Cubist picture seen as a portrait make a similar
          point, but are less explicit about the sequence of recognition. See
          p.291. See also Central Questions, p.91.
III-34 n.3  Flatland, p.44.
III-36 n.1  Wasserzeichen Buchstabe P - Teil 2, ed. Gerhard Piccard, Stuttgart,
1977, Section VII, Nos. 194 and 195.
III-40 n.1  See below, Chapter IV.
III-42 n.1  On the several kinds of spaces, see above, Chapter I.
III-43 n.1  On some problems of this sort, see my paper, 'Berkeley's Rejection
of Anselm's Argument', in Studies in Anselm, ed. Gillian Evans, London, 1982;
and discussion of the incommensurable in 'Notions: the Counter-Poise of the
Berkeleyan Ideas' in Giornale di Metafisica, (Nuova Serie,) III, 1981, pp.246;
251-54; 258-59.
III-49 n.1  See Persons: pp.93-107.
     n.2  McGill University is a major center for this work. Some papers by
          surgeons there include: a chapter by Julia K. Terzis et al. in
          Microsurgical Composite Tissue Transplantation, eds. Donald Serafin &
          Harry J. Buncke, Jr., St. Louis - Toronto - London, 1979. See also
          Microsurgery, ed. Sherman J. Silber, Baltimore, 1979, Chp. I,
          'Microsurgical Technique'; and Microscopic and Endoscopic Surgery
          with the CO2 Laser, eds. A.H. Andrews, Jr. and T.G. Polanyi, Boston -
          Bristol - London, 1982, Chp. I, 'History of the CO2 Laser in Surgery'
          by Polanyi.
III-51 n.1  Persons, pp.66-75.
                                                           txtfnIII-1
*    'Sense data' is written here instead of 'qualia' to conform with the usage
favored by the contributors of the papers to which Ayer is replying. (cf.
p.278.)
                                                              IV-1
Chapter IV - Perspicio: I Observe
     Ordinary observations and most of our informal empirical claims reflect a
belief in a continuous external world which is generally stable. This world is
admitted to include objects which move about in it, such as animals; and it
also is said to undergo predictable changes, like the ordered procession of the
seasons. More complex information about observable changes are not excluded,
but they typically are thought to be performed before a backdrop of reliable
scenery and well-schooled minor players. To all appearances and for most
purposes therefore, the external world is judged to be fundamentally at rest.
     This result is a direct consequence of the emphasis that we give to visual
information in preference to that derived from the other senses. Our claims are
none the worse for this choice; on the contrary, they suit our case admirably.
Still it is useful to know what our biases about information actually include.
     As well as the preferred, continuous visual space that provides the arena
in which objects may be perceived, there is also the sensible perspective which
governs the order and sequence of sensory information. Even the casual observer
traces pathways in the world, noting in turn his ideas as they succeed one
another. Deliberate scientific observation obviously is not so easily depicted,
but it is essentially the same sort of exercise whenever the investigation
includes literally perceived ideas.
Perspective and Representation:
     The perspective from which all ideas are judged is implicit in
perception. Whether one is relying on the traditional perceiver or on the
sensible perspective, it is relatively easy to overlook the role which must be
filled by some organizer of logically independent ideas. Generations of Humeans
indeed have succeeded in omitting this problem of organization altogether,
largely because Humean impressions were easily transformed into more or less
continuous objects. Nevertheless, once the question is addressed, it is
difficult to admit heterogeneous, independent ideas and then altogether to
reject some sort of perceiver.
     If the various given elements of perception require a sensible
perspective, it is all the more apparent that physical objects must be observed
from some point of view. An abiding assumption of physical object theory is
that the object is continuous and not wholly perceived, because it has an
unseen, or far, side. From this it follows that the object also possesses a
near side, and both of these relative concepts presuppose some observer whose
point of view is reflected in such judgments about location and visibility.
James' squirrel concentrated minds wonderfully on just these issues, and has
rightly remained important for this reason.1
     In the representation of sensory experience, the central function of the
sensible perspective is explicitly acknowledged. This is one of several
features that distinguishes empirical observation claims and the ways in which
they can be represented, from claims based on purely theoretical knowledge. In
the latter case, it is granted that anything can represent anything else. Where
there is no sensory evidence to be considered, it is necessary only that the
rules for representation be clear, and that the whole collection of rules be
made consistent with one another.
     Once empirical information must be taken into account, the case is
fundamentally different. The elements of perception, or ideas, determine the
types of possible spatial relationships, and any would-be sensory
representation is required to include a sensible likeness of the original.
Representations of sensory experience imitate more or less convincingly the
object of interest, and it is noteworthy that of all such imitations, the most
successful is visual representation.
     Visual representation carries greatest conviction because first, the
spatial relations commonly attributed to the objects to be represented are the
relations that were originally borrowed from the characteristic features of
visual space. The external world is generally supposed to be at rest in a
                                                              IV-2
perceptual space that never is found to be empty, and which accomodates several
ideas at the same time. This is precisely the description that identifies the
perceptual space of visual ideas.
     Second, the physical object that is to be represented is agreed to be both
visible and tangible, by definition. The representation similarly is governed
by what is thought possile for the object. This is shown when the
representation is judged to be literally out of reach. Like the object it
represents, there is then no inclination to impugn its reality merely because
it cannot at that moment be tested for its tangibility. Let us suppose that a
human face is represented visually. If such a face were diminished in size so
as to suggest to us that it is too distant to provide us with tangible
information, we need not for that reason judge it to be less real. We might
instead be content simply to examine its visual appearance for the likeness
which we seek.
     The third reason for the success of visual representation is the most
interesting and in some respects the most far-reaching one. A visual
representation is peculiarly satisfying because it can imitate life in
precisely the ideas offered by its original, and its representation need not be
further pursued. On hearing a song, we might look for a singer and find a
recording, but the seen face is just that. We know, of course, that human faces
do not feel like painted canvases, but the painted canvas can imitate the look
of a human being with complete fidelity to the original, because we can
literally see on the canvas every seeable element that belongs to that view of
the subject in life. By contrast, what is heard is necessarily transient and
provokes questions about its source.
     These are the reasons that underlay the triumph of the visual
representation, or the painted scene, in the great Renaissance disputes
concerning the paragone. The ideal to be realized by the artist was a life-like
representation.
     The paragone was the argument concerned with whether painting or sculpture
should be judged the superior art. In the 15th century it is recorded that
Antonio Filarete, a 'minor Florentine sculptor and architect', replied to the
Duke of Milan who had been praising sculptors because of the difficulty of
their art in the following manner:
[Filarete:]* 'Your lordship speaks truth, for carving in marble is a matter of
great mastery. In the same way, as far as the eye's vision goes, and aiming to
counterfeit those colors that nature makes, those [paintings]* are great things
too. For however good they are, the one [sculpture]* always seems to be of the
material they really are, but what is painted seems to be the actual thing. And
many are taken in, believing the object to be real. And not only men but
animals have been taken in by this power of colors,...'(p.90)1
     If the artist's goal is to produce a life-like representation, there can
be no doubt that Filarete is right, no matter how carefully he must tread in
venturing to disagree with his patron. The existence of trompe-l'oeil clinches
his argument, for in the imitation of nature, the other senses introduce
insoluble problems of continuity. It is altogether more difficult first, to
delineate the subject to be imitated, and second, to sustain the representation
of individuals that are either heard or felt. A brief inquiry into these two
usually informative senses will indicate the scope of the problem.
     If one attempts to imitate a pitch heard in nature, this is not at first
very complicated. Birdsong and the calls of animals evoke the animal easily
enough, but then the demands of representation make themselves felt. The
supposition is that the song of, say, a greenfinch is being produced by a
greenfinch, but his portrait in imitated sound ought to include as well other
auditory information that suits his species. It would seem however that only
his particular call and the supposed kicking of dry leaves or of some other
background shrubbery can give any indication of his presence. At this point,
the sequential character of auditory space becomes awkward. For auditory space
is such that the pitches that can be interpreted as the song of the greenfinch,
                                                              IV-3
or some other related audible activity, must continue until the finch's
departure is signaled' But his natural mode of travel is silent flight. The
result is that the auditory representation of a physical object like a
greenfinch is inevitably incomplete.
     One who seeks out the living greenfinch by following his song may well be
rewarded by seeing him, but the assurance given by a sighting reflects the
inadequacy of sound recognition for all but the most knowledgeable of bird
watchers.
     Typically, sound portraits of animals are recordings taken from nature,
not imitations of nature. Radio nature broadcasts manage the recorded auditory
portrait as well as it can be done. 'Manage' is however the key word in the
technique, and such broadcasts employ a wide range of straightforward
descriptions and conventional signals for a change of scene, like crunching
footsteps and splashing water. Any of these effects can, of course, be imitated
just as birdsong can be, but they all suffer eventually from the sequential
order of audible space and its essential silences. For in a portrait drawn by
sound, a prolonged silence is indistinguishable from a failed representation of
a continuous physical object.
     From the example of the greenfinch two principles of representation can be
identified. There is the evident requirement that the right kind of idea should
be perceived, and also meet the terms of its appropriate perceptual space. A
successful audible representation of a greenfinch then must exhibit a
qualitative likeness with the song of the greenfinch. It is further required
that the representation should be in a context that is characteristic of the
greenfinch as the object here imitated. The failure of an audible context is
considered first.
     It is evocative of a warm sunny day to hear the buzz of a bumblebee
together with presumed rustling leaves and the chirpings of birds. When
combined these audible ideas might be thought to emanate from a garden in
summer. The same buzz, if heard against a background of pitches associated with
a howling winter wind, immediately sounds wrong. The representation of the
bumblebee fails to convince us of his presence simply because bumblebees and
winter gales are not found together.
     Representations can also fail to meet the condition of likeness. This need
not just be a question of poor perceptual imitation or a near miss; there is
also a type of failure whose shortcomings are clear beyond dispute.
     Consider the representation of a conventional, indeed prosaic, melody.
(melody only, of 'None More Shrill Than Thou')
     The composition is not in any way extraordinary, except that the range
indicated is quite inaudible to human ears. The notes are to be sounded eight
octaves above middle-C, a pitch which exceeds our auditory capacity by more
than 40,000 Hertz.1 The alternative title of the piece, 'Duet for Long-eared
Bats', gives the game away, but it is not a fault of the context that causes
this imitation of an ordinary written duet to fail. It fails because a musical
score is essentially an injunction, and this injunction cannot be followed
because it is sensorily impossible for us to do so. Yet if the pitch were
lowered, for instance to the upper reaches of the piano, the score is easily
played. In short, there is nothing amiss with the terms in which the piece is
written, except for the impossibility of hearing it played accurately. The
human ear is simply the wrong ear for the purpose, hence the human being is out
of scale with the representation. The human scale is a condition of perception
to which the Renaissance artists early directed their interests. As we shall
have occasion to notice, this is especially true of the new theory of
painting. Perspective, after all, implicitly includes the observer and judge of
life-like representations.
     It is rare to find a life-like representation of a physical object based
                                                              IV-4
solely on tangible information. This is so because we tend to begin with visual
information about an object and then to correct our judgment by consulting the
tangible evidence thought relevant to the case. It does not follow from this
however that tangible information inevitablyu reveals what there is and
therefore cannot represent anything else. If the purpose is to produce a
life-like representation of a physical object, then the tangible representation
can be tested for the required tangible likeness and context.
     Consider a shape like a rabbit sitting in a field. When this
representation is first seen, it might look convincing and lead one to suppose
that the figure is that of a live rabbit. Its context can be tangibly noticed
when approaching it, and the discovery that it is a stuffed rabbit, or even a
life-like toy rabbit, can be delayed until it is firmly touched. The objection
that in these circumstances a really convincing rabbit would hop away long
before it is reached can be met with the reply that the rabbit could be either
tame or sick. No doubt the observation that the rabbit figure does not move
away will arouse some suspicion about its apparently standard look, but the
test is finally to be made by touch. And tangibly the figure is found to be
unlike a live rabbit.
     The unyielding shape of a toy rabbit or a stuffed one would make the
representation fail. The same result would follow from the incoherent
floppiness of some kinds of toy rabbits, or of dead ones. Literally at first
touch, an imitation fur might be convincing, but subsequent tangible
exploration of this furry shape is required by the sequential perceptual space
that belongs to touch. The lack of muscular tension in the rabbit's body would
quickly reveal the deception, and show whether it is a toy or stuffed or dead.
Warmth or the lack of it need not be invoked to confirm the judgment, although
a very chilly rabbit shape is most unlikely to be a live rabbit. A particular,
predictable body temperature is not of course applicable to cold-blooded
animals, and so it is worth recording that the muscles of animals like frogs
also exhibit a characteristic tension only when the animal is alive.
     Even from this example, it is not difficult to appreciate why tangible
imitations generally are not used to represent physical objects. The artistic
representation of furs, as distinct from animals, is however to be found in
another quarter. One fur is readily employed as a surrogate for another and
usually more expensive one, but then the imitation is presented as some type of
garment or upholstery. There is no question of providing a tangible
representation of the living fur-bearing animal, although its outline may be
preserved as in the example of a mink scarf. Certainly no believable context
for the tangible likeness of an animal is even attempted in such productions.
     A most interesting example of artistic imitation that includes certain
features of a tangible representation is life-like sculpture. This is the
imitation of tangible perception 'at a distance' so to speak, but its analysis
is especially revealing.
     A tinted sculpture in wax can be an extraordinarily good imitation of the
original human being but only to the eye. The touch of the wax and the immobile
figure at once destroys the illusion. Still, the genuine grounds for its
limited success are not immediately obvious.
     The advantage enjoyed by the solid waxen figure over the painted surface
figure appears at first to be overwhelming. This is a consequence of the fact
that the sculpted figure is three-dimensional, and so it is readily supposed
that it can represent more accurately a three-dimensional physical object. The
objection to this uncritical opinion is that the third dimension of such an
object is in fact a tangible dimension,1 and therefore cannot literally enhance
the illusion of life. As we have noted, any genuinely tangible information is
fatal to the belief that the figure is a living human being.
     The whole advantage of the sculpture is found in its availability for
viewing from several perspectives, a feature that we associate with informative
views of human beings. To exploit this possibility, the ideal sculpted figure
                                                              IV-5
might at first be presented so as to allow any observer to walk around it  and
so see it from every side. Obviously it is necessary to ensure that the
observer is always kept well out of reach of the representation while noticing
its life-like features. The result is that each viewing of the figure conforms
to expectations and inspires belief in its human reality.
     But now, a second issue arises. Because the sensory information is wholly
visual, the space that is exploited in this representation is not the
sequential space of touch, however much the observer may himself move from
place to place. Instead, the space is the continuous, stable space of sight. It
is not surprising therefore to find that even the waxen figure appears to be
most life-like when it is seen in a tableau. So placed, together with living
actors, and provided that none of the actors seemed to move, for a short period
it would not be possible to distinguish the imitation from the real. The
observer would then be supposed to look at the figures in the tableau from a
comparatively limited number of places, and all from the front of the scene, as
on a stage with a procenium arch.
     In these conditi ns it is clear that the successful representation of a
living human being not only is founded entirely on the colors perceived, but it
also uses to the full the advantages of stable, visual space. The sculpture is
effectively a painted figure in a painted scene, and the test that the
representation is genuinely founded on single views, each complete at the
moment, is to select any scene with the sculpted figure and substitute for it a
painted one. If the resources of stage lighting are used correctly, it would be
impossible to tell the sculpture from the painting, because there is no
discernible difference in the two representations. They both are composed of
perceived colors, and such colors can be repeated so as to be judged
indistinguishable, hence identical. On the evidence therefore, Filarete was
right, as well as courageous, to plump so boldly for the life-like superiority
of the painted image.
     To sum up so far, the results of our analysis of the painted waxen figure
reveal that the success of this life-like representation rests entirely on its
separate, isolatable visual appearances. Each appearance is complete at the
moment of perception and is located in a stable perceptual space. Like the
carefully lighted painting, the sculpted representation is visible because the
observer is presented with contrasting colors which he interprets as a human
figure. The problematic far side of the supposed figure is, as in life, quite
unobservable; and such perceptible qualities as it might show from a different
perspective are nothing to the point.
Lights and Pigments:
     It is not the least of the painters' virtues that their work directs
attention to the relation between those colors we are inclined to call lights
and those called pigments. The centuries since Newton especially have led many
discussions about colors into analyses of light, beginning with the visible
spectrum revealed by the prism and developing to accounts of wavelengths. Just
how an object actually looks, or what colors it may be said to exhibit, are
questions not infrequently ignored by this approach, with the result that there
is a considerable lack of clarity about what we literally see. The puzzlement
provoked by the color continuum is a monument to obscurity about visible ideas.
     Visible ideas effectively introduce the solution to several puzzles. This
is so because these ideas simply are the colors that we see whenever we see
anything at all. The separate question as to whether one is viewing a light or
a pigment, or indeed lighted pigments, is properly one step removed from the
sensory experience. The physiological requirement which states that a certain
level of light is necessary in order for us to see any ordinary objects also
can be identified as belonging to physiology rather than to perception.
     As to what is seen, even the white light of Newton's experiment is a color
which may be seen under the classical conditions so often described. There is
too the familiar yellow-white beam of a good bicycle lamp seen from the side,
and therefore against the dark background that it does not illuminate. More
brilliant and more rare is the white beam of a skyscraper searchlight which
sweeps the night sky above the city as a warning to friendly air traffic.
     Equally we are surrounded by pigmented surfaces whose reflective
properties determine the colors we see and attribute to the perceived planes.
Again it is specifically color that we see. The reasons for a color's being
that hue rather than another one can be analyzed, traced to its source and
conditions, and predicted on subsequent occasions. Perceived colors thus have
two known sources or conditions, and these influence each other in ways that
can be known.
     It is the manipulation of colors that brings out the specific differences
between lights and pigments. Where lights are to determine changes in color, it
is presumed that the object being illuminated is a constant surface with fixed
pigments. Exercises in mixing lights rely on this stability. To test lighting
for example, one might simply focus a succession of colored lights on a white
screen. It is then easy to show that the standard mixing of lights produces
quite different effects from the standard mixing of pigments. It is well-known
that red and green lights combine to produce yellow, an effect notably
different from the rather muddy results of mixing red and green pigments. A
proscenium stage lends itself to innumerable transformations resulting entirely
from well-controlled lighting. In every instance however, the working
assumption must be that the surfaces to be illuminated are stable, and their
pigmentation is known. A predictable, not to say desirable, result of a
lighting effect depends on a reliable constant; and for lighting the constant
is the visible surface to be transformed.
     The complementary exercise in the manipulation of pigments relies instead
on a source of light of a constant color. It is not unexpected that the
standard light is the white light of the sun, since the overwhelming number of
objects that we see are lighted by it. The painter who wishes to make a
life-like representation of an object seen out of doors will usually take his
colors from its daylight appearance. He will in any event suppose that the
light by which he selects his pigments is the same as the light by which his
painting will be seen. Otherwise the spectator will not see even the colors it
is presumed that the painter saw.1 And whether he intends to make a realistic
painting or not, the variables in his repertory are the pigments and surfaces
which he employs; the light is deemed to be a constant.
     The fact that these two kinds of colors may be qualitatively
indistinguishable makes painted life-like representations possible, and a
rather simple example of one peculiarly convincing. Imagine a full pale yellow
moon. If this moon is seen through a window on a summer night, and no stars are
visible, it would be quite indistinguishable from a moon painted in pale yellow
pigments, were the painting suitably lighted. Ex hypothesi, any observer would
be out of reach of the painting and, as in the case of the real moon, have no
tangible ideas about it at all. There is consequently nothing but the ideas
available to sight, which are the two pale yellow discs, and the dark
backgrounds against which each is seen. Nevertheless the fact remains that one
is a painted disc and the other is a satellite of the earth.
     The explanation of this impasse in judgment between things which are so
different is contained in the analysis of their elements and of visible ideas.
When lights and pigments are understood as ways of classifying colors, it
readily follows that each pale yellow disc can be a necessary and sufficient
condition for visual evidence for a moon. Moreover it is only visual evidence
which can count in this instance because of the terms of the example. But even
though the elements are all colors, the lights and pigments cannot be mixed or
exchanged, because their variables and constants are different. Any detectable
change in the colored light of the real moon produced by the atmosphere could
subsequently be matched by a change in the pigments of the painted moon, but
the technique would be noticeably different. Drawing a fine curtain over the
                                                              IV-7
window would again require the artist to dim the lustre of his moon by
resorting to his paints not to the light. Still, as ideas, the colors can be
made qualitatively indistinguishable. The painted moon then succeeds to
perfection in its imitative role, and continues so for some considerable
period.
     To conclude this section, the exercise of examining the two pale yellow
discs calls attention to some recurring features about visible
representations. One is that the perceived colors are simply given, and
speculation about how they may be altered does not offer any clues for deciding
between their present appearances. A second point which is illustrated in the
moon example is its evident dependency on a carefully controlled perspective,
including the distance from which any observations of the painted moon are to
be permitted. Naturally the spectator is ignorant as to which pale yellow disc
is being governed by this rule, but the control is still systematically
applied. A similar care in the viewing of life-like representations is
characteristic of the early 15th century Renaissance painters and sculptors and
architects, among whom Leone Battista Alberti is happily most clear and
informative.
Systematic Life-like Representation:
     In 1436 there appeared in Florence a little work entitled Della
pittura.1 It is 'the first modern treatise on the theory of painting' and
introduces Alberti's description of linear perspective and its use in depicting
accurately the appearances of things. Alberti also set out for the aspiring
painter the principles of his art and the techniques by which he could achieve
mastery. To this end the pupil must learn to look at his subject intelligently
and record what he sees accurately. Alberti himself was much concerned with the
suitable education of the painter and his knowledge of classical literary works
and educated opinion. The whole tenor of the book is to affirm that the best
type of painter is a humanist and artist, rather than a craftsman whose skills
are properly directed in executing the will of his patron. The skills are not
for this reason to be despised, but they are best exhibited when they are
thoroughly understood.
     Book One of Della pittura virtually opens with a statement about the
proper subject matter of painting, as distinct from the mathematical concepts
of which Alberti makes extensive use.
No one would deny that the painter has nothing to do with things that are not
visible.8 The painter is concerned solely with representing what can be seen.1
(p.43)
In his note to the translation, Spencer remarks that:
8.   solo studia il pictore fingiere quello si vede (MI, 120v.). The Latin
varies the statement slightly to give it a more philosophic turn: Nam ea solum
imitari studet pictor quae sub luce videantur (O, iv). For the painter attempts
only to imitate that which is seen in light. (Italics mine.)* (p.100)
     In Book Two, the three concepts which govern the technique the reception
of light. The flavor of Alberti's approach to his subject is nicely illustrated
in the passage with which he begins the discussion. Again, we are left in no
doubt of the subject at hand.
Painting is divided into three parts; these divisions we have taken from
nature.
     Since painting strives to represent things seen, let us note in what way
things are seen. First, in seeing a thing, we say it occupies a place. Here the
painter, in describing this space, will say this, his guiding an outline with a
line, is circumscription.
     Then, looking at it again, we understand that several planes of the
observed body belong together, and here the painter drawing them in their
places will say that he is making a composition.
     Finally, we determine more clearly the colours and qualities of the
planes. Since every difference in them is born from light, we can properly call
                                                              IV-8
their representation the reception of light.
     Therefore, painting is composed of circumscription, composition and
reception of light. (pp.67-8)
Alberti then develops each concept in turn, always preserving the emphasis on
what is seen, and how it is best to be represented.
     Of circumscription he says in the following paragraph:
Circumscription describes the turning of the outline in the painting. (p.68)
The nature from which circumscription is taken obviously is the border produced
by contrasting adjacent colors. Visible shapes are determined by such contrasts
in color, but the edge is not different from the colors which make it
visible.1 And so Alberti warns the novice painter:
Because circumscription is nothing but the drawing of the outline, which when
done with too apparent a line does not indicate a margin of the plane but a
neat cleavage, I should desire that only the movement of the outline be
inscribed. (p.68)
Alberti, the gentle guide, then immediately becomes the stern master as he
continues this passage with:
To this, I insist, one must devote a great amount of practice. No composition
and no reception of light can be praised where there is not also a good
circumscription. It is not unusual, however, to see only a good circumscription
- that is, a good drawing - which is most pleasant in itself. (p.68)
The stress given here to the importance of good drawing is inspired partly by
Alberti's recognition that the one-dimensional line of the mathematicians is
not the two-dimensional, though never so thin, line which the painter must
use. It is possible to indicate boundaries by juxtaposing comparatively
prominent shapes or 'planes' by the use of shading, thus producing the result I
understand by that curious phrase, 'the movement of the outline'. The
alternative is to draw so as to suggest the outline of objects, not the
presence of attenuated planes, or lines, which is what is actually seen.
Alberti indeed states that good drawing is pleasing, yet however good it may
be, it remains only a necessary condition for the life-like representation of a
thing.
     In one respect, circumscription is also concerned with the space inclosed
by the outlines, the 'planes' as Alberti uses this word. The purpose of his
invention of linear perspective is precisely to preserve visible resemblances
between a representation and its original. In painting this is done by the
placing of planes so as to preserve the visible relations of any object that is
observed. And where there are planes, there are inevitably outlines of planes.
It is not surprising then to find Alberti adding somewhat later when he
discusses composition that circumscription "pertains not a little to
composition" (p.70). This is evident when he states,
I say composition is that rule in painting by which the parts fit together in
the painted work. The greatest work of the painter is the istoria. Bodies are
part of the istoria, members are parts of the bodies, planes are parts of the
members. Circumscription is nothing more than a certain rule for designing the
outline of the planes, since some planes are small as in animals, others are
large as those of buildings and colossi. (p.70)
The techniques for preserving the visible relationships between men and
buildings is mentioned again, but this subject is dealt with primarily in Book
One.
     The istoria is a concept of the greatest interest and importance to
Alberti, though it has little to do with contemporary requirements for
realistic painting. Essentially by istoria Alberti means the occasion that is
depicted in a scene, including the expression of emotions by the attitudes of
the figures shown. The assumption is that some identifiable kind of event is
the usual subject matter for great painting, but it need not be historical in
any usual meaning of the word. A work of imagination on some universally
interesting and edifying theme derived from the classics is preferred by
Alberti. The important conditions are that life-like representations of a
                                                              IV-9
suitable subject should be accurate to the eye and convincing to the emotions.
     The istoria which merits both praise and admiration will be so agreeably
and pleasantly attractive that it will capture the eye of whatever learned or
unlearned person is looking at it and will move his soul. (p.75)
Good composition must include therefore both the accurate representation of
visible planes, and the suitable use of them. Alberti's careful exposition of
suitability need not detain us.
     The third division of painting,
     The reception of light remains to be treated. In the lessons above I have
demonstrated at length how light has the power to vary colours. I have taught
how the same colour, according to the light and shade it receives, will alter
its appearance. I have said that white and black express to the painter shade
and light; all other colours for the painter are matter to which he adds more
or less shadow or light. (pp.81-2)
     The colors of the objects to be depicted vary with the light or shade in
which they are seen. To match such variations, the painter must be especially
sensitive to the use, and limitations, of black and white, which are his only
means of introducing those differences produced in nature by sunlight. However
the attention of the artist is to be given not to objects considered as units,
but to the planes of the composition. Alberti's analysis of figure founded on
lines and planes is explicitly applied to the techniques of coloring.
     I prefer a good drawing with a good composition to be well coloured.
Therefore let us study first of all light and shade, and remember how one plane
is brighter than another where the rays of light strike, and how, where the
force of light is lacking, the same colour becomes dusky. It should also be
noted that the shadow will always correspond to the light in another part so
that no part of a body is lighted without another part being dark.
     As for imitating the bright with white and the shadow with black, I
admonish you to take great care to know the distinct planes as each one is
covered with light or shadow. This will be well understood by you from nature.
(pp.82-3)
     It is obvious that good coloring makes colored figures more like their
originals, but there is more to Alberti's preference than that. Here we are no
longer concerned solely with the lights and shadows of objects themselves, but
with the principles underlying their accurate representation. By the use of
black and white, and its effect on the other pigments, the artist can color the
planes of his drawn objects so as to reveal the place of each figure in a
composition. The consequences of this result are considerably more extensive
than even Alberti realized, although we shall find that his analysis provides
an effective reply to critics who flourished hundreds of years later.1
     Alberti's insistence on the accurate representation of lighted and
shadowed planes led him to deplore the use of gold paint in any picture. The
habit until then was to decorate as well as to represent; thus the saints might
be given a golden nimbus, or the Virgin a golden crown, or again, Dido a quiver
and girdle painted in gold. According to Alberti, in the painting proper none
of these things should be done. The objection is that gold tends to reflect
light on its own account. Consequently gold cannot be managed as the other
pigments can be managed by the careful placing of the source of light used to
illuminate the panel. The comment on the subject near the end of Book Two is
wholly characteristic of the author. Indecisiveness is hardly a fault of one
who writes:
     There are some who use much gold in their istoria. They think it gives
majesty. I do not praise it. (p.85)
     Book Two is concluded with a summary of the divisions of painting, and the
proper scope of the painter's art. Alberti is careful again to call attention
to the visible planes on which all accurate representation depends. Once again
too he implicitly distinguishes the concerns of the painter from those of the
mathematician. Like a good advocate Alberti closes by reminding his readers of
what they have been told, however briefly.
                                                             IV-10
We have treated of the circumscription, of the larger and smaller planes  we
have treated of colours as we believe them to pertain to the use of the
painter. Therefore, we thus express all painting when we say it is made up of
these three things: circumscription, composition and the reception of light.
(p.85)
     And so the painter who follows the injunctions of Alberti can arrange his
pigments so as to produce a life-like scene. This approach to painting is just
the reverse of the analysis of an object and its visible surroundings into
colors that literally are seen. Alberti is of particular interest too because
his divisions of painting explicitly distinguish the representation to be
painted from the perspective of the painter, yet his treatise takes both into
account. We have been told by him that for the painter colors produce planes;
organized planes produce objects; and objects in place produce a life-like
representation of a scene. Moreover, a scene is always observed from some point
of view, and for Alberti the eye of the beholder is the point from which linear
perspective is developed.
     The height of the observer's eye gives the "position of the central ray'
or line of sight",1 and together with the distance of the eye from the picture
plane,2 provides the conditions for Alberti's theory of recession. To develop
the theory he introduced his 'visual pyramid' in Book One of Della pittura in
the following terms.
The pyramid is a figure of a body from whose base straight lines are drawn
upward, terminating in a single point. The base of this pyramid is a plane
which is seen. The sides of the pyramid are those rays which I have called
extrinsic. The cuspid, that is the point of the pyramid, is located within the
eye... (pp.47-8)
Alberti notes too that most objects are judged with reference to man, and
therefore it is necessary when representing men and objects together to
maintain the latter's true proportion in relation to any human figure that
appears in the same plane. This is required no matter how remote these
representations may be from the picture plane. The positions of the observer
and the representation to be viewed are then fixed by Alberti.
     First of all about where I draw. I inscribe a quadrangle of right angles,
as large as I wish, which is considered to be an open window through which I
see what I want to paint. Here I determine as it pleases me the size of the men
in my picture. I divide the length of this man in three parts. These parts to
me are proportional to that measurement called a braccio, for in measuring the
average man it is seen that he is about three braccia. With these braccia I
divide the base line of the rectangle into as many parts as it will receive. To
me this base line of the quadrangle is proportional to the nearest transverse
and equidistant quantity seen on the pavement. Then, within this quadrangle,
where it seems best to me, I make a point which occupies that place where the
central ray strikes. For this it is called the centric point. This point is
properly placed when it is no higher from the base line of the quadrangle than
the height of the man that I have to paint there. Thus both the beholder and
the painted things he sees will appear to be on the same plane.
     The centric point being located as I said, I draw straight lines from it
to each division placed on the base line of the quadrangle. These drawn lines,
[extended]* as if to infinity, demonstrate to me how each transverse quantity
is altered visually. (p.56)
A sketch of the described relationships will make this exercise clearer. The
one given below is borrowed in part from Spencer (p.122).
     One of the more striking features of Alberti's theory quoted above is his
use of the observer to determine the height of human figures in the
representation. Furthermore, Spencer has traced Alberti's opinions about the
proper viewing distance for a convincing painting to his work surveying
monuments in Rome during the years 1431-1434.1 Quite apart from this evidence
is of course Alberti's distinguished career as an architect. It is the less
                                                             IV-11
unexpected then to encounter on the following page the warning:
Know that a painted thing can never appear truthful where there is not a
definite distance for seeing it. (p.57)
     This remark has sometimes been held to show that Alberti's analysis
commits the observer to a monocular view of a painted scene, observed literally
through a pinhole. Against this rather fatuous interpretation, one can begin by
reviewing the passages of Della pittura already cited. It is true that some
point of view is required, but Alberti's recognition of the resources of the
painter and the conditions that rule a life-like representation give him ample
means of responding to such criticism. Mistaken theories of the pinhole view,
the rounded eye and the moving object are treated below. We now turn to the
observer and his significance for Alberti, and for the analysis of visual
perception.
Painted Representation and Visual Perspective:
     The chief interest of Della pittura for our purposes is Alberti's obvious
conviction that the systematic placing of colored shapes and the construction
of an ordered perspective belong to the study of painting. The analysis of
visual perception which begins with colors and the visual space in which they
occur has an obvious parallel with the painter's use of pigments. The further
claim that any plausible account of visual perception sooner or later reveals
an implicit perceiver, or sensible perspective, is not very far removed from
the function that Alberti bestows on his observer. In both cases, whether of
representation or of perception, the point of view of the perceiving subject
provides the ground for a systematic interpretation of what can be seen.
     Alberti's observer is the painter, in the first instance, and his purpose
is to reproduce what he sees in a way that is credible. He must, in
consequence, recognize and understand what he literally sees, so that he can
produce the effects he intends. The credibility of the painting is a condition
that ought not to be underrated. Not only does it justify the art of the
painter as Alberti understands painting, but it also enables some
misapprehensions to be exposed and corrected.
     The task of the painter, according to Alberti, is to produce an image of
reality, which also includes a dramatic subject of a suitably edifying kind.
This entails making the painted objects to look like their originals, and
endowing the painted actors with expressions acknowledged to be appropriate to
their several functions, ages, social ranking and the like. When the
representation imitates life in all of these respects, the painter has
accomplished his highest purpose, for his istoria has succeeded. Moreover,
Alberti can be assured that the painting and original scene will in fact look
like each other because the scene has been analyzed in terms of the colors it
shows, and the colored planes have been drawn so as to reproduce their visible
relationships on a flat surface.
     Unlike his immediate predecessors and indeed a good many of his
contemporaries, Alberti's prescription for painting is intended to produce a
result that is descriptive, rather than primarily evocative. Long tradition, by
contrast, had often presented highly decorated saints in order to impress the
viewer with the grandeur of the figure, and no doubt to encourage a response
that included confidence in the powers of an intercessor who could be so
represented. This is one origin of the use of gold and the peculiar problem it
caused when used to decorate the painted figure. Alberti's specific and firm
rejection of this unreliable coloring was no idle exercise in petty tyranny.
His insistence on the proper scale of painted objects also ran counter to the
customary ranking of figures which represented the kings of the earth, saints,
angels and any person of The Trinity as being much larger than ordinary human
beings.1 Rank varied with one's companions in the painting; kings were
comparatively humble and therefore small, when they appeared with angels, but
were appropriately grand if seen with townsmen. All these conventions were
undercut by a theory of painting that insisted on a life-like representation,
                                                             IV-12
and it is Alberti's special virtue that he provided a means of doing what he
advised.
     Alberti's description of a painted scene, like all descriptions of sensory
experience, is from a point of view. For the painter however, the point of view
is explicit. The theory promulgated in Della pittura even enlarges on the
riches of perspective. In effect it is claimed that, if the observer were to
occupy the correct point from which to view the whole painting, he would see
the objects represented as if he were standing in the ideal spot in the
painting itself, or in an extension of it just in front of the picture plane.
It is hardly an exaggeration to state that one can apparently walk into a
painted Albertine scene, if indeed one is not already apparently a part of it.
     The painter who follows Alberti's advice can readily think of his work as
being set in a frame like the 'open window' mentioned in Book One. But it is
not necessary to be a disciple of Alberti to adopt this imaginative view,
because in one important respect any painter frames the visible world. The
scene as he paints it must be frozen in place and given limits just as if it
were in a frame. More interesting is the fact that this restriction does not
inhibit the apparent faithfulness of the painted scene, because we see the
original essentially at rest. Painted life-like representations are life-like
because, as we have noted, the external world is deemed to enjoy the stability
characteristic of the visible world. A world depicted apparently at rest does
not therefore strike us as artificial, but rather we are apt to judge that it
is a good likeness of the original.
     The program described in Della pittura places the viewer before the
frame. If he is a painter, then his highest purpose is to use his pigments to
produce an istoria. Added to his technical knowledge of colors and perspective
is his judgment of visible reality, and his opinions about what is best.
Alberti's pupil does not slavishly follow even his own calculations. In
practice he may, with the blessings of his master, complete the placing of a
figure guided by his judgment.1 The question now to be asked is in what this
judgment is thought to consist.
     Alberti frequently speaks of the painter as being taught by nature, or
even of the three divisions of painting as having been taken from nature.
Sometimes he mentions too that the novice painter will naturally place himself
in a spot that gives him the best view of an object which he proposes to draw.
The natural view is, as these sources suggest, one which provides the observer
with information to his purpose at the time. Apart from such special interests
as belong to the artist, it is everyone's purpose at least to identify objects
in the world; hence information that promotes recognition is universally
valued. We are thus led by self interest to the analysis of reliable sensory
information, and thence to the role played by the most favorable perspectives
from which to judge objects.
     There are rules for judging objects, of which one part consists in the
rules for viewing buildings. If the viewer is an architect, he is less
concerned with the painted scene, and more interested in establishing the most
favorable point of view for revealing the shape of the object. This is the
perspective which offers the greatest amount of undistorted information. In
most buildings which have four walls and four right angles, the most favorable
perspective shows flat walls which, if they were drawn, would be parallel with
the picture plane. Each wall is an elevation of the building, one definition of
elevation being, "the external faces of a building".1
     Among the best, because most informative, views of any building is a view
of one of its elevations, which conventionally is seen at right angles to the
observer's line of vision. If a face of the building is viewed from an oblique
angle, the view may be comparatively informative about the shape of the
building, but only provided that the face is clearly focussed. To see any
object clearly, we must look straight at it, as is our natural practice. We
rightly do not seek information about the appearance of objects by casting on
them sideways glances.2
                                                        IV-13
The architect's conventional representation of a building includes the
second definition of elevation. This meaning of elevation is, "a drawing made
in projection on a vertical plane to show any one face (or elevation) of a
building."3 The rules for looking at the drawing of a building are in some
respects like those for looking at the building itself. In viewing each drawn
elevation, the observer is presumed to occupy those places that preserve the
look of the drawn face and show it at right angles to the line of vision. Like
the face of the building proper, its drawn elevation has a desirable viewing
distance which is largely determined by how much of the object one wishes to
see. It is true that the angle of vision from which a drawing can be seen is
more restricted than the angles tolerated by a building. Still, the reason for
preferring a straightforward view of the drawn elevation is the same as that
for preferring to look straight at the building it represents. We require to be
informed, and perspectives are preferred because of the amount of coherent
information they provide. To reject information is therefore not only odd, but
contrary to the value we give it. Consequently it is more than strange to view
a drawn elevation at an an le that apparently is other than 90 degrees. For
this is to distort information that has been presented, and perversely to
introduce ignorance where knowledge has been offered.
     The perceiver or observer is given many opportunities to exercise his
judgment in selecting the perspectives from which to view either objects, or
their representations. The object must above all be identified, and so the most
informative sightings of it are those favored. The conventional representation,
the drawn elevation of a building, captures and makes systematic the principles
of enlightened viewing. Life-like representations for their part depict the
familiar looks of familiar things. In each kind of observation, the common
feature is to be found in the rules that point to the most informative
perspective. It is not therefore an eccentricity of Alberti to state rules for
the viewing of things and their representations. He is simply making explicit a
practice we happily indulge, but usually overlook. The rules for seeing things
include the placing of the observer, and his rational use of his vision,
together with a recognition of its limits. The same general rules apply to the
seeing of things that are represented, either in their full colors or in the
darker outlines which visibly constitute architectural drawings.
     To sum up, the framed picture is a natural choice for the painter. It
explicitly arrests a visible scene, yet still seems faithful to the original
because a painted representation takes full advantage of the assumed stability
of the objects represented. Exploiting the coincidence of visual space and
conventional "real space", the painter can make a naturally moving object, like
an animal, appear life-like although quite still, with the result that it is
the more easily recognized. Again, the viewer can be brought to notice one of
the more informative aspects of a still object, like a building, which he
habitually sees from less enlightening angles. In either case, the framed
picture presents a good view of the object, and by its own shape and dimensions
indicates the most favorable points from which the representation may be
viewed.
     In viewing a painting, as in standing before a large building, one's
working assumption is that it is to be looked at from the most advantageous
place. For a painting, this means any place which shows the whole of the
painted surface and its figures; for a large building, one ought to see the
whole of the near side of the building and any surrounding area thought to be
interesting. Alberti's prescribed techniques for painting succeed in producing
life-like representations because they bring order to customary practice. We
habitually use the same techniques to see and judge as those he sets out for
his pupil who proposes to see, judge and represent.
Criticisms and Replies:
     It is obvious that a life-like representation must present a recognizable
object. Equally obvious is the fact that some perspectives are to be preferred,
                                                             IV-14
since familiar objects and even good friends are unrecognizable from some not
very extravagant points of view. In architecture, the study of representation
includes a systematic treatment of perspective and scale. For the purposes of
our discussion, one point to be noticed is that a drawn elevation represents a
building from some ideally informative perspective.
     The face of a building, viewed at right angles to its surface is the best
way to view its permanent features. As a physical object, a building is
generally presumed to have permanent features, but how these are best seen is
not often considered. For this reason Alberti's rules for painted
representations of buildings may at first seem to restrict the viewer's freedom
to look at the object from many different angles, but this complaint is not
well-founded. Most angles which are radically different from those of a
standard elevation are not interesting as representations of the building,
except possibly as an exercise in applied geometry. This is a crucial point
when the production of a life-like representation is the goal of the painter.
     For the architect, the accurate representation of each face of a building,
with the placing of its windows, doors, chimneys and decorations, provides him
with a guide to the eventual total effect of the finished structure. His
unspoken rule is that, in general, if the perpendiculars are correct, the
diagonals will take care of themselves. Recessed features or curved surfaces
can be represented by shading and hatchmarks.
     As an architect Alberti was well aware of the relationship between the
placing of objects and their life-like representation. It was partly for this
reason that he gave so much attention to the perspective of the observer and
his judgment of the painted scene. Certainly presented with any object or
credible representation of one, Alberti could prescribe an ideal place from
which to look at it. It is indeed both possible and desirable to hang a
painting so as to determine the place from which it is seen. Similarly the
drawn elevation indicates that there is a preferred perspective from which to
view the permanent features of the face of a building. In each case, as before,
the preference is founded on the superior information given by the favored
point of view.
     One difference between Alberti and some of his critics is that his
representations had as their goal a likeness to life. The concepts underlying
his advice about painting any object are addressed to what is to be seen. A
description of the method of representing a Campanile standing on the opposite
side of the piazza might have been as follows: If you were gazing at the
Campanile across the piazza from here, this is what you would see; not this is
what an optically correct method of focussing from a central perspective would
reveal, much less what a wide-angle lens camera would record. And Alberti was
right, because he looked carefully and intelligently and straight.
     Because Alberti's use of perspective was to aid in representing the
natural scene, he was not much exercised by the special problems of monocular
vision where it would make no difference in the look of things. And despite
much influential talk to the contrary, it rarely does make a difference to a
life- like representation. The object to be depicted must be relatively small
and have sharply contrasting colors quite close together for the difference
between its being seen by one eye, rather than by the other, to be of any
moment. As a general rule, the slight shift in focussing by a change of the
viewing eye is not so much a problem for the painter as a matter for decision.
If one view is preferable because it includes more of some plane, then that one
can simply be chosen. Alternatively, a slightly different viewing angle can be
selected for the representation, or the painted scene can be enlarged, and the
effect diminished by introducing a longer viewing distance. The point is that,
if one proposes to build an optical instrument and fit it with lenses, then the
proposed range of the instrument and the number of eyes to be assisted are
important facts for the maker to know. The painter is not concerned only with
enhancing the natural limits of his vision when he depicts what he sees.
     Most objects that he notices are more distant from him than a single arm's
                                                             IV-15
length, and are located sufficiently far apart from each other for him to
select a vantage point. The painter, like any other observer, is accustomed to
look at objects from some informative angle, no matter what it is, when he is
walking about in the world. He need not focus first one eye and the the other,
in order to see objects; he takes as given the colors and immediately inferred
colored shapes which he encounters, and interprets them according to his
information, interests, culture, prejudices and so on. What he does not do is
entertain paralyzing doubts about the precise angles of vision of a particular
subject seen first by one eye and then by the other. This is a problem to be
solved by the maker of optical instruments in the practice of his calling, but
has nothing to do with the painter's practice of his.
     One eye may be used in order to focus on some point of detail, but the
calculation of angles is not a part of accurate representation and does not
belong either to customary pursuits. The eye is not just a lens, nor indeed any
kind of camera. As anyone may confirm for himself, when looking at buildings or
other large objects from some favorable perspective, the difference between a
left-eyed view and a right-eyed one is negligible.
     Alberti's choice of the visual pyramid signals his awareness of what
belongs to perception and life-like representation, and what belongs to
theories about some related subjects. Certainly he did not divide principles
along the lines of our contemporary university faculties, but he is quite
specific about the difference between the concepts of geometry and those used
in the systematic development of the painted likeness. The visual cone promoted
by Euclid has about it a peculiar echo of the shape of the eye itself. But we
do not see the world either as a circle of colors or as two overlapping circles
of colors, much less do we deliberately 'split the difference' in the angles of
vision indicated by the locations of two such circles.
     Alberti's disregard for strict monocular perspective, in favor of
circumscription and composition, is shown throughout Della pittura. There he
describes a method of drawing a circular figure in perspective on a receding
pavement. He then directs the pupil, mentioned above, to finish his drawing by
using his judgment rather than by calculating the least details of the
representation. The part played by judgment and the practised hand is prominent
too in Alberti's advice about shading the great and small planes of a
composition. We have already seen that he was especially sensitive to the use
of black and white pigments as the only ways of depicting shade and light, and
emphasized the need to preserve natural looking proportions between the lighted
side of an object and its shaded side. Then there is the placing of the
spectator of the finished painting. Alberti never says, 'stand on this spot',
but talks more generally about the proper height for viewing a work in relation
to the centric line. He is on firm ground here since any representative
painting is best seen from an identifiable range of heights, distances and
angles.
     These several interests, as reflected in his writing, indicate both
Alberti's freedom from the strictures of monocular perspective and his
appreciation of the naturalness of a painted scene. It is not unreasonable to
suppose that Alberti knew as well as anyone how much variation we accept as
characteristic of the appearances of things. Few theorists, if any, ever looked
at objects more carefully than he did, or wrote more tellingly about their
visible features. And most of the time he was patently right.
     It is simply the case that we tolerate a range of views of relatively
large objects, provided that nothing we judge essential to the look of the
thing is altered. And, in this context, we understand 'essential' as tending to
preserve our assumptions about how things are arranged. The arrangements also
include ourselves, and we recognize as unusual a view of an adjacent city
street as seen from the top of a skyscraper. Even this perspective remains
credible however, provided the sides of the building and distant figures in the
street conform to what we already know and are disposed to expect. For we
accept as natural great variations in the appearances of objects that are
                                                              IV-16
thought to be familiar. It is not unexpected then that we should be inclined to
call 'life-like' a wide variety of representations of these objects. What we do
not tolerate, because it is visually unclear, is an unfocussed life-like
representation. The static space of visual perception is static, hence even an
indistinct view of an object is clearly indistinct. The failure to grasp the
implications of this point has led several eminent critics to waste time and
paper.
     Alberti invented the painter's velo or veil. This is a very fine woven
cloth to which some heavier threads are added to mark out parallels, as may be
required. When hung between the object to be drawn and the artist, the veil
divides the scene into regular sections. The purpose of the veil is to enable
the beginning painter to learn the ways in which the objects in a scene will
appear in a single vertical plane. Later, the veil was also used in fresco
painting. For the beginner however, Alberti's veil principally shows the
correct placing of the odjects seen, and thereby aids the learner in his study
of representation. This, in any event, is what Alberti says.1 It is not
therefore entirely clear why Kenneth Clark mildly deplores this aid, although
his suspicions about a monocular perspective seem to lurk in the background.
For against Alberti, Clark comments:
The objection, [to the use of the velo] which seems valid to us, that it ties
the artist down to a one- eyed, static view-point, was a recommendation to
Alberti;...2
If 'to us' is not the imperial 'we', then Clark is mistaken. The supposed
perils of the 'one-eyed, static view-point' are avoided by Alberti's
knowledgeable mixture of vision and judgment mentioned above. In viewing a
scene we, all of us, are tied down only to the recognizable. As to Clark's
criticism of the 'static', this is an objection to visual representation that
deserves to be as notorious as it is misconceived. How, pray, are we to see
anything clearly that is not clearly focussed? And who among Alberti's critics
would undertake to draw a life-like representation of an ordinary object seen
only when it was in motion? Is there anyone who would not prefer to arrest the
object for the sake of obtaining a more accurate view of it, even if the object
is to be depicted as moving? This is not just a simple case of depicting an
object at rest with a static drawing of it. The issue is that of recognizing
that the object is best seen when it is apparently at rest because that is the
condition under which our vision is most subtle.
     Vision also signals a much larger world to us of course, and we assume
that this greater external world is essentially at rest, because rest is
characteristic of continuous visual space. It is admitted that we might have
had some other efficient sense for detecting comparatively remote objects; we
might have been possessors of sonar, but the fact is that we are not so
equipped. The world that we can know best while it is yet at some presumed
distance from us is the world that we suppose we see. We have learned too that
the most favorable sighting of an object occurs when it shows its several
planes in a steady and unchanging manner. Alberti's veil would capture one of
these static views, and provide the observer with a great amount of
recognizable information. It is designed to enable the artist to place any
objects accurately in his drawing, and so make his representation as nearly
like the living scene as possible. But again, the artist is not obliged to
depict what he would not ordinarily see. His eye is not a camera; neither a
movie camera, nor a pin-hole camera nor one with a wide-angle lens.
     On the evidence of his paper entitled, 'The mask and the face: the
perception of physiognomic likeness in life and in art', E.H. Gombrich seems to
believe that the eye would have been improved if it produced effects more like
the changing views shown by a scanning camera. At least he tirelessly points to
the unreality of the frozen scene.1 Now, given our present capacities and
related theories, this is tantamount to holding that we could somehow judge
things better if we could not see them so well. A sample comment runs:
     But though the snapshot has transformed the portrait it has also made us
                                                              IV-17
see that problem of likeness more clearly than past centuries were able to
formulate it. It has drawn attention to the paradox of capturing life in a
still, of freezing the play of features in an arrested moment of which we may
never be aware in the flux of events. (p.16)
     It may be suspected that Gombrich is under several identifiable
misapprehensions about sight and the analysis of things seen. Certainly he
writes as if he believes that tangible and visual information is already
combined in some indivisible whole, so that isolated visual information tends
to lack reality, and static visual information is even farther removed from the
object it depicts. This is not an uncommon interpretation of perceptible
objects, but it does rely on fundamental mistakes about the elements of
perception, or ideas, their logical independence and its implications, and the
special claims of the sensible perspective. It simply is useless to argue about
the best representation of some object when the perceptible features of the
object and their several relationships have not been adequately considered.
     The most positive statement that can be made about the visual likeness of
a human being and moving picture frames is that moving picture frames do not
confuse us. It is small thanks to film technique that all is not chaos,
although the development of equipment capable of producing a sufficient number
of frames per second undoubtedly made the picture clearer. The chief credit for
the success of representation by moving frames belongs however to our natural
bias toward the intelligible. In short, we make sense of them.
     Moving picture frames do not confuse us physiologically because we cannot
literally see them move, provided the speed is sufficient. A scene in which no
one appears to move at all therefore exactly resembles a still photograph of a
single frame.
     Moving picture frames considered as representations do not confuse us
psychologically because we are accustomed to there being changes in figures,
which we see as moving figures. We identify the selected figure as being in
motion rather than as being replaced. Even though the figure may change all of
its colors, by passing from apparent brilliant sunlight to a shadowed light, we
still interpret the perceived colors as being the same figure. When presented
with the colors of a moving film, we act just as we do in judging the colors
presented by nature. In both cases, we interpret the colors as parts of
familiar physical objects which are picked out by our language. The colors are
organized and, if possible, arrested for a better view.
     If this is so, it would seem that the virtues of the moving picture frame
are purely negative, or at least very limited. Our preference for a still
photograph has a solid, rational foundation in that a still picture gives a
clearer view of the object. This is not to deny that some still photographs are
unsatisfactory, but the cause of failure can be traced to the difficulty of
recognizing the object. If our preference in viewing objects is to view them
when they are at rest, it is equally important for the representation to
provide a most 'significant' or 'characteristic' appearance of the thing
represented. The sole advantage of a moving film is to be found in the case of
the odd perspective, and our naive confidence that the moving camera will
sooner or later offer a more favorable perspective. This problem and the hope
for its disappearance of course will apply only when a life-like representation
is the one intended.
     The main reason that a moving film of someone we know well is less
satisfactory as a representation than a good, still photograph is that the
individual represented is thought of as a constant, and in a moving film is
depicted artificially as continuously changing. The individual as constant is
the covert bias here, but it is I think a part of our concept of a continuous
physical object. If this is the case, it is not unexpected to find that the
continuous object ought ideally to be constant in any of its appearances. This
taste for stability is readily associated too with the fact that the steady
object is the one most clearly seen.
     The special features of continuous visual space go far to account for our
                                                             IV-18
visual preferences. It is the continuous, hence apparently stable, visual space
that so firmly anchors visible ideas. There is therefore no need for a good
likeness of a face to change, because the depicted face is a complete,
life-like view at the moment it is seen. In the most favorable case, a good
moving film may provide a sequence of representations that are equally
satisfactory, but the first likeness is not thereby made less true to life. A
characteristic appearance is what counts, hence change for its own sake seems
artificial when a natural likeness has already been achieved. Once again, the
properties of static visual space vitiate the supposed special claims of moving
film.
     The essentially sequential character of auditory space, on the contrary,
tends to favor the sound track of a film. Here there is no dissimilarity
between the words heard one after another in a recording and in nature. An
auditory record of a human voice is not strictly a representation at all, but
rather is a preserved sequence of pitches. A good imitation of an individual's
voice succeeds in evoking the speaker, but the effect soon palls because, if
the speech is rigidly determined, it fails as a conversational voice. An
imitation can of course be a lecturing voice, but this is natural only to
lecturers and, happily, not all of the time. The set speech inevitably
finishes, and the illusion of there being the real speaker and not an imitation
finishes too. Sequential auditory space requires life-like continuity, and that
is not available to any pre-determined speech.
     The most successful auditory representation of human beings is found in
theatrical productions. Scenes are constructed to carry conviction,
conversations succeed one another naturally; but what the drama represents are
universal characteristics, not individual human beings. In the rare portrayal
of historical figures, they commonly are judged quite unconvincing by specially
knowledgeable hearers.1
     Auditory representations of individual human beings labor under
inescapably disadvantageous conditions. First, there is the problem that
eventually the voice must be associated with a visible and tangible object as
it is in ordinary life. Voices, after all, belong to people who are supposed to
be at least visible and tangible. There is a further, impossible requirement
that follows from the sequential character of auditory space. No matter how
good the imitated voice, an auditory representation, strictly interpreted, has
no end. For when the voice falls silent, the representation fails.2
     To conclude this section, visual recognition is ideally directed to static
objects because the static object can be seen clearly. It follows that a
life-like painting, so far from being an artificial representation of a moving
object, is instead a true representation of that object seen under the most
informative conditions.
     Some years ago M.H. Pirenne posed a nice question about the painted
representation of a scene, as compared with the results given by a pin-hole,
and therefore strictly monocular, camera.1 He showed that a sphere set well out
to one side of the vanishing point would appear in the photograph as a
misshapen oval. He also noted that Raphael's 'School of Athens' includes
several perspectives, no doubt in order to give a clear representation of the
different groups of philosophers depicted across a rather large area. Raphael's
solution would have been applauded by Alberti, if we take seriously the stress
that he gave to the judgment of the painter. Neither of them we may be certain
would have allowed a misshapen oval to represent a sphere. Indeed Raphael
painted Ptolemy holding a highly respectable though, from most perspectives,
quite impossible circular globe.*
     It is apparent that in practice, painters were not usually oppressed by
the laws of linear perspective, or of any other system. There is, as I have
suggested, much more tolerance of technical inconsistencies in painted
representations than the manuals would lead one to suppose. The reason for this
however is not just a certain carelessness about details, but the continual
experience of different visible aspects of objects, and therefore a wide range
                                                             IV-19
of recognizable perspectives. Provided we believe that we are dealing with a
standard physical object, we can accommodate a good many very different
perspectives of it, before becoming uncertain of the object itself. Thus,
Alberti's tolerance of minor adjustments is not an inconsistency in a painter's
theory, though it would be a fault in an instrument maker. Painters do not
require theories founded on an ideal observer devoid of judgment.
     Leonardo's famous objection that Alberti's theory of perspective would
allow more distant columns standing in the picture plane to appear larger than
nearer ones, reflects the preoccupations of the instrument maker. As Pirenne
remarks, this was never a problem for painters, since they simply made the
columns less wide. There is nothing unusual in this; the tradition of
eliminating undesirable incidental effects has a long history in the arts. The
Greeks invented entasis to keep their columns from appearing to curve inwards,
and Vitruvius is eloquent on the best ways of preserving visible symmetry in
rows of temple columns, while falsifying tangible symmetry to do it.1
     Alberti as a student of Vitruvius' De Architectura knew all of these
techniques and a good many more. He did not however use them to deviate from
his understanding of a life-like representation. On the subject of perspective,
the difference between Leonardo and Alberti is that Alberti emphasized what is
to be represented; where the objects in the painted scene are to be placed, and
how they are to appear to be lighted. Alberti exploited the fact that the
viewer of the painting, like the painter himself, prefers to look at the work
from its most informative perspective. Few who wish to look at a painting
insist on viewing it out of the corners of their eyes, and the same is true of
looking at ordinary objects. Alberti could therefore make a row of columns
diminish from the viewer's ideal perspective, and that would be sufficient. He
could produce by coloring what would appear most natural, following his own
advice to his pupil:
     Remember that on a flat plane the colour remains uniform in every place;
in the concave and spherical planes the colour takes variations, because what
is here light is there dark, in other places a median colour. (p.83)
     0ne feature of Alberti's theory of painting deserves further attention.
This is his care in separating circumscription and composition, or the placing
of drawn objects; from the reception of light, or their coloring. No
requirements of Alberti's linear perspective resulted in his misplacing of
objects relative to one another, for he genuinely had devised one way of
recording the scene. Coloring clarified what even good drawing must sometimes
leave indeterminate, with the result that a life-like representation could be
produced very nearly according to rule.
     For our purposes it is especially interesting that Alberti proposed to
teach the placing of planes by use of the veil. The fact that the veil could so
readily divide the scene to be painted into its constituent parts, and do so
exhaustively, has implications beyond the production of frescoes.
     Finally, Alberti argued correctly that, by the judicious use of colored
pigments, the two-dimensional painted scene could capture the original to the
life. In writing Della pittura he shows how the painter reverses the process of
perceptual analysis, and uses his art to build colors into things. Following
the prescribed divisions of painting, the artist presents the painted scene
first to his own eyes and then for those of spectators. Seeing and judging
belong as ever to the observer.
                                       fnIV-1
Footnotes for Chapter IV
IV-2 n.1  See Persons: on perspective and physical object theory, pp.20-31.
IV-5 n.1  Creighton E. Gilbert, Italian Art 1400-1500, Sources and Documents,
          Englewood Cliffs, N.J., 1980, p.90.
IV-8 n.1  The human ear has an effective range of about 20 to 20,000 Hertz, or
          cycles per second. Middle-C is 256 Hertz, because the A above
          middle-C is set at 440 Hertz. This is British Standard Concert Pitch.
IV-11 n.1 This is a consequence of the heterogeneity of sight and touch even
          though the same words, such as 'shape' and 'distance' are used for
          both kinds of spaces.
IV-16 n.1 The presumption is necessary because the colors that someone else
          sees cannot ever be known to be qualitatively identical with those
          one sees oneself. It doesn't matter, but it is worth knowing.
IV-18 n.1 The original text was in Latin. Alberti omitted many of its copious
          examples drawn from classical authorities when he made the Italian
          translation. All English translations of Della pittura used below are
          those made by John R. Spencer in Leon Battista Alberti on Painting,
          New Haven and London, 1977.
IV-19 n.1 Della pittura, (Spencer,) p.43.
IV-20 n.1 See below, Chapter V.
IV-24 n.1 See below, section on Criticisms and Replies.
IV-25 n.1 Della pittura, p.115.
     n.2  The picture plane is the plane of the board itself or other flat
          surface to be painted. Its chief interest is that if it is used
          directly in a painting, it is the extreme foreground of the
          representation; it is always for Alberti the plane from which any
          more distant object is made to recede, and any plane parallel to it
          is known not to distort straight lines. Thus two receding lines of
          columns which form a corridor to the observer are all drawn straight
          and parallel to those columns that appear in the picture plane.
IV-28 n.1 Della pittura, pp.112-17.
IV-30 n.1 There are of course a number of exceptions to this treatment of
          scale, though it might be noticed that the artists are generally
          thought of as the great forerunners of the early Renaissance.
IV-32 n.1 Della pittura, pp.71 and ff.
IV-33 n.1 The Penguin Dictionary of Architecture, eds. John Fleming, Hugh
          Honour, Nikolaus Pevsner, 3rd edn., Harmondsworth, 1981, p.105,
          col.A.
     n.2  Distorted representations introduce special issues, but these do not
          affect the general claim.
     n.3  Fleming et al., Op. cit.
                                                             fnIV-2
IV-42 n.1 Della pittura, pp.68-70.
     n.2  Kenneth Clark, Leon Battista Alberti on Painting, Prceedings of the
          British Academy, Vol.XXX, London, 1944, p'9'
IV-44 n.1 E.H. Gombrich, Julian Hochberg, Max Black, Art, Perception and
          Reality, Baltimore and London, 1972, p.16. See also pp.28 and 32.
IV-48 n.1 The imitated voice in a set-piece recorded speech is the great
          exception to this rule. The most famous example is the imitation by
          the actor Norman Shelley of Winston Churchill's speech to the House
          of Commons on 4 June 1940. The deception was only recently admitted.
          The historical references were kindly supplied by the BBC who further
          state that, "Mr. Shelley never actually impersonated Sir Winston
          Churchill on any BBC broadcasts but he was employed by a commercial
          recording company to read some of Churchill's speeches and these were
          sold to American radio stations." Angela Gilchrist, International
          Broadcasting Audience Research, BBC London, in a letter dated 24
           November 1982.
     n.2  The final words of someone who dies would escape this objection, but
           not the first one; unless we presume that all bodies are immediately
           thrown overboard with a resounding splash. Even then the telling
           questions are only delayed.
IV-49 n.1 This is only one of the issues discussed most interestingly in his
          volume, Optics, Painting and Photography, Cambridge, 1970.
IV-50 n.1 Vitruvius, De Architectura, Book IV; Edited and translated by Frank
          Granger, Loeb Classical Library.
                                                            txtfnIV-1
*     Editor's brackets
*    That is, Editor's italics.
*    Editor's brackets.
*    Ptolemy is holding the globe in his left hand; the figure holding a
starred sphere in his right hand is said to be Zoroaster.
                                                               V-1
Chapter V - Ideas and the Four-Color Map
     The use of Alberti's veil shows clearly that whatever appears before one's
eyes can be placed accurately on a vertical plane. There are no blank spots in
the visual scene, and nothing that is perceived need be omitted from a
life-like representation.
     The converse of the concept revealed by Alberti's technique is also true,
though not generally recognized. I shall argue therefore that whatever can be
placed on a plane can appear before one's eyes, and that this relationship
between sight and a plane surface transforms the problem of the four-color map.
     The first point to make is that the coloring of a plane surface is
properly judged by sight because first, colors are necessarily perceived
colors; and second, all perceived colors can be seen as if on a vertical
plane. Alberti's veil succeeds precisely because of the latter condition, and
the former is true by definition. If, on the contrary, anyone wishes to
entertain imperceptible colors, he is welcome to them; but it is not plausible
to hold that they are the colors intended by those who talk of the ways a map
drawn in the plane can look. It should also be noted that, because the
literally visible scene can always be placed on a flat surface, the case of the
planar map and perceived colors is unique. No other shape to be divided and
colored stands in the same relationship to sight, although of course
topologically equivalent shapes can be treated in the same way.
     By using the concept of direction, it is not difficult to apply the
concept of a travelling perceiver whose own place on a plane is designated as
the central division. As the perceiver moves, the area called the central
division moves also. This is necessary because all other areas of the map are
described with reference to the central division.
     The theoretical perceiver can be omitted from the account, and the areas
themselves described with reference to their several neighboring areas. Still,
in every description given of a map, there must be some area deemed the central
division, since all other areas mentioned are designated by referring to it. In
effect, when it is convenient, a theoretical perceiver governs the concept of
the central division; when the perceiver is omitted, a central division is
still required if anything is to be said about the map and its colors.
     Alberti's veil organizes the visual plane exhaustively. He obviously did
not attempt to solve problems about map coloring, but the original veil
illustrates some simple and telling relationships. When the veil is placed
before one's eyes, the areas produced by the heavier threads are rectangles.
This is the simplest kind of division of a plane because it is one which
requires only two colors.
     The figure above can be thought of as Alberti's veil, with only the heavy
threads indicated.
     The intersections are mathematical points, and any area A is seen to have
just one immediate neighbor in each of the major compass directions. Thus if a
perceiver occupying any part of area A were to move at all, he would either
cross into a neighboring area of a different color; e.g. a' or b', or pass over
a mathematical point to an area of the same color; e.g. B. In the latter case,
the second area, B, is not a neighbor of area A because A and B are not
adjacent, nor are their surrounding areas adjacent. Some of their surrounding
areas are evidently identical, e.g. a' and b', but this is different from being
a neighboring area. For neighboring areas stand in a significant and limiting
relationship for the purposes of coloring a planar map.
     In the course of developing the following solution to the four-color map,
it will be shown: First, that the concept of a neighbor is one that is
determined by direction; second, that directions can be multiplied
systematically in relation to areas so as to require the use of four colors to
distinguish four areas; and third, that it is direction which shows how further
multiplication introduces the possibility of always repeating one of the four
                                                               V-2
colors, rather than requiring a fifth color. I shall argue further that the
concept of direction, as the way in which a perceiver could move on a map and
note what is seen, is the key to recognizing that the problem of the four-color
map is a problem of perception, and accordingly can be solved as one.
     There is one further preliminary comment to be made. No one who is even
casually acquainted with the history of science or philosophy should be in the
least surprised to learn that there is more than one type of approach to a
given problem, no matter how venerable; much less that the conventional terms
of the question might be misleading. It is not in any way extraordinary to
discover that topology can provide ways of coloring a map drawn on a torus, and
long since has decided on the minimum number of colors required for the
exercise. It might however have been thought that the steady resistance of a
map drawn in the plane to similar treatment was not without significance. The
very recalcitrance of the planar map should have invited suspicion about its
apparent blandness.
     The discussion which follows will show that the problem of the four-color
map is best thought of as a problem of perception. This approach is rewarding,
not least because it then makes sense to use the relationships that are
exhibited in visual space, where in fact colors are to be seen.
Part I*
     The classic map problem, it will be recalled, is to determine the number
of colors both necessary and sufficient to delineate a map drawn on a plane
surface or, what is the same thing, on the surface of a sphere. The reply I
suggest is that four colors are in fact sufficient for all such maps, though
this is more readily seen in simple maps than in complex ones.
     A simple map may be defined as one which extends in the four basic
directions only, whereas a complex map includes as well a multiple of one of
these directions. The concept of direction is fundamental to this distinction
between maps. Thus the thesis advanced is that a simple map uniformly preserves
the four directions in terms of which all maps of plane surfaces are described,
and accordingly is the fundamental type of map. The complex map, by contrast,
exhibits doubled directions which are indicated by parallel lines and whose
practical result is to require more or less complicated asymmetrical coloring.
Both maps need four colors only.
Directions:
     The account begins with recognizing that there are only four wholly
different directions in which any object on a flat surface, or any part of the
surface itself, may move or be extended. These are in a vertical direction, a
horizontal direction, in a leftwards or rightwards diagonal, the latter two
hereafter to be called 'W' and 'E'. The vertical and horizontal directions
retain their customary designations of 'Y' and 'X', respectively. (See Figure
1.)
     The accumulation of figures, like rectangles, in- a row from left to right;
e.g.,                 shows an extension of areas in one direction only, +X, and
illustrates the ready repetition of non-adjacent colors where this pattern
occurs. An instance of multiple directions which requires an additional color
would be produced by the same figures, with a line added parallel to a
horizontal line. Thus we see the figure                      requires a third
color. Relationships sufficiently complex to capture all of the different
directions that can be exhibited are best seen by introducing definitions of
areas and their several kinds of neighbors.
Areas and neighbors:
     An area is a visible, hence colored, shape, and as such forms one part of
a planar map. The color of an area spreads to its edges where the coloring of
any different area marks its limits.
     A neighbor is an area that stands in one of several specified
                                                               V-3
relationships to another area' A neighbor may be either a second area adjacent
to the central area; or it may be a third area having a common border with the
second area; or it may be some other area whose borders are reciprocally
related to the central area. Neighborhood ceases when adjacent shapes or
inter-related borders cease. This is a crucial point because not all of the
areas in a planar map have a fixed relationship to a given method of coloring.
As we shall see, genuine alternative colors are always to be found in the
process of coloring a map, and the reason for this is that the same doubled
directions which require an additional color will, when increased in the same
direction, revert to a set of relationships in which no additional color is
required. A simple case can be shown using the previous example. The line
parallel to the horizontal line which required a third color in the figure
                     , cannot be repeated to the same effect. A second
horizontal line simply introduces a more remote neighbor in a vertical
direction. Thus we find                        . It should be noted too that
none of these colors is decided before one begins, since it is necessary only
that all areas with common borders should exhibit colors that are different
from one another.
     Neighbors can also be identified by directions, and here direction implies
motion. A neighbor may lie in one or more directions from an area deemed to be
the central division. In the figure       , area N lies in direction +X from
area C: that is, if C were to move toward N or replace N, it would move only in
a horizontal rightwards direction. Similarly, if a traveller in any part of
area C proposed to move toward N, motion in a +X direction would be sufficient
to encounter N. It is to be noted that motion in other directions would not be
sufficient for travelling from any part of area C. For example, motion in a
promising diagonal direction like +E might lead a traveller to miss area N
altogether, as in           .
Exhaustive list of areas:
     The areas of a planar map are of the following types.
(a) There is first the central division which provides the reference for all
other areas. This division is taken to be central no matter where it happens
for the moment to be located on a map. (Figure 2, wedge B.)* The assumption is
of course that the map exhibits at least two areas.
(b) There are the two converging neighbors of the central division which,
together with it, extend in all directions without repetition. (Figure 2,
wedges A and C.)
(c) There are the bordering neighbors (of the converging neighbors) which are
comparatively remote from the central division. (Figure 2, wedges E and D.)
(d) There is the surrounding neighbor (of the central division and its
neighbors) which encloses the perimeter of the whole group. (Figure 2, the
rectangle JKLM surrounding the circle.) There is moreover a partly-surrounding
neighbor which may border fewer areas than the whole group, but usually extends
in not fewer than five directions.
(e) Finally there is the intruding neighbor (or neighbors) of the central
division and its converging and bordering neighbors. The intruding neighbor
borders on and thereby forms a barrier to two or more adjacent neighbors in the
direction in which it lies. (Figure 2, the semi-circle of wedges abcd bordering
the quadrilaterals A, B, C, D.)+
     In every case it is to be noted that to be a neighbor is a reciprocal
concept such that (i) if A is a neighbor of B, then B is a neighbor of A; and
(ii) if area A is a neighbor of area B, then A forms a barrier to B in every
direction in which B might extend, if B has a border with A in that direction;
and (iii) given condition (i), vice-versa. (See Figures 3 and 4 and also Figure
5.)
representation of the directions in which colored shapes can be extended, and
stand to one another. The several neighbors, with their adjacent borders and
                                                               V-4
more remote relationships, are presented as wedges that extend in all of the
directions admitted by a plane surface. These directions may be multiplied, it
is true, but the demand for an additional color generated by a parallel line is
not repeated, but rather is terminated, by the addition of a second parallel
line. The consequence is that pressures for additional colors do not
accumulate. Multiple directions do not entail unpredictably multiple colors,
although asymmetrical coloring is often required, as we shall see.
     For now, taking Figure 2 as a schematic representation of any flat surface
we find the following:
     Any direction is either X, Y, W or E, or some combination of these.
     Any area may be accurately described by indicating the directions in which
it extends from point O. Thus one wedge is determined by X and W, the others by
W and Y, Y and E, and E and X. The movement of any area could similarly be
described by direction. The description would then indicate the path that such
an area must follow in crossing the border of a neighboring area, or of any
other area on the same map.
Colors:
     Again using Figure 2 to represent the relationships found on a planar map,
we see:
     Each central division* has at most two converging neighbors.
     Since all neighbors must be distinguishable by color, it follows that each
central division and its converging neighbors require only two colors.
     A central division and its converging neighbors include the four possible
directions; hence bordering neighbors only repeat some direction already
employed. It follows that some comparatively remote color can be used again to
delineate bordering neighbors.
     Intruding neighbors may lie along the boundaries of a central division and
one of its converging neighbors and thus require a third color. If the boundary
of a third area which is a bordering neighbor is also involved, the color of
the original central division may be repeated in the bordering neighbor. Thus:
     The central division requires one color.
     Converging neighbor-1 requires one color different from that of the
central division.
     Converging neighbor-2 requires one color different from that of the
central division, but which may be the same as that of converging neighbor-1.
     A bordering neighbor requires a color different from that of the adjacent
converging neighbor, but may repeat other colors, especially that of the
central division.
     The surrounding neighbor requires a color different from all the areas it
borders in surrounding them.
     The intruding neighbor typically is a third color. Its usefulness is a
consequence of the limits its shape imposes on those areas it borders, for it
effectively reduces the need for varied neighboring colors by its own uniform
presence. Thus if it has a common border with the central division, a
converging neighbor and a bordering neighbor, it has extended in every
direction and locks them into a two-color pattern. There then remains one color
to surround the whole, making four colors.
     To sum up, as Figure 2 shows, a simple map displays only four possible,
irreducible directions on a plane surface before repetition begins. From a
given point, a two-dimensional expanse of color must be depicted in at least
two of these directions. It can be extended in three or more directions, and
finally, it can completely surround some other expanse making eight directions,
which are the four basic ones repeated in regular sequence. The complex map
mentioned above introduces an anomaly among neighbors, but not one that is
fatal to our argument. We may therefore conclude this section with the
following claim:
     By the use of four colors only, the conditions set out for delineating or
otherwise mapping a plane surface, or the surface of a sphere, may be met.
                                                          V-5
These are the only conditions that need be met.
Therefore, only four colors need be employed.
The April 1975 number of Scientific American included as a seasonal
diversion a so-called five-color map. The relationships it exhibits are not
without interest because the apparently symmetrical figure does indeed require
an asymmetrical pattern of colors. This is a consequence of its being a complex
map; that is, of its having multiplied one of the four basic directions.
     Let us designate the upper horizontal and vertical border area 'S', its
top diagonal neighbor area 'R', R's similar neighbor 'Q', the block adjacent to
R, 'P', and the area bordering Q and S, 'T'. (See Figure 5.)1
     Area S can be seen to have the curious property of surrounding R in no
fewer than seven directions (three of which are, of course, repeated) and yet
failing to isolate R from Q in two of the directions in which S borders R
completely. It does not  order R exclusively however, as a consequence of the
two parallel vertical lines one of which is common to Q and R and the other
common to R and S. Thus S lies in directions -Y and -E from Q as well as from
R.
     The issue turns on the use of directions. A direction that continues in a
straight line through 0 proceeds in its reciprocal direction. (See Figure 1.)
In coloring a plane map, one direction of a pair of reciprocal directions is
counted as one of the four possible directions, its reciprocal being counted as
a repeated instance. A color may therefore be repeated in the same direction
(or its reciprocal) because either the area is continuous, or it is divided by
some intervening area, and the color is taken up again on the 'far side', as it
were, of the intervening area.
     In the case before us, area S borders area R in seven directions. R and S
are reciprocally and respectively intruding neighbor and partly-surrounding
neighbor. (See figure 6.)
     The reciprocal directions +E and -W are among those directions in which S
surrounds R and partly borders the -Y-most extremity of R. The same reciprocity
is true of directions +Y and -Y. S does not however isolate R in direction -W
as is customary for a surrounding neighbor. This is the case because S also
borders Q in direction -W from R.
     The vertical line common to Q and R introduces to S a second intruding
neighbor which is Q. Q lies in the same direction, from the -Y-most extremity
of S, as does the first intruding neighbor R. The map therefore displays two +Y
vertical directions from S instead of the one characteristic of a simple map.
     Ordinarily this configuration would simply require the use of a fourth
color to preserve the distinction between say, areas Q and P, and all would be
well. This is still what is done, but symmetry is abandoned at the same time.
For the pattern of colors required in the remainder of the drawing makes
symmetrical coloring impossible. More generally, in every case of this sort
which includes the relationships exhibited by areas P, Q, R, S and T (but no
others), it is necessary to make use of four colors. A multiplied direction,
such as an additional vertical direction, demands an additional color.
Consequently, given the particular figure of the April number, an asymmetrical
treatment is required in order to distinguish the boundaries.
     The justification for insisting on the four basic directions, and the
related tactical use of four colors, is that this approach illuminates an
abiding feature of plane surfaces. On occasion, the need for asymmetrical
coloring may be less apparent, but it nonetheless is required only when a
multiple of one of the original directions is introduced.* As we have noted,
the most interesting case of multiplied directions is that partly shown in
Figures 5 and 6. This is so because it has by far the most radical effects on
symmetry. The advantage of attending to repeated directions is seen in Figure
7. Here the effect of the complete map is to require markedly asymmetrical
coloring, though certainly not a fifth color.
                                                          V-6
In summary, it would appear that any map drawn on a plane surface or on
the surface of a sphere may be delineated with four colors. No doubt
asymmetrical coloring demands greater attention in practice, but even the most
carefully devised asymmetry can be organized in terms of the directions that it
exhibits. For asymmetry in maps evidently is a complication addressed more to
the pleasures of the eye and the limits of the imagination than to any
systematic account of directions. Given therefore that it is the concept of
direction on which our argument rests, we may conclude that the four-color
planar map can have no five-color counter-example.
Part II:
Coloring Technique
     It is a feature of this approach to the four-color map that the two
concepts of direction and neighbor are exploited in uncommon ways.
     The several basic directions mentioned above characterize the simple map
and show the use of repetition in the coloring of such maps. Equally, multiple
directions provide the foundations of complex maps and their resulting
asymmetrical coloring. The two sorts of directions supply between them the
concepts necessary for a more detailed description of neighbors.*
     Neighbors, for their part, designate areas which need not have common
borders, but only reciprocal relations. The different types of neighbors
include therefore those pairs of areas which are comparatively remote from one
another, but whose relationships affect the range of available colors. In turn,
it is these relationships which support the claim that pressures on the choice
of color are not cumulative because it can be shown; (1) that neighbors are
wholly determined by directions, and (2) that some of these directions must be
repeated at just that junction in a coloring scheme which might be thought to
require a fifth color. Now as we have noted, a repeated direction permits a
repeated color; hence four colors suffice for any such map as ours.
     The interplay of directions and neighbors may be seen by considering the
following examples.
     There is first the simple map which most easily shows the straightforward
use of directions in coloring, and the inherently movable center of any
coloring plan. (See Figure 8.)
     If wedge B is the central area, then converging neighbors A and C must
obviously have colors different from B, but may themselves share a color. This
is so because the path that wedge A must follow in order to come to be adjacent
to wedge C is wholly blocked by B. In such a case, wedge A would move in
directions +Y and +E, and it is clear that wedge B lies precisely in these two
directions from A.
     Similarly, if the quadrilateral B in Figure 9 and the smaller b' are
thought of as two areas, then it is clear that wedge b" could repeat the color
of B without being lost to view. In this case, b' forms a barrier between B and
b" and lies wholly in the directions of -Y and -E from B.
     A different sort of barrier is provided by the mathematical point here
designated O. Wedges H and b" are separated by the absence of a border, but
related by the reciprocity of the directions in which a traveller would move in
order to pass from the one to the other. For on such a map as this, travelling
from b" to H would entail proceeding in directions -Y and -E, whereas the
reverse sequence; that is, of proceeding from wedge H in directions +W and +Y
would lead to b" in the first instance. Both types of barriers then,
mathematical points as well as intervening areas, reveal that up is related to
down and right is related to left not solely by exclusion, but by the
possibilities of repeated directions and therefore of repeated colors. For the
purposes of coloring, there are a number of occasions when up is down and right
is left. See Figures 10 to 18.
     The coloring technique which we shall consider simply designates the
central area of a map as that area in terms of which neighboring areas are
                                                               V-7
first described. This central division therefore changes as the colors of the
map progressively are decided. Once again, the pressure to choose one color
rather than another has a definable limit beyond which repetition begins.
     Irregular complex maps can be colored systematically by repeating colors
which lie in the same or reciprocal directions. (Figure 19.) The technique of
isolating areas in several directions is shown in the use of the intruding
neighbor Figure 20, and the partly-surrounding neighbor Figure 21.
Simplest four-color configurations:
     It is a general characteristic of our maps that the number of required
colors is increased when the directions in which the areas lie are multiplied
rather than repeated. Consequently those four-color maps which have only four
areas must multiply their directions with the greatest profligacy, and they can
easily be seen to do so.
     The typical simplest four-color map exhibits four contiguous areas, no two
of which are isolated from each other.
     A map which includes an inner island, as in Figure 22, shows the island
standing in every direction from its three contiguous neighbors and yet failing
to form a barrier between any pair of them. The island 4 plainly stands in a
+X-direction from area 1, but is not the only area contiguous with 1 to do so,
since this is equally true of parts of areas 2 and 3. Three parallel lines are
needed to illustrate the +X-direction in which the several contiguous neighbors
of area 1 are to be found. The same is true of the +Y-direction of the three
contiguous neighbors of area 3.
     A similar inner island can be constructed which includes the parallel
lines of multiple directions in the figure. Area 2 of Figure 23 manifestly
stands in every direction from its three contiguous neighbors, yet like Figure
22 equally fails to form a barrier between any pair of them. The vertical lines
which separate areas 1 from 2, 3 from 4, and 2 from 4 obviously are parallel,
and so give the result that area 4 doubles the areas contiguous with it in both
the -X and -Y-directions. It therefore does not isolate either area 1 in the
+Y-direction or area 2 in the -Y-direction. By way of contrast, an inner island
which does isolate all of the areas contiguous with it and therefore requires
only three colors is area 1 in Figure 24.
     A second type of simplest four-color map is that shown in Figure 25. In
this case the fourth color is required by an area which might be called the
surrounding sea. This sea again lies in every direction from the other,
mutually contiguous areas; and they, in turn, lie in several parallel
directions from one another.
     The grounds for supposing that four colors are not sufficient for coloring
any map drawn on a plane surface or the surface of a sphere is the suspicion
that a configuration which requires four colors in isolation may later,
unexpectedly support a demand for a fifth color because the effects of the
earlier four-color pattern prove to be cumulative. This suspicion that an
ultimately recalcitrant surprise may be gathering force is not justified for
the reason that surprises and irremedial pressures are not problems of the same
type. No one denies that the possibilities of asymmetry provide exercise beyond
the scope of pictorial imagination, but it does not follow from this that the
demands of a four-color configuration are cumulative. On the contrary, the
juxtaposition of two such unyielding patterns provides a barrier just where the
areas are thereby made adjacent, and consequently allows at least one color to
be repeated beyond the barrier so formed.
     It is not therefore to be expected that when a map such as that shown in
Figure 23 is repeated, and the two maps are given some contiguous areas, that a
fifth color will be required to distinguish all the new relationships. Repeated
directions, and hence repeatable colors, ensure that this is not so.
Straightforward repetition of the pattern, in Figure 26, and the original
figure together with its mirror image in Figure 27 illustrate the relationships
                                                               V-8
between directions and colors.
     In practice, because there is no cumulative effect of four-color patterns
when they are repeated, flexibility in the choice of color can be noted in the
course of coloring any map. This is done by signalling that there may be an
alternative color in each appropriate area. If it later happens that the map
appears to require a fifth color, it is necessary only to refer to the more
closely related areas which gave room for choice, and change one or several
colors to the alternatives noted. The other colors are then adjusted by
following some definite direction from the newly-chosen colors toward the
problem area. Frequently the alternative will permit a clear barrier to be
drawn between the area or areas which offered a choice and the problem area,
with the result that the influence of the four-color pattern which caused the
difficulty is readily seen to be limited. But whether it is readily seen or
only discovered laboriously, the principle holds good. The fact is that in any
map of five or more areas, there may be portions of the map which require the
systematic use of four colors. Nevertheless, there must also be other,
neighboring portions of the same map which offer a genuine choice of colors,
and which consequently interrupt the more or less remote influence of the
former portion. The map printed in Scientific American gives a good
illustration of both the restricted and the alternative use of colors. See
Figure 28.
Conventional Lines:
     A conventional line is one which might be imagined to be drawn on a map in
order to separate two areas which are not separated on the map as given, and
thereby to eliminate the effects of multiple directions. This is a most useful
device where the ordinary effects of a partly-surrounding neighbor are
diminished by the presence of parallel lines, which of course require an
additional color to separate the resulting contiguous areas.
     In a regularly drawn map such as that of Scientific American, a
well-placed conventional line has the dramatic effect of transforming an
asymmetrical map into a symmetrical one, with all the benefits to the human eye
and visual imagination that this bestows. A second and related advantage is
that the very existence of a proper site for a conventional line, especially in
the comparatively complex case of partly-surrounding neighbors, signals that
the map concerned is asymmetrical. See Figure 29.
     Obviously from the point of view of map-coloring, this forewarning of
asymmetry is very useful. One knows then that the map is to be treated by
coloring first those areas which clearly require a four-color pattern. The
second step is to fill in the remainder of the map in systematically chosen
directions and in the process to note alternative colors as they occur. See
Figure 28.
Conclusion:
     There are in fact a relatively small number of relationships in which any
area of a map may be involved for the purposes of delineation by color.*
Whether a map is simple or complex, when the perimeter of an area has been
traced while preserving the individual boundaries of its adjacent neighbors,
then its fundamental relationships with the remainder of the map have been
decided. Any problems which arise subsequently strictly refer to another area.
This does not mean that adjustments in the color of the earlier-determined area
need not be made, but it does mean that the solution lies in choosing an
alternative color where one can easily be noted, and then distributing the
remaining colors so as to continue to preserve the required boundaries, as we
have illustrated.
     The two points to be insisted on are; first, that there are alternatives
because the pressures which demand a fourth color are not cumulative; and
second, that any asymmetrical coloring scheme which exploits our concept of
                                                               V-9
directions can take due notice in passing of those areas which permit
alternative colors. Adjustments then become an exercise in retracing the
directions originally followed. There is no question of having either to decide
on or restrict the number of areas to be colored. The map need only be some
specific map and therefore finite.
     Finally, there is a curious historical echo in the problem of the
four-color map. This is found in the attitude that admits to some doubts about
the sufficiency of four colors after all.* These residual suspicions are odd
ones however, for they rely on the haunting possibility that the demand for
four colors might prove cumulative in some future configuration. In effect,
critics raise the spectre of the unforeseeable, and then worry because it
cannot be foreseen. But the answer is that there is no spectre; nor can one be
produced merely by invoking the logic of the concept unforeseeable.
                                       fnV-1
Footnote for Chapter V
V-13 n.1  Part of figure that appeared in Scientific American, April, 1975,
          p.128.
                                                            txtfnV-1
*    For the record, the solution presented in Part I was worked out in all its
essential features in June 1975. It therefore pre-dates the computer-based
solution of Kenneth Appel and Wolfgang Haken.
*    Wedge B is assumed to include the smaller wedge b unless otherwise noted;
so too with the other similar pairs of wedges.
+    Here the wedges and quadrilaterals must be distinguished.
*    For example, wedge B.
*    See figures in Part II below.
*    In some cases the repetition of parallel lines can cancel asymmetry and
produce a more elaborate symmetrical map, but not a simple map. See below,
Figure 30.
*    See above, Part I.
*    This now takes the form of wondering whether the computer-based proof
might contain some flaw not yet detected.
                                                               C-1
Conclusion
     Two advantages follow from recognizing that strictly interpreted ideas are
the genuine elements of perception. The first is that the sensory evidence is
accurately distinguished from the theories in which it figures. Simple
descriptions are then more readily separated from valid inferences, with the
result that observation claims can be given due weight, and no more.
     A second advantage of attending to ideas is derived from their descriptive
limitations. Because each idea is logically independent of every other idea,
and because all observation claims are founded on ideas, the sensible
perspective has an obvious function in organizing these perceptual elements. By
recognizing this perspective, we can make rather better sense of the usual
conditions of observation, not least the perceptible discontinuity of
supposedly continuous physical objects.
     James' squirrel, who shyly resolved to remain on the far side of his tree,
and did so, reads us a lesson in the benefits to be gained by exploiting
perspective. Other problems of perception that are untangled by revealing their
constituent ideas include the puzzle set by Hempel's ravens, and the oddities
produced by the color continuum. The classic four-color map problem also yields
to an analysis based on ideas and the special features of visual perception.
Here I have argued that a map drawn on a plane surface, or on the surface of a
sphere, is the
unique case in which the principles used in coloring the figure are directly
related to the visual space in which all colors must be perceived.
     The concept of presence has emerged too as having a useful role in
descriptive theory after all. The price of acknowledging a perceiver often has
been rejected as being too high, but it seems to me that the advantages are
even greater. For presence, when allied with the sensible perspective, provides
the essential distinction between sensory evidence here and now, and the
neutral descriptions of empirical theory.
     The claims made for a rational skepticism are not unrelated to presence.
The sensible perspective admits, and indeed seizes on, the consequences of
privacy and the limits of one's certain knowledge. Put briefly, this skepticism
clarifies the issues. For the rational skeptic can deplore ill-founded
descriptive theories of external reality, and yet argue that a sympathetic
imagination bridges gaps which logic cannot close. The important point is to
recognize where valid inference ends and imaginative resourcefulness begins.
     To conclude, I have argued that strictly interpreted ideas are irreducible
and lead to a sensible perspective. These two aspects of experience together
provide the foundations of empirical claims. No observation can dispense with
them, although empirical descriptions can be elaborated indefinitely. Still,
description has its limits, and cannot venture beyond the borders
of observation and valid inference. Accordingly, it is at this juncture that
the critical imagination enters into its kingdom, carefully provided with the
baleful eye of skepticism.