I

Words, Works, Worlds

1. Questions

Countless worlds made frorn nothing by use of symbols — so might a satirist summarize some major themes in the work of Ernst Cassirer. These themes — the multiplicity of worlds, the speciousness of 'the given', the creative power of the understanding, the variety and formative function of symbols — are also integral to my own thinking. Sometimes, though, I forget how eloquently they have been set forth by Cassirer,[1] partly perhaps because his emphasis on myth, his concern with the comparative study of cultures, and his talk of the human spirit have been mistakenly associated with current trends toward mystical obscurantism, anti-intellectual intuitionism, or anti-scientific humanism. Actually these attitudes are as alien to Cassirer as to my own skeptical, analytic, constructionalist orientation.

My aim in what follows is less to defend certain theses that Cassirer and I share than to take a hard look at some crucial questions they raise. In just what sense are there many worlds? What distinguishes genuine from spurious worlds? What are worlds made of? How are they made? What role do symbols play in the making? And how is worldmaking related to knowing? These questions must be faced even if full and final answers are far off.

2. Versions and Visions

As intimated by William James's equivocal title A Pluralistic Universe, the issue between monism and pluralism tends to evaporate under analysis. If there is but one world, it embraces a multiplicity of contrasting aspects; if there are many worlds, the collection of them all is one. The one world may be taken as many, or the many worlds taken as one; whether one or many depends on the way of taking.[2]

Why, then, does Cassirer stress the multiplicity of worlds? In what important and often neglected sense are there many worlds? Let it be clear that the question here is not of the possible worlds that many of my contemporaries, especially those near Disneyland, are busy making and manipulating. We are not speaking in terms of multiple possible alternatives to a single actual world but of multiple actual worlds. How to interpret such terms as "real", "unreal", "fictive", and "possible" is a subsequent question.

Consider, to begin with, the statements "The sun always moves" and "The sun never moves" which, though equally true, are at odds with each other. Shall we say, then, that they describe different worlds, and indeed that there are as many different worlds as there are such mutually exclusive truths? Rather, we are inclined to regard the two strings of words not as complete statements with truth-values of their own but as elliptical for some such statements as "Under frame of reference A, the sun always moves" and "Under frame of reference B, the sun never moves" — statements that may both be true of the same world.

Frames of reference, though, seem to belong less to what is described than to systems of description: and each of the two statements relates what is described to such a system. If I ask about the world, you can offer to tell me how it is under one or more frames of reference; but if I insist that you tell me how it is apart from all frames, what can you say? We are confined to ways of describing whatever is described. Our universe, so to speak, consists of these ways rather than of a world or of worlds.

The alternative descriptions of motion, all of them in much the same terms and routinely transformable into one another, provide only a minor and rather pallid example of diversity in accounts of the world. Much more striking is the vast variety of versions and visions in the several sciences, in the works of different painters and writers, and in our perceptions as informed by these, by circumstances, and by our own insights, interests' and past experiences. Even with all illusory or wrong or dubious versions dropped, the rest exhibit new dimensions of disparity. Here we have no neat set of frames of reference, no ready rules for transforming physics, biology, and psychology into one another, and no way at all of transforming any of these into Van Gogh's vision, or Van Gogh's into Canaletto's. Such of these versions as are depictions rather than descriptions have no truth-value in the literal sense, and cannot be combined by conjunction. The difference between juxtaposing and conjoining two statements has no evident analogue for two pictures or for a picture and a statement. The dramatically contrasting versions of the world can of course be relativized: each is right under a given system — for a given science, a given artist, or a given perceiver and situation. Here again we turn from describing or depicting 'the world' to talking of descriptions and depictions, but now without even the consolation of intertranslatability among or any evident organization of the several systems in question.

Yet doesn't a right version differ from a wrong one just in applying to the world, so that rightness itself depends upon and implies a world? We might better say that 'the world' depends upon rightness. We cannot test a version by comparing it with a world undescribed, undepicted, unperceived, but only by other means that I shall discuss later. While we may speak of determining what versions are right as 'learning about the world', 'the world' supposedly being that which all right versions describe, all we learn about the world is contained in right versions of it; and while the underlying world, bereft of these, need not be denied to those who love it, it is perhaps on the whole a world well lost. For some purposes, we may want to define a relation that will so sort versions into clusters that each cluster constitutes a world, and the members of the cluster are versions of that world; but for many purposes, right world-descriptions and world-depictions and world-perceptions, the ways-the-world-is, or just versions, can be treated as our worlds.'[3]

Since the fact that there are many different world-versions is hardly debatable, and the question how many if any worlds-in-themselves there are is virtually empty, in what nontrivial sense are there, as Cassirer and likeminded pluralists insist, many worlds? Just this, I think: that many different world-versions are of independent interest and importance, without any requirement or presumption of reducibility to a single base. The pluralist, far from being antiscientific, accepts the sciences at full value. His typical adversary is the monopolistic materialist or physicalist who maintains that one system, physics, is preeminent and all-inclusive, such that every other version must eventually be reduced to it or rejected as false or meaningless. If all right versions could somehow be reduced to one and only one, that one might with some semblance of plausibility[4] be regarded as the only truth about the only world. But the evidence for such reducibility is negligible, and even the claim is nebulous since physics itself is fragmentary and unstable and the kind and consequences of reduction envisaged are vague. (How do you go about reducing Constable's or James Joyce's world-view to physics?) I am the last person likely to underrate construction and reduction.[5] A reduction from one system to another can make a genuine contribution to understanding the interrelationships among world-versions; but reduction in any reasonably strict sense is rare, almost always partial, and seldom if ever unique. To demand full and sole reducibility to physics or any other one version is to forego nearly all other versions. The pluralists' acceptance of versions other than physics implies no relaxation of rigor but a recognition that standards different from yet no less exacting than those applied in science are appropriate for appraising what is conveyed in perceptual or pictorial or literary versions.

So long as contrasting right versions not all reducible to one are countenanced, unity is to be sought not in an ambivalent or neutral something beneath these versions but in an overall organization embracing them. Cassirer undertakes the search through a cross-cultural study of the development of myth, religion, language, art, and science. My approach is rather through an analytic study of types and functions of symbols and symbol systems. In neither case should a unique result be anticipated; universes of worlds as well as worlds themselves may be built in many ways.

3. How Firm a Foundation?

The non-Kantian theme of multiplicity of worlds is closely akin to the Kantian theme of the vacuity of the notion of pure content. The one denies us a unique world, the other the common stuff of which worlds are made. Together these theses defy our intuitive demand for something stolid underneath, and threaten to leave us uncontrolled, spinning out our own inconsequent fantasies.

The overwhelming case against perception without conception, the pure given, absolute immediacy, the innocent eye, substance as substratum, has been so fully and frequently set forth — by Berkeley, Kant, Cassirer, Gombrich,[6] Bruner,[7] and many others — as to need no restatement here. Talk of unstructured content or an unconceptualized given or a substratum without properties is self-defeating; for the talk imposes structure, conceptualizes, ascribes properties. Although conception without perception is merely empty, perception without conception is blind (totally inoperative). Predicates, pictures, other labels, schemata, survive want of application, but content vanishes without form. We can have words without a world but no world without words or other symbols.

The many stuffs — matter, energy, waves, phenomena — that worlds are made of are made along with the worlds. But made from what? Not from nothing, after all, but from other worlds. Worldmaking as we know it always starts from worlds already on hand; the making is a remaking. Anthropology and developmental psychology may study social and individual histories of such world-building, but the search for a universal or necessary beginning is best left to theology.[8] My interest here is rather with the processes involved in building a world out of others.

With false hope of a firm foundation gone, with the world displaced by worlds that are but versions, with substance dissolved into function, and with the given acknowledged as taken, we face the questions how worlds are made, tested, and known.

4. Ways of Worldmaking

Without presuming to instruct the gods or other worldmakers, or attempting any comprehensive or systematic survey, I want to illustrate and comment on some of the processes that go into worldmaking. Actually, I am concerned more with certain relationships among worlds than with how or whether particular worlds are made from others.

(a) Composition and Decomposition

Much but by no means all worldmaking consists of taking apart and putting together, often conjointly: on the one hand, of dividing wholes into parts and partitioning kinds into subspecies, analyzing complexes into component features, drawing distinctions; on the other hand, of composing wholes and kinds out of parts and members and subclasses, combining features into complexes, and making connections. Such composition or decomposition is normally effected or assisted or consolidated by the application of labels: names, predicates, gestures, pictures, etc. Thus, for example, temporally diverse events are brought together under a proper name or identified as making up 'an object' or 'a person'; or snow is sundered into several materials under terms of the Eskimo vocabulary. Metaphorical transfer — for example, where taste predicates are applied to sounds — may effect a double reorganization, both re-sorting the new realm of application and relating it to the old one (LA: II).

Identification rests upon organization into entities and kinds. The response to the question "Same or not the same?" must always be "Same what?"[9] Different soandsos may be the same such-and-such: what we point to or indicate, verbally or otherwise, may be different events but the same object, different towns but the same state ,different members but the same club or different clubs but the same members, different innings but the same ball game 'The ball-in-play' of a single game may be comprised of temporal segments of a dozen or more baseballs. The psychologist asking the child to judge constancy when one vessel is emptied into another must be careful to consider what constancy is in question —constancy of volume or depth or shape or kind of material, etc.[10] Identity or constancy in a world is identify with respect to what is within that world as organized.

Motley entities cutting across each other in complicated patterns may belong to the same world We do not make a new world every time we take things apart or put them together in another way; but worlds may differ in that not everything belonging to one belongs to the other. The world of the Eskimo who has not grasped the comprehensive concept of snow differs not only from the world of the Samoan but also from the world of the New Englander who has not grasped the Eskimo's distinctions. In other cases, worlds differ in response to theoretical rather than practical needs. A world with points as elements cannot be the Whiteheadian world having points as certain classes of nesting volumes or having points as certain pairs of intersecting lines or as certain triples of intersecting planes. That the points of our everyday world can be equally well defined in any of these ways does not mean that a point can be identified in any one world with a nest of volumes and a pair of lines and a triple of planes; for all these are different from each other. Again the world of a system taking minimal concrete phenomena as atomic cannot admit qualities as atomic parts of these concreta.[11]

Repetition as well as identification is relative to organization. A world may be unmanageably heterogeneous or unbearably monotonous according to how events are sorted into kinds.

Whether or not today's experiment repeats yesterday's, however much the two events may differ, depends upon whether they test a common hypothesis; as Sir George Thomson puts it:

There will always be something different.... What it comes to when you say you repeat an experiment is that you repeat all the features of an experiment which a theory determines are relevant. In other words you repeat the experiment as an example of the theory.[12]

Likewise, two musical performances that differ drastically are nevertheless performances of the same work if they conform to the same score. The notational system distinguishes constitutive from contingent features, thus picking out the performance-kinds that count as works (LA, pp. 115-130). And things 'go on in the same way' or not according to what is regarded as the same way; 'now I can go on',[13] in Wittgenstein's sense, when I have found a familiar pattern, or a tolerable variation of one, that fits and goes beyond the cases given. Induction requires taking some classes to the exclusion of others as relevant kinds. Only so, for example, do our observations of emeralds exhibit any regularity and confirm that all emeralds are green rather than that all are grue (i.e. examined before a given date and green, or not so examined and blue — FFF, pp. 72-80). The uniformity of nature we marvel at or the unreliability we protest belongs to a world of our own making.

In these latter cases, worlds differ in the relevant kinds they comprise. I say "relevant" rather than "natural" for two reasons: first, "natural" is an inapt term to cover not only biological species but such artificial kinds as musical works, psychological experiments, and types of machinery; and second, "natural" suggests some absolute categorical or psychological priority, while the kinds in question are rather habitual or traditional or devised for a new purpose.

(b) Weighting

While we may say that in the cases discussed some relevant kinds[14] of one world are missing from another, we might perhaps better say that the two worlds contain just the same classes sorted differently into relevant and irrelevant kinds.

Some relevant kinds of the one world, rather than being absent from the other, are present as irrelevant kinds; some differences among worlds are not so much in entities comprised as in emphasis or accent, and these differences are no less consequential. just as to stress all syllables is to stress none, so to take all classes as relevant kinds is to take none as such. In one world there may be many kinds serving different purposes; but conflicting purposes may make for irreconcilable accents and contrasting worlds, as may conflicting conceptions of what kinds serve a given purpose. Grue cannot be a relevant kind for induction in the same world as green, for that would preclude some of the decisions, right or wrong, that constitute inductive inference.

Some of the most striking contrasts of emphasis appear in the arts. Many of the differences among portrayals by Daumier, Ingres, Michelangelo, and Rouault are differences in aspects accentuated. What counts as emphasis, of course, is departure from the relative prominence accorded the several features in the current world of our everyday seeing. With changing interests and new insights, the visual weighting of features of bulk or line or stance or light alters, and yesterday's level world seems strangely perverted — yesterday's realistic calendar landscape becomes a repulsive caricature.

These differences in emphasis, too, amount to a difference in relevant kinds recognized. Several portrayals of the same subject may thus place it according to different categorial schemata. Like a green emerald and a grue one, even if the same emerald, a Piero della Francesca Christ and a Rembrandt one belong to worlds organized into different kinds.

Works of art, though, characteristically illustrate rather than name or describe relevant kinds. Even where the ranges of application — the things described or depicted — coincide, the features or kinds exemplified or expressed may be very different. A line drawing of softly draped cloth may exemplify rhythmic linear patterns; and a poem with no words for sadness and no mention of a sad person may in the quality of its language be sad and poignantly express sadness. The distinction between saying or representing on the one hand and showing or exemplifying on the other becomes even more evident in the case of abstract painting and music and dance that have no subject-matter but nevertheless manifest — exemplify or express — forms and feelings. Exemplification and expression, though running in the opposite direction from denotation — that is, from the symbol to a literal or metaphorical feature of it instead of to something the symbol applies to — are no less symbolic referential functions and instruments of worldmaking.[15]

Emphasis or weighting is not always binary as is a sorting into relevant and irrelevant kinds or into important and unimportant features. Ratings of relevance, importance, utility, value often yield hierarchies rather than dichotomies. Such weightings are also instances of a particular type of ordering.

(c) Ordering

Worlds not differing in entities or emphasis may differ in ordering; for example, the worlds of different constructional systems differ in order of derivation. As nothing is at rest or is in motion apart from a frame of reference, so nothing is primitive or is derivationally prior to anything apart from a constructional system. However, derivation unlike motion is of little immediate practical interest; and thus in our everyday world, although we almost always adopt a frame of reference at least temporarily, we seldom adopt a derivational basis. Earlier I said that the difference between a world having points as pairs of lines and a world having lines as composed of points is that the latter but not the former admits as entities nonlinear elements comprised within lines. But alternatively we may say that these worlds differ in their derivational ordering of lines and points of the not-derivationally-ordered world of daily discourse.

Orderings of a different sort pervade perception and practical cognition. The standard ordering of brightness in color follows the linear increase in physical intensity of light, but the standard ordering of hues curls the straight line of increasing wavelength into a circle. Order includes periodicity as well as proximity; and the standard ordering of tones is by pitch and octave. Orderings alter with circumstances and objectives. Much as the nature of shapes changes under different geometries, so do perceived patterns change under different orderings; the patterns perceived under a twelve-tone scale are quite different from those perceived under the traditional eight-tone scale, and rhythms depend upon the marking off into measures.

Radical reordering of another sort occurs in constructing a static image from the input on scanning a picture, or in building a unified and comprehensive image of an object or a city from temporally and spatially and qualitatively heterogeneous observations and other items of information.[16] Some very fast readers recreate normal word-ordering from a series of fixations that proceed down the left-hand page and then up the right-hand page of a book.[17] And spatial order in a map or a score is translated into the temporal sequence of a trip or a performance.

All measurement, furthermore, is based upon order. Indeed, only through suitable arrangements and groupings can we handle vast quantities of material perceptually or cognitively. Gombrich discusses the decimal periodization of historical time into decades, centuries, and millennia.[18] Daily time is marked off into twenty-four hours, and each of these into sixty minutes of sixty seconds each. Whatever else may be said of these modes of organization, they are not 'found in the world' but built into a world. Ordering, as well as composition and decomposition and weighting of wholes and kinds, participates in worldmaking.

(d) Deletion and Supplementation

Also, the making of one world out of another usually involves some extensive weeding out and filling — actual excision of some old and supply of some new material. Our capacity for overlooking is virtually unlimited, and what we do take in usually consists of significant fragments and clues that need massive supplementation. Artists often make skillful use of this: a lithograph by Giacometti fully presents a walking man by sketches of nothing but the head, hands, and feet in just the right postures and positions against an expanse of blank paper; and a drawing by Katharine Sturgis conveys a hockey player in action by a single charged line.

That we find what we are prepared to find (what we look for or what forcefully affronts our expectations), and that we are likely to be blind to what neither helps nor hinders our pursuits, are commonplaces of everyday life and amply attested in the psychological laboratory.[19] In the painful experience of proofreading and the more pleasurable one of watching a skilled magician, we incurably miss something that is there and see something that is not there. Memory edits more ruthlessly; a person with equal command of two languages may remember a learned list of items while forgetting in which language they were listed.[20] And even within what we do perceive and remember, we dismiss as illusory or negligible what cannot be fitted into the architecture of the world we are building.

The scientist is no less drastic, rejecting or purifying most of the entities and events of the world of ordinary things while generating quantities of filling for curves suggested by sparse data, and erecting elaborate structures on the basis of meagre observations. Thus does he strive to build a world conforming to his chosen concepts and obeying his universal laws.

Replacement of a so-called analog by a so-called digital system through the articulation of separate steps involves deletion; for example, to use a digital thermometer with readings in tenths of a degree is to recognize no temperature as lying between 90 and 90.1 degrees. Similar deletion occurs under standard musical notation, which recognizes no pitch between c and c# and no duration between a sixty-fourth and a one hundred-and-twenty-eighth note. On the other hand, supplementation occurs when, say, an analog replaces a digital instrument for registering attendance, or reporting money raised, or when a violinist performs from a score.

Perhaps the most spectacular cases of supplementation, though, are found in the perception of motion. Sometimes motion in the perceptual world results from intricate and abundant fleshing out of the physical stimuli. Psychologists have long known of what is called the 'phi phemomenon': under carefully controlled conditions, if two spots of light are flashed a short distance apart and in quick succession, the viewer normally sees a spot of light moving continuously along a path from the first position to the second. That is remarkable enough in itself since of course the direction of motion cannot have been determined prior to the second flash; but perception has even greater creative power. Paul Kolers has recently shown[21] that if the first stimulus spot is circular and the second square, the seen moving spot transforms. smoothly from circle to square; and transformations between two-dimensional and three-dimensional shapes are often effected without trouble. Moreover, if a barrier of light is interposed between the two stimulus spots, the moving spot detours around the barrier. Just why these supplementations occur as they do is a fascinating subject for speculation (see further V below).

(e) Deformation

Finally, some changes are reshapings or deformations that may according to point of view be considered either corrections or distortions. The physicist smooths out the simplest rough curve that fits all his data. Vision stretches a line ending with arrowheads pointing in while shrinking a physically equal line ending with arrowheads pointing out, and tends to expand the size of a smaller more valuable coin in relation to that of a larger less valuable one.[22] Caricaturists often go beyond overemphasis to actual distortion. Picasso starting from Velasquez's Las Meninas, and Brahms starting from a theme of Haydn's, work magical variations that amount to revelations.

These then are ways that worlds are made. I do not say the ways. My classification is not offered as comprehensive or clearcut or mandatory. Not only do the processes illustrated often occur in combination but the examples chosen sometimes fit equally well under more than one heading; for example, some changes may be considered alternatively as reweightings or reorderings or reshapings or as all of these, and some deletions are also matters of differences in composition. All I have tried to do is to suggest something of the variety of processes in constant use. While a tighter systematization could surely be developed, none can be ultimate; for as remarked earlier, there is no more a unique world of worlds than there is a unique world.

5. Trouble with Truth

With all this freedom to divide and combine, emphasize, order, delete, fill in and fill out, and even distort, what are the objectives and the constraints? What are the criteria for success in making a world?

Insofar as a version is verbal and consists of statements, truth may be relevant. But truth cannot be defined or tested by agreement with 'the world'; for not only do truths differ for different worlds but the nature of agreement between a version and a world apart from it is notoriously nebulous. Rather — speaking loosely and without trying to answer either Pilate's question or Tarski's — a version is taken to be true when it offends no unyielding beliefs and none of its own precepts. Among beliefs unyielding at a given time may be long-lived reflections of laws of logic, short-lived reflections of recent observations, and other convictions and prejudices ingrained with varying degrees of firmness. Among precepts, for example, may be choices among alternative frames of reference, weightings, and derivational bases. But the line between beliefs and precepts is neither sharp nor stable. Beliefs are framed in concepts informed by precepts; and if a Boyle ditches his data for a smooth curve just missing them all, we may say either that observational volume and pressure are different properties from theoretical volume and pressure or that the truths about volume and pressure differ in the two worlds of observation and theory. Even the staunchest belief may in time admit alternatives; "The earth is at rest" passed from dogma to dependence upon precept.

Truth, far from being a solemn and severe master, is a docile and obedient servant. The scientist who supposes that he is single-mindedly dedicated to the search for truth deceives himself. He is unconcerned with the trivial truths he could grind out endlessly; and he looks to the multifaceted and irregular results of observations for little more than suggestions of overall structures and significant generalizations. He seeks system, simplicity, scope; and when satisfied on these scores he tailors truth to fit (PP:Vll, 68). He as much decrees as discovers the laws he sets forth, as much designs as discerns the patterns he delineates.

Truth, moreover, pertains solely to what is said, and literal truth solely to what is said literally. We have seen, though, that worlds are made not only by what is said literally but also by what is said metaphorically, and not only by what is said either literally or metaphorically but also by what is exemplified and expressed — by what is shown as well as by what is said. In a scientific treatise, literal truth counts most; but in a poem or novel, metaphorical or allegorical truth may matter more, for even a literally false statement may be metaphorically true (LA, pp. 51, 68-70) and may mark or make new associations and discriminations, change emphases, effect exclusions and additions. And statements whether literally or metaphorically true or false may show what they do not say, may work as trenchant literal or metaphorical examples of unmentioned features and feelings. In Vachel Lindsay's The Congo, for example, the pulsating pattern of drumbeats is insistently exhibited rather than described.

Finally, for nonverbal versions and even for verbal versions without statements, truth is irrelevant. We risk confusion when we speak of pictures or predicates as "true of" what they depict or apply to; they have no truth-value and may represent or denote some things and not others, while a statement does have truth-value and is true of everything if of anything.[23] A nonrepresentational picture such as a Mondrian says nothing, denotes nothing, pictures nothing, and is neither true nor false, but shows much. Nevertheless, showing or exemplifying, like denoting, is a referential function; and much the same considerations count for pictures as for the concepts or predicates of a theory: their relevance and their revelations, their force and their fit — in sum their rightness. Rather than speak of pictures as true or false we might better speak of theories as right or wrong; for the truth of the laws of a theory is but one special feature and is often, as we have seen, overridden in importance by the cogency and compactness and comprehensiveness, the informativeness and organizing power of the whole system.

"The truth, the whole truth, and nothing but the truth" would thus be a perverse and paralyzing policy for any worldmaker. The whole truth would be too much; it is too vast, variable, and clogged with trivia. The truth alone would be too little, for some right versions are not true — being either false or neither true nor false — and even for true versions rightness may matter more.

6. Relative Reality

Shouldn't we now return to sanity from all this mad proliferation of worlds? Shouldn't we stop speaking of right versions as if each were, or had, its own world, and recognize all as versions of one and the same neutral and underlying world? The world thus regained, as remarked earlier, is a world without kinds or order or motion or rest or pattern — a world not worth fighting for or against.

We might, though, take the real world to be that of some one of the alternative right versions (or groups of them bound together by some principle of reducibility or translatability) and regard all others as versions of that same world differing from the standard version in accountable ways. The physicist takes his world as the real one, attributing the deletions, additions, irregularities, emphases of other versions to the imperfections of perception, to the urgencies of practice, or to poetic license. The phenomenalist regards the perceptual world as fundamental, and the excisions, abstractions, simplifications, and distortions of other versions as resulting from scientific or practical or artistic concerns. For the man-in-the-street, most versions from science, art, and perception depart in some ways from the familiar serviceable world he has jerry-built from fragments of scientific and artistic tradition and from his own struggle for survival. This world, indeed, is the one most often taken as real; for reality in a world, like realism in a picture, is largely a matter of habit.

Ironically, then, our passion for one world is satisfied, at different times and for different purposes, in many different ways. Not only motion, derivation, weighting, order, but even reality is relative. That right versions and actual worlds are many does not obliterate the distinction between right and wrong versions, does not recognize merely possible worlds answering to wrong versions, and does not imply that all right alternatives are equally good for every or indeed for any purpose. Not even a fly is likely to take one of its wingtips as a fixed point; we do not welcome molecules or concreta as elements of our everyday world, or combine tomatoes and triangles and typewriters and tyrants and tornadoes into a single kind; the physicist will count none of these among his fundamental particles; the painter who sees the way the man-in-the-street does will have more popular than artistic success. And the same philosopher who here metaphilosophically contemplates a vast variety of worlds finds that only versions meeting the demands of a dogged and deflationary nominalism suit his purposes in constructing philosophical systems

Moreover, while readiness to recognize alternative worlds may be liberating, and suggestive of new avenues of exploration, a willingness to welcome all worlds builds none. Mere acknowledgement of the many available frames of reference provides us with no map of the motions of heavenly bodies; acceptance of the eligibility of alternative bases produces no scientific theory or philosophical system; awareness of varied ways of seeing paints no pictures. A broad mind is no substitute for hard work.

7. Notes on Knowing

What I have been saying bears on the nature of knowledge. On these terms, knowing cannot be exclusively or even primarily a matter of determining what is true. Discovery often amounts, as when I place a piece in a jigsaw puzzle, not to arrival at a proposition for declaration or defense, but to finding a fit. Much of knowing aims at something other than true, or any, belief. An increase in acuity of insight or in range of comprehension, rather than a change in belief, occurs when we find in a pictured forest a face we already knew was there, or learn to distinguish stylistic differences among works already classified by artist or composer or writer, or study a picture or a concerto or a treatise until we see or hear or grasp features and structures we could not discern before. Such growth in knowledge is not by formation or fixation or belief[24] but by the advancement of understanding.[25]

Furthermore, if worlds are as much made as found, so also knowing is as much remaking as reporting. All the processes of worldmaking I have discussed enter into knowing. Perceiving motion, we have seen, often consists in producing it. Discovering laws involves drafting them. Recognizing patterns is very much a matter of inventing and imposing them. Comprehension and creation go on together.

I shall return in Chapters VI and VII to many of the questions surveyed here. Now I want to consider two much more specific topics: in Chapter II, a subtle categorization peculiarly significant for the arts; and in Chapter III, a sample tracing of a notion across versions in various systems and media.