Hcmpel, Carl G. (1993), "Empiricism in \he Vienn:l Circleand in the Berlin Society for Scientific Philosophy:Recollections and Reflections," in Friedrich Stadler(~d.). Scientific Philosophy: O,.igins and De,'efopmel/ts.Dordrecht, Netherlands: Kluwer, 1-10.

Kaufmann, Felix ([1936} 1999), Melhodenfehre der Sozial-wi.w!1lschajten. Vienna and New York: Springer.

Kraft. Viktor (1950), Der Wiener Kreis. Del" Ursprulfg des,'\!I!()po.ritil'ismus. Vienna and New York: Springer.

Menger, Karl (1979), Selected Paper.~ ;1/ Logic and Fowzda-(;""s. Didactics, Economic.f. Dordrecht. Netherlands:Reidel.

,,-- (1994), Reminiscences of the Vienna Circle and the.'tJalhematical Colloquium. Edited by Louise Galland,Bri.m McGuinness, and Abe Sklar. Dordrecht, Nether-lands: Kluwer.

N;lcss- Arne (2003), "Pluralism of Tenable Worldviews," inF. Stadler (ed.), TIre Vienna Circle and Logical Empiri-dvm: Reel'olualion and FuJure Perspeclil'es. Dordreeht,Netherlands: Kluwer.

~kmelh, Elisabeth, and Friedrich Stadler (eds.) (1996),Emyclopedio and Utopia: The Life and Work ojOflo Neuroth (/882-/945). Dordrecht, Netherlands:Kluwer.

:-J..:urath, Otto (1921), Anti-Spengler. Miinchcn: Callwey.English translation in M. Neurath anti R. Cohen (cds.)11973), Elllpirici:ml am! Sociology. Dordrecht, Nether-hinds: Reidel, 158-213. .

- (1931), Empirische So=iologie. Der \t';s.\'en..fchajl!ichf?(i"fwlt del' Ge.tclticllle una Nutionalokonolllh:. Vienna:Springer. English translation in M. Neuralh and R.Cohen (cds.) (1973), Empiridsl11 and Sod%gy. Oor-drecht. Netherlands: Reidel, 3/9-421.

. - (1946) "Tt,e Orchestration of the Sciences by theEncyclopedia of Logical Empiricism." in PIIi/os()phy andPhenomenological Research VI/4: 496-508. .

Nt:urath, Olto, Rudolf CaTnap, and Charles Morris (cds.)( 1971). FOUlldoliOlIS of the Unity of Scielfce: TQward allIIIIt'rnaf;On(11 Enc-yclopt>d;(J of Unified Science (Vol. I.110S. 1-10; Vol. II, nos. 1-9). Chicago and London:Chicago University Press.

Quine, Willard Van Orman (1953), From a Logical Point ofView: Nine Logko-PI1/Josopltica/ Essays. Cambridge.MA: Harvard University Press.

Schlick, Moritz ([1918, 1925] 1974), Gellel'u/ Theory ofKl1owledgfl. Tran"Jated by Albert E. Blumberg. Viennaand New. York: Springer 1974.

H- (1934), "Ober das Fundament der Erkenntnis," iT!El'kenntnis 4: 79-99. .

~

VISUAL REPRESENTATION

~

Graphs, diagrams, drawings, sonographs, and x-raysare commonly used in contemporary science in theprocess of research, in communicating results, and

VISUAL REPRESENTATION

- (1950), "Moritz Schlick," in Philosophen-uxikon.~di~d by Werner Ziegenfuss and Gertrud Julig. Berlin:oe uru)'Icr.

Stadler, Frie~ric~ (2001), The. ~il!!ma Circj~ SI.ud~e:..b1 ~h~Urigtns. Uel'eJopment, ana InJluence oJ LogIcal unpin-,-ism. With the first publication of the protocols (1930-31) of tbe Vienna Circle and an interview with Sir KarlPopper (1991). Vienna and New York: Springer.

- (2002), "The Emigration and Exile of AustrianIntellectuals," in Rolf Steininger, Gunter Bischof, andMichael Gehler (eds.), Austria in the Twentieth Century.New Brunswick, NJ, and Lom1on: Transaction Publish-ers, 116-136.

- (ed.) (2003a), The Vienna Circle and Logical Empil'i-d.rm: Reel.ulualion and Future Perspecliw:.t. Dordrecht,Netherlands: Kluwer.

- (2003b), "The 'Wiener Kreis~ in Oreat Britain: Emi.. grabon and Interaction in the Pmlosophy of Science," in

E. Timms and .J. Hughes (OOs.) Inlell~rtuQI Migration andCulrural TraIT.yo,'mation: Refugee.~ fi'om National Sodal-ism in ,he English-Speaking World. Vienna and NewYork: Springer, 155-180.

-- (2003c), "Transfer and Transformation of LogicalEmpiricism: Quantitative and Qualitative Aspects," inG. Hardcastle and A. Richardson (eds.) Logical Empiri.cism in .,",'orlh Aml'rica. Minneapolis: University of Min-nesota Press, 216-233.

Stadler, Friedrich, and Peter Weibel (eds.) (1995), Ve,.,,'ei.bung d(!r VernUl!{r [The Cultural Exodus from Austria).Vienna and New York: Springer.

Timms, Edward, and Jon Hughes (eds.) (2003). IntellectualMigration and Cui/llral Tran.r{urmcllion: Refugee.f fromNatj()1/u/ Socialism il1 the EIIgli.fh-Speak ing World.Vienna and New York: Springer.

Uebel, Thomas E. (2000), Vel'11u/!fikrit/k und Wi.rsenxchaft.. Oiro /"<?t/mth t/ncl del" E".~te Wie/ter K,.(~is. Vielma and

New York: Springer.\Ion Mists. Richard (\951), PClsitMsl1I: A Sludy in Human

1IIIfl('n/(Jllflim~. New York: Dover.

See also Analyticity; Carnap, Rudolf; Conventional-ism; Demarcation, Problem of; Empiricism; Hahn,Hans; Hempel, Carl Gustav; Logical Empiricism;Mach, Ernest; Neurath, Otto; Phenomenalism;Popper, Karl Raimund; Rational Reconstruction;Quine, Willard Van; Schlick, Moritz; Unity andi>isuni~' of Science; Unity of Science Movement;Verifiability ,

in education. In contrast to more familiar images-paintings, snapshots, children's drawings-visualrepresentations in science often, though not always,

863

VISUAL REPRESENTATION

depict phenomena that cannot be seen: structurestoo small to see with visible light (electron micro~graphs), relations among properties (graphs), stepsin a mechanism (diagrams). Philosophers ofsclencehave studied linguistic and mathematical represen-tations in order to understand science. but they haveonly recently begun to investigate what visual repre-

. sentations contribute, and how they do so. Visualrepresentations appear to play philosophically sig-nificant roles in scientific reasoning. They are prev-alent in journal articles, where scientists express anddefend hypotheses. These papers are relatively for-mal communications, subject to disciplinary stan-dards of clarity and objectivity, and reviewersscrutinize figures as well as text in evaluating thearguments presented. Some figures appear to ex-press scientific hypotheses (e.g., the diagram of thedouble helix), while others,are presented to providesupport for a hypothesis. Can a visual representa-tion express a hypothesis? What kind of inferencescan a visual representation support? How does thevisual format of a figure relate to its role? Scientistsfrequently express concern about the accuracy offigures, just as they do about the accuracy of lin-guistically or mathematically expressed claims.Can pictures be accurate-or true? In general,what advantages do visual representations offerover linguistic and mathematical representations?

In order to answer these questions. it is essentialto understand the nature of visual representationsas such, and to know in what ways they differ fromother types of representations. An analysis that canapply to all symbols used in science is required toavoid dependence on assumptions about the kindsof representations involved. Thus, the first step inunderstanding visual representations in science isclarification of key representational features. Dif-ferent kinds of visual representations can then becompared with each other, and with linguisticrepresentations. This preliminary step is also re-quired in order to understand the epistemic roles>played by figures-fundamentally, to explain howvisual representations express and support scientific.claims.

Visual Symbols

Visual representations, like written or spoken sen-tences and numerical formulas, are external objectsthat function as symbols. No object conveys con-tent on its own; symbols. must be interpreted.Goodman (1976) shows that resemblance is neithernecessary nor sufficient for representation: Justabout any thing can be designated to refer tosome other thing-Wellington does not represent

864

his portrait even though they resemble one another.Comprehension of symbols, including pictures,involves interpretation, which is conventional inthe sense that the relation between symbol formand content is not detennined just by either intrin-sic features of the symbol or a resemblance relationbetween the form of the symbol and its referent;something extrinsic to both objects (symbol andreferent) is necessary to detennine that one refersto another. This is obvious for linguistic represen-tations, whose form does not bear a visible relationto its referent. Comprehension of pictures oftenfeels so natural and automatic that viewers are notconscious of it, but application of the appropriateinterpretive conventions is necessary to compre-hend visual representations. For example, in orderto understand a watercolor of a landscape, one has

'to ap'ply the appropriate interpretive conventions to,'the colors and shapes in order to comprehend it as arepresentation of a landscape. These are differentconventions from those used to interpret a differentkind of picture, such as a black-aDd-white photo-graph. A gray tone in the watercolor must be inter-preted differently from a gray tone in the photo.All fonns of representation used in a scientific arti-cle share this most general feature of symbols: Theyrequire application of the appropriate interpretiveconventions in order to know what the symbolrefers to. The interpretive conventions govern rela-tions between symbol and referent for particularsystems of symbols, so that although it is temptingto try to analyze pictures by focusing on individualspecimens, the full understanding (as with linguisticrepresentations) requires knowing the systems ofwhich they are components.

The content of visual representations is not en-tirely conventional in the above sense; relationsbetween the visible form of visual symbols andtheir referents are also involved in detennining thecontent of pictures. There is a fundamental differ-ence between textual and visual symbol systems.Visual systems are based on a spatial fonnat: Visu-al representations are symbols in which some spa-tial relations are interpreted to mean somethingabout the referent. In some visual symbol systems,spatial features of the symbol refer to spatial fea-tures. For example, spatial relations among circlesin a ball-and-stick diagram of a molecule refer tospatial relations among the atoms in the molecule.In other visual systems, however, spatial features ofsymbols refer to nonspatial features of the objectrepresented. A spatial feature of a time line-length-represents a temporal feature: duration. '

Graphs are visual symbols in which spatial featuresrepresent relations among properties, like the

relation between gas volume and pressure. Othervisible features such as color may also contribute tothe meaning of visual representations. However,the referential role of spatial relations is the funda-mental feature of visual representations.

F or this reason, the visible fOl'1HS of visual repre-sentations are related to their referents. This rela-tion varies among visual symbol systems, but eachsystem is characterized by a relation between sym-bol form and content that holds for that system,and this relation is the basis for interpreting, andthus comprehending, the symbol as such. This rela-tion holds between the interpreted visible featuresof the symbol, on the one hand, and the propertiesand relations represented, on the other (not be-t ween all features of the symbol and all those ofits subject).

In contrast to the spatial format of visual rep-resentations, linguistic representations have a se-quential format; the sequence of letters and spacesa lone is suffident to determine the meaning of text.Serial symbol systems typically comprise symbolswhose spatial fonn is arbitrary with respect to theirmeaning. Though some serial systems, such aswritten Chinese, include pictographic characters,this is not necessary for serial representation, andthe relationship between symbol form and referentin the pictographic characters serves a mnemonicpurpose, but is not systematic (not all Chinese char-ul.:ters are pictographic). Chinese is a serial systembcea use the meanings of statements are determinedby the ordering of characters, rather than by spatialrelations among them. For serial systems like alpha-betical and numerical symbol systems, the shapes ofletters are entirely unrelated to the referents of the\-\"Drels and sentences they compose. Relative spatialposition of serial characters can contribute tomeaning-poets might vary between-word spacingfor emotiona] effects-but it is not necessary; thesequence of characters is sufficient 'to detennine.symbol meaning.

Types of Visas) Symbo)s

This difference in format does not account forimportant differences among visual representations,so it cannot explain why scientists use differentkinds of visual representations. Further analysis ofthe properties of visual symbol systems allows forca tegorizing two different kinds of visual represen-tation and explaining what makes them differ fromeach other, as well as identifying an importantf(;alure that one of these visual types, but not theother, shares with serial representations. Diagram

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VISUAL REPRESENTATION,

systems, such as those of electrical circuitry andchemical structures, look different from visual rep-resentations that appear much more like pictures,such as electron micrographs and satellite photos.This is because the former symbol systems sharesome features with Jinguistic representations-inaddition to having the spatial fornlat shared by anvisual representations.

Some symbol systems consist only of markingsthat can each be identified as instances of a par-ticular character-unless they are simply illegible(Goodman [1976] calls these syntactically articulatesystems). Text, numerical formulas, and wiringdiagrams have this type of syntax. It anows forcompositionality: All these systems consist of un-ambiguously recognizable atomic characters (e.g.,numerals, letters, Chinese characters) combined inrule-governed ways. In a visual symbol system withthis kind of syntax, some spatial relations amongthe atomic characters will also be interpreted torefer to some relation among the referents of theatomic character. The meaning of a molecular dia-gram is a function of the reference of the atomiccharacters and how they are arranged (see Figure 1).These are compositional symbol systems, like writ-ten languages and numerical systems, all of whosesymbols consist of atomic characters that arealways identifiable as particular characters. Theirmeanings are a function of the identity and compo-sition of atomic characters, whether the composi-tion is sequential (for serially formatted systems) or

0 0 QII II IIc -"- p -0 - P -':"'0 -P -:""c °-

I I I0- 0- 0-

ATP

Fig. 1. Diagram of adenosine triphosphate (ATP). In thisdiagram, lines and letters serve as atomic characters thatrefer to bonds and different kinds of atoms, respectively.Spatial relations among those atomic characters are alsointerpreted: for example, contiguity of a P, a single line,followed by an 0, to refer to the bond between aphosphorous and an oxygen atom. In this way, the atomiccharacters and spatial relations among them are used torepresent the structure of the molecule.

865

VISUAL REPRESENTATION

Fig. 1. Electron micrograph of inner mitochondrial membranes. The image is produced by aprocess in which a very thin sample is prepared with a stain that does not mix well withbiological material. and also repels electrons. A beam of electrons is aimed at the sample, andelectrons go through the areus where biological material is present but are deflected by thestain. This process produces a pattern of light areas on the image whose shape matches the waythe electrons passed through the sam~le. From Fermindez-Monin 1962.

spatial. Because of this compositionality, which is inpart due to the fact that visible forms of atomiccharacters are arbitrary with respect to their mean-ing, diagrams have some of the convenience andflexibility of textual representations (whose spatialfeatures are entirely arbitrary with respect to mean-ing). These are formats with which it is easy toexpress very abstract or general ideas. For thisreason they are useful for representing mechanisms.

Photographs, natural history drawings, and elec-tron micrographs have some important syntacticand semantic differences (Figure 2 is an exampleof this type of figure). These images are not com-posed of discrete atomic elements. They are char-acters from systems in which any diITerence.--for atleast one interpreted spatial feature of the figure.such as the shape of a curve on a graph-corre-sponds to a difference in the character that figureinstantiates. And every different character has adifferent referent. So two electron micrographswith different two-dimensional arrays of light-to-dark scaling represent different structural features.Because the smallest spatial difference correlateswith a different referent. visual representationsfrom these systems can represent very complexproperties (like the particular shape of a subcellularstructure), and these systems comprise symbols thattogether represent a dense range of these properties.

Another prominent difference among visualrepresentations is their degree of abstraction. It isnot possible to explicate this difference in terms ofdiscrete categories. but studies of the relation be-tween abstractness of symbol form and sym bol con-tent in scientific contexts have presented someinteresting results. Michael Lynch (1988) discusses

866

figures in which an electron micrograph and a sche-matic drawing are paired together, showing thatfigures with different degrees of abstraction canplay different epistemic roles. In these. pairs, themicrographs serve as evidence for the more abstractvisual representation. Lynch describes the visibledifferences between the two and relates those dif-ferences in symbol form to differences in the con-tent each conveys, in order to support his claimthat the inferential move from less to more abstractrepresentatioll b not a matter of mere simplifica-tion of form in terms of a reduction of visualstimuli. The schematic drawings are idealizations.generalizations. or extrapolations from the picturesthat support them. There is a difference in the kindof fact depicted by each of the two representationsin the pair. The picture refers to a particular case..while the schematic drawing expresses a claimthat is general (applying to multiple cases), in addi-tion to being more abstract (leaving out featuresrepresented in the picture).

The use of figures that vary in abstraction alsoraises questions about the relationship betweenabstractness of representation and accuracy. Hall(1996) argues that the degree of naturalism of apictorial style is distinct from its capacity for ac-curate representation. He supports his thesis withcontrasts of realistic pictorial styles that misrepre-sent human anatomy with very schematic dia-grams that convey accurate information. Giventhe role of interpretation in comprehension ofvisual representations. this phenomenon can nowbe explained. Accurate visual representations areinterpreted to represent a state of affairs thatobtains. There is no warrant for assuming that

visual representations are meant to represent allproperties of their subjects; the properties repre-sented, as wen as the visible features of the sym-bol used to convey them, vary among visual symbo]systems. Very schematic figures, then, are not in-accurate just because they do not represent indetail the features of their referents. Thus, under-standing figures as elements of visual symbol sys-tems that vary according to system conventionsclarifies the relation between representational stylesand semantic value. .

Scientific Reasoning and VisualRepresentationsAlo(lel-Based Reasoning

Most contemporary philosophers of science whohave discussed the use of figures focus on the con-tent of the figures, rather than presenting an analy-sis of how that content is conveyed-what the visualformat contrihu1es. Nersessian (1992) and Giere(1996) discuss scientific visual representa lions,and. while these papers also focus on content, theirmodel-based accounts of scientific reasoning offer apromising route to understanding how figuresmight be involved in that reasoning. (see ScientificModels). Nersessian (1992) discusses the develop-men t of the theory of electromagnetism, arguing foran important role for analogical reasoning, whichinvolves a systematic mapping of relations betweena source and a target domain. Nersessian supportsher claim with a discussion of Maxwell's figure,which she describes as "a visual representation ofan analogical model" (Nersessian 1999, italics inoriginaL). Nersessian suggests that anaJogicalthinking involves mental models, which embodythe relations holding among the events and entitiesinvolved in the object of thought (see ScientificMetaphors). The 't:1s-efulness of a visual representa-tion to this kind of analogical reasoning can beexplained by the distinctive feature of visual repre-sentations: their spatial formatting. A visual repre-sentation of a model might be particularly efficientfor mental modeling, since the content is conveyedthrough spatial and other visible relations.

Comprehending the representation requiresmapping the perceived visible features to the ap-propriate relations and properties of the referent.An independent step of generating a mental imageof the model is not required, as it would be if the.model were conveyed through a serial representa-tion. Consider the difference between a linguisticdescription of an analog clock face and a picture ofone. The statement that the big hand is on the eight

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VISUAL REPRESENT A TJONI

and the small hand is just below the ten providesinformation from which it is possible to infer thetime. Most people would comprehend the descrip-tion, then create a mental image of the clock, andfrom that image determine the time. Comprehend- .

ing a picture of a clock seems to eliminate a step bycombining the comprehension of the representationwith the construction of the mental image.

Giere (1996) focuses on external, rather thanmental, models: Scientific theories are abstractobjects that need not have linguistic character.Judgments about models are made by comparingthem with real objects, because a model serves as aprototype to assess similarity to putative instancesof the model. Giere considers diagrams embodi-ments of completely abstract models; he claimsthat, as such, they can serve as prototypes for simi-larity judgments. The ubiquitous nature of resem-blance relations makes it difficult to account forthe particular similarities that are relevant for aparticular judgment. This is another area in whichfurther study of scientific visual representations assuch could have an interesting payoff: understand-ing visual representations as isomorphic symbolsprovides some resources to explain how diagramsmake certain features salient. The isomOJ'phic rda~lion stands between some, but not all, of the visiblefeatures of the figure and its content, as determinedby the interpretive conventions for that symbol.system. So the capacity to understand a figure asa representation explains the capacity to identifythe features by which similarity should be assessed.

Evidential RolesVisual representa lions often appear to be present.

ed as support for scientific claims. Brown (1997)describes severa] diagrams from mathematics andargues that they function as proofs. Folina (1999)respo"nds by pointing out that these diagrams arenot proofs in the sense of deductive demonst-rations, though she concedes that the diagramsmay contribute some other form of ~upport.Some diagram systems have been shown to supportproofs. Hammer (1995) presents analyses ofseveral logical diagram systems (Venll, Euler, andPeirce), including soundness and completenessproofs. However, the~e demonstrations do notshed light on how an individual visual diagramcould function as a proof.

Giere (1996) presents examples of figures fromresearch in geology, in which the patterns of twodifferent types of data are placed in visible corre-spondence with one another, in accordance withthe model in question. However, while in this case

,

~

867

VISUAL REPRESENT AnON

the form of the figures is recognized as important toconfinnation, the relation between form and con-tent that distinguishes visual representations is notdiscussed.

Wimsatt (1991) provides examples of figuresfrom various disciplines that facilitate inferences,including cases in which the use of multiple kindsof figures are involved. Wimsatt does not give anexplicit account of how figures support inferences,but the paper emphasizes the usefulness of visualrepresentations in handling data that vary alongmore than one dimension. The analysis of visualrepresentations can clarify how figures do this:For making inferences from a single figure, thetwo-dimensional ronnat is an advantage, because'the dimensions can be used to express relations that'hold among the data. For example, by plotting.experimental results on a graph, in which the posi-tion of each data point is detennined by its value oneach of the axes, relations among the data can bedetermined very efficiently. Thus graphs provide away to represent the data themselves, by usingspatial location along the axes to refer to values.In addition, graphs facilitate inferences of higher-order properties, because the spatial relations amongthe plotted points are meaningful: They are inter~preted according to the conventions governing theinterpretation of location with respect to the twoaxes. So spatial relations among the plotted pointssupport inferences about relations among theproperties represented by individual data points.

In addition to being spatially formatted, andthus representing relations among parts of theirreferents, some figures provide evidence for a hy-pothesis because the figure is causally related towhat it represents. An electron micrograph, forexample, is made by beaming electrons through avery thin biological sample stained with materialthat does not mix with biological material and thatdeflects electrons. The electrons can go through theslide only in areas without stain, so the array ofdetected electrons reflects the array of unstainedarea on the slide, thereby producing the light areasof the image. The process of producing the micro-graph correlates the form of the image (light versusdark areas) with the shape of the sample. The mi-crograph thus represents the structure of the sam~pie. Note that this does not guarantee that thesample has the structure the micrograph represents:The procedure might produce such an image, dueto problems in staining or machine malfunction.Accuracy is not guaranteed. .

But if researchers think their procedure is reli-able, they will take the micrograph as an accuraterepresentation of the sample structure. One could

868

draw the same structure, but the fact that the fonnof this visual representation is causally relatedto the sample that the figure represents is an im-portant source of the epistemic warrant of the mi-crograph. Pictorial representations generated byimaging techniques gain this status because of thecausal relation between symbol and object. For thisreason pictorial representations can playa role very.similar to evidence claims: Their epistemic warrantderives primarily from causal interactions betweenthe object studied and a detector, rather than byinference from other representations. This is simi-lar to perceptually grounded linguistic observationstatements. The veracity and the evidential rele-vance of such figures depend on the procedure bywhich they are produced. In order for a figure tos~rve as evidence, scientists need some assuran~ethat the technique that produced the image gener-ates accurate representations of the subject matter.This assurance can come in the form of under-standing appropriate causal connections betweenthe technique and the representations it generates,or through experience of the reliability of a meth-od. The critical difference between a figure like amicrograph and a linguistically expressed observa-tion claim is that the form of the figure is causallyrelated to its content.

The micrograph also exemplifies another way inwhich the kind of visual symbol involved makes animportant contribution to science. Imaging tech-niques produce visual symbols with distinctive,"pictorial" representational features describedabove. The characters are not composed of unam-biguously identifiable atomic characters, and thesesystems have the capacity to represent a dense setof referents, due to the precise correlation betweensymbol form and referent.

This system-level feature grounds another im-portant advantage of visual representations: Manyimaging techniques provide an experimental meth-od that results in a comprehensible representationof a state of affairs, even if the precise vocabularyneeded to describe that state of affairs throughlinguistic representations does not yet exist. Theircontent is a function of the visible form of thesymbol and does not depend on a vocabulary ofarbitrarily associated symbols and meanings. So aperson who knows how to interpret such a symbolcan do so even if it represents a novel phenomenon.For example, a person who knows how to interpretmicrographs like Figure 2, in which the light areasrepresent biological material, 'can comprehend amicrograph from the same system even if it has ashape the viewer has never seen or heard of before.That means that the person can comprehend the

i

micrograph, as a representation of the form ofthe sample structure, even if it represents a struc-ture that was completely unknown prior to theproduction of the micrograph. This is quite differ-ent from alphabetical systems; because the connec-tion between symboJ form and referent is arbitrary,one cannot comprehend an unfamiliar word simplyby looking at it. Pictorial symbol systems offeran important advantage in science, allowing newlydiscovered and extremely complex phenomena tobe represented and fully comprehended. Once arepresentation of the phenomenon is in hand, it ispossible to assign a linguistic name to it, but havinga hypothesis about this structure is not a prerequi-site. Imaging techniques provide tools to compre-hensibly represent phenomena that do not yet havea linguistic laber.

Finally, the capacity of visual representation tosupport scientific know1edge requires that suchrepresentation be usable objectively. Like linguisticrepresentations, pictures can be used for both rhe~torical and nonrhetorical purposes. The capacityof figures to represent phenomena gives them thepotential to contribute objective support for a sci-entific hypothesis. Identifying how to use visualrepresentations objectively is not a trivial matter,and scientists have expressed active concern in thisarea. A historical study by. Daston and GaIison(1992) shows that chokes "about what images topublish can be influenced by scientists' beliefsabout appropriate ways to avoid subjectivity inscientific communication.

NecessityAre visual representations necessary for contempo-rary science? In some cases, human cognitive limita-tions make the use of visual representationsnecessary for comprehension of the conte.nt the au-thor wishes to convey (Perini 2001). For example,diagrams of macromolecular structures are externalrepresentations whose contents can be expressedthrough seriaHy formatted symbo]s: The coordi-nates for atomic locations can be printed out as alist as weB as used to make a diagram. But, whilehumans readily understand the diagrammatic rep-resentation and can understand the individua] items

. on the serially formatted ]ist of atomic coordinates,

they cannot use that ]ist to generate a mentalrepre-sentation of the structure of the molecule. Compre-hension of the structure requires a representation ofthe spatial re]ations among the parts of the mole-cule, and the computational task involved in calcu-lating those relations from the list of individualatomic coordinates is simply too complicated.

VISUAL REPRESENT AnON

A different set of circumstances that would makevisual representations necessary is if they conveyedcontent that was both essential to science andnot expressible with serial representations suchas linguistic or numerical symbols. There are twodifferent reasons why the content of visual repre-sentations might fail to be expressible with serialrepresentations. First, pictorial content would notbe linguistically expressible if pictures conveyed adifferent kind of content from linguistic representa-tions. However, the analysis in terms of symbolsystem features provides no reason to think thatthere is such a difference. The difference betweenlinguistic and, visual representations concerns fea4tures of the symbol system (of its characters on theone hand ang of the referent set on the other), andnot the nature of the content conveyed. Second,pictorial content would not be linguistically ex-pressible if the amount of content conveyed by thevisual representation could not be symbolized withserial representations. If an infinite set of represen-tations were the only possible linguistic translationof a figure, actual expression with physical symbolswould be impossible. Kitcher and Varzi (2002)argue that a map of Manhattan is worth a nonde-numerable set of linguistic representations. Theyreach this conclusion after claiming, without sup-port, that the real map is not the physical symbol,but an abstract object. This abstract objectamounts to a shape consisting of infinitely manycontiguous line segments, each of which can belinguistically described. The question of necessitydoes not turn on whether the map is really thephysical symbol or an abstract object, so this aspectof their paper can be taken as given. The paperdoes not show that the map is necessary due toamount of content, however, because Kitcher andVarzi's analysis does not provide any reason to-think that the ~ap could not also be .expressed bya finite serial symbol. There is no reason why onecomplicated linear expression describing that shapewould not serve equally well as a translation.

The question of translatability tends to drawphilosophical attention because of the disciplinaryfocus on linguistic representations, but it is impor-tant to bear in mind that the philosophical signifi-cance of visual representations in science does notdepend 011 whether or not they are necessary toconvey the content they do. Diagrams and tablesboth can be easily translated into serially formattedlinguistic or mathematical representations, yet theyare the preferred expression of the data. This sug-gests that the visual fom1at itself contributes toscientific reasoning. Perini (2004) offers a prelimi-nary analysis of the role of two-dimensional

869

VISUAL REPRESENTATION

formatting in the presentation of evidence, and con-cludes that tables-consisting entirely of numericalsymbols, but formatted in two dimensions-serveas evidence in part because that way of presentingthe data facilitates inferences of higher-order rela-tions among the data. Furthermore, while the sameconclusion can be drawn from the data set pre-sented serially, the reasoning involved would bedifferent. Thus those wishing to understand thereasoning actually presented in a scientific paperemploying a table would need to consider the datain their two-dimensional presentation. The previ-ous section showed that imaging techniques likeelectron microscopy have distinctive capacities forevidential support because of the pictorial nature ofthe representations they produce. Even if figuresare fully tran~latable,. they stilI make philosophi-

. cally significant co'ntributions to science as' visual'

representations-and must be understood as suchin order to understand the reasoning contemporaryscientist~ ::Ictually use.

LAURA PERINI

References

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Daston, Lorrait:'le, and Peter Galison (1992), "The Image ofObjectivity," Representations 40: 81-128, .

Fernandez-Monln, Humberto (1962), "Cell-MembraneUltrastructure:: Low-Temperature Electron Microscopyand X-Ray Diffraction Studies of Lipoprotein Compo-nents in Lamellar Systems," CirClflution 26: 1039-1065

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870

Use of Arr in Science. Toronto: University of TorontoPress.

Goodman, Nelson (1976), L"ngllage.~ of Art: All ApproClc"to (J Theory of Symlwls. Indianapolis. IN: Hackett Pub-lishing.

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Hammer, Eric (1995), Logic wid Visual InjOn1lOtioll. Stan-ford, CA: CSLI Publications.

Kitcher, Philip, and Achille Varzi (2000). "Some Picturesare Worth 2NO Sentences," Philosophy 75: 317-381.

Lynch. Michael (1988), "The Externalized Retina: Selectionand Mathematization in the Visual Documentationof Objects in the Life Sciences." Hw1/ull Studies II:201-234.

Nersessian. Nancy (1992), "How Do Scientists Tnink?Capturing' the Dynamics of Conceptual Change inSdcuu:." in Ronald Giere (ed.). Cogllitive Modelsoj Science: Minnesota Studies in the Philosophy of &i.el1l:e, vol. 15. Minneapolis: University of MinnesotaPress.

- (1999), "Model-Based Reasoning in ConceptualChange," in Lorenzo Magnani, Nancy Nersessian,and Paul Thagard (eds.), J~!odef-Based Reasonillg illSci(mfijlc DI:"('O,'eIJ'. New York: Academic/PlenumP"hli.h..ro. H-~-__~-

P~rini. Laura (200 I). '.Explanation in Two Dimensions:Diagrams and BiologiC<11 Explanation," presentation atthe biannual mei'.rin<J nflh.. Tnt..rn"';n,,,,1 fnr ,hI" J..f;~t".."uu --un_non_-. .-- ~.Philosophy and SocTal Science of Biology, Hamden, CT,July 18-22.

- (2004), "Visual Representations and Their Role inConfirmation:' presentation at the unmml meeting ofthe Philosophy of Science Associ<ltion, Austin. TX, No.vember 18-20.

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See a/so Confirmation Theory; Scientific Models