On Alberti's "sign": vision and composition in quattrocento painting - Leon Battista Alberti's commentary 'On Painting'

Jack M. Greenstein

Historians of art have long regarded composition as a major achievement of Renaissance painting. In making this assessment, they are echoing the views of Leon Battista Alberti, whose commentary On Painting offers the first critical appreciation of composition in pictorial art. Written in Latin in 1435, On Painting was translated into Italian in 1436 and reissued in a definitive Latin edition around 1440.(1) Scholars treat Alberti's famous account of one-point perspective construction as the key to, and reason behind, the commentary.(2) But this account is only a small part of a work whose prime purpose is to demonstrate that painting is a liberal art when its practice conforms with three rules (rationes) or underlying logical principles. This paper argues that these rules locate the kind of painting that Alberti admires most within a philosophical tradition according sight a central role in human cognition.

For Alberti, composition is the second and most important rule of art. Composition follows "circumscription," the rule for drawing outlines, and precedes "the reception of light," the rule for applying colored pigment. Circumscription and coloring are common topics in ancient, Byzantine, and medieval art literature; composition is not. Before Alberti, it was seldom (if ever) discussed in connection with painting, and he devotes more attention to it than to any other topic.(3) As his definition makes clear, composition produces the painter's "greatest work":

Composition is the rule of painting by which the parts are brought together to form a pictorial work. The greatest work of painting is not a colossus, but historia. For the praise of ingenuity is greater in historia, than in a colossus. The parts of a historia are bodies, part of the body is a member, part of a member is a surface. Thus the prime parts of the work are surfaces, because from them come members, from the members come the bodies, and from those comes the historia, indeed the ultimate and absolute work of painting.(4)

In Giotto and the Orators, Michael Baxandall shows that the four-level model of artistic organization that Alberti calls composition was familiar to every Renaissance student of rhetoric) Rhetoricians described a period - a sentence consisting of three, four, or more clauses - as an arrangement of words to form phrases, phrases to form clauses, and clauses to form the complete sentence. Baxandall argues that the style of sentences was a matter of controversy in the 1430s for Latin authors of neoclassical training. Humanist teachers like Guarino da Verona (1374-1460) promoted a style of Latin prose that emulated Greek ekphratic literature. They admired the abundance, diversity, and splendor of descriptions that enumerated the vivid details of scenes put before the reader's eyes in loose series of appositive phrases, clauses, and simple sentences. Humanist rhetoricians like George of Trebizond (1396-1486), on the other hand, criticized Latin ekphratic prose as weak and dissolute. They favored the dignity, gravity, decorum, and restraint of a more composed style in which descriptions are organized into lengthy, well-rounded periods with clearly delimited phrases and clauses. Baxandall maintains that Alberti applied George of Trebizond's critical standards for composed and dissolute prose to painting. In his view, Alberti's discussion of composition is predicated on a belief that painting and writing have "cognate styles of organization." Accordingly, he maintains that historians "can make out a polarization of styles common to both painting and writing" when they apply Alberti's categories to early quattrocento art. Baxandall concludes that the rule of composition expresses Alberti's preference for pictorial works in a composed style parallel to that of a Latin periodic sentence.

Nonetheless, identifying particular paintings with which to illustrate Alberti's visual standard for composed and dissolute works is no easy matter. Alberti discusses only two pictorial works that he and his contemporaries might actually have seen. Both works, which unfortunately are now lost, were located in Rome. One is an ancient relief of the Death of Meleager (II. 37), the other, a famous fresco of the Navicella by Giotto (II. 42). Alberti presents them as successful compositions. All other works that he holds up as exemplary, including those praised for composition, were familiar only from ekphrases in classical literature. In fact, Alberti explicitly warns his readers that most of the ancient works that they might see do not provide a trustworthy standard for composition:

As we may easily judge [intelligimus] from the works of former times, this matter probably remained completely unknown to our ancestors, because it is obscure and difficult. For you will scarcely find any historia of antiquity to be aptly composed, not in painting, not in relief, not in sculpture. (I. 21)

Giotto is the only postclassical artist mentioned in the body of the commentary. Although Giotto had been dead for more than a century, readers may well assume that his work provided a standard for the kind of composition that Alberti admired. However, the preface to the Italian edition explicitly links Alberti's commentary with the artistic situation in contemporary Florence. In the preface, Alberti dedicates his commentary to five Florentine artists whose talents, he says, are in no way inferior to those of the most famous artists of antiquity and whose accomplishments convinced him that contemporary practitioners have the ability to discover things about the arts and sciences that even their most illustrious predecessors did not know.(6) Four of the artists to whom the commentary is dedicated were working in Florence while Alberti was writing it: the architect Filippo Brunelleschi and the sculptors Donatello, Lorenzo Ghiberti, and Luca Della Robbia. The only contemporary painter singled out for praise is Masaccio, who died prematurely in 1428 or 1429 without leaving artistic heirs capable of carrying his artistic program forward. Alberti's praise for Masaccio stands in sharp contrast to the negative allusions to contemporary painting scattered throughout the commentary (for example, 1.12; II.39, 46; III.56). In a commentary advocating a new form of artistic practice, the favorable reference to Masaccio in the dedication is sufficient to show that his work exemplifies the kind of contemporary painting that Alberti wished to promote. A1berti may even have written his commentary with the hope of reviving the practice of neo-Giottesque, humanist painting, which Masaccio pioneered and which in 1435 was in danger of passing away with him.

A comparison between the work of Masaccio and that of Gentile da Fabriano illustrates Alberti's visual standard for the polarization of styles in Florentine painting. One standard for humanist artistic patronage in Florence was set by the pioneer Greek humanist Palla Strozzi, when he commissioned Gentile to paint the Adoration of the Magi. Historians (including Baxandall) agree that Alberti's commentary offers an implicit criticism of Gentile's painting. In Gentile's Strozzi Altarpiece [ILLUSTRATION FOR FIGURE 7 OMITTED], a multitude of richly attired figures and an abundant diversity of plants and animals, including birds, dogs, monkeys, dozens of horses, and even a leopard, are rendered with painstaking attention to details of costume, accessory, ornament, material, and texture. Alberti explicitly condemns such characteristic features of Gentile's art as the liberal use of gold (II.46), the tumultuous crowding of figures (II.39), and the too plentiful diversity that results from packing the picture plane with an unbridled mixture of people, goods, animals, and architecture (II.40). Masaccio, on the other hand, rendered the same subject [ILLUSTRATION FOR FIGURE 9 OMITTED], as Cristoforo Landino put it, "simply and without ornament."(7) In his Adoration of the Magi [ILLUSTRATION FOR FIGURE 9 OMITTED], visual attention is concentrated in the restrained and dignified actions and interactions of a small company of characters. Alberti praises such characteristic features of Masaccio's art as the expressive representation of bodily movement (II.36, 41-42), the modest variety in the dress, poses, ages, and features of the figures (II.38-40), and the clear presentation of three-dimensional form through tonal modeling (II.46-47). The result is a coherence of narrative that Gentile's deliberately casual composition eschews.

Some might object that these differences in handling are due to differences in the scale, format, scope, and social function of the two paintings. Gentile's painting is the main scene of an altarpiece for the sacristy of S. Trinita, Florence. Measuring 173 by 223 centimeters, it joins four episodes of the Magi story into a single scene spread over three panels. Masaccio's painting is a predella from a (disassembled) altarpiece for the Chapel of St. Julian in the Chiesa del Carmine, Pisa. Measuring 21 by 60 centimeters, it shows only the culminating episode of the story in which the Magi offer their gifts to Christ. Although both are devotional narratives painted on panels for important subsidiary altars in urban churches, these factors surely conditioned the way that the two artists handled the subject.

Yet the internal organization of painting is more important to Alberti than these other factors. Before Alberti, art was most often discussed in terms of its format and function. Manuals written by craftsmen focused on the materials, media, and shop techniques of artists. Tracts written by theologians focused on the religious content, appropriate placement, and devotional significance of images. By contrast, Alberti is most concerned with the pictorial aspects of painting. A signal characteristic of his commentary is that the rules of art apply equally to works of different scale, format, medium, subject, and use. For this reason, a comparison between Gentile's altarpiece and Masaccio's predella may serve to illustrate Alberti's visual standard for composed and dissolute painting.

In Giotto and the Orators, Baxandall argues that Alberti's standard for composition is narrowly stylistic. He claims that parallels between Alberti's discussion of pictorial composition and contemporary discussions of rhetoric are evidence of a historical analogy between style in humanist Latin prose and style in Albertian painting. This article argues that pictorial composition is about something far more important, pervasive, and profound than style as it is understood by Baxandall. It places Alberti's rule of composition in the context of late medieval and early Renaissance theories on the role of vision in providing knowledge of the material world. These theories explain that the visual properties by which things are known are diverse and that different properties are perceived and understood in different ways. Accordingly, they describe vision as a series of cognitive processes involving both sense and intellect. Composition is one process by which sense and intellect comprehend the visual properties of things. A lengthy comparison near the end of this article shows that Gentile's and Masaccio's Adoration of the Magi emphasize different kinds of visual properties. Masaccio's painting is well composed by Alberti's standards, because it gives greatest prominence to visual properties comprehended by cognitive composition. Conversely, since different properties are comprehended by vision through different cognitive processes, the internal organization of visible qualities in painting structures the way in which paintings are perceived and understood. By expressing a preference for composed works, therefore, Alberti also expresses a preference for paintings that advance the use of cognitive composition in perception and thought. The emphasis on cognitive composition in visual experience gives Albertian painting a distinctive social function.

Whatever the cogency of Baxandall's textual argument, it is difficult to see how composition as a four-level structure of organization applies to the kinds of stylistic distinctions that he attempts to draw. Baxandall explains that Alberti's rule of composition calls for a "total interdependence of forms" in which "planes go to make up members, members go to make up bodies, and bodies go to make up the coherent scene of narrative painting."(8) Gentile's painting may be described as "dissolute" because it is packed with a splendid diversity of things, rendered in vivid detail. Yet his figures have bodies made up of members and surfaces. Masaccio's narrative historia may be described as "composed" because it is more concentrated, restrained, and dramatic than Gentile's theatrical display. But what has this to do with using surfaces to compose members, and members to compose bodies? If the overall formal coherence of pictorial narrative was his primary concern, Alberti could have found a more direct way to say it.

Medieval literature contains many terms for describing the overall coherence of works of art. As Meyer Schapiro demonstrates, churchmen often praised the beauty resulting from proportio (proportion), formositas (shapeliness), dispositio (arrangement), integritas (totality), and symmetria (symmetry) in painting, sculpture, and architecture. Likewise, D. W. Robertson, Jr., shows that literary critics were much concerned with ordine (order), dispositio, symmetria, numerus (number), and convenientia (agreement).(9) Alberti passed over these terms in favor of compositio, a term that emphasizes not only the unity of the whole but also the nature and variety of the parts.

Alberti's rule of composition places surfaces at the confluence of two key aspects of painting. Surfaces are at once the "prime parts" of the pictorial work and the smallest visible components of the depicted bodies (II.35). These two aspects of the surfaces have a well-established pedigree within Aristotelian philosophy. A passage from Aristotle's On Interpretation (16a4-b25), a required text for a bachelor's degree in fifteenth-century universities, discusses what a "prime part" is in an expressive system.(10) Aristotle explains that words are the prime parts of speech, because they fulfill the function of speech, which is to direct the mind to concepts, while their component parts - that is, syllables - do not. Conversely, two passages from Metaphysics (1041b9-33 and 1043b4-6), a more advanced but also widely read text, describe what a component is. According to Aristotle, components are the material parts out of which things are formed. These components are necessary for the thing to exist, but by themselves, detached from the composite whole, the components do not fulfill the function of the thing that they compose. He gives as examples a syllable, a house, and flesh. Syllables are composed of letters; houses, of some building material, such as bricks; and flesh, of the material elements (earth, air, water, and fire). If the letters of a syllable, the bricks of a house, or the elements of flesh are separated from one another, the syllable, the house, or the flesh would cease to exist, but the letters, bricks, and elements would remain. Separated from one another, however, letters alone do not serve as the sounds of speech; bricks alone do not provide shelter; and the elements alone do not constitute the flesh of a human being. Only by virtue of being composed do the components fulfill the function of the whole.

By treating composition as a stylistic principle, Baxandall obscures one of Alberti's most remarkable critical insights. None of the various parties to the quattrocento dispute cited by Baxandall questioned the primacy of words in speech. Alberti's definition of composition gives surfaces the same primacy in painting that words have in speech. This analogy between words and surfaces is, to my knowledge, unprecedented and suggests that surfaces are the prime parts of painting for the same reason that words are the prime parts of speech. As Aristotle maintains, words are the prime parts of speech because they fulfill the expressive function of speech, while their component parts - the syllables - do not. If the component parts of bodies are the four elements - earth, air, water, and fire - then the component parts of paintings are the materials that make up its pigments, mediums, grounds, and supports. Yet the surfaces of which Alberti speaks are not the material surfaces of the pictorial work of art (nor the material surfaces of real, natural bodies). Rather, as component parts of depicted bodies, these surfaces are already products of the representational process. For only in the context of a representational work do the material components of painting fulfill their expressive function by taking on the visual qualities of depicted bodies, say, by appearing fleshlike. Conversely, it may properly be said that the artist composes members out of surfaces, bodies out of members, and the completed work out of bodies, only if surfaces are thought somehow to provide the fleshlike material for the members, bodies, and historia. Alberti designates depicted surfaces, not pigments, the "prime parts" of painting because depicted surfaces are the smallest units that fulfill the expressive function of painting, which is directing the eyes and minds of viewers to the depicted objects. Alberti's rule of composition, then, invests depicted surfaces with a visual and logical priority within painting. As the prime units of the pictorial work and the smallest components of the depicted bodies, surfaces are where representation begins. By making composition the focus of his art of painting, Alberti draws attention to, and explains the significance of, this defining feature of Renaissance art.

The Parts of Byzantine and Medieval Painting

Alberti's contention that depicted surfaces are the "prime parts" of painting signals a fundamental change in representational art. Byzantine and medieval image theorists treat the depicted persons and things - that is, what Alberti calls bodies - as the prime units of painting. A passage from the fourth-century Greek father Saint Athanasius of Alexandria gives the classic explanation for how images are related to their prototypes. Often repeated by Byzantine iconophiles, such as Saint John of Damascus, it circulated also in medieval Latin translation:

In the image is the appearance [species] and form [forma] of the Emperor, and in the Emperor is that appearance which is in the image. For the likeness [similitudo] of the emperor is not different in the image; so that a person who sees [videat] the image views [inspiciat] the Emperor in it; and again he who sees the Emperor recognizes [intelligat] that it is he who is expressed [sit expressus] in the image. From which moreover the likeness does not differ. . . . For the image is his form and appearance.(11)

Athanasius held that images are connected to their prototypes through a "shape," "form," or "appearance" seen in both. E. H. Gombrich argues that this shape, form, or appearance is a product of artistic practice rather than a naturally occurring visual likeness, but that it nonetheless "somehow partakes of the nature of Platonic truth."(12) Moshe Barasch clarifies the philosophical status of this artistic likeness when he shows that Byzantine theorists associated the pictorial schema that produced it with what they called "circumscription," or the principle of delimiting. Barasch cautiously proposes that circumscription in Byzantine painting is connected to the theological idea that all created things are by nature "circumscribed," that is, limited in time, place, shape, and so forth.(13) If so, Byzantine artistic practice would, at least in theory, rest on a culturally specific approach to understanding the natural world through sight.(14) Even within this theory, however, the shape, form, or appearance linking images and prototypes does not pertain to the material of the icons or the substance of the prototypes; rather, as the iconophile Nicene Council of 787 put it:

No one, of course, has thought to reproduce with colors his divinity, for "No one," it says [John 1:18], "has ever seen God." He is uncircumscribable, invisible, and incomprehensib le, although circumscribable according to his humanity. For we know Christ to be of two natures, that is, a divine and a human one, without division. The one, therefore, which is uncircumscribable and the one which can be circumscribed are seen in the one Christ. The icon resembles the prototype, not with regard to the essence, but only with regard to the name and to the position of the members which can be characterized. . . . An icon lacks not only a soul but also the very substance of the body, I mean flesh, muscles, nerves, bones, and elements, that is, blood, phlegm, fluid, and gall, the blending of which it is impossible for one to see in an icon. If these were seen in the icon, we would call this a "man," and not an "icon of a man."(15)

Byzantine discussions of artistic practice often have the painter begin by circumscribing the namable parts of a figure and proceed by filling in the delineated areas with color.(16) The linear schema describes the overall shape, figure, or appearance of the prototype; the areas of color make the schema more distinct and easily discernible. In mosaic and fresco, the linear schema remains visible as dark and light bands or golden striations [ILLUSTRATION FOR FIGURE 1 OMITTED]. As John Gage emphasizes, the visual effect of Byzantine mural art depends on the fluctuating lighting in churches, the viewer's distance from the images, and the size of the tesserae or color patches on the mural surface.(17) When viewed in situ, Byzantine art often produces what he terms an "optical mixture" whereby light reflected from adjacent but discrete areas of color fuse to form a more or less continuous visual image. In this fused image is a shape, figure, or appearance of the prototype, so that a person who sees the fused image recognizes the prototype in it. Nonetheless, the texture of the picture plane usually remains visible through and within the optical mixture. The tesserae or discrete color patches are often large enough in relation to the delineated features to be visible from a distance; they are often deployed on the picture plane in decorative linear patterns that emphasize the artistic schema; and areas of sharply differentiated colors are often juxtaposed in a way that interrupts the optical mixture. These features combine with the fluctuating illumination of the church interior to draw attention to the physical presence and material character of the artistic schema on the colored mural surface. The shape, figure, or appearance of the prototype seen in the optical mixture is thereby distinguished from the crafted work of art that bears the artistic schema.

In panel painting, color often obscures whatever lines of the artistic schema might actually have been drawn on the picture plane. Yet here, too, the visual schema may be discerned. Even in a deliberately classicizing, preiconoclastic work such as the icon of S. Maria de Urbe, Rome [ILLUSTRATION FOR FIGURE 2 OMITTED], the namable features are clearly outlined, the transitions between light and shade are abrupt, and the face loses flesh color in some areas of full illumination and in most areas of full shadow, even though the latter are gray, not black.(18) As in mural painting, the appearance of the prototype is associated with light reflected from a body rather than with the surfaces of a body seen under light. Within such a conception of art, the smallest units of recognition - comparable to words in speech - are the figures themselves or perhaps their namable parts (the members). Lines and color patches on the picture plane are logically and visually, if not practically, posterior to - or derivative from - an overall schema that makes the depicted persons and things recognizable. The shape, figure, or appearance that the schema produces is the primary unit of recognition. Lines and color patches themselves have little independent representational value and certainly cannot be said to compose the members and bodies in the way that Alberti says that surfaces do.

Medieval Latin handbooks on art also emphasize the schematic aspect of the crafted image. Paul Hills shows that these handbooks treat pictorial modeling as analogous to sculpting the picture plane. Dark lines indicating recession are called incisions, "a term taken over from gem carving or engraving on metal or glass." According to Hills, "the adoption of a term from carving suggests how closely painters conceived of their linear modeling with a dark tone as analogous to gouges in the surface: the modeling furrows on ivories offer a likely prototype."(19) Conversely, the projection at the center of each area is indicated by a white stripe called matizatura, which Hills convincingly interprets as luster rather than highlight, or the lightest tone of local color on an illuminated object. Like luster, Hills explains, white stripes of matizatura

obliterate . . . the local color; they do not blend with it at the edges. Their location does nothing to indicate a consistent direction of light and their dynamic mobility may even seem like a painter's attempt to capture the mobility of lustre - a mobility the painters would have noted on their models, antependia in metalwork and enamel.(20)

Hills's insightful analysis points to a conclusion that he does not sufficiently stress: incisions and luster are qualifies of the crafted picture plane, not of the depicted person or thing. If they serve to model the prototype, it is through reference to a shape, form, or figure that the artist has impressed as if in relief into the painting.

The discussion of dark lines and white stripes in the art manual De diversis artibus, written by a German monk named Theophilus, probably in the early twelfth century, strongly suggests that the shape, form, or figure of Latin medieval art is the same as the linear schema of Byzantine art.(21) Theophilus advises painters to designate (designare) with shadow

the eyebrows and eyes, the nostrils and mouth, the chin, the hollows around the nostrils and the temples, the lines of the forehead and neck, the curves of the face, the beards of young men, the joints [articulos] of the hands and feet, and all the parts which may be distinguished [distinguuntur] in the nude body. . . . [Conversely with luster (prima lumina)] you will illuminate [illuminabis] the eyebrows, the nose in its length and on each side above the openings of the nostrils [nasum in longitudine et super foramina narium ex utraque parte], the fine lines around the eyes, below the temples, above the chin, near the nostrils and on each side of the mouth, the upper forehead, between the wrinkles of the forehead - [but these only] sparingly, the neck in the middle, around the ears, the joints of the hands and the outside of the feet [ac articulos manuum et exterius pedum], and every rotundity in the middle of the hands, feet and arms [et omnem rotunditatem manuum et pedum et brachiorum in medio] .(22)

Like Byzantine iconophiles, Theophilus has the artist circumscribe the

namable parts of the prototype. Dark lines mark with shadow the divisions between these parts; white stripes indicate luster at their projecting centers. No attempt is made to show how the parts flow together on the surface of the represented body. These incisions and projections pertain directly to a linear schema inscribed on the painting and only indirectly, through this schema, to the prototype; they model the schema, not the prototype. Here, too, the primary unit of recognition is the prototype and its namable parts, not its surfaces.

Devotional Vision

The primacy of the prototype is crucial for the devotional function of medieval art. For monks, nuns, and lay religious, prayer is a specialized discipline whose goal is an affective contact with God. Devotion to images is a form of this specialized discipline. The broad acceptance of Byzantine image theory by medieval Latin theologians may, I suggest, be linked to its seeming applicability to a practice of praying with images that was taught in monasteries.(23) In this devotional practice, images function like sacred texts in oral prayer, as gateways to memory. However, whereas prayer concentrates the mind in memory, devotional vision concentrates mind and memory in sight.

Devotional vision was sometimes practiced in conjunction with a two-line poem. Composed by a Benedictine poet in about 1100 for use as an inscription on cult images,(24) this distich circulated widely in manuscripts and on images (many of which are now damaged or lost).(25) It is quoted in about 1287 by William Durandus in support of the official position that images have a commemorative role in worship:

(Neither God nor man is the present image, which you perceive, But God and man is he whom the sacred image figures.)(26)

The diction varies in inscriptions, but if surviving evidence is reliable, the following is its most common form in art:

(Neither God nor man is the present image which you perceive, But God and man is he whom the present image signifies.)(27)

Modern scholars claim that the "Nec Deus" distich is a philosophical poem warning against idolatry.(28) However, this reading slights the second line, which draws attention to the close iconic connection between image and prototype. Rupert of Deutz (1076-1129), for example, cites the second line as a proof that worshipers become like the prototypes signified by the images that they revere.(29) Likewise, the Augustinian canon Gerhoch of Reichersberg (1092/93-1169) uses the distich to explain how one might see God in a painted crucifix:

Understand that neither God nor a hanging man is the image that you perceive, but God and man is he whom the perceived image figures [nec Deus est, nec homo pendens, quam cernis imago, sed Deus est et homo, quem certa figurat imago]. While therefore you perceive [cernis] with your eyes the life-giving image of the poor and destitute man hanging on the cross, understand deep in your heart that you see the Lord face to face, so long as with sound faith you know him to be God whom you perceive [cernis] as man.(30)

That the "Nec Deus" distich urges viewers to regard the image as a sign for the prototype is also evident in inscriptions adapted to particular iconographies. In a twelfth-century ivory relief from Flanders, Christ treads on a pair of beasts as he displays a cross (now broken) and an open book [ILLUSTRATION FOR FIGURE 3 OMITTED].(31) An inscription incorporating the second line of the distich explains the meaning of this "simple image":

(God king and man is he whom the simple image signifies. By whom is thrown down death, shown by the serpent [and] lion.)

The devotional function of the "Nec Deus" distich is confirmed by a retable from the chapel of St. Firmin in St-Denis, Paris [ILLUSTRATION FOR FIGURE 4 OMITTED].(32) An inscription surrounding the enthroned Christ reminds worshipers why they should revere the figure signified by the "sculpted image":

(This is God and man whom the present image signifies, Therefore man will pray to him whom the sculpted image figures.)

These artistic and literary examples suggest that the "Nec Deus" distich is a disciplinary tag - a verbal reminder of inner psychological processes to be performed before sacred images. It might even have served as a text for murmuring, for, as Jean Leclercq and Mary Carruthers show, murmuring necessarily accompanied both prayer and memory work.(33) This ruminative function would explain, at least in part, why Durandus quotes the "Nec Deus" distich in support of an official position drawn nearly verbatim from the Decretum.(34)

The present context permits only a brief description of the psychological processes invoked by the "Nec Deus" distich. Since it goes without saying that everything other than God is not God, the first line is meaningful only in a devotional context, where a connection with God is sought.(35) The distich reminds worshipers how to activate this connection. Its first line calls for perceiving (cernere) the image as a crafted, material object that is not God; its second, for perceiving how the image "signifies" or "figures" God. Byzantine theory and medieval art manuals describe the sign or figure in images as a circumscribed schematic pattern. Devotional vision disciplines worshipers to sort out - the root meaning of cernere - those visible qualities of the image that pertain to this pattern. This sorting out leads to the perception of an abstract shape, form, or appearance that the image as sign has in common with Christ. By focusing on this shape, form, or appearance, devout worshipers attain an affective contact with God. Since this appearance is held by theorists to present the likeness of Christ as seen by the Apostles, images serve a commemorative function in worship, as the church maintains.(36)

In all the versions of the "Nec Deus" distich, the fundamental unit of devotional significance is a sign or figure for Christ, the man who is God. Signification and figuration are closely linked in medieval thought.(37) In the version of the distich cited by Durandus, the image "figures" (figurat) both God and man; in the version most often used as an inscription in art, it "signifies" (signat) him; and in the inscription on the retable from St-Denis, it both "signifies" (signat) and "figures" (figurat) him. This interchangeable use of the words figurat and signat indicates that the unit of the image comparable to the word in speech is Christ, the God-man. It is by virtue of a figure or sign for Christ that the image fulfills its expressive function, which is to lead the worshiper's mind to God. The figure or sign discerned in the image is therefore the fundamental unit of meaning and hence the prime part of medieval painting.

Where Latin thinkers and artists differ from their Byzantine counterparts is in the attention that they give to - and the value that they place on - the object bearing this sign for Christ.(38) Like the Byzantine texts cited above, the "Nec Deus" distich characterizes the relation between image and prototype as likeness within dissimilarity. The decree of the Nicene Council of 787 implies that despite this essential dissimilarity, the likeness conveyed by the pictorial sign is more or less exact and unmediated. By contrast, Western devotional practice emphasizes the worshiper's active role in discerning this likeness. Contemplating the dissimilarity between God and the crafted object is a crucial component of this activity.(39)

Thomas Aquinas on Sense and Cognition

A most telling account of the cognitive processes involved in image worship is found in the work of Saint Thomas Aquinas. In the Middle Ages and the Renaissance, speculation on the human capacity for understanding the world through sense took the form of a vast corpus of direct and indirect commentaries on Aristotle's De anima. As an expert on Aristotle, Aquinas brings his deep knowledge of this tradition to bear on his discussion of devotional art.

Aristotle's philosophy is predicated on the conviction that all knowledge originates in sensory experience. Although the intellect is the seat of knowledge, thinking is not possible without the apprehensions of sense.(40) In Aristotle's theory, sense includes not only the perception of external things but also such internal functions as common sense, estimation, memory, and imagination (phantasia). Medieval commentators attributed these internal functions to distinct faculties termed the "inner senses."(41) For Aristotle, however, they are functions of sense that resemble the functions of intellect and thus serve as a kind of interface between sense and intellect.

Aristotle holds that sensing and thinking are connected and analogous operations of the soul. In books 2 and 3 of De anima, both sense and intellect are described as potentials that are activated and become productive in operation. Sense and intellect are potentials because they are affected, moved, or changed by perception and learning; they are productive because their potentials are realized when they are activated or exercised. The activation of sense is triggered by objects in the environment; for this reason, objects are said to act on sense by affecting it. The intellect, on the other hand, is self-activated. Yet active thinking requires active sensing because sense cognitions serve as objects of thought in much the same way that things in the environment serve as objects of sense.

Since sense and intellect function analogously, one way of distinguishing them is by describing the things that affect them and that they produce. Aristotle maintains that sense is affected by "forms" without matter. In Aristotelian philosophy, form is a technical term for any quality of a real thing that may be comprehended by sense or intellect. Aristotle compares sense perception (aisthesis) to the impression of a signet ring in wax (424a17-22).Just as the wax receives the "sign" of the ring without its matter, so, too, sense receives the "sign" of sensible objects without their matter. When sense is active this sign is somehow equivalent to the object that produces it, so that "sensation is in a way what is sensible" (431b23-24; cf. 425626). Sensation becomes what is sensible through the production of phantasms (phantasmata) by phantasia (cf. 429a1, 42). Martha Nussbaum argues that since "what is sensible" are things heard, felt, smelled, touched, and seen, phantasms are interpretations of perceptions as the "appearances" of things.(42) However, before Wittgenstein, most translators, commentators, and philosophers referred to phantasms as mental "images," even though they are not restricted to visible things.

A central thesis of De anima is that phantasms are necessary for thought. "For the thinking soul," Aristotle explains, "phantasms serve as if they were the contents of perception. . . . That is why the soul never thinks without a phantasm" (431a14-16). Yet phantasms are comprehended differently by sense and intellect. "While the faculty of sensation is dependent upon the body," Aristotle reasons, "thought is separable from it" (429b4-5). Accordingly, while "phantasms are like sensuous contents except in that they contain no matter" (432a9), the objects of intellect are "separated" from their sensuous contents as much as possible (429b21-22). "The faculty of thinking. . ." Aristotle insists, "thinks the forms in the phantasms. . . . Thought is the form of forms, and sense the form of sensible things" (431b2, 432a2). Aristotle cryptically describes the potential of intellect to abstract forms from phantasms as "a virtue for becoming all things" (430a14) and the activity of intellect in thinking these forms as "a virtue for making all things" (430a15). Consequently, he holds that "in every case the mind which is actively thinking is the objects which it thinks" (431b 16-17; cf. 429b20, 431a1).

Aristotle's idea that the thinking mind is the objects thought poses a problem. Since the intellect thinks forms without matter, how can it think bodily things, composed of matter? Saint Augustine solves this problem by proposing that active thinking is an interior vision of things in their true, immaterial reality as divine ideas. Thomas Aquinas, however, rejects the immanent Platonism of Augustine's position. He argues that if knowledge originates in sense, thought has to comprehend not just abstract ideas but also the material qualities of bodily objects.

Thomas Aquinas maintains that the active intellect thinks bodily things in a formal way. His explanation of the formal character of thought depends on his interpretation of the Aristotelian concepts of form, matter, substance, and accident. The treatment of these concepts in this article is necessarily compressed and draws heavily on the incisive analysis of Aquinas's theory of mind by the philosopher Anthony Kenny.(43) As Kenny explains, Aquinas defines 'form' as "that by which, or in virtue of which, a thing is what it is" (id quo aliquid est).(44) In Aristotle's system of categories, a thing is what it is by virtue of the properties that distinguish it from other things. Aquinas follows Aristotle in identifying ten kinds of properties that distinguish one thing from another.(45) These properties include both accidental and substantial forms. Accidental forms are sensible qualities attached to material things that vary without an object losing its identity.(46) In Aristotelian philosophy, the nine kinds of accidental forms are: quantity (which includes shape), feature (or quality proper), possession (or habit), relation, time, place, posture, action, and passion. Substantial form, on the other hand, is the property or properties that determine what a thing is, so that if the substance of an object changes, the object itself ceases to exist. In this theory, 'substance' is a composite of form and matter, and 'matter' is a technical term for that which has the capacity for substantial change. (For example, when cream becomes butter, the substance changes but the matter remains.) Since form determines what an object is, it correlates with species or the classification of things by type; since matter "receives" form, it correlates with genus or the classification of types by kind (see Aquinas, S, 1.50.2.1, ad 1). Although the form of matter might change, matter always exists in some form or another. Aquinas insists that prime or formless matter does not exist. Instead, he holds that the simplest substances into which bodies decompose - that is, the four elements, earth, air, water, and fire - are four genera of minimally formed "preexistent matter" (S, III.75.3; cf. 1.50.2, 66.1-2). Conversely, all forms are the forms of something. Accidental forms are the changeable, sensible properties of individual material things; substantial form is the property or properties by virtue of which a thing exists as what it is. Aquinas agrees with Aristotle that each material thing has its own substantial form (S, I.50.2). Since every parcel of matter is distinct in place, every form-matter composite is different. Accordingly, matter necessarily differentiates the substantial form of material things. Peter, Paul, and John are three men, whose identity is defined by the substantial form of humanity. However, there is no single form of humanity in which they all share. Rather, being three men and not one single man, each has his own individual substantial form of humanity. For Aquinas, therefore, the substantial form of material things is always individuated, never specific.

The intellect becomes like corporeal things by thinking the forms in phantasms of individual substances. Aquinas points out that Aristotle attributes to the intellect two kinds of active thinking with respect to sense: apprehension and judgment.(47) Apprehension abstracts the whatness (quidditas), or "what it is," of individual things from phantasms (S, 1.84.7. res.).(48) Through apprehension, the intellect understands individual things as members of a specific class: for example, when phantasia interprets a perception as the appearance of a woman, intellect apprehends what makes this appearance a woman Because every individual is unique, this apprehension is necessarily vague and general. On deeper consideration, the intellect might further apprehend the whatness of the class to which the individual belongs; for example, it might understand that womanhood is female humanity. Aquinas calls the object of this apprehension a "species," or universal phantasm. Once apprehended, universal phantasms are stored in memory, where they aid in perception and thought. As objects of thought, species are comparable to mathematical forms and nounal meanings (S, 1.85.1, 6). Since individual women exist but "female humanity" does not, species are abstractions, not physical entities. Yet like abstract mathematical forms underlying the magnitudes of existing things, species inhere in substance and cannot be considered without reference to real things. And, like nounal meanings, species are, in Aquinas's view, neither true nor false, only more or less completely understood; for example, all competent speakers understand in a vague and general way that the noun gold means precious yellow metal, but chemists can give a precise and unambiguous definition of gold as a specific element. Since the intellect always apprehends by means of species, it cannot fully comprehend individuated substantial forms by apprehension alone.

Instead, understanding material things in their particularity requires judgment. For Aquinas, judgment is "a certain kind of reflection" through which species are compared with phantasms (S, 1.86.1). Like Aristotle, Aquinas terms this process "composition and division."(49) Unlike apprehension, composition and division are subject to "truth and falsehood . . . just as in the complex utterance which is its expression" (S, 1.85.2. ad 3). "Composition" affirms by bringing together two or more unitary concepts called "indivisibles"; "division" denies by separating indivisibles. Aquinas identifies three types of indivisibles.(50) Two are "whatness" and "species"; the third, "separated substances." Separated substances are accidental properties - such as color, size, texture, and so forth which are known by comparison through sense. For example, redness is a separated substance commonly perceived in apples. It is not possible to define redness except through reference to red things like apples, but just as redness does not figure in the definition of these things, so, too, these things do not define what red is. Following Aristotle, Aquinas characterizes separated substances as "privations" standing "in opposition to corporeal things, whose whatness the intellect receives first and by itself" (S,1.85.8 res.). If species are comparable to mathematical forms, separated substances are comparable to mathematical points. All sensible things, Aquinas explains, have magnitude. Since a point has no magnitude, it is not a sensible thing. But when understood negatively as the smallest possible division between perceived things, a point may be sensed as "a sort of sign of division" between magnitudes.(51) It is the same with color and texture, for black is the privation of white, and smooth the privation of rough. Thus, "separated substances" are sensible forms that are not themselves sensible or intelligible things.

The intellect actively thinks individual things by composition and division. Aquinas explains:

The human intellect must understand by composition and division.... In first apprehension, the human intellect does not immediately attain perfect cognition of a thing; but first it apprehends something of it, namely its whatness [quidditas ipsius], which is the first and proper object of the intellect. And then it understands [intellegit] properties, accidents and conditions [habitudines] circumstantial to the essence of the real thing. Accordingly, it must necessarily compose or divide one apprehension with others; and from one composition or division proceed to others. . . .

The likeness of things is received in intellect according to the mode of the intellect and not of things. . . . For in material things there is a twofold composition. First, indeed, of form with matter, and to this corresponds composition in the intellect by which a universal whole [that is, species] is predicated of its part. . . . The second is composition of accident with subject [that is, substance]; to this composition in reality [reali] corresponds composition in the intellect according to which accident is predicated of subject. . . . Nevertheless composition in intellect differs from composition in reality, because those [things] which are composed in real things are different; in intellect composition is a sign for the identity [compositio est signum identitatis] of those [things] which are composed. . . . According to this rule of identity [identitatis rationem], our intellect composes by predicating one [indivisible] of another. (S, 1.85.5. res., ad 3)

Since the "whatness" of individual objects is imperfectly understood by apprehension, the intellect turns back to inner sense in order to compare species with phantasms. Through this process, the intellect judges which separated substances pertain to an object as an individual and which do not. Judgment is subject to error; circumstantial or accidental qualities might be attributed to substantial form. Nevertheless, the process results in a series of affirmative and negative propositions about the compound nature of real things. On the basis of these judgments, imagination composes a new phantasm (or interpretation of appearances) by joining separated substances to species. This new phantasm is "a sign for the identity" of the real object, because it consists entirely of those perceptions - and according to Aristotle perceptions are "signs"(52) - that the intellect judges to pertain to the object. In this way material things are understood through composition.

Thomas Aquinas on Sacred Images

For Thomas Aquinas, devotion to images leads to apprehension of the prototype. In his commentary on Aristotle's On Interpretation, Aquinas uses the example of a statue to show how judgment requires apprehension.(53) A statue of Hercules, he explains, may be understood both as bronze and as the likeness of a man. The intellect understands the statue as a real thing when it composes and divides these two indivisible characteristics. However, apprehension is needed to understand what bronze is and what a man is. Since the statue is the likeness of a man and the intellect apprehends what a man is, the intellect apprehends what the statue represents.

In the Summa theologiae, Aquinas extends this discussion to devotional art. The context shows that his interest lay in the attention paid to art, not in art itself. Having already established that reverence is due to Christ as both God and man, he continues:

As the Philosopher says [Aristotle, On Memory 450b27], there is a two-fold movement of the mind towards an image: one indeed towards the image itself as a certain thing [res quaedam], another, towards the image in so far as it is the image of something else [imago alterius]. And between these two movements there is this difference, that the former by which one is moved towards an image as a certain thing, is different from the movement towards the [represented] thing, but the latter movement, which is towards the image as an image, is one and the same as that which is towards the [represented] thing. Thus we must say that no reverence is shown to Christ's image as a thing - for instance, carved or painted wood - because reverence is not due save to a rational creature. It follows therefore that reverence should be shown to it only in so far as it is an image [of Christ]. Consequently the same reverence should be shown to Christ's image as to Christ himself. Since, therefore, Christ is adored with the adoration of latria, it follows that his image should be adored with the adoration of latria. (S, III.25.3 res.)

According to his earliest biographer, William of Tocco, one night while Thomas Aquinas was praying in the Chapel of Saint Nicholas in S. Domenico, Naples, a crucifix spoke to him.(54) Whatever its truth, this story accurately expresses the strong presence of God that Aquinas felt before sacred images. For the passage quoted above, which was written in Naples around the time when the miracle of the crucifix reportedly took place, surpasses the arguments of even the most fervent Byzantine iconophiles in defending image worship. Byzantine iconophiles argue that since the likeness between image and prototype is partial, Christ is to be adored with latria, or worship, but images only with dulia, or reverence. Aquinas reasons that since images are adored solely for this likeness, they deserve the latria due to Christ himself.

Aquinas's defense of image worship turns on the meaning of "image" as both a crafted object and the appearance of persons and things. Following Aristotle, he maintains that both aspects attract the attention of beholders. Images as certain things are corporeal objects, which, as the example of the statue confirms, are understood through composition and division as things in themselves. Since composition and division are cognitive processes that involve turning from intellect to corporeal sense, I propose to call the attraction of images as objects their 'embodiment function.'(55)

For Aquinas, however, it is the attraction of images as likenesses of something else that justifies image worship. He describes this attraction as "one and the same" as the attraction of that other thing. If this other thing were a material object, this formulation would contradict the example of the statue, in which the intellect apprehends the thing of which the statue is a likeness. But reference to Aristotle's On Memory (450b20-451a1) shows that there is no contradiction. There Aristotle compares remembrance with contemplating the likeness of a sitter in a portrait. Remembrance occurs when the soul recalls a phantasm produced by a previous perception or thought. Like a portrait, this phantasm is both a thing in itself and an icon of something else. When understood as an icon, it is a likeness of something previously perceived or thought, which derives from a prior cognition of that thing. So, too, when a portrait is contemplated as an icon of a sitter, it is a likeness of a prior cognition (for example, of what the artist saw and thought when painting), even if a viewer has not previously seen the sitter in person.(56) In a commentary, Aquinas seizes on Aristotle's discussion to argue that likenesses in paintings, even those of particular men, are objects of intellect. Like things remembered, sitters in portraits are present to viewers only as phantasms. These phantasms are cognitive likenesses, not objects of outer sense. Accordingly, "when the soul devotes itself to a phantasm insofar as it is phantasm of something else, it considers that thing as an image which we sensed and understood previously, just as is said about the painting. . . . [In both cases, the movement of the soul] is like an act of phantasia or imagination or even of intellect, when considering a universal thing."(57) Thus, like universals and prior cognitions, the likenesses of things represented in images are intelligible to the soul by apprehension.

I propose to call the apprehension of images as likenesses the 'signification function.' According to a famous definition by Saint Augustine, which is quoted by Thomas Aquinas and many other medieval and Renaissance thinkers, a sign is "a thing [or property] proper to appearance [praeter speciem] that causes the senses to fashion something other than itself in cognition."(58) Aquinas's discussion conforms perfectly with this definition. His image is a "certain thing" whose appearance causes the viewer to recognize the likeness of "something other than itself." Even if the prototype is a real thing, it is understood by apprehension, not composition and division, because it is recognized as an appearance of what the thing is rather than as a material object. This appearance makes the crafted image a sign.

Aquinas's defense of image worship accords with the devotional practice urged by the "Nec Deus" distich. For Aquinas, understanding holy images requires both judgment and apprehension, but it is apprehension that justifies image worship. The distich is a complex utterance instructing worshipers to divide and compose in order to apprehend. The first line urges division by denying that the present image is God; the second line urges composition by affirming that the sacred image signifies God. Through composition and division, worshipers fashion a phantasm of the present image. This phantasm consists of signs for the identity of the image as both a crafted material object and a likeness of God. The signs for God in the image cause sense to fashion a likeness of God in cognition. Judgment composes this cognitive likeness on the basis of what the intellect apprehends to be God in the image. In this way, devotional vision disciplines worshipers to perceive God in the image.

The practice of image worship urged by the distich and discussed by Thomas Aquinas inverts, as it were, the cognitive processes by which vision comprehends the natural world. As shown above, Aquinas holds that the human intellect first apprehends the whatness of an object, then distinguishes its nonessential properties, and finally composes and divides these indivisibles. Both the distich and Aquinas's discussion presuppose that viewers already apprehend that the image is an image (its whatness), and in both, this apprehension is followed by composition and division. However, natural vision is directed to judging objects as material things among other material things, but devotional vision is directed toward apprehending an appearance fashioned in cognition as a likeness of what the prototype is known to be. This further apprehension invests devotional vision with its transcendental or super-natural character. It also explains why things and their nameable parts, rather than corporeal surfaces, are the prime units of recognition in devotional art.

Signification and Embodiment in a Devotional Image

A Sienese panel of the Redeemer, which was produced in 1215 as an antependium and later used as an altarpiece [ILLUSTRATION FOR FIGURE 5 OMITTED], provides an example of how the cognitive practices urged by Aquinas and the "Nec Deus" distich correlate with the representational structure of medieval devotional art. The antependium consists of a nearly square central panel flanked by six rectangular panels stacked three on each side. The grid frame is adorned with an asterisk frieze that is punctuated by rosettes at the corners of the lateral rectangular panels. All visible surfaces not given over to figural representation are gilded, except for the decorative vermilion bands that border the various pictorial fields. The seven panels are recessed with respect to the frame, but the ground within the mandorla in the central panel is raised and the sculpted figure of Christ projects from it so that it sticks out beyond the plane defined by the frame. This unusual combination of flat pictorial imagery, painted ornamental borders, pastaglia-work friezes, and painted relief sculpture draws attention to the singular physicality of the altarpiece and so encourages the use of composition and division to understand it.

Through composition and division, the Redeemer is understood as both an object in itself and as a likeness of Christ. The coloring and craftsmanship characterize the antependium as a precious and splendorous material object: precious because it is laboriously crafted out of gold and other expensive pigments; splendorous because it reflects scintillating light, which is termed splendor in late medieval optics. Within the crafted object, the part figuring Christ is given the greatest emphasis: it not only dominates the center, it also projects most strongly. However, the modeling of the figure is not proportional to the three-dimensional form of Christ's body, for the projection of each section is only slightly greater at the center than the edges, and the divisions between the nameable parts (such as the eyes, nose, cheeks, and chin) are marked with the deepest incisions. Instead, the relief works together with the gilded lines and changes in color to mark a linear schema of Christ's circumscribed form. Thus, the modeling does not refer to Christ himself; instead, it serves to embody a crafted sign for him. The embodiment of this sign encourages worshipers to attend to how Christ is signified.

Worshipers activate the signification function by composing and dividing signs for the identity of the crafted image. Some of these signs pertain to the image as a crafted object, others pertain to the image as a likeness of Christ. Hills argues that the scarlet disks and opaque white dots set into the decorative vermilion bands mimic the lustrous splendor of jewels, which were set into the ornamental framework of metalwork antependia and even occasionally into that of painted wooden panels.(59) Opaque white is used with similar optical effect in the narrative scenes, where it renders lustrous the highlights of garments, of buildings, and even of Christ's exposed flesh. Conversely, in the scene at upper left, the highlighted surfaces of the tablecloth are gilded. Thus, the coloring, which characterizes the crafted object as precious and splendorous, also helps produce the pictorial imagery, when this imagery is associated not with the material qualities of the altarpiece but with the splendorous light reflecting from it. By attending to the circumscribed figure of a man in the reflected light, worshipers perceive with their eyes a luminous dematerialized image of what the intellect apprehends to be Christ.

Alberti on the Visible

Alberti's commentary On Painting offers a radical reassessment of the cognitive relation of image and prototype. The opening paragraph leaves little doubt that Alberti was familiar with scholastic theories of cognition (probably from his doctoral studies at the University of Bologna). In university curricula, fields of knowledge based on sense experience, such as optics, music, mechanics, and astronomy, were classified as "middle" or "intermediate sciences" (scientiae mediae) because they applied mathematical analyses to the ever-changing appearances of the material world studied by the natural sciences.(60)

Alberti's opening paragraph claims the same intermediate status for painting (I.1):

so that our oration would be clearer, we will take first from mathematicians [a mathematicis] those things which seem pertinent to the topic. . . . [Then] we will explain the rules of painting from nature herself. . . . [Mathematicians] measure the species and forms of things [species et formas rerum] with mind [ingenium] alone, divorced entirely from matter. But since we wish things to be placed under sight [sub aspectu], in writing we will utilize, as they say, a more fleshy wisdom [pinguiore Minerva]. And we will judge ourselves to have done well, if our readers truly understand us on this difficult subject, which no one else whom I can see has treated in writing. Therefore I ask that our writings be read not as if by a mathematician alone but more as if by a painter.

Alberti's reference to "the species and forms of things . . . divorced entirely from matter" accords with scholastic definitions of intellectual knowledge. The references to nature and mathematicians locate his topic within the intermediate sciences. The word aspectus in the phrase "placed under sight" is a technical term from optics, the most developed intermediate science. Moreover, his ensuing paragraphs on permanent and changeable qualities of surfaces rehearse scholastic definitions of special and common sensibles.(61)

Yet Alberti does not address his commentary only to highly educated readers. Since his audience includes painters, patrons, and, as Baxandall shows, students in humanist schools, he avoids, wherever possible, the technical vocabulary of scholasticism. For this reason, he asks that his commentary be read more as the writings of a painter than of a mathematician and later claims "to speak" as a painter (I.1). This claim leads some modern critics to suppose that On Painting is a straightforward text with no epistemological significance. But this supposition projects into the Renaissance modern romantic ideas about artists (which are difficult to sustain even in a modern context). Renaissance artists did not speak or write in Latin, and in the Italian version Alberti changes "speak" to "write," as if to insure that the commentary not be confused with shop talk. More important, Alberti's commentary transformed the way that artists themselves wrote about art. The writings of earlier artists, like Theophilus and Cennino d'Andrea Cennini, focus on craft techniques; the writings of later artists, like Ghiberti, Piero della Francesca, and Leonardo da Vinci, address the specialized epistemological issues that Alberti raises. If Alberti wrote as a painter, it was as a Renaissance humanist artist-educator whose introductory teaching is informed by advanced knowledge.

Alberti's teaching begins with a series of definitions, which are interrupted by one of the boldest assertions in the history of art (1.2):

At the outset it is necessary to know that a point is a sign, which, as one might say, cannot be divided into parts. In this place I call a sign anything that is in a surface so that it can be beheld by the eye [possit oculo conspici]. No one would deny that nothing pertains to the painter that is not truly received by visual contemplation [intuitum, literally, intuition]. For the painter studies to represent only that which is seen by light [sub luce videantur]. Points joined together continuously in a row constitute a line. So for us a line will be a sign whose length can be divided into parts but it will be so slender in width that it cannot be split. . . . If many lines are joined together like threads in a cloth, they will make a surface. A surface is the outer part of a body, which is recognized not by depth, but by width and length and in like manner by its qualities.

In the ensuing paragraphs, Alberti distinguishes between permanent and changeable qualities of surfaces. The permanent qualities are outline and curvature. These qualities are "permanent," he explains, because they cannot be changed without altering the surface itself: if they are changed, the surface "loses its original name and form [faciem], and what before might have been perhaps called a triangle will now be known [nuncupabitur] as a quadrangle or afterward as multiangled figure [that is, a polygon]" (I.3). As the geometric analogy makes clear, the permanent qualities define the intelligible character of the surfaces. The changeable qualifies are apparent extent (including size and shape) and apparent color (including the degree of brightness). Alberti calls the latter quality the" reception of light." These qualities are "changeable" because they vary without the surface itself being altered. In particular, they vary with the distance and position of the viewer and the direction and conditions of light. Alberti's changeable qualities, therefore, do not make manifest changes in the bodies themselves. For this reason, they differ from "accidents," which for Alberti and most scholastics are changeable properties of objects themselves.(62) Considered in relation to these initial definitions, Alberti's famous description of perspectival construction takes on a new significance: it provides proof that painting can make known the permanent qualities of depicted surfaces even though the visual rays convey to the viewer only the changeable ones.(63)

These initial definitions seem so clear and self-evident that the sentences equating the visible with signs (which they purport to explain) have for the most part escaped critical attention.(64) But I have long been troubled by them. Presented as a consensus view, Alberti's statement that the painter is concerned only with "what is seen by light" marks a fundamental departure from previous opinions. Just three decades earlier, for example, the Tuscan painter Cennino Cennini described painting as "an art for which it is necessary to have fantasia and skill of hand in order to find things not seen, seeking them under the shadow of natural objects . . . thereby showing that which is not as if it were" (emphasis added).(65) Alberti's treatment of the sign, point, line, and surface is hardly less puzzling. Why would he give simple definitions of these Euclidian elements but not define such complex, specialized, and important concepts as historia, ingegno, invention, and function (officio)? Why does he equate the visible with signs, and why define points and lines as certain kinds of signs? Signs for what?

The answers to these questions emerge from a consideration of medieval literature on optics - or perspectiva, as it is called in Latin. Scholars have long acknowledged the importance of this literature for Alberti's discussion of vision. However, most treatments have centered on how optics contributed to his explanation of constructed perspective. Little attention has been given to the broader epistemological issues raised by Alberti's adoption of optics as a model for the cognitive processes involved in painting.(66)

But as Graziella Federici-Vescovini, A. I. Sabra, David Summers, and Katherine H. Tachau emphasize, medieval and Early Renaissance optical science presents vision not simply as a form of perception but as a paradigm for cognitive knowledge of the material world.(67) Because vision is a cognitive process involving inner sense and intellect, optics links sight with semantics, semiotics, and theories of the soul. It makes use of such fundamental Aristotelian concepts as form, substance, accident, quality, individual, universal, species, and whatness. More important, it explains how the intellect might comprehend material things fully as individual objects, instead of merely approximating them to abstract species. For this reason, it provides late medieval and Early Renaissance thinkers, especially those with nominalist leanings, with an alternative to scholastic models of cognition.

In optics, the contribution of Arab thinkers, especially Abu Ali al-Hasan ibn-al-Haytham (ca. 965-ca. 1039), known as Alhazen, is crucial. From the thirteenth century on, Latin translations of Alhazen's major optical treatise circulated under the title Perspectiva or De aspectibus. This treatise influenced every major European writer on optics from Roger Bacon (ca. 1214-1294),John Pecham (d. 1292), and Witelo (13th century) to Johannes Kepler (1561-1630).(68) Moreover, an Italian translation by Guerruccio di Cione Federighi circulated in quattrocento Florence, where it was read by Ghiberti and other artists.(69) Indeed, all the major points of Alhazen's theory discussed here are summarized in book 3 of Ghiberti's Commentarii.(70)

As a student of optics, Alberti was keenly attuned to the epistemological significance of vision. His definition of points and lines as signs, his description of the visual pyramid, his rules for the art of painting - including composition - and his suggestions for applying these rules to practice condense and conflate epistemological arguments commonly advanced in optical literature. Because of Alhazen's seminal importance, the following discussion focuses on him. However, most of the ideas were common currency among thirteenth-century perspectivists, who along with Alhazen served as sources for Alberti, Ghiberti, Leonardo da Vinci, and other fifteenth-century students of optics.

Points and Lines

Since vision takes place along straight lines, ancient, medieval, and Renaissance optics proposes geometric models for how lines of sight convey the forms of objects to sense and intellect. These lines of sight are called visual rays - species or radii - and theorists debate whether they issue from the eye or from the objects seen. Realists treat the forms conveyed by the rays as real properties of the things seen. Nominalist thinkers, however, question the epistemological status of the rays and of the forms.(71) They point out that real objects exist in three dimensions, but in mathematics, points, lines, planes, circles, spheres, and so forth are purely conceptual entities that lose their defining geometric character when given physical embodiment. Accordingly, they argue that when medieval perspectivists speak of points, lines, planes, and so forth, they are discussing fictional qualities constructed by the mind and not the properties of real things.

An anonymous commentary on Euclid's Optics written in Florence at the end of the fourteenth century shows what is at stake. Originally, this treatise contained chapters on points, lines, angles, surfaces, and bodies, but the last two are missing.(72) The chapter on points opens with three definitions: (1) in geometry the point is the end of a line; (2) in physics it is an object seen at a very great distance; (3) in optics it is the end of a visual ray, such as falls in the eye. (Alberti utilizes all three definitions.)(73) It then considers whether the point terminating a line (definition 1) or falling at the end of a visual ray (definition 3) can be seen. Citing Euclid's theorem that everything visible is seen under a visual angle - that is, forms the base of a triangle whose apex is in the eye - the author concludes that these points cannot be seen. Likewise, lines cannot be seen "under visual angles" because they have no width.(74) Nonetheless, it is possible to distinguish lines in visible things through geometric laws and optical experience.

Biagio Pelacani da Parma (d. 1416) takes this argument a step further. Robert Klein accords Pelacani, whose works were read by Leonardo da Vinci, a central place in shaping and transmitting the ideas on which pictorial perspective rests.(75) Although Pelacani spent most of his career at universities in northern Italy, he taught at the Studio Fiorentino, the public university of Florence, in 1388.(76) Moreover, a manuscript copy of the definitive version of his Questions on Perspective (written about 1390, revised and expanded in 1403) was produced in Florence in 1428.(77)

Pelacani draws on but modifies a definition of the visible developed by Alhazen. Euclid defines the visible as a lighted, colored, opaque body seen under a visual angle. However, as Sabra explains, Alhazen treats vision in terms of "punctiform elements" rather than angles.(78) Since Aristotle establishes that immediate corporeal vision comprehends only color and light (De anima, 418a26 - 419a24), Alhazen describes visible bodies as aggregates of illuminated points radiating colored light in all directions.(79) This analysis leads him to define the visible as a lighted, colored opaque body of moderate size placed before the eye at moderate distance, and this definition is adopted by Pecham and Bacon.(80)

Alhazen's punctiform analysis poses a problem. If every point radiates light and color in all directions, rays from different points can reach the eye at the same place. How then does visual sense sort out which ray corresponds to which point? For students of optics the physiology of the eye provides the answer to this question(81) [ILLUSTRATION FOR FIGURE 6 OMITTED]. Alhazen holds that the sensitive part of the eye is "a small, delicate, white and humid" lentil-shaped globe mounted within the uveal sphere at the end of the optic nerve directly opposite the pupil. This small globe is filled with two gelatinous liquids of differing density, which are separated by a very thin, frail membrane (indicated in Fig. 6 by a dashed arc): at the front is the "crystalline humor," which resembles ice in its transparency; behind it is the denser but clearer "vitreous humor." Sight occurs when rays pass through the crystalline and vitreous humors to the optic nerve, which transmits sensations to the brain. Rays entering the cornea obliquely are refracted to the periphery as they pass from one humor to another; this refraction weakens them so that they make little if any impression on the optic nerve. Rays perpendicular to the anterior surface of the crystalline humor (which is concentric with the cornea) pass unrefracted to the vitreous humor, which refracts them toward the back of the eye where the optic nerve is most sensitive. Although they do not actually converge in the eye, these perpendicular rays form a "visual cone" or "round pyramid" whose apex is at the center of the eye and whose base is at the object seen. The clearest impression is made by the incident ray at the center of this pyramid, because it passes unrefracted through the crystalline and vitreous humors to the center of the optic nerve. This sorting out of rays into a visual pyramid preserves the "structure" and "order" of visual form.(82)

Nonetheless, perception by a single pyramid is imperfect. Although the centric ray gives a clear perception of apparent color and indicates the direction of the gaze, the other rays, being refracted, give only an uncertain sense of apparent size, shape, and extent. Only by sweeping the centric ray over the surfaces of perceived objects does the viewer obtain a secure knowledge of visual form. This secure knowledge is then certified by judgment - a faculty that is like reason but that belongs to inner sense, not to intellect.

Pelacani seizes on this description to argue that in visual perception color is always united with shape.(83) He contests the distinction drawn by medieval perspectivists between perception by the eye, or naked sense, and comprehension by inner sense. The faculty of vision, he insists, resides not in the eye but in the "common sense," which not only receives visual impressions but also assembles and judges them. Since the visible is a lighted, colored magnitude, shape and size are comprehended at the same time as color and light. Points, lines, and so forth are imaginary constructions used for judging shape and size. They are not physical entities; yet, as "instruments of vision," they are visible properties comprehended by sense.(84)

Alberti's description of the visual pyramid presupposes Pelacani's revision of medieval optics. Like Alhazen and his followers, Alberti analyzes the visible object into "punctiform elements." Vision, he explains, is accomplished by a pyramid of visual rays connecting every point of a visible surface with the eye. Each pyramid contains three kinds of rays: extrinsic rays fall at the edges of the surface; median rays fill the pyramid; and the centric ray strikes the surface perpendicularly (I.5-8). Each kind of ray has a different function: the centric ray determines the viewer's distance from the visible surface; the median rays convey its apparent color and light; and the extrinsic rays measure its apparent size. Thus, like Pelacani, Alberti regards the perception of shape and apparent size as united with that of color and light.

Alberti also follows Pelacani in describing optical points and lines as instruments of vision. He explains how vision measures a surface (I.6):

Quantities are measured by the extrinsic rays. For quantity is a space between two separated points on the edge [fimbria] running around the surface, which the eye measures by these extrinsic rays almost as if with that instrument called a compass [for drawing circles]. There are as many quantities in a surface as there are separated points on the edge corresponding to one another [sese correspicientia]; for we use these many extrinsic rays whenever we recognize in aspect [aspectu recognoscimus] the height from top to bottom, the width from left to right, the depth from near to far, or any other dimensions. This is why it is usually said that vision occurs by means of a triangle whose base is the quantity seen and whose sides are those same rays which are stretched to the eye from [extreme] points of that quantity.

Thus, for Alberti as for Pelacani, points and lines are instruments of visual sense.

One aspect of Alberti's discussion seems to have provoked particularly harsh criticism. After citing Euclid's rule that apparent size is measured by the angle of vision, Alberti offers an alternative explanation, which casts Pelacani's definition of the visible into terms that his less advanced readers might more easily comprehend (I.7): "I usually expound this rule among my friends: the more rays are employed in seeing, the greater the prospective quantity is estimated to be; and the fewer [rays] the less." Apparently, this "rule" was criticized by mathematicians, for Alberti felt it necessary to defend it in a Latin tract of one paragraph entitled On Points and Lines for Painters (ca. 1450-55):

Here among painters points and lines are not what they are among mathematicians, where infinite points fall in a line. From our definition, a point is a sign [signum], because the painter senses [sensiat] it as something median [medium quoddam] between the mathematical point and a quantity which falls under number, such as atoms perhaps are. And when the painter takes from nature, which is imitated, first lines and angles and then lights and colors of surfaces, [he takes] whatever of it falls under number and consists of the divisible parts not in the thing made but in nature. Moreover, who said that there are as many rays of light in a line of one foot as in a line of two feet? In short, because of this, possibly existing things, not infinite ones, are to be posited by reasoning about possible works [sunt . . . possibilia fieri . . . infinita not sunt ex rationibus possibilium operum]. May this small thing be enough to have responded to my detractors.(85)

Alberti's response rehearses the status of painting as intermediate between mathematics and natural philosophy. Intermediate sciences use geometric demonstrations to explain the changing world of sense. In mathematics, the elements of geometry are abstract intelligibles, which by definition cannot be embodied in sense or imagination. However, because objects of perception are finite and material, the intermediate sciences construct their models out of finite units, which are thought to exist, rather than out of purely abstract intelligible units, which cannot exist. Aristotle credits to Democritus the theory that all corporeal things are composed of possibly existing, finite, indivisible units of matter termed atoms.(86) Atoms also figure prominently in an early theory of vision, advanced by Democritus, which was known to Alhazen and Thomas Aquinas and taken up by Henry of Langenstein and others.(87) This theory explains vision as a "reflection" in the eye, brought about by atoms or "material likenesses" imprinting themselves in sense like a seal in wax.(88) (Alberti alludes to this theory when he suggests that "images are figured in the surface of the eye, as in an animate mirror" [I.6].) Because they are material, these atoms inhere as discrete parts of corporeal bodies; yet, because they are too small to be perceived or measured, they are discovered only through reasoning. Conversely, in Metaphysics (1016b25-29), Aristotle argues that mathematical points are indivisible quantities that have position.(89) The points with which painters are concerned, Alberti argues, are halfway between the immaterial, indivisible, positioned points of mathematics and the discrete, indivisible packets of matter called atoms in natural science. Like points in Aquinas's discussion of "separated substances," they are sensed as the smallest possible division between perceived things, even if they cannot be perceived by themselves.

Samuel Edgerton, Jr., offers Alberti's brief tract On Points and Lines for Painters as justification for translating signum in the commentary On Painting as" 'figure' or 'mark' - in other words, something tangible, like a dot on a piece of paper."(90) This translation is doubly misleading. First, it suggests that "signs" are made by artists. In both works, however, Alberti's discussion of points and signs centers on the perception of real bodies, not depicted ones. Points are signs, Alberti says, because they are sensed. Indeed, if a sign is "anything that is in a surface so that it can be beheld by the eye" (I.2), all visible things present to visual sense a myriad of signs, only some of which are points. Associating signum with painters' marks inverts this relationship. Second, a "dot on a piece of paper" is discrete, divisible, perceptible, and potentially measurable. In his Elements of Painting, Alberti claims that a point "which they make during the work of painting [opus pingendi] . . . is an inscription so tiny like atoms that nothing smaller can be made by hand."(91) Strictly speaking, even the smallest inscription made by hand is a surface, not a point. However "tiny like atoms" an inscription may be, as long as it remains visible on the surface of the painting as a tangible mark made by hand, it "falls under number" to a greater degree than atoms, which, though discrete, are too small to be perceived by corporeal sense .(92) In the tract On Points and Lines for Painters, Alberti describes the point-as-sign as something halfway between a fully abstract mathematical point and a discrete but indivisible quantity such as atoms might be. Even the smallest inscription made by a painter is too large, too divisible, and too material to fall halfway between atoms and mathematical points. Thus, the description of the point-assign in the tract On Points and Lines for Painters provides compelling evidence that insofar as the definition of sign in the commentary On Painting explicitly includes points, the signum cannot be "something tangible, like a dot on a piece of paper."

Nonetheless, Alberti's discussion suggests that points may be sensed as signs in paintings as well as in natural bodies. Alberti does not claim that the smallest inscription made by a painter is as small as atoms. Rather, he explains that it is "so tiny like atoms" inasmuch as "nothing smaller can be made by hand." This explanation adapts to the practice of painting a definition of atoms put forth in natural philosophy. As noted above, in philosophy atoms are the smallest possible units that may be thought to exist in nature. In Alberti's formulation, points made by painters are the smallest inscriptions that are thought possible in painting. When an inscription made by hand is beheld by the eye as "something tangible" on the material surface of the painting, it is sensed as a delimited surface with measurable extent, not as a point. An inscription is a sign sensed as a point only when it is beheld as the smallest possible unit inhering in a surface. Beholding the smallest units that are thought possible requires the application of intellect to sense. Without this application of intellect, there are no points in painting. For Alberti, then, optical points are signs, not dots, because points are signs and signs are points only in consciousness, where sense and intellect meet.

Alberti's discussion of how the three rules of painting should be applied in practice clarifies the visual status of points and lines. With regard to circumscription or "marking the edges" (notitia fimbriarum), he warns the painter to use "lines as tenuous as possible and nearly fleeing from sight [visum]. . . . For . . . if it is done with clearly visible lines, they will appear not as the margins [margines] of surfaces in the painting, but as some little cracks [rimulae aliquae]" in it (II.31). Alberti's discussion makes it clear that all lines drawn on the surface of a painting are beheld as inhering in some surface. Drawn lines beheld as tangible marks inhering in the surface of the painting appear as cracks, or gaps of measurable width, in the surface of the painting itself, because they are seen as dark areas, not as edges. Drawn lines beheld as the smallest inscriptions that are thought possible in painting appear as edges, or linear divisions inhering in the surfaces of the depicted bodies, because they are sensed as signs "whose length can be divided into parts but [are] so slender in width that [they] cannot be split" (I.2). Next, when applying the rule of composition to practice, a painter uses lines for "designating these conjunctions of surfaces in their places" (II.30). It will be shown below that the surfaces being discussed here are also those of the depicted bodies. Drawn lines designate the surfaces of the depicted bodies in their places only when they are beheld as edges or arrises of the depicted surfaces and not as marks on the picture plane. Then, according to the rule of reception of light, the painter "fill[s] the places described with colors" (I.12; cf. II.30). Transitions between planes are to be gradual so that "color on contiguous parts dissolves like smoke" (II.46-47). Thus, in the finished painting all drawn lines are covered with pigment; they are sensed not as marks but as signs that make visible the form underlying the colored surfaces of depicted things.

Optical Signs

In order to understand Alberti's equation of optical points and lines with "signs," it is necessary to look in greater detail at Alhazen's theory of vision. The aspects of this theory previously summarized constitute only the start of a three-stage process that results in secure and full visual comprehension of individual objects.(93) In Alhazen's Optics, the interconnections are as important as demarcations between these stages, which are performed continuously, so that visual sensation from the first stage provides what is certified at the second and discriminated at the third. The three stages are clearly distinguished, and the connections and demarcations between them are well understood by Roger Bacon and other medieval Latin perspectivists who take up Alhazen's theory. The first stage, described above, is "pure sensation," or the perception of apparent color and light.(94) In Latin translations, this kind of vision is termed "superficial comprehension" (comprehensione superficialis) or vision "under aspects" (de aspectibus) and is associated with sight by means of a single visual pyramid.(95) Since only the centric ray passes unrefracted into the eye, vision under aspects is imperfect; viewers may be certain that a colored, illuminated body lies before them in a certain direction but do not clearly apprehend its shape, size, distance, or other properties.

Alhazen's second stage involves the use of the mind's estimative powers and imagination - what others call "common sense"(96) - to ascertain visual form. By sweeping the centric ray over an object, the eye sends to the mind a series of verified or veridical impressions. These impressions are then certified by estimation and assembled by imagination into an image of the object as a whole.(97) In Latin, the sweeping of the visual ray is termed "intuiting" (intueor), the estimation and assembly of the impressions "certification," and this stage of the visual process "intuition" (intuitio) or "intuitive cognition." The resulting "certified" image comprehends all twenty-two "special sensibles" by which things are known to sight.(98) These visual sensibles include not only light and color, which are perceived by pure sensation, but also distance, position, solidity, figure (including contour and three-dimensional form), size, motion, texture, shadow, beauty, and similarity and dissimilarity. The special sensibles of Alhazen are equivalent to the "separated substances" of the scholastics, as Thomas Aquinas recognizes.(99) Both are visual properties known through sense by comparison. In material objects, these separated substances are always mixed; accordingly, the visual sensibles or "intentions" by which they are comprehended are "composed" in a certified image.(100)

Alhazen insists that intuition provides secure knowledge of individuals and species.(101) Certified images, he explains, are fixed in memory in proportion to the frequency that they are ascertained. Since intuition comprehends similarity and dissimilarity as well as the special sensibles, features common to several certified images are fixed most strongly. In this way, memory becomes a storehouse not only for individual likenesses but also for "universal forms" produced by the accretion of certified images. Unlike Aquinas's species, which are abstracted from sense perceptions, Alhazen's universal forms are conglomerates of visual properties usually found in members of a species. As such, they include what Aquinas terms accidents and "separated substances" as well as whatever - if anything - is visible of substantial form. (For example, the universal form of milk is white for Alhazen, not for Aquinas.) Intuition recognizes individuals through the similarity of new certified images to memory images of individuals, and it recognizes species through the similarity of new certified images to memory images of universal forms. Thus, Alhazen's intuitive vision comprehends the whatness of objects in both their individual and their specific identity. For this reason, Bacon calls it "comprehension through knowledge,"(102) and such fourteenth-century philosophers as William of Ockham define "intuitive cognition" as the immediate and full intellectual knowledge of individual things.(103)

Alhazen's final stage of vision involves the use of memory and reason by the "discriminative faculty" (virtus distinctiva del cogitiva). Intuitive vision comprehends the true forms of a visible object, certifies that it exists, and recognizes what it is. Now, by contemplating the object at length, the viewer sorts out the visual qualities that pertain to its substantial nature.(104) Since appearances change as light and position change, discriminating the visual properties of individual objects takes time. Discriminative vision uses reason to make distinctions between appearances of the same thing at different times. In this way, each of the special sensibles of an object is discerned and judged. For example, the virtus distinctiva discerns proper local color by comparing different shades of green on the same object and then makes inferences about the object on the basis of the green color proper to it. Through such discriminations, the viewer comprehends how an object moves, whether it is beautiful or ugly, and so forth. As Sabra explains, "according to this manner of speaking visual perception is perception of 'forms' understood as 'composed of' a multitude of particular visual properties possessed by material objects, and perception of the compound form is considered to take place in advance of perceiving the constituent properties in the form."(105) Or as Alhazen puts it: "sight perceives every one of the particular properties [intentiones] in conjunction with the others; then by distinguishing the properties in the form, it perceives them separately."(106) Alhazen regards discrimination as a kind of inference, which resembles the "composition and ordering of a proposition" but differs from verbal syllogizing in the ordering of its parts. Whereas verbal syllogizing proceeds from a universal premise, to a particular premise, and then to a conclusion, discrimination comprehends the conclusion at the same time as the universal premise, because sight comprehends the particular directly. In addition, the universal premises of discrimination are often "primary notions" such as "a whole is greater than a part," which the intellect comprehends immediately without having to deliberate about them.(107) For this reason, Bacon terms this stage of vision "syllogistic comprehension," attributes it to the "cogitative faculty," and argues that the inference involved is analogous to, but not the same as the process of rational inference in logic.(108)

Signs enter optical theory in relation to visual recognition. Alhazen's treatment of signs is scattered throughout books 1 and 2 of the Optics.(109) No definition is given, but signs are always associated with recognition by memory or "prior cognition" (cognitio antecedens or praecedens).(110) Prior cognition takes two forms. The first involves recognition of objects; the second, recognition of visual properties.

A sign by which an object is recognized is a distinctive feature or property that serves as an index or clue to its identity. When perceiving an object, viewers scan their memory for images of something similar. If the object itself was previously seen or is similar to something previously seen, it is recognized at a glance without a certified image. Alhazen explains:

Now recognition may be of an individual object or a species. Recognition of an individual object occurs as a result of likening the form of the visible object which the sight perceives at the time of recognition to the form it has formerly perceived of it. Recognition of a species occurs as a result of likening the form of the visible object to that of similar individuals of the same species which the sight has formerly perceived. . . . [This] recognition does not occur as a result of inspecting all the properties in the form [that is, by certified vision], but rather through signs. For when sight perceives one of the properties in the form [of the visible object], while remembering the first form [that is, the previously seen object], it recognizes the form. But that is not so with all that is perceived by inference [that is, by discriminative vision], for many such things are perceived only after inspecting all or many of the properties of the individual object. . . . (111)

Alhazen likens the recognition of objects by signs to the reading of a script by a literate person. Literate readers recognize familiar words at a glance, without having to discern each and every letter. But unfamiliar words are recognized only by inspecting each letter in order to discern their sound and meaning.(112) According to Alhazen, visual recognition by signs might proceed from part to whole, from one individual to another, from types to individuals, from individuals to types, and so forth.(113) However, since appearances are always changing and nothing appears in precisely the same way at two different times, intuitive and discriminative vision are still necessary for full visual comprehension of an object.(114) Thus, recognition of objects by signs precedes intuitive vision. It abstracts some features (the signs) and yields an immediate (but vague) comprehension of what a thing is. Accordingly, Alhazen's recognition of objects by signs is analogous to Thomas Aquinas's "simple apprehension of whatness."

Recognition of properties by signs, on the other hand, serves intuitive vision. In an important passage, Alhazen explains how visual properties are recognized by signs:

Now recognition [cognitio] is not pure sensation [solo sensu]. For the sense of sight perceives the forms [intentiones] of visible objects from forms [that is, primary sensibles(115)] that come to it from the colors and lights of those objects. And its perception of lights qua lights and of colors qua colors is by pure sensation. But those properties in the form, which, or the like of which, it has previously perceived and which, or the like of which, it remembers having perceived, are at once perceived by recognition from signs in the form [of visible objects].(116)

Sabra shows that the properties of things recognized by signs include all the special sensibles comprehended by intuition.(117) In this case, recognition by signs assists intuition just as - to return to an earlier analogy - knowledge of the alphabet aids the letter-by-letter recognition of unfamiliar words.

Since memory is built up from childhood, most adult perception takes place by means of signs. Indeed, Sabra argues that for Alhazen the primary sensibles are not pure sensations but the qualities or properties of things:

what Ibn al-Haytham [Alhazen] seems to mean by "perception by pure sensation" is perception of either of these qualities [that is, apparent color and light] as a quality of some object. It is identical neither with the impression produced in the eye nor with awareness of such an impression.(118)

According to Alhazen, recognition of properties by signs is more or less immediate and almost always accompanies intuitive and discriminative vision.(119) For this reason, the visible consists not of apparent color and light as such, but of the visible qualities (or sensible forms) by which the properties of things are understood.(120) Thus, the signs used in intuitive and discriminative vision are analogous to Thomas Aquinas's "indivisibles" because both function as "signs for the identity of those [properties] which compose real things" (S,I.85.5 ad 3).

Latin thinkers understood this difficult concept implicitly, for they termed the visual forms that convey the sensible properties of things "intentions."(121) They used this term not because these forms are products of will but because they "intend to" or "lead the mind to think" the visual properties of objects. As Roger Bacon explains, a species (or visual ray) "is called an intention in the common usage of naturalists, on account of the weakness of its being in comparison to the thing, for they say that it is not truly the thing but rather the intent of the thing, that is, its similitude."(122)

In book 4 of the Opus Majus, which is devoted to mathematics, Bacon makes the association of the visible with signs explicit. Previously, he argued that the species "produces every action in the world, for it acts on sense, on intellect, and on all matter of the world for the generation of things."(123) Then, in a section entitled "On Signs," he explains how species act on intellect.(124) Species are "natural signs" of objects.(125) Unlike words, which are "imposed" by common consent and therefore are arbitrary and conventional, natural signs are "ordered by the soul towards signification. They are called natural, moreover, because they signify [signi rationem recipiunt] by their essence and not by the intention of the soul."(126) Since words signify by the intention of the soul, they refer directly to concepts, and through concepts to things; conversely, since natural signs signify by their essence, they refer directly to things, and indirectly to concepts.(127)

Albertian Vision

Book 2 of Alberti's commentary condenses Alhazen's optics into three rules for pictorial practice.(128) Alberti's rules emphasize the importance of delimiting the parts before adding the colors. Because works painted in fresco and tempera have to be brought to completion section by section, historians of art connect these rules with quattrocento studio practice.(129) But Alberti insists that they derive from the way that people see (II.30):

We divide painting into three parts and these divisions we have from nature herself. For inasmuch as the painter studies to represent things seen, we note in what way things themselves come under aspect [sub aspectu veniat]. First, when we look at [aspicimus] something, we see [videmus] it to be something that occupies a place. The painter indeed circumscribes the space of this place, and he will aptly name this rule of drawing the edges [ducendae fimbriae] circumscription. Next, intuiting [intuentes] we come to recognize [dignoscimus] how the many forward-facing surfaces fit together on the body [plurimae prospecti corpotis superficies inter se conveniant]; and designating [designans] these conjunctions [coniunctiones] of the surfaces in their places, the artist will rightly name [this rule] composition. Finally, looking with greater discrimination we discern [aspicientes distinctius . . . discernimus] the colors of the surfaces; in painting the representation of this thing, which receives all differentiation [differentia] from light, will appropriately be called by us reception of light.(130)

This account of vision employs a model familiar from Alhazen. Alberti's viewer first sees under aspects [aspicimus]; then recognizes by intuition [intuentes . . . dignoscimus]; and finally discerns with greater discrimination [aspicientes distinctius . . . discernimus].

Alberti's description of vision adapts Alhazen's optics to the conditions of painting. For Alhazen, seeing under aspects yields a clear perception of apparent color and direction, but only an uncertain comprehension of extent. For Alberti, it yields a comprehension of place and thus extent, but not color. This modification follows from Alberti's conviction (based on Pelacani's argument) that the visual pyramid includes extrinsic rays that measure the surface "as if with that instrument called a compass." Inasmuch as seeing under aspects comprehends relative direction, the viewer sees the extent as "something that occupies a place." Alberti's decision to link color perception with discriminative vision will be discussed below.

Alberti's treatment of intuition follows from his account of seeing under aspects. In Alhazen, intuitive vision ascertains visual form by sweeping the centric ray over the many surfaces of an object. The resulting certified image comprehends, albeit in composite form, all twenty-two sensible properties by which objects are known by sight. At the outset, Alberti associates composition with recognizing how surfaces fit together on a body. Since this recognition enables painters to designate the edges and arrises of surfaces, it certifies, so to speak, their circumscribable form. However, intuitive vision, he explains (II.35, 36, 38, and elsewhere), involves far more than this. Proper composition takes account of place, size, function, appearance (species), color, motion, beauty, grace, and "other things," including light and shade and roughness and smoothness. Alberti does not mention sweeping the centric ray. Yet this action might be implicit in his description, for he uses the word "intuiting" as a gerund to describe the optical activity that results in recognizing how the surfaces fit together.

More telling is the association of perspective construction with composition. In book 1, Alberti explains that a single visual pyramid is composed of as many small pyramids as there are surfaces being seen (I.12):

I have explained how, in seeing [visendo], a pyramid is built of triangles. We have proven how extremely important it is that the distance and position of the centric ray and the reception of light should be fixed [certam]. But we intuit [intueamur] not one, but many surfaces with one aspect, and as we have already written in some detail about single surfaces, we must investigate how surfaces joined together [coniunctae] present themselves. As we have taught, all single surfaces enjoy their own pyramid which carries their colors and light. Since bodies are covered with surfaces, all forward-facing [prospectae] quantities of bodies carry a single pyramid weighed down by as many small pyramids as there are surfaces comprehended by that prospect [eo prospectu] .

Alberti identifies two types of surfaces (I.13-17).(131) Surfaces parallel to the picture plane are "equidistant quantities"; they retain their characteristic shape and proportions when circumscribed in painting. Surfaces oblique to the picture plane are "nonequidistant quantifies"; they lose their characteristic shape and proportions when circumscribed, and the more extreme the angles of the extrinsic rays the greater the changes in their appearance. Perspective construction assembles the many small visual pyramids of intuition into a single large visual pyramid in which both types of surfaces stand in relation to the same centric ray.

Organizing the small pyramids into a single large pyramid guarantees that all the surfaces will be recognizable (I.17-21). Alberti argues that if the world were shrunk to half its size, nature would appear the same, because all things are recognized by "what philosophers call accidents" (I.18), which are known by comparison. Artificial perspective preserves the comparability necessary for recognition by fixing the extent of equidistant and nonequidistant surfaces "in a certain ratio" to the centric ray of the large pyramid and hence to one another. In book 2 (31-33), Alberti explains how to project the ground plans of rectangular and circular buildings onto a perspectival grid. He recommends that portrait painters use a perspectival veil to establish the "site [situs] of the outlines and boundaries of the surfaces" of the eyes, nose, mouth, chin, forehead, temples, and so forth. Among the "many advantages" of this method, "the first [is] that it always refers to certain immobile surfaces, so that you can return to the apex of the [visual] pyramid by means of the position of those boundaries."

Inasmuch as perspective construction involves drawing outlines, it pertains to circumscription as well as composition, especially since circumscription fixes the "space of this place." But Alberti realized that place or space as such is less important for painting than is insuring the comparability of visible properties.(132) (Place is one of these visible properties, but place understood as the location of an object, not as an abstract site within a continuous void.)(133) Since intuition ascertains these visual properties, Alberti associates perspective construction more with composition than with circumscription. He explains: "this rule of dividing up the pavement pertains especially [maxime] to that part of painting, which, when we come to it, we shall call composition" (I.21).(134)

The idea that intuition applies to vision from a single viewpoint distinguishes Alberti from Alhazen. Since Alhazen is concerned with vision in its everyday context, he allows that viewers move during certification. Alberti, however, restricts painting to only those "many surfaces comprehended by [a single] prospect" because the walls and panels on which painters work are single surfaces (I.12). Much has been written about the single viewpoint in Renaissance painting. What is important (and new) here is that Alberti regards the prospect from a single viewpoint as a composite of certified images. Among the many factors behind this insight, probably the most significant is Brunelleschi's first perspective demonstration panel. As is well known, Brunelleschi's first perspective demonstration featured a careful rendering of the Florentine Baptistery, which was viewed reflected in a mirror by looking from behind the panel through a small hole piercing the painted building at a point corresponding to the position of the painter standing before the actual building. Kemp argues that the thickness of the panel and the small size of the hole so severely restricted the field of view that the entire baptistery could not have been seen in a single glance.(135) He concludes that it was necessary to maneuver the eye while looking through the hole. If so, Brunelleschi's demonstration showed the importance of intuition - or changing the direction of the gaze - while looking from a single viewpoint.

Alberti's description of the visual pyramid as a composite of many small pyramids clarifies why he calls the rule of painting derived from intuition "composition."(136) In the Posterior Analytics (71a1-72a23), Aristotle explains that cognitive "units" of the arts and sciences are significant and believable things: things are significant when intellect apprehends what they are; things are believable when it is possible to affirm that they exist. By these criteria, the certified images of Alhazen cannot be broken down into smaller cognitive units by intuition alone. For Alhazen's certified image is an aggregate of clearly discerned points of colored light, and these points of light are not themselves existing things. Although the certified image comprehends all twenty-two visual sensibles, these sensibles are intermixed at each point and cannot be discerned separately without discrimination. Through discrimination the points and the sensibles are sorted out, the one by privation, the other by comparison. In this discriminated form, points and sensibles are possibly existing objects of thought. For this reason, Alhazen compares discrimination, not intuition, with composition. Alberti, on the other hand, accepts Pelacani's argument that the fundamental units of vision are colored magnitudes, each of which contains all the different kinds of visual qualities. Although the various sensibles are everywhere intermixed, they belong to different magnitudes. If intuition recognizes how surfaces fit together, it also necessarily apprehends the colored magnitudes as distinct surfaces (their whatness), which can be affirmed to exist. For Alberti, then, intuitive vision is compositional because it comprehends objects as aggregates of cognitive traits.

Alberti's association of intuition with composition brings Alhazen's optics into conformity with medieval Aristotelian thought. Thomas Aquinas maintains that even though Aristotle called the operation of intellect twofold, his works actually describe three distinct operations.(137) In addition to apprehension and judgment by composition and division, there is the reasoning by which intellect proceeds from things known to the investigation of things unknown. And just as apprehension is necessary for composition, so, too, composition is necessary for reasoning. According to Aquinas, Aristotle treats reasoning in the three books of the Organon devoted to syllogizing. When Alhazen compares discrimination with composition, he follows Aristotle in treating composition as a form of syllogizing. But Aquinas argues that syllogizing is reasoning, not judgment by composition and division. Thus, when Alberti links composition with intuition, he associates the presyllogizing form of cognition described by Aquinas with the presyllogizing form of vision described by Alhazen.

Alberti's rule for the reception of light closely follows Alhazen's understanding of discriminative vision. For Alhazen, discriminative vision involves sorting out and judging which visual qualities actually belong to an object. Alberti likewise links the reception of light with the "differentiation" of things. In book 1 (7-11), he explains that conditions of viewing affect apparent color and light: a man walking in a sunlit meadow is tinged with green, and the air weakens the apparent hue of distant objects. However, his rules for the reception of light exclude such local and transient effects (II.46-49).(138) Instead, Alberti promotes a theory of color based on a correspondence between hue and matter.(139) This theory holds that, in Alberti's terminology, all "species" of colors derive from "four true kinds [genera]" of color, which correspond to the four material elements out of which all bodies are composed. This terminology rehearses a fundamental Aristotelian argument that the four elements constitute the genera of matter.(140) Accordingly, Alberti maintains that the admixture of pigments in local color can be made to match the composition of elements in bodies.(141) Conversely, variations in the incidence of light, by which three-dimensional form is seen, should be rendered only by the gradual and sparing addition of white and black, since white and black are not "true," elemental colors and hence do not change the "kind" (genus) or elemental mixture of the hue (I.10; II.46). For Alberti, then, hue is directed to expressing material substance as local color, and tone to expressing form through illumination. This clear separation of hue and tone, local color and illumination, makes it easy for the viewer to discriminate how matter and form contribute to the properties of things "seen under light."

Alberti's association of color with discriminative vision rather than seeing under aspects follows directly from his equation of the visible in painting with signs. For Alhazen and Bacon, signs are visible qualities that promote recognition of objects or their properties. Recognition of objects by signs results in immediate identification without intuition; recognition of properties by signs serves intuition, which builds up knowledge of things by certifying the forms (or, more properly, intentions) of their surfaces. In Albertian painting, proper composition insures that all the surfaces and members of a body "should agree in species" (specie omnia conveniant; II.37). As previously shown, both Alhazen and Aquinas maintain that the "species" of things seen are stored in memory as universal forms or phantasms, where they constitute a person's knowledge of what makes things what they are. Alhazen further explains that these universal forms are conglomerates of visible qualities, built up through repeated acts of observation. Alberti recommends that painters study the appearances of bodies in nature and fix the things that they have learned deeply in memory (II.36). In this way, he explains, they understand how to accommodate members to one another in size, function, and appearance. These repeated acts of observation build up a memory of universal forms and thereby constitute the painter's knowledge of what makes things what they are. Accordingly, when the surfaces and members are properly composed, the species of the depicted things are immediately recognizable by prior cognition.

Yet because painters are concerned only with what "is received by visual contemplation [intuitium]," Alberti discusses only signs for visual properties.(142) He reduces this concept of the sign to a simple, clear formula. "In this place," he writes, "I call a sign anything that is in a surface so that it can be beheld by the eye" (I.2). For Alberti, any visual quality that makes a surface recognizable as "the outer part of a body . . . not by depth, but by width and length and in like manner by its qualities" (I.2) is a sign.(143)

Although his definition of a sign as anything beheld "in a surface" might seem to apply to marks, figures, or brushwork on the picture plane, Alberti never refers to the pictorial works or their material elements as signs. Instead, in a famous passage comparing painting to an intersection or transparent plane, he calls on painters to subordinate the visual qualities of the crafted object - what Aquinas calls the "certain thing" - to the visual properties of the depicted bodies. He writes (I.12):

When they [painters] go around a surface with lines and then fill the described places with colors, nothing is to be sought more than that on this one surface are represented many forms of surfaces, and not otherwise than if this surface, which they work on with colors, were wholly transparent and so glasslike [admodum vitrea et perlucida huiusmodi] that the entire visual pyramid passed through it. . . .

Historians of art routinely cite this passage as evidence that Alberti conceives of painting as a window. But some clarification is necessary.(144) Alberti draws the analogy with a window not in this passage but in the course of describing a perspective diagram. His demonstration of "how the intersection [of the visual pyramid] is expressed by the art of painting" begins with a drawn rectangle, which "is to me like an open window from which the historia is contemplated [contueatur]" (I.19). Since Renaissance open windows do not have glass or transparent screens to look through, this simile does little to explain the qualifies of finished paintings as crafted objects. Instead, it prepares readers to see the transversals and orthogonals subsequently drawn within the rectangle as features of a depicted horizontal surface rather than marks on a sheet of paper. That is why Alberti refers to the demonstration as "this rule for dividing up all pavement."

Like the analogy of the window, Alberti's description of the intersection as "transparent" and "glasslike" emphasizes that the visual qualities of painting should belong primarily to the depicted surfaces rather than to the artwork as crafted object. These qualities are signs to the extent that they make the surfaces of depicted bodies recognizable. Thus, signs figure in Alberti's theory of representation not because a painting is a sign but because surfaces are perceived by means of them. Conversely, surfaces, not signs, are the prime parts of painting because visual qualities are signs only in relation to the depicted things that they make recognizable.

As components of represented bodies, depicted surfaces also make known the bodies underlying them. Alberti recommends that painters study anatomy to learn how the proportions of surfaces reveal the body underneath (II.36). He concedes that some might object to this advice, because

I said above that nothing pertains to the painter of visible things which is not seen [earum rerum spectare quae non videantur]. They would be right, except that just as in dressing [a figure] it is necessary first to draw the nude underneath [nudum subsignare], so in painting a nude you should first dispose the bones and muscles, which you cover with moderate flesh and skin so that the places where muscles are may be understood without difficulty. Since nature herself exhibits all these measures unfolded in everyday life [explicatas in medium], the studious painter discovers [inveniet] great utility in recognizing them. . . .

Because the movements of bodies are exhibited in everyday life, muscular action can be recognized from bodily surfaces by prior knowledge. For this reason, painters should commit to memory the "forms" and "differentiations" of all the members of the body (III.55).(145)

Recognition of muscular action is crucial to Alberti's understanding of the expressive power of painting. In a famous passage, he observes that the corpse in an ancient Death of Meleager seems truly dead because all limbs hang flaccidly and without motion (II.37). Accordingly, if every member is given a slight articulation so that it seems self-supporting, depicted bodies seem to live and move. Since these motions are innate to human bodies, viewers understand what they express about the motions of the soul through a corporeal empathy linking creatures of like nature (II.41). Thus, for Alberti, as for Alhazen and Bacon, the visible world is composed of qualities familiar from experience, which serve as signs by which things and their properties are recognized. But whereas Alhazen and Bacon emphasize the recognition of persons and objects as a whole, Alberti focuses attention on recognition of their component parts. What is most relevant to painters are signs for depicted surfaces, because these make visible the motions of body and soul, through which human nature is understood.(146)

Elsewhere I have shown that Albertian composition invests painting with the same multilevel significance that medieval and Renaissance theologians attribute to written historia.(147) Painting has the literal significance of historia when it presents "something done and seen" to corporeal sense; it has the moral significance when it moves the soul (that is, inner sense), because, as Augustine shows, all emotions reveal moral habits when considered as ethical responses to a person or event; and it has the allegorical significance when it is the invention of a timeless, intellectual truth. Each level of significance results from cognitive composition. Understanding the literal significance requires bringing together "everything they [the depicted bodies] carry out among themselves and with respect to the spectator [so that it] corresponds to performing and teaching the historia" (II.42); understanding the moral significance requires affirming or denying the various emotions as good or evil responses to the central action; understanding the allegorical significance requires comprehending the intellectual "force" of "beautifully setting up the composition of historia" (III.53). This intellectual force is the artistic "invention," and, as the word invention implies, it is "discovered" in the visible world through cognitive composition rather than abstracted from it by apprehension.

Alberti's conception of the visible in painting stands in marked contrast to earlier art theory. In Byzantine and medieval art theory, the primary units of recognition are prototypes and their namable parts. They are recognized through signs, which are embodied in the crafted object as distinct in material and essence from the prototype. The signs of optical theory, on the other hand, bear a "natural" relation to their prototypes. As Bacon explains, they signify "by their essence and not by the intention of the soul," because they pertain by nature to the objects that they make visible. Alberti adapts this concept of signs to painting. He calls on painters to subordinate the embodiment of the painting as an object to the embodiment of the represented figures by equating the signs of painting with the superficial visual properties of the represented things.

This change in the character of pictorial signs entails a change in the cognitive processes for viewing painting. Devotional vision transcends the material world of natural vision by putting composition and division at the service of a deeper apprehension. Albertian painting appeals to the cognitive processes used for visually comprehending material objects in the natural world by putting apprehension at the service of composition. In this way, Alberti at once explains and justifies the emergent naturalism of Renaissance painting.

Renaissance Embodiment and Albertian Painting

Alberti's equation of the visible with optical signs discloses a fundamental shift in the character of art. In medieval devotional art, signification and embodiment have different referents. The image is embodied as one thing - a crafted, material, sign-bearing object - and signifies another - the prototype. Renaissance art subordinates the embodiment of the image as a "certain thing" to the embodiment of the represented bodies.(148) Rather than serving as a crafted sign for a dematerialized likeness, Renaissance painting presents depicted bodies for contemplation by both mind and corporeal sense.

Like most Renaissance paintings, Gentile da Fabriano's Adoration of the Magi [ILLUSTRATION FOR FIGURE 7 OMITTED] embodies what it represents. With the exception of the golden haloes and background, all the shapes and colors within the pictorial field may be read, from moderate viewing distances, as optical signs for depicted persons, animals, and objects. Although the liberal use of gold advertises the preciousness of the crafted image, much of the gold is used for representing golden things and hence makes visible the materiality of dep