Baudelaire’s Critique of Sculpture

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KSDJournal of Aesthetic Education, Vol. 49, No. 3, Fall 2015 © 2015 Board of Trustees of the University of Illinois

Baudelaire’s Critique of Sculpture

ARNOLD CUSMARIU

Am şlefuit materia pentru a afla linia continuă.

—Constantin Brâncuşi1

Und das Problem ensteht: was is das, was übrigbleibt, wenn ich von der Tat-sache, daß ich meinen Arm hebe, die abziehe, daß mein Arm sich hebt?

—Ludwig Wittgenstein, Philosophical Investigations2

1. Introduction

Acknowledged to have launched modern poetry with Les Fleurs du mal (1861), Charles Baudelaire was also a prolific and influential art critic, a close friend of Edouard Manet, and an early champion of Eugène Delacroix. At one time decidedly not a friend of sculpture, Baudelaire published a critique of this art form in a section of his Salon de 1846 titled “Pourquoi la sculpture est ennuyeuse” (“Why Sculpture Is Boring”)3:

Sculpture has several disadvantages inherent in the medium itself. Crude and direct like nature, sculpture is nevertheless vague and elusive owing to the many sides that can be seen at the same time. It would be useless for the sculptor to insist on observation from a unique angle. Moving around the sculpture, the spectator can choose at will a hundred different angles, missing the right one and often discovering through the accidental effects of light and shadow some-thing embarrassing to the artist: beautiful attributes he did not intend at all. A painting is not whatever one would like it to be; there is no way of looking at it other than on its own terms. A painting can be

Arnold Cusmariu holds a PhD in philosophy from Brown University and has pub-lished in metaphysics, epistemology, logic, and aesthetics. He began making sculp-ture in 1984, producing about one hundred pieces to date in all media but currently works exclusively in stone. His work has appeared in juried exhibits and is in private collections. The present article follows up on his initial attempt to explain his work-ing aesthetic in “The Structure of an Aesthetic Revolution” (Journal of Visual Arts Prac-tice 2009).

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viewed from only one, rigidly determined angle; similarly, what has the most weight is the meaning the painter intends to convey. That is also why it is difficult in sculpture to know what is to count as making a mistake.4

Considerable analytical effort turns out to be required to state and then meet the objections Baudelaire raises here, with far- reaching implications for sculpture—its aesthetics, its pedagogy, and, ultimately, the nature and practice of the art form itself.5

2. Article Outline

Sections 6–8 state Baudelaire’s objections in valid argument form so that only the truth of premises is at issue. Philosophical concepts are used to define a ruling paradigm in sculpture. Section 9 presents a response to Baudelaire based on comments by fellow sculptor David Smith and shows it amounts to capitulation. Sections 10 and 11 propose and motivate a new paradigm for sculpture that allows us to deny key premises in Baudelaire’s arguments. Section 13 identifies these premises and explains why they no longer hold. Section 12 illustrates paradigms old and new with photos of my own work, accompanied by detailed analyses. Finally, sections 14–19 note aesthetic benefits of the new paradigm to encourage other sculptors to consider transitioning to the new paradigm.

3. Pedagogical Impact

Opportunities abound to derive educational material from this article, in matters of substance—theory and applications—as well as method. For example,

• TheargumentssettingforthBaudelaire’sobjectionscanbeusedincourses comparing and contrasting the aesthetics of painting and sculpture. Section 5 gives an example of the sort of dialogue that can be helpful in a classroom setting.

• Courses surveying developments in contemporary art can drawextensively from this article’s high level of detail, for example, the definition and motivation of a new paradigm for sculpture and its practical consequences.

• Verifiablehistoricalclaimsaremade,towhichIdrawattentioninthe text and in footnotes. Teachers can use the verification of these claims as a basis for lectures, classroom assignments, term paper topics, and even final exam questions.

• Akeyobjectiveofasculpturecoursewouldsurelybetoprovidestudents a clear understanding of the concepts unique to the third dimension in art. This objective can be met in part by studying the sculpture paradigms carefully defined here.

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• Educatorswhobelievethatconceptualanalysisisavaluablepre-cursor to progress in art will find a powerful ally. Philosophical training made possible the analytic effort described here, which, in turn, led to the production of artworks.6

• Afamiliarcomplaintfromstudentsisthattheoriesaretooabstract,too “out there,” too disconnected from reality to be of practical use. The article illustrates formal paradigms with photos of “before” and “after” artworks, accompanied by detailed analyses, to facili-tate comprehension and connect theory with practice.

• Books on the subject generally agree that innovation involves“thinking outside the box.” The present approach concurs but adds that a thorough understanding of “the box” is a necessary precondition and would lead to genuine advances not by eliminat-ing “the box” but rather by building a better one.

• Thenewparadigmdescribedhere, though rigorously analytical,turns out to promote far greater creative freedom than its predeces-sor, as art students and working sculptors would quickly discover.

• Iwould like nothing better than to see art schools use the newsculpture paradigm. I am hoping its benefits will be motivation enough for art- school teachers to consider incorporating my theo-ries and working methods into their curricula.

• Section18explorestheimpactofthenewparadigmonsculptureinstruction. I argue that direct carving is the preferred method of the new paradigm because it allows the high level of composi-tional freedom the paradigm requires. This paradigm is unique to sculpture; thus, training unique to sculpture is called for.

• Applyingphilosophical concepts andmethods to solve aestheticproblems is nothing new. What is new is that such application proves able to solve problems working artists face in the studio every day. Accordingly, closer “crossover” co- operation between art schools and philosophy departments is warranted.

• I have communicated this very point to the PhilosophyDepart-ment at Brown University, where I obtained my PhD, and the nearby art school with which Brown is affiliated, the Rhode Island School of Design.

4. Baudelaire’s Objections Summarized

Baudelaire implies that the relativity of vision, a common fact of ordinary life, does not render ordinary objects “vague and elusive”7 but that sculpture is a different story. Here a question arises that is neither obvious nor avoid-able: How do we decide what angle of vision is appropriate for the purpose of recovering8 the aesthetic content of a three- dimensional art object? As I interpret him, Baudelaire argues that, unless sculpture behaves like paint-ing, two consequences follow that are sufficiently serious to question the aesthetic value of the third dimension in art9:

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(1) “aesthetic skepticism” in the form of doubt that knowledge of aes-thetic content in sculpture is possible.

(2) a situation that I will call “aesthetic anarchy” that is even more trou-bling.

The challenge is how to make sculpture that avoids these consequences without collapsing into painting—in effect, how to rescue the third dimen-sion in art.

5. Aesthetic Skepticism: A Classroom Dialogue

TEACHER: We studied paintings, as well as sculptures, during our field trip to the museum last week. Let’s make an effort today to get at the differences between the two art forms in basic terms. I know this is a difficult question, and I don’t expect a definitive answer. The floor is open.

STUDENT 1: Sculptures are objects; paintings are images—some-times of objects, sometimes not.

STUDENT 2: Paintings are objects, too. The painted canvas has a frame around it and occupies space. Weight and physical dimen-sions are all measurable.

STUDENT 1: The properties I have in mind are aesthetic. Those of a painting can be fully appreciated while it is hung on a wall. Sculp-tures need a pedestal located well away from a wall.

STUDENT 2: Surely, sculptures can also be displayed against the wall. Museums do that routinely, probably for reasons of space.

STUDENT 1: Displaying a sculpture this way blocks appreciation of all its aesthetic properties. A sculpture exemplifies aesthetic prop-erties in all three dimensions; a painting only in two.

STUDENT 2: What does that mean?STUDENT 1: To fully appreciate the aesthetic properties of paintings,

the viewer only needs to stand in front of them, which is why put-ting them up on a wall is sufficient for such purposes. Sculptures exemplify aesthetic properties in all three dimensions and, thus, require 360- degree access to appreciate them all.

STUDENT 2: Okay; but how does a viewer decide physical loca-tion with respect to a sculpture to be certain that he or she is able to appreciate the aesthetic properties the artist intended? Is such certainty even possible? What if it isn’t?

6. Aesthetic Skepticism: The Argument

The following sequence captures what I think is Baudelaire’s argument for aesthetic skepticism in sculpture (“TDAO” abbreviates three- dimensional art object):

(1) Viewer V can succeed in recovering the aesthetic content of TDAO X that sculptor S intended X to convey only if the visual perspectives of

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X chosen by V to view X match the visual perspectives of X revealing the aesthetic content that S intended X to convey.10

(2) It is doubtful that such a match can occur because

(i) viewers may simply be unaware which visual perspectives the sculptor considered special or unique and which not.

(ii) even if they knew what these perspectives were, viewers are not “accountable” to the artist and can ignore or overlook the visual perspectives revealing the aesthetic content the sculptor intended.

(iii) viewers may well prefer perspectives revealing aesthetic content the sculptor did not intend, possibly for reasons the artist would reject.

(iv) viewers are likely to match the sculptor’s intended perspectives by accident, luck, or guesswork.

Therefore,

(3) It is doubtful that viewer V can succeed in recovering the aesthetic content of TDAO X that sculptor S intended X to convey.

(4) If (3), then it is doubtful that viewers can attain knowledge of the aesthetic content of a TDAO X that sculptor S intended X to convey.

Therefore,

(5) It is doubtful that viewers can attain knowledge of the aesthetic con-tent of a TDAO X that sculptor S intended X to convey.

To connect this argument to the contents of the passage: Baudelaire notes that, in painting, there is no matching problem of the sort described in (2), meaning that he holds that there must be a match between artist and specta-tor in the choice of viewing angles for sculpture as well, which I stated in the form of a necessary condition in (1). His comments that “the spectator can choose at will a hundred different angles, missing the right one . . . often dis-covering something embarrassing to the artist through the accidental effects of light and shadow: beautiful attributes he did not intend at all” go beyond doubt that a match can occur between artist and spectator in the choice of viewing angles, so I think Baudelaire would have no problem accepting (2), which is all that is needed here. Point (3) follows logically from (1) and (2). Baudelaire does not assert (4), though I think he would have no problem accepting it, given the emphatically negative tone of his comments. Point (5) follows logically from (3) and (4). Baudelaire seems to assert (2) as an empirical fact about encounters with TDAOs, based most likely on his own experience.11 His “vague and elusive” comment about the multiple perspectives possible with respect to TDAOs seems also meant as a factual observation, another reason that he would accept the matching requirement in (1). To take the sting out of this argument, one must show that the circum-stances (i)–(iv) noted in (2) can be mitigated. As we shall see, this is not a simple matter at all.

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7. Aesthetic Anarchy: The Ruling Paradigm

Though we are able to see only one side of a three- dimensional object at a time—as Baudelaire notes—we do not usually consider this a limitation on our knowledge. Under normal conditions, changing visual perspective is unnecessary because it would not tell us anything we did not already know. The surface configuration of physical objects is consistent throughout with the kind of objects they are, a fact learned early on in life and confirmed by experience time and again thereafter. Virtually any viewing angle is suf-ficient for the purpose of determining what we are looking at; knowledge of attributes perceived now together with prior knowledge of objects of the same kind is usually sufficient to allow prediction of what is not seen from what is seen. Concepts of a philosophical theory enable us to state the issues more sharply. According to ontological phenomenalism,12 physical objects are collections of actual and possible sense data—a sense datum being what is immediately apprehended at a given time.13 For the majority of physical objects, we have the ability to take a particular sense datum and leap beyond the present, correctly predicting other sense data in the set of all and only sense data identical with that object, including sense data hidden from view at a given moment. We are able by and large to carry out basic epistemic tasks such as identifying and reidentifying ordinary physical objects as well as predicting comembership in the same set of sense data based on a single sense datum regardless of viewing angle. Our lives and safety often depend on it. More precisely, where X is an ordinary physical object (OPO), X is an ordered n- tuple of (actual and possible) sense data, A = <sd1, sd2, sd3 . . . sdn>, such that

1. membership in A is determined by a single concept, the concept of X.2. sense data in A are, in principle, predictable from other sense data in

A.3. the concept of “the same X” is inferable from any sense datum in A.4. the concept of X determines the ordering sequence of sense data in

A.14

Call these four conditions “Paradigm A.” Explanations of its conditions are in order.15

Condition 1 states that properties of sense data associated with OPOs stem from the applicable concept. Thus, all trees share basic properties such as roots, a trunk, branches, and leaves, along with their surface configura-tion, so that sense data apparent in the presence of a tree must be consistent with properties expected to be apparent. Likewise, sense data associated with a sculpture representing—or, in the case of art readymades (for exam-ple, Marcel Duchamp’s), identical with—a familiar object of experience will be consistent with the properties of the represented object.

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Condition 2 captures the idea that, for any OPO, one can infer from sense data apparent now what sense data would be apparent if one shifted posi-tion; there are no “vague and elusive” OPO sense data. The opacity of solid objects is not an obstacle to assenting to the truth of subjunctive conditionals about them. Such inferences transfer once again to representational as well as many modern sculptures. Condition 3 reflects the fact that having the concept “tree” entails the ability to identify (and reidentify) trees from a single sense datum. Shown photos of the same tree taken from different angles, most people would be able to tell that they are photos of the same tree. If A is a sculpture of a man, just about any sense datum in A will allow an inference to the effect that A is of the same man and that the object in view is the same sculpture despite shifts in position that render different sense data apparent. Condition 4 rules out discontinuities in the ordering sequence of OPO sense data because they would be inconsistent with the applicable concept.16 Walking around a tree will not reveal anything inconsistent with the concept “tree.” Bark, branches, and leaves will appear to be just where they are sup-posed to as one shifts position. Here there is a corollary for sculptures as well, ruling out discontinuities in the ordering sequence of sense data with the concept of the object represented. Sculptures Baudelaire might have seen in Paris—in the Louvre, the Lux-embourg Gardens, the Père Lachaise Cemetery, the Notre Dame Cathedral, and the lesser- known Eglise Saint- Gervais—were all figurative and, there-fore, consistent with Paradigm A. But more than that: A review of sculpture, regardless of period or tradi-tion, will reveal not a single counterexample to this paradigm.17 Though all are TDAOs, figurative, quasi- figurative, and even abstract sculptures never-theless are consistent with 1–4. Predictable sense data comembership under a defining and ordering concept holds equally for such famous sculptures as Michelangelo’s David (1504), Rodin’s Thinker (1879), Brâncuşi’s Mlle Pog-any (1912), and Giacometti’s L’Homme qui marche I (1961); identification and reidentification can also proceed just the way it does for ordinary physical objects. The David, the Thinker, and Walking Man are rigidly bound by the concept of the male figure, while the female head and hands concepts deter-mine sense data in Mlle Pogany just as rigorously. Condition 3 means that it can safely be anticipated from any viewing angle that what will be apparent from another viewing angle is (as well as of) the same thing, in regard to both the sculpture and what it is about. The rear views of Mlle Pogany, the David, and the Thinker are all anatomically correct. It is compatible with Paradigm A that the surface configuration of the David is smooth, while that of the Thinker and the Walking Man is not. Mlle Pogany proves that minimally represented facial features and hands can nev-ertheless be consistent with the female concept guiding the composition. The experience of what is clearly a work of modern art does not place an

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undue doxastic burden on the viewer, who may well notice that diminished adherence to literal representation actually enhances aesthetic properties because potentially distracting details have been omitted. The Giacometti piece is epistemically as straightforward as its many illustrious predeces-sors. These conclusions apply to many other Paradigm- A sculptures.18

Museum visitors and art students can also verify that moving away from a perspective such as the traditional angle—front and slightly off to the right—can reveal aesthetic content that can diminish the impact of stronger, earlier perspectives. Thus, consider views of the four famous sculptures just mentioned from behind, a perspective their creators almost certainly would have preferred viewers avoided. This leads to another serious problem, as we shall see shortly. The consistency of sculpture with Paradigm A shows something aes-thetically as well as philosophically surprising: Despite differences that would be immediately evident if a traditional treatment of (for example) the female figure and a modern one were seen side by side—for example, the ancient Venus de Milo and Alexander Archipenko’s Woman Combing Her Hair (1915)—a good deal of modern sculpture only exemplifies a range of variations of an existing paradigm, Paradigm A, not a different paradigm. Conceptually speaking, the Archipenko piece is not as different from the ancient Venus as one might think. I would argue that, without the analytical details Paradigm A provides, this fact would not be apparent.

8. Aesthetic Anarchy: The Argument

Recall the following key passage from Baudelaire:

Moving around the sculpture, the spectator can choose at will a hun-dred different angles, missing the right one, often discovering some-thing embarrassing to the artist through the accidental effects of light and shadow: beautiful attributes he did not intend at all.

It follows from Paradigm A that sense data in the set associated with OPOs are seldom if ever epistemically special in the sense of being uniquely necessary for purposes of identification, reidentification, or predicting comembership to that set. Any sense datum will do for such purposes. The same is also true of TDAOs that fall under Paradigm A. The fact that such objects have aesthetic properties seems irrelevant: Here identification, reidentification, and predicting comembership can also occur based on arbi-trarily chosen sense data, as can easily be verified relative to the four famous sculptures cited above as well as many others, regardless of period, style, or tradition.19

Knowledge of shape and configuration attributes of the male figure would be sufficient to allow anyone (including people not interested in art) (a) to predict what is not seen from what is seen from any arbitrarily

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chosen angle of view relative to the David, the Thinker, and the Walking Man in regard to the anatomical features of the male figure; (b) to predict what would be next in the sequence of sense data associated with these sculptures as representations of the male figure based on arbitrarily selected sense data; and (c) to identify and reidentify these sculptures as representations of the male figure and as the same sculptures from any arbitrarily selected sense data. Hence, there are no epistemically special sense data for these sculp-tures. While abstraction in Mlle Pogany may pose additional challenges, viewers should still be able to predict from one sense datum the remaining sequence of sense data based on their knowledge of the female head and hands, as well as carry out other tasks entailed by Paradigm A. The absence of epistemically special sense data is not limited to sculp-tures intended as representations of the human figure. The many sculptures David Smith executed as part of his Cubi series, for example, which are complex aggregates of familiar geometric volumes, are also such that even viewers unschooled in the geometric properties of those volumes would be able to predict from one sense datum the remaining sequence in the compo-sition.20 Moving thirty degrees of arc from some arbitrary spot would not reveal sense data inconsistent with the geometry apparent thirty degrees of arc earlier. A cube is a cube is a cube all the way around and so are cylinders, spheres, ellipsoids, and tetrahedra; there are no epistemically special sense data for geometric sculptures either. While sculptors (for example, cubists) have found in geometry fresh aesthetic inspiration as they searched for a new analysis of the human form, none has taken liberties with geometry itself—realizing perhaps what philosophers have known for a while, that changing the properties of mathematical objects will yield a new object and perhaps even a new category of object. (Compare the meaning of “triangle” in Euclidean and non- Euclidean geometries.) Sculptures such as Smith’s Cubi series can be considered figurative (rather than abstract) in that geo-metric volumes are depicted as they are in a textbook. I will have more to say about abstraction in art below and how it can be redefined. To return to Baudelaire, he takes the absence of a “rigidly determined angle” in a new direction to argue for a different sort of breakdown in com-munication between artist and spectator in sculpture. Here is a reconstruc-tion of the argument:

(1) There are no epistemically special sense data associated with sculp-ture.

(2) If (1), then viewers can select viewing angles of a sculpture as they see fit.

Therefore,

(3) Viewers can select viewing angles of a sculpture as they see fit.(4) If (3), then viewers are free to seek aesthetic content in a sculpture as

they see fit.

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Therefore,

(5) Viewers are free to seek aesthetic content in a sculpture as they see fit.(6) If (5), then the sculptor has lost control over recovery of the aesthetic

content he or she intended a sculpture to convey. This is aesthetic anarchy.

Therefore,

(7) Sculpture entails aesthetic anarchy.

There is no aesthetic anarchy in painting because there is only one aes-thetically special sense datum—a painting is seen from one “rigidly deter-mined angle.” Once again, the apparently unavoidable disconnect between artist and viewer in sculpture seems to pose a serious problem for three- dimensional art objects.

9. One Response to Baudelaire: Capitulation

David Smith made the following comment in a 1961 interview21:

SMITH: Sculpture and painting aren’t very far apart.SYLVESTER: This is one of the great twentieth- century discoveries,

isn’t it?22

SMITH: I hope so.

I have stated Baudelaire’s position that sculpture and painting should not be very far apart to mean that there is a need in both art forms to exemplify epistemically and aesthetically special sense data. Smith’s comment that sculpture and painting “aren’t very far apart” is factually correct as a report of what many sculptors produced during the twentieth century, including Smith himself, as even a cursory review will show, in effect conceding both elements of Baudelaire’s critique.23 Smith and others have escaped aesthetic skepticism and aesthetic anarchy by producing “flat,” painterly sculptures that exemplify epistemically and aesthetically special sense data, for which the matching problem cannot arise because there is no such thing as free-dom to select viewing angles when there is only one significant viewing angle. Paradigm A is irrelevant to such sculptures just as it is for painting and for the same reason. Aesthetic three- dimensionality has effectively dis-appeared—and with it an entire art form.

10. My Response: Paradigm Shift

Baudelaire’s critique is not a cause for despair but rather an opportunity to rethink the aesthetics of the third dimension. It is clear what problems must be solved to avoid the skepticism and anarchy objections. First, it must be shown how a three- dimensional art object can be composed in a way that ensures a match between the visual perspectives carrying the aesthetic

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content the sculptor intended and those chosen by a viewer seeking to cap-ture that content. Second, it must be shown how sculptures can be com-posed so as to exemplify aesthetically and epistemically special sense data without becoming “flat,” that is, without collapsing into painting. The solution I wish to propose is in the form of a paradigm shift. To jus-tify such radical conceptual change, a proposal is expected to show that doing so is necessary as well as sufficient to solve a fundamental problem. Aesthetic skepticism and anarchy surely qualify as fundamental prob-lems for sculpture. Once an alternative paradigm has been defined and its workings have been explained, showing that a shift to the new paradigm is sufficient to solve Baudelaire’s problems entails showing how artwork pro-duced under the new paradigm is free of those problems, which I do below at length. Showing that a shift away from Paradigm A is necessary to solve Baudelaire’s problems is another matter entirely, however. Two familiar precedents can be cited by way of guidance as to why a paradigm shift might be necessary. The first is the discovery of an internal inconsistency at the foundational level, which is usually possible only in a formal system closed under deduction. This happened when Bertrand Rus-sell derived a contradiction in the naïve conception of a set expressed in Gottlob Frege’s abstraction Axiom V, which led to a shift Russell himself ini-tiated to what came to be known as the iterative conception of a set.24 After a lot of hard work, iterative sets, which would have been a good way to think about sets in the first place, proved able to carry out the work Frege and Georg Cantor intended. The second precedent also involves the discovery of an inconsistency but of an external sort, in the form of incompatibility of a scientific theory with empirical evidence. Thus, Albert Einstein showed that two fundamental postulates of special relativity, though contradictory in classical mechanics, in fact agreed with experimental data: The laws of phys-ics are the same for all observers in uniform motion relative to one another; and, as the Michaelson- Morley experiment showed, the speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the light source. What had to go was the Newtonian paradigm for thinking about space and time in absolutist terms, to be replaced by the space- time- continuum paradigm. Among other things, special relativity was able to explain the behavior of all inertial physical phenomena except gravity—which general relativity explained as the warping of space by mas-sive objects rather than a force like magnetism. Neither consideration seems relevant to showing that replacing Para-digm A is necessary to solve Baudelaire’s two problems. Aesthetic skep-ticism and anarchy, though serious and fundamental, do not constitute a proof of inconsistency of Paradigm A as a model for sculpture. Baudelaire’s two problems also do not amount to experimental evidence with which

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Paradigm A is inconsistent with aesthetic facts; nor do they point to aesthetic facts that the paradigm cannot explain. While these precedents from mathematics and science are not a good fit, nevertheless there is something they have in common that is relevant and instructive. Recall that Baudelaire’s two problems stem from a single cause: the failure of consistency between sense data carrying the aesthetic content the sculptor intended and sense data experienced by viewers free to seek aesthetic content in a sculpture as they see fit. Paradigm A leads to (or fails to block) inconsistency between the artistic intent and viewer experience, so that I am able at least to argue for the necessity of replacing Paradigm A in the form of a conditional claim that replacement is necessary to restore consistency between the artistic intent and viewer experience provided it is important to have such consistency for the sake of achieving a connec-tion between artist and audience. I admit this is not absolutely conclusive because someone may well succeed in getting around Baudelaire’s prob-lems while retaining Paradigm A. Before moving on to state the new paradigm, I wish to add a justification for a shift away from Paradigm A, speaking as a working artist. The Wittgenstein quote at the beginning of this article is my way of stat-ing the view, which is part of my working aesthetic, that a sculpture is not just an ordinary physical object plus something—the way an action has been said to be just movement plus intention—but rather is a sui generis, extraor-dinary sort of object. A shift to a paradigm that ordinary physical objects do not—indeed, cannot—satisfy is, therefore, in order, to signal a categorical difference between sculptures and ordinary physical objects. The trend in modern sculpture toward the abstraction—about which I will have more to say later—seems to me evidence of a recognized need to get away from ordinary physical objects. Had the analysis presented here been undertaken and applied earlier, perhaps the history of the art form would have unfolded very differently.

11. A New Paradigm for Sculpture

Paradigm replacement means producing sculptures that are ordered n- tuples B = <sd1, sd2 sd3 . . . sdn> of (actual and possible) sense data, such that

1*. Membership in B is determined by an overarching narrative or theme.

2*. Few or no sense data in B are predictable from other sense data in B.3*. The concept of the same X is not inferable from every sense datum in

B.4*. Theme or narrative determines the ordering sequence of sense data

in B.25

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Call these four conditions “Paradigm B.” Explanation of its conditions is in order. Under Condition 1*, sculpture is composed “in the round” by group-ing sense data around a narrative or theme. Even if mimetically accurate with respect to surface, shape, or volume, properties of an ordinary material object, including geometric ones, this approach removes the need to focus on “copying” as the vehicle of composition. Also gone is the need for a com-position to be restricted to a consistent set of surface, shape, or volume prop-erties associated with a single object or one and the same such. The experience of viewing sculpture changes under Condition 2* because of the presence of epistemically special sense data. What is not seen is no longer readily inferable from what is seen, so viewers must travel the full length of the circle around the sculpture to take it all in, which they will want to do in any case because unpredictably new sense data will become apparent as they move around the sculpture. Memory now plays a key role in connecting temporally disparate sense data. Under Condition 3*, sculptors need no longer be bound by “the” art object idea, as were Michelangelo, Rodin, Brâncuşi, Giacometti and many others working under the traditional Condition 3—consciously or not. Compositions can suggest association with one object or parts thereof now; association with another object or parts thereof fifteen degrees of arc away; association with yet another object or parts thereof fifteen more degrees of arc away; and so on. Continuity in the composition is dictated entirely by aesthetic factors, not mimetic ones. Unlike Brâncuşi, I see not reason “to seek a continuous line.” As we shall see shortly, viewers shown photos of the same Paradigm B sculpture from different angles may well fail to recognize that they are pho-tos of the same sculpture, which would be a virtual impossibility for Par-adigm- A sculptures. Under Condition 3*, it can only be safely anticipated that sense data degrees of arc apart bear some relation to the overall theme, which it will be up to the viewer to discern. We shall see below what a dra-matic difference this can make. Discontinuities in the ordering sequence of sense data are problematic under Condition 4* only if inconsistent with the theme or narrative guid-ing the composition. This should not be a problem because the determining condition is very liberal and one that artists would follow anyway as part of the customary aesthetic practice of achieving overall unity in a composition.

12. Sculpture, Old and New

With this conceptual framework behind us, I now turn to my own work for a side- by- side comparison of Paradigm- A and Paradigm- B sculptures. Show-ing how Paradigm- B sculptures avoid Baudelaire’s aesthetic skepticism

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and anarchy objections is reserved for the next section, where I also explain which steps of Baudelaire’s (valid) arguments are false. Let us look first at a piece I made based on Paradigm A, which is as vulnerable to Baudelaire’s critique as other sculptures falling under this paradigm.26

The two Ariadne views are orthogonal and capture two aesthetically spe-cial sense data. The “accidental effects of light and shadow” support Baude-laire’s point that lighting and display conditions can reveal properties the artist did not intend to be highlighted. A museum exhibit probably would use more generic lighting than seen in the photos, which would allow or even encourage viewers to prefer visual perspectives I would not neces-sarily have agreed revealed aesthetically special sense data, or ignore those I did intend. Result: It is doubtful that recovery of the aesthetic content I intended would occur, leading to aesthetic skepticism. The absence of epis-temically special sense data means there is nothing I could do to prevent aesthetic anarchy, nor could any other Paradigm- A sculptor. The aesthetic content of sense data apparent from viewing angles other than the two photos is less and, in some cases, much less interesting. This is as true of my Ariadne as it is of many Paradigm- A sculptures: “Once you’ve seen one sense datum, you’ve seen them all.” Predictability, a friend in sci-ence, is an enemy in art.27

Figure 1. Ariadne: View 1 Figure 2. Ariadne: View 2

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Eve (2001) is one of many Paradigm- B compositions I made—I moved away from Paradigm A in less than one year. Sense data here are indepen-dent, and the range of narrative options has been increased significantly.

• Thesequenceofviewsisdeterminedbyaestheticfactorsrelatedtothe overall theme of the composition rather than predictably exem-plifying attributes of one and the same object.

• Scale and surface configuration are not consistent from view toview.

• View2showsEve tobepregnant,whileView4 implies it, sug-gesting sacredness in human terms independent of the biblical story in View 3, where she is shown holding the apple, lost in thought.

• Eve’s pregnancy is not inferable fromView 1 or View 3; Eve isshown at different stages of life, without indicating temporal order.

• The carving techniques used—in-the-round in View 1 and bas-relief in View 3—amount to different narrative styles.

Figure 3. Eve: View 1 Figure 4. Eve: View 2

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• Contrasting aspects of the Eve story are expressed in the samepiece: in View 1, she is carefree before the apple; in View 3, she ponders the dilemma whether to take a bite.

• EveisshowncloseupinView1,soherbeautycanbeadmiredandthe viewer can glimpse what Adam saw that led him to fall in love.

• EveisshownfromadistanceinView3atamuchsmallerscale,togive her privacy as she contemplates an important decision.

An audience member at an American Society for Aesthetics meeting where I presented sections of this paper asked me to explain why the pri-mary base (mahogany) and the intermediate base (marble) are elliptical and the stone sits at one of the foci. My reply: The ellipse is the shape described by our planets as they revolve around the sun, which is situated not in the center—an ellipse does not have a center—but rather at one of the foci. Eve is in the sun position as a way of indicating (a) that the theme of Eve is Woman- as Life- Giving- Force, (b) that my working aesthetic has the female figure as the primary focus and inspiration, (c) that I agree with Baudelaire in associ-ating beauty with the female figure, a venerable tradition in art and poetry.

Figure 5. Eve: View 3 Figure 6. Eve: View 4

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13. Skepticism and Anarchy Avoided

Recall that Baudelaire asks what angle of vision is appropriate for the pur-pose of recovering the aesthetic content the sculptor intended a sculpture to convey, raising two challenges. The first challenge is how sculpture can be made so that visual perspectives chosen by viewers consistently match the visual perspectives revealing the aesthetic content the sculptor intended to convey. The second problem is how sculpture can be made that exemplifies aesthetically special sense data so that viewers are not free to seek aesthetic content as they see fit, irrespective of whether the sense data they would experience viewing a sculpture are aesthetically special. For the time being, I propose to explain how Paradigm- B sculptures can meet these challenges by reference to my own work pictured above, showing how Eve succeeds where Ariadne failed. For Eve and other Paradigm- B sculptures, Baudelaire’s doubts that a match is possible between artistic intent and viewer perspective do not arise, so premise (2) of the aesthetic skepticism argument is false. It does not matter (i) whether viewers are aware which visual perspectives the sculptor considered special—they all are; that (ii) viewers can choose at will visual perspectives revealing the aesthetic content—they all reveal the sculptor’s intent; that (iii) viewers may prefer perspectives revealing aesthetic content the sculptor did not intend—there are not any; finally, that (iv) accident, luck, or guesswork are not in the least involved in matching the sculptor’s intended perspectives. There is no need to guess or hope to luck out when getting it right is assured. There is an important reason that twice as many photos of Eve were shown than of Ariadne. For Paradigm- A sculptures, one sense datum is suf-ficient to anticipate the configuration of the others in the same set. Showing two (or three) more photos of a Paradigm- A sculpture such as Ariadne would not have been necessary for the above- noted epistemic purposes and would have mattered little for aesthetic purposes. Some readers probably already concluded that one photo of Ariadne is enough to “get it” epistemically as well as aesthetically. The same is true (no disrespect intended) of the four famous sculptures discussed earlier. Another exercise for art students would be to examine sculpture photos available online and decide whether more than one photo is necessary to “get” those compositions. On the other hand, fewer than four photos of Eve would not have been enough to recover the aesthetic content of this composition, and I feel sure that readers will won-der what the piece looks like from other perspectives. (I will be building a website soon and posting videos of this and other Paradigm- B pieces.) Identification, reidentification, and predicting comembership cannot be based on a single arbitrarily chosen sense datum of Eve—which is another useful exercise for art students. Thus, the four views of Eve, which are

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forty- five degrees of arc apart, represent epistemically special sense data. Viewers are free to select angles only in that they can start the experience of looking at Eve with any of the four views shown in the photos, or reasonably close to these perspectives—and even then will find that the composition captures and holds attention no matter the starting place. I have since made over a dozen sculptures featuring epistemically special sense data only a few degrees of arc apart, so that a video of them on a rotating carousel would be much better than photographs. All sense data are aesthetically special in a Paradigm- B sculpture, so premise (1) of the aesthetic anarchy argument is false. The freedom to seek aesthetic content in a sculpture does not mean that the Paradigm- B sculptor has lost control over recovery of the aesthetic content he or she intended a sculpture to convey. Therefore, step (6) of the aesthetic anarchy argument is also false, and this argument is rendered doubly unsound. Viewers walking around a Paradigm- B composition would travel the same path the sculptor did in creating it, experiencing sense data that contribute uniquely to the overarching theme in a way that is not predictable from what other sense data contribute. People who have seen the four photos of Eve shown above without being told anything about them have asked me whether they are photos of four different sculptures. Evidently they noticed that they are not photos of the same female figure and, being used to seeing only Paradigm- A sculptures of which Condition 3 holds without exception, inferred fallaciously that the photos must be of four different sculptures. While they noticed that the bases were identical, they discounted this fact because the stone looked so different in the four views and, rather than contravene a familiar paradigm, assumed I had made four identical bases and positioned four sculptures at the same angle on top of them. When I told them they were wrong, they were surprised as well as confused; they felt as if the rug had been pulled from under them. Of course, they would have found nothing confusing about the two views of Ariadne or any other Paradigm- A sculpture.

14. Paradigm B Benefit 1: Invariance Defied

Leonardo da Vinci’s Vitruvian Man (ca. 1487) illustrated invariance in bilat-eral objects with respect to the sagittal plane, that is, the imaginary vertical plane dividing objects into left and right volumes that are approximate mir-ror images of one another (LR- invariance). A second type is invariance with respect to the coronal plane, dividing bilateral objects into front and back volumes (FB- invariance). It is easy to see that Paradigm- A sculptures are LR- and FB- invariant and that Paradigm- B sculptures are not,28 which explains why one or two images of Paradigm- A sculptures are sufficient to illustrate the composition, but not Paradigm- B sculptures.29

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The sequence of sense data in Paradigm- A sculptures exemplifies a third type of invariance, concept invariance (C- invariance), which can be con-firmed by placing one on a rotating carousel: Sense data in Ariadne follow one another exactly as specified by the concept of the female torso all the way around. Except for aesthetic details owing to the medium, we see just what we would expect to see if a “real” female torso were present, striking the pose of Ariadne. Modern sculptures are also C- invariant with respect to the concept guiding their design, despite wide variations in surface configura-tion and style. Paradigm B, on the other hand, at most suggests consistency with an overarching theme, leaving it to the sculptor to decide how to achieve it. Some of the sense data in Eve, for example, Views 1–3 (but not 4), while individually C- invariant, are not part of a sequence consistent with the same female figure all the way around, only the concept of one. Paradigm- A sculptures also exemplify rotational invariance (R- invariance): if such sculptures are placed on a rotating carousel, sense data unfold accord-ing to LR- and FB- invariance. Thus, spinning the carousel 180 degrees from the front view reveals the back view of the same object and vice- versa, while spinning from the left side 180 degrees reveals a right side that is its (approxi-mate) mirror image. A full 360- degree view reveals only C- invariant sense data—yet another exercise for art students. R- invariance breaks down for Paradigm- B sculpture. Sense data in Eve change soon after they are rotated, but not according to LR- , FB- or C- invariance, which do not hold. For this reason, my sculptures are best displayed on a rotating carousel.30

15. Paradigm B Benefit 2: Abstraction Redefined

The contrast between Paradigm A and Paradigm B is also a contrast between concepts of abstraction that are mirror images of each other. The two ele-ments of the phenomenalist view of physical objects—sense data and their ordering sequence—help clarify the difference and show that the figurative and the abstract are not as incompatible in art as is usually thought. Thus, a sculpture is considered abstract if sense data of it lack or show at best minimal correspondence to sense data of familiar or recognizable objects. However, note that a sculpture can be considered abstract even if its ordering sequence of sense data nevertheless corresponds to the ordering sequence of sense data of familiar or recognizable objects. As the reader can easily verify, Paradigm- A sculptures such as those of Archipenko and Moore are abstract in this sense—the sense that art critics and aestheticians usually have in mind. However, a sculpture can also count as abstract if the reverse is the case. That is, sense data of a sculpture may correspond to sense data of familiar

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or recognizable objects; but it is the sculpture’s ordering sequence of sense data that does not match the ordering sequence of sense data of any familiar or recognizable objects. As noted above, some views of Eve do correspond, albeit minimally, to what we would expect to see in a sculpture of a female figure. Eve is abstract in the second sense, in that such correspondence does not hold for the sequence of views of Eve. There is no familiar or recogniz-able object to which this sequence corresponds. The title of Eve refers not to a person but rather to a theme, as required by Condition 4 of Paradigm B.31

16. Paradigm B Benefit 3: Greater Emotive Impact

Emotive impact at the macro level seems to be a function of emotive impact at the micro, individual sense- datum level. Roughly, emotive impact at this level is an ordered set <P, S, <A, R>, E, I> relating a person P, a sense datum S, P’s cognitive mode with respect to S (apprehension A of S now or recol-lection R later), P’s interpretation I of S, and P’s emotive response E to S as interpreted under I. (We need to distinguish cognitive modes because S as apprehended now may well draw a different emotive response than recol-lection of S later, even under the same interpretation I.) Emotive impact can vary from person to person even if I is the same for all because of variations in E. Even simple Paradigm- B compositions can have greater overall emotive impact than more complex Paradigm- A compositions because of the consis-tently high emotive impact possible at the individual sense- datum level. In a Paradigm- A composition, emotive impact may well decrease, albeit gradu-ally and imperceptibly, the further one moves away from a dominant view-ing angle, for example, the traditional one of front and slightly off to the right from which Paradigm- A sculptures are usually photographed.

17. Paradigm B Benefit 4: Telling Stories in the Round

Viewing order makes little aesthetic difference to Paradigm- A sculptures. While sense data in such sculptures must be made “in a way that is equally convincing”32 to ensure invariance—all must fit together in the correct sequence as aspects of the same object—that is the extent of it. It is inessential for purposes of interpretation where one starts the viewing experience; in what order one continues; whether one returns to a previously viewed sense datum and continues in sequence or out of it; whether one continues after an interruption exactly at the placed one stopped; whether one keeps going in one direction until completion as opposed to going back the other way; and so on. The viewed sequence of sense data for most Paradigm- A sculpture is more than likely to be a small subset in any case because gallery visitors will often “get the point” with one look and move on to another sculpture.

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Viewing sequence as well as where the viewer starts are very much rel-evant in Paradigm- B compositions. A Paradigm- B sculpture such as Eve will have at least four ordered sequences of sense data and at least four view-ing scenarios: <1,2,3,4>, <2,3,4,1>, <3,4,1,2>, and <4,1,2,3>. Art students are invited to study each carefully. Scenario I, <1,2,3,4>, for Eve is this: View 1, interpreted as glorifying the female figure and showing her as the beautiful woman Adam loved, derives its emotive impact from the two faces of love, the erotic and the aesthetic. Emotive impact in View 2 changes character, interpreted as showing Eve’s pregnancy, the result of Adam’s love for her, love having acquired sacred meaning. Dramatic considerations drive emotive impact in View 3, where Eve puzzles over a decision with far- reaching consequences. View 4 is emo-tively neutral.

Scenario I <1,2,3,4,>: <erotic/aesthetic love; sacred love; conundrum; neutral>.

Scenario II <2,3,4,1>: <sacred love; conundrum; neutral; erotic/aesthetic love>.

Scenario III <3,4,1,2>: <conundrum; neutral; erotic/aesthetic love; sacred love>.

Scenario IV <4,1,2,3>: <neutral; erotic/aesthetic love, sacred love; conun-drum>.

Some viewers might prefer Scenario I because the neutral view offers a breather as the last and least emotionally charged sense datum of the sequence; some might prefer II because of its exciting last view; those reli-giously inclined might opt for III; others might prefer IV because it ends in a puzzle. I would not find viewer preferences humiliant pour l’artiste because I intended them all, so aesthetic anarchy does not arise.

18. Paradigm B Benefit 5: Composing in the Round

For centuries, sculptors and painters were taught that drawing should be the starting point of all work. Sculptors were to generate sketches until the desired aesthetic result was visualized—effectively composing on a flat sur-face—build a small model from drawings in plaster or clay, and then create the stone sculpture from the model. If a casting was needed, a wax model or a mold would be made from the completed sculpture. I learned the “lost wax” method in art school, though I eventually decided to leave such work to a foundry. Alex Bigler and his team at Equestrian Forge of Leesburg, Vir-ginia, have done all my castings, including Study in Motion (edition of five, from my first stone completed in 1999), Andromeda (1998 casting of the 1987 wood original), and A Musical Note (2001 casting of the 1985 wood original).33

For Paradigm- A sculptures, traditional painterly methods are quite suf-ficient to achieve the desired aesthetic result. Visualization would require

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only a few drawings, just as only a few photos are necessary to picture a Paradigm- A sculpture, for example, Ariadne. Interestingly, modern artists such as David Smith still worked from drawings.34 The sculpture instructor in my art class also encouraged students to make drawings first; luckily for me, he was not dogmatic about it. Direct carving was my method from the beginning and still is. For Paradigm- B sculptures, painterly methods are not just inadequate: they are counterproductive. For one thing, the drawing process essentially forces a three- dimensional brain to think in two dimensions, which can harm sculptors—how exactly is a story for another time. The key problem is philosophical and has serious aesthetic consequences. A drawing is a representation of only a single sense datum, even allowing for perspective. Unlike Paradigm- A sculptures, sense data of a Paradigm- B sculpture are not easily inferable from a single sense datum, so a single drawing would not enable the sculptor to visualize what should come next in the composition, and thus potentially inhibit creativity. Making twenty or thirty sketches a few degrees of arc apart to overcome this problem is not a practical solu-tion, for obvious reasons. Far better to rotate the stone slowly after the initial degree of arc has been composed, bringing into view new sense data and fresh leads. The first full cycle completed, it can be followed by reworking in a second cycle, then a third, then a fourth, then . . . That is how I work. Direct carving is not just simpler and more efficient; it represents far greater compositional opportunities and would assist sculptors seeking to transition to Paradigm B. Practicing this method over time can yield the sort of mental rewiring that eventually will dispense with visualization on paper. Now that we have a paradigm that is unique to sculpture, it is time for sculp-tors to receive training unique to their art form. Art schools need not elimi-nate drawing from sculpture curricula, only offer direct carving training, and credit toward a degree, to students interested in making Paradigm- B art.

19. Paradigm B Benefit 6: Yes, It’s Art

Though it took a while for the reorientations to gain acceptance, the para-digm shifts in mathematics and physics described earlier did not occasion doubts that the new systems belonged to their respective disciplines in mathematics and physics. Questions whether progress was achieved aside,35 iterative set theory still counted as mathematics and special relativity still counted as physics and for the same reasons that their predecessors did. Results were still expressed in languages recognized as appropriate by their respective communities, that is, the language of set theory and the language of physics; basic concepts accepted by researchers as implicit in the nature of the discipline such as “axiom,” “theorem,” “validity,” and “confirmation” did not change; and so on.

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What about the shift in sculpture I have advocated from Paradigm A to Paradigm B? The question is whether the result is art. After all, Paradigm B entails thinking about the concept of an object in sculpture in a radically dif-ferent way. Because I am suggesting that Paradigm- B sculptures be displayed on a rotating carousel, it is event ontology that now applies.36 Therefore, it is nec-essary to speak to the issue of compatibility between sculptures produced under Paradigm B and definitions of art that philosophers have proposed. A paper of this scope cannot hope to provide a complete answer, so, for the time being, I can indicate only briefly why I think the Paradigm- B piece discussed earlier, Eve, is consistent with three main attempts in the literature to define art: the institutional, historical, and functional definitions of art. For present purposes, I do not need to decide which definition is correct nor evaluate objections that have been raised. I also do not need to provide a definition of my own. The institutional definition says roughly that X is an artwork if and only if X has been conferred art status by someone with appropriate authority in an art- world system.37 It would seem that Eve is not, strictly speaking, an artwork according to this definition. Eve has been on display only once, on a rotating carousel, at the Philadelphia meeting of the American Society for Aesthetics in April 2011, where I read an earlier version of this paper. To my knowledge, only philosophers were in the audience, who, I suppose, prob-ably lack the “appropriate authority in an art- world system” to confer art status upon Eve even if they wanted to—though, I should add, no one in the audience questioned whether Eve was a work of art. I can report, however, that other sculptures of mine have been in juried exhibits in the Washington, D.C., area over the years—I have been making sculpture since 1984—so I have had art status conferred upon other work of mine by exhibit jurors who presumably have the “appropriate authority in an art- world system” and, by implication, the status of artist has been conferred upon me by someone who has the “appropriate authority in an art- world system.” Perhaps I can claim that Eve is an artwork according to the institutional definition on grounds that it was produced by someone who has had the status of artist conferred upon him by someone who has the “appropriate authority in an art- world system.” This may be good enough evidence to show that Eve’s status as an artwork is not inconsistent with the institutional definition of art. Robert Stecker has shown that the historical definition of art cannot be stated quite so simply.38 After a ten- page discussion of various counterex-amples to Jerrold Levinson’s proposal,39 Stecker presents a definition in disjunctive form, consisting of four components and three subcomponents. This means, in effect, that I am free to pick the disjunct that most readily yields consistency and leave it at that. Thus, Stecker’s condition (iii) says that X is a work of art if X arose from artistic processes or impulses within

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the mind of X’s creator. I can attest that Eve came into being just this way, as the discussion above made clear. Therefore, Eve counts as an artwork according to the historical definition of art. Quite possibly Eve also counts as an artwork according to the first disjunct of Stecker’s definition, which says that X is an artwork if X is seriously intended for regard- as- a- work- of- art. It was by me. Stecker presents and defends a functional definition of art.40 His defi-nition, which he describes as a “multitrack system for classifying items as art,”41 is also in disjunctive form. The first disjunct of the “somewhat simpli-fied version”42 says that X is an artwork if X is one of the central art forms and is made with the intention of fulfilling a function art has. It is easy to see that Eve qualifies as an artwork according to this condition. Sculpture is indeed one of the central art forms, and I can attest that I made it precisely with the intention of fulfilling a function art has. Though the ontology and the epistemology of Eve are very different from those of the David, my inten-tions in making it were the same as Michelangelo’s. I am unsure what to say about Stecker’s second disjunct, which is about achieving excellence in ful-filling a function of art, because it is not for me to say whether Eve achieves such excellence—a critic will get a chance to have a go at that issue soon enough. Perhaps the fact that Eve responds to Baudelaire’s critique can be counted as an argument for excellence on grounds that the successful com-munication of aesthetic content is a key function of art. So, Paradigm B is consistent with a functional definition of art as well.

20. Summing Up

The conjecture- refutation model, a modern version of the Socratic method that requires theories to be tested against reason and experience, is sound dialectics not just in science. I have treated Baudelaire’s critique as such a test, passing which I have argued entails giving the third dimension a new aesthetic paradigm linked to powerful concepts far removed from common-sense assumptions. Freed from the geometric and epistemic tyranny of the obvious and the mundane, sculptors can now “strive toward something lying beyond the limits of experience”43 and create extraordinary artworks.44 Assisting them in their efforts will be a new narrative flow; significantly increased emo-tive impact; compatibility between the figurative and the abstract; and far greater control over interpretation. Displayed on a rotating carousel, Paradigm- B sculptures exemplify “the weaving together of forms”—Plato’s beautiful metaphor in the Sophist. The new paradigm may also hold the key to resolving the famous “ancient quar-rel” between art and philosophy in Book X of the Republic—but that is a story for another time.45, 46

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Notes

1. Here is the full quote: “Brâncuşi ar fi fost întrebat de cineva de ideea care a stat la baza înfăptuirii Maistrei şi Brâncuşi ar fi răspuns: ‘Am şlefuit materia pentru a afla linia continuă şi când am constatat că nu o pot afla, m- am oprit. Parcă cineva mi- ar fi dat peste mâini.’” (Responding to a question about the idea that led him to create the Maistra, Brâncuşi said: “I kept polishing the surface looking for a continuous line and once I realized that I could not find it, I stopped; it was as if someone had slapped my hands.”). Vavila Popovici, Centrul Cultural Pitesti, “Jurnal american, 21 septembrie 2006, altă zi la New- York” (American diary, 21 September 2006, another day in New York), http://www.centrul- cultural- pitesti.ro/index.php?option=com_content&task=view&id=406 (accessed March 11, 2015).

2. “And the problem arises: what is left over if I subtract the fact that my arm goes up from the fact that I raise my arm?” Ludwig Wittgenstein, Philosophical Investi-gations, trans. G. E. M. Anscombe (London: Macmillan, 1953), §621.

3. Charles Baudelaire, Salon de 1846 XVI, Œvre complète, ed. Claude Pichois (Paris: Gallimard, 1976), 487.

4. Here is the French original:

La sculpture a plusieurs inconvénients qui sont la conséquences néces-saire de ses moyens. Brutale et positive comme la nature, elle est en même temps vague et insaisissable, parce qu’elle montre trop de faces à la fois. C’est en vain que le sculpteur s’efforce de se mettre à un point de vue unique; le spectateur, qui tourne autour de la figure, peut choisir cent points de vue différents, excepté le bon, et il arrive souvent, ce qui est humiliant pour l’artiste, qu’un hazard de lumière, un effet de lampe, découvrent une beauté qui n’est pas celle à laquelle il avait songé. Un tableau n’est que ce qu’il veut; it n’y a pas moyen de le regarder autrement que dans son jour. La peinture n’a qu’un point de vue; elle est exclusive et despotique: aussi l’expression du peintre est- elle bien plus forte. C’est pourquoi ils est aussi difficile de se connaître en sculpture que d’en faire de mauvaise.

Baudelaire’s “brutale et positive” language poses a translation challenge because the literal rendering, “brutal and positive,” is unhelpful. What must be taken into account is the well- known fact that Baudelaire is essentially a city poet (of his beloved Paris), for whom nature in the countryside is wild, uncouth, and unpredictable; and lacks the comforts, order, and, above all, cultural opportu-nities that only a city can offer. “Crude and direct” seems to me an adequate rendering of what Baudelaire was getting at.

5. L. Cassandra Hamrick has suggested that Baudelaire changed his mind about sculpture in Salon de 1859 and comments that the change is hard to explain:

Plus précisément, ce qui reste difficile à expliquer, c’est l’ostensible aver-sion exprimée par cet auter [Baudelaire] en 1846 pour un art auquel il va (paradoxalement semble- t- il), attribuer un ‘rôle divin’ treize ans plus tard dans son Salon de 1859. (More precisely, what remains difficult to explain is the aversion this author [Baudelaire] expressed in 1846 toward an art form to which he would attribute, seemingly paradoxically, a “divine role” thirteen years later in Salon de 1859.)

L. Cassandra Hamrick, “Baudelaire et la sculpture ennuyeuse de son temps,” Nineteenth- Century French Studies 35, no. 1 (2006): 110–11. Though an article of this scope is not the place for textual comparisons and analysis, I will make two points: As we shall see, (a) Baudelaire’s objections are fundamental and, thus, apply to more than the sculpture “de son temps”; (b) Hamrick’s comment (116) that sculpture is “un art qui présente des inconvénients particuliers pour ceux

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qui la practiquent” (an art that poses problems only for those who practice it) is even more off the mark. For discussion of the historical and cultural context of Baudelaire’s critique, see Alfred Boime, Hollow Issues: The Politics of Sculpture in Nineteenth- Century France (Kent, OH: The Kent State University Press, 1987); and Wolfgang Drost, “L’Evolution du concept baudelairean de la sculpture,” Gazette de Beaux- Arts 1508 (1994): 39–52.

6. My artistic development has relied heavily on my philosophical training in ana-lytical metaphysics and epistemology—though not aesthetics, which I did not study in school. No doubt there are artists who agree with the famous remark Barnett Newman reportedly made at the Fourth Annual Woodstock Conference in 1952: “Aesthetics is for me like ornithology must be for the birds.” As a general comment about philosophy, it is evidently false.

7. Marc Eigeldinger states that Baudelaire was familiar with Plato’s Republic (though it is unclear whether he read it) and enjoyed talking about Plato’s philo-sophical views:

Un passage de l’étude sur Théophile Gautier [Baudelaire’s friend and mentor, dedicatee of Les Fleurs du mal] laisse éventuallement entendre que Baudelaire connassait La République. . . . cette allusion à La République n’implique pas que Baudelaire ait lu le dialogue. En revanche un passage du Salon de 1859 prouve que le poète connassait la philosophie de Platon et aimait à en parler.

Marc Egeldinger, Le Platonisme de Baudelaire (Paris: Les Éditions de la Baconnière a Boudry, Neuchatel, 1951), 7–8.

8. I owe this useful term to my Tampa commentator William Seeley: “Recogniz-ing Sculpture: Comments on Arnold Cusmariu’s ‘Baudelaire’s Critique of Sculp-ture,’” presented at the October 28, 2011, meetings of the American Society for Aesthetics in Tampa, Florida.

9. Small wonder that two paragraphs later Baudelaire offers more negative com-ments on sculpture (Baudelaire, Œvre, 488):

Once past its primitive period [the original is more pointed: “l’époque sauvage”] sculpture became nothing more than an auxiliary art form (“un art complémentaire”) even in its most magnificent achievements. Diligently carved statues existed only in humble association with paint-ing and architecture, serving their goals. Cathedrals reaching up to the sky filled thousands of empty spaces with sculptures that were nothing more than a memorial to flesh and body—painted sculptures, note this well—whose pure and simple colors, though admittedly unique, had to be in harmony with everything else to help achieve the poetic effect of the building. Versailles found shelter for its many statues by placing them in the shade or in groves where waterfalls splashed them with a thousand diamonds of light. Throughout history, sculpture has played an auxiliary role (“un complément”); whether in the past or the present, it has been a solitary art form (“un art isolé”).

10. Baudelaire’s comment that “what has the most weight is the meaning the painter intends to convey” qualifies as intentionalist. However, premise (1) of the argu-ment is not intentionalist as such because it only states a necessary condition of what must be the case for a viewer to be in a position to recover the aesthetic content put there by the artist, from which it does not follow that the only mean-ing a work of art can have is due to the artist. The matching problem Baudelaire raises does not entail intentionalism. As I do not see clear commitment on his part to such a view, so I do not plan to address familiar objections to it. Recent philosophical work on intentionalism includes Berys Gaut, A Philosophy of Cin-ematic Art (Cambridge: Cambridge University Press, 2010); Paisley Livingston,

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Art and Intention: A Philosophical Study (Oxford: Oxford University Press 2005); and Robert Stecker, Artworks: Definition, Meaning, Value (University Park: The Pennsylvania State University Press, 1997).

11. Years ago, before becoming a sculptor, I recall having the same questions as Baudelaire while viewing a massive steel construction somewhere in Washing-ton, D.C. I kept walking around it wondering where I was supposed to stand to “get the point.”

12. See George Berkeley, A Treatise concerning the Principles of Human Knowledge and Three Dialogues between Hylas and Philonous, in Principles of Human Knowledge and Three Dialogues, ed. H. Robinson (New York: Oxford University Press, 2009).

13. As in a previous article, I am speaking of sense data as entities only for the sake of presentational simplicity, borrowing an aesthetically useful way of thinking about TDAOs. I realize that ontological phenomenalism is intended as a theory about all physical objects, but for the time being only its implications for TDAOs are relevant. See Arnold Cusmariu, “The Structure of an Aesthetic Revolution,” Journal of Visual Arts Practice 8, no. 3 (2009): 163–79.

14. Cusmariu, “Structure,” presents two more paradigms that define essential dif-ferences between my work and that of every other sculptor. One of the two para-digms is metaphysical and redefines mereotopological attributes.

15. Teaching suggestion: Art educators are invited to test the four sculpture corollar-ies below through classroom assignments and museum field trips.

16. The view that sets have members essentially extends no less to ordered n- tuples, which are sets of sets. For a defense, see James Van Cleve, “Why a Set Contains Its Members Essentially,” Nous 19, no. 4 (1985): 585–602.

17. Teaching suggestion: Art educators are invited to test this claim through class-room assignments and museum field trips.



20. Teaching suggestion: Smith’s sculptures can be studied in major museums and the large Bolton Landing collection in upstate New York where he lived and worked.

21. David Smith, interview with David Sylvester, in David Smith: Sculpture and Draw-ings, ed. Jörn Merkert (Munich: Prestel- Verlag, 1986), 162.

22. The knowledgeable reader will likely note that sculpture in the form of reliefs is a very old practice indeed—e.g., Goujon’s reliefs from Fontaine des Innocents, 1548–49—therefore, the idea of “flat” sculpture epistemically resembling paint-ing is hardly a twentieth- century innovation.

23. To assist art educators and their students, here is a partial list that includes sev-eral works by Smith himself: virtually everything by Nevelson; Judd installa-tions that barely rise above ground level; Calder mobiles; Matisse’s Nu de dos (1909–30); Archipenko’s Femme à l’évantail (1914); Picasso’s Glass, Knife and Sand-wich on a Table (1914), Lipschitz’s’ Still- life with Musical Instruments (1918), Reclin-ing Woman with Guitar (1928), and Birth of the Muses (1944–1950); Arp’s Bird Man (1920) and Two Heads (1929); Vantongerloo’s Triptych (1921); Schwitters’s Mertz-bild (1924); Giacometti’s Head (1928); Tutundjian’s Relief with Cylinder (1929); Torres- Garcia’s Composition (1931–34); Domela’s Composition in Relief (1936); Biederman’s Structurist Work No. 3 (1937); Nicholson’s Relief (1939); Noguchi’s Contoured Playground (1940–41); Callery’s Amity (1946–47); many by Smith him-self, such as Song of an Irish Blacksmith (1949–50), The Banquet (1951), Agricola I (1951–52), and Cubi XXVII (1965); Paolozzi’s Cage (1950–51); Morris’s I- Box (1962); Hepworth’s Two Figures (1964); Flavin’s Monument for V. Tatlin (1966); Kowal’s Biotic Myth (1968); Smithson’s Six Stops on a Section (1968); Hesse’s Unti-tled (1970); Cragg’s New Stones (1978); Long’s Stone Line (1980); Serra’s Titled Arc

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(1981); and Ruckriem’s Double Piece (1982). The third dimension has disappeared in Christo projects involving lengthy spans of fabric hung on wire, such as Run-ning Fence (1979) and the 7,500 identical panels, The Gates (2005), placed in New York’s Central Park along a path 37 km. long. Educators are invited to expand the list.

24. For a discussion of the issues, see George Boolos, “The Iterative Conception of a Set,” The Journal of Philosophy 68, no. 8 (1971): 215–32.

25. Is there a danger that structuring an artwork according to a theory that belongs to a different conceptual category (epistemology) would eliminate, through reductionism, the aesthetic dimension? I do not think so. The key point to realize is that “structured” does not mean “reduced”: Paradigm B pertains to only con-ceptual structure, not content. (a) While aesthetically and epistemically special sense data are constant companions under my paradigm, as Baudelaire argued they should be, this is only true in the sense that the epistemic “is” of my para-digm is necessary by way of formal guidance for the aesthetic “ought,” not that it is necessary or sufficient as an analysis of it. (b) The composition of individual sense data is linked exclusively to a theme’s aesthetics character. (c) Aesthetic factors also determine the choice of ordering sequence relating sense data in the piece, which can be as discontinuous relative to one another and in as many different ways as the sculptor deems necessary. Thus, I can agree with Sibley that aesthetic attributes are irreducible and am not guilty of the naturalistic fal-lacy. See Frank Sibley, “Aesthetic Concepts,” Philosophical Review 68, no. 4 (1959): 421–50. On the naturalistic fallacy, see G. E. Moore, Principia Ethica (London: Cambridge University Press, 1903).

26. Like many sculptors, I also started out working under Paradigm A, though I can-not claim to have been aware that I was doing so. Had it not been for my training in philosophy, it is unlikely I would have been able to identify the conditions that define this paradigm or understood what changes need to be made to replace it.


28. For example, Views 1 and 2 of Eve are not LR- invariant because she is pregnant in View 2 but not View 1; hence, View 2 is not a side view of View 1. Mirror imaging plays no role at all in how Views 2, 3, and 4 are related. Views 2 and 4, both side views, are also not mirror images of each other. View 1 suggests FB- invariance in View 3, while View 3 suggests LR- invariance in View 1; but neither is the case. A photographic record of Eve would require at least four images to show what each major sense- datum contributes to the composition.

29. To assist art educators and their students, here is a partial list of FB and LR invari-ant sculptures: Maillol, Bourdelle, and Lachaise figures are invariant, e.g., Femme (1905), Pénélope (1909), and Elevation (1912–27). The two figures of Brâncuşi’s The Kiss (1907–8) are nearly mirror images of one another. Archipenko’s Woman Combing Her Hair (1915), Boccioni’s Unique Forms of Continuity in Space (1913), and virtually all Giacometti figures are invariant. Moore’s scattered- object ontol-ogy does not break invariance, e.g., Recumbent Figure (1938) and Reclining Figure (1934). Picasso’s Man with a Sheep (1943) is invariant in both subjects, as is Lip-chitz’s Prometheus Strangling the Vulture (1943–52). Segal is back to literal invari-ance, e.g., The Diner (1964–66). Picasso’s Daley Plaza cubist statue (1967) is per-fectly LR- invariant. Art educators are invited to expand this list.

30. Paradigm- B sculpture placed against the wall next to a painting would also make for an interesting contrast between dynamic and static art. Such an effect could not be produced with a Paradigm- A sculpture. Thus, Paradigm B changes the ontology of sculpture from static object to dynamic event understood as prop-erty exemplification. See Jaegwon Kim, “Events as Property Exemplifications,” in Action Theory, ed. Miles Brand and Douglas Walton (Dordrecht: D. Reidel Pub-lishing Co., 1976), 159–77.

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31. What about geometric sculptures such as David Smith’s Cubi XIX (1964)? Here sense data correspond faithfully to sense data of familiar and recognizable vol-umes such as spheres and hexahedra. The sculptures are rigidly LR- invariant along several axes (among other predictable properties); surfaces are defined by equations that control every point; each volume type is defined by a differ-ent equation; finally, the ordering sequence of sense data matches the order-ing sequence of sense data of geometric objects catalogued in books studied in school. Thus, Cubi XIX do not seem to be abstract sculptures in either sense. Apparently, avoiding correspondence to the human figure is not sufficient for abstraction!

32. Théophile Gautier, “Exposition de 1836,” Le Cabinet de lecture, (1836): 13–14. The French original reads, “… à disposer d’une manière également satisfaisante.”

33. Information about my artistic development can be found in Cusmariu, “Struc-ture,” 165–66.

34. See his sketches in David Smith, 39 and 106–7.35. Readers familiar with the history of set theory will recall that Cantor’s work met

with resistance bordering on hostility from such illustrious contemporaries as Kronecker, Poincaré, Weyl, and Brouwer, some of whom did not think set theory was mathematics. Halmos says this in the “Preface” of his set theory book (prob-ably tongue in cheek): “[G]eneral set theory is pretty trivial stuff really, but, if you want to be a mathematician, you need some, and here it is; read it, absorb it, and forget it.” Paul R. Halmos, Naïve Set Theory (Princeton, NJ: Van Nostrand, 1960).

36. Kim, “Events as Property Exemplifications.”37. See Stecker, Artworks, 84. My wording is a slight paraphrase of Stecker’s

definition.38 Ibid., 97.39. Jerrold Levinson, “Refining Art Historically,” Journal of Aesthetics and Art Criti-

cism 47, no. 1 (1979): 21.40. Stecker, Artworks, chap. 3.41. Ibid., 51.42. Ibid., 50.43. Immanuel Kant, Kritik der Urteilskraft (1790; Wiesbaden, Germany: Insel Verlag,

1957), §49: B194/A191. Here is the original: “Man kann dergleichen Vorstellun-gen der Einbilungskraft Ideen mennen: eines Teils darum, weil sie zu etwas über die Erfahrungsgrenze hinaus Liegenden wenigstens streben.”

44. A working axiom for me is that art ought to transcend the banal and the com-monplace, e.g., soup cans, urinals, Brillo boxes, and piles of bricks—bilateral objects all, incidentally—rather than aim at glorification or “transfiguration.” Compare Arthur Danto, The Transfiguration of the Commonplace: A Philosophy of Art (Cambridge, MA: Harvard University Press, 1997.) I agree with Martha Gra-ham, who famously remarked that she did not want people to come into the theater off the street to see . . . the street.

45. An interesting take on what form such a response might take is Christopher Jan-away, Images of Excellence: Plato’s Critique of the Arts (Oxford: Oxford University Press, 1995), chap. 8.

46. Earlier versions were presented at 2011 American Society for Aesthetics meet-ings in California, Pennsylvania, and Florida. Thanks to attendees for helpful questions and comments, especially Aili Bresnahan, Saul Fischer, Nicole Hall- Elfick, Garry Hagberg, James Shelley, Dabney Townsend, and my Florida com-mentator William Seeley. Thanks also to the editor of this journal for suggesting that I make the connection to art education more explicit. All translations are mine unless otherwise noted.

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Baudelaire’s Critique of Sculpture