Analytical Conceptualism

The term “meta-art” is an analogue to meta-mathematics. Meta-art is a set of every and all known and possible sentences about art. For the purposes of this article, any concrete set of connected sentences about art is considered a theory.

In what follows I will consider a number of fundamental constraints preventing the construction of a single, general, unified theory of art. Determing that such a theory is impossible, I will consider a number of incomplete special theories, which can serve as models of various aspects of art. I will call “Analytical Conceptualism” the discipline concerned with the systemic construction of models of art. I will discuss various such concrete models, along with gnoseological problems associated with general modeling.

1. Duchamp’s Fundamental Question

At the end of the nineteenth and the beginning of the twentieth century, art went through an explosive development. Traditional drawing, painting, and sculpture were joined by new forms: collage, photography, cinema, ready-made objects, texts, performance … In 1913 Marcel Duchamp asked his fundamental question: “Can one make works that are not works of art?”1 We call this question “fundamental” because it marked the change from an intuitive notion of art based on history and aesthetics to the pointed and unrestricted questioning of the foundations of art. It signified the point in art’s development when enough discomforting art facts and concepts had accumulated to show that the old paradigm was breaking up and a new paradigm was forming on fundamentally new principles.

Around the same time a number of other disciplines also blossomed. The need to investigate the foundations of such disciplines as mathematics and logic was felt very strongly by such remarkable scientists as Bertrand Russel and David Hilbert, and led to the creation of meta-mathematics, now better known as formal logic.

To answer Duchamp’s seemingly simple question, we have to know two things: what art is and what art is not. Duchamp and a number of other artists tried to answer the question by example. Here we will try to build an analytical apparatus to deal with Duchamp’s fundamental question systemically. Fortunately, a great deal of work was done in the 1960s and ’70s that can help us.

2. Kosuth’s Criterion

In 1969 Joseph Kosuth published “Art after Philosophy.”2 Numerous breakthrough ideas were presented in his remarkable essay, two of which are particularly important for us here. The first was Kosuth’s declaration of the independence of art from aesthetics. To achieve this, Kosuth uses the “principle of verification” championed by the British philosopher A. J. Ayer.

According to Ayer: “A sentence had a meaning if and only if the proposition it expressed was either analytic or empirically verifiable.”3 For example, the sentence “Two plus two equals four” can be verified analytically and proved to be correct. The sentence “The sun rises in the west” can be verified by observation and proved to be incorrect. So these sentences have meaning that can be verified. But the sentence “Pegasus has beautiful wings” cannot be verified, either by means of logic or by observation or experiment. It is meaningless as an assertion, though we understand what it says. According to Ayer, scholarly fields like ethics, theology, and aesthetics are made up of meaningless sentences and are thus themselves meaningless.

Kosuth used Ayer’s principle to declare the independence of art from aesthetics. Art, argued Kosuth, was free from the capricious judgments of so-called “taste.” Aesthetics became just one of many qualities of art, and artists could consider it or not. While some questions lingered about Ayer’s principle of verification, the conceptual independence of art from aesthetics, psychology, politics, economics, and other disciplines was an inevitable discovery that can be confirmed by other means.

The history of art tells us that art changed from the ancient era to the Middle Ages, from the Renaissance to modernism and postmodernism. The driving force behind this evolution is claimed to be external forces: social, political, even personal. As soon as these forces change, art changes—or so goes the argument. The trouble with this picture is that it describes well what happened, but it gives no idea of what will happen next. And it cannot tell us this precisely because it looks backward and assumes the driving forces to be external to art.

But art is a discipline. It evolves internally. In mathematics, the Pythagorean theorem is important not because it was proved five hundred years before Christianity and not because of the rich culture of the Hellenic world at the time. No, it is important because all of analytic geometry and trigonometry and calculus and numerous other areas of mathematics are based on this theorem.

Art evolves. It becomes more complex. It feeds on new ideas and technologies. It conquers new territories. Fundamentally, art is driven by the question: “What is there that was not known to art before?” And this question will be asked by future artists, just as it was asked by artists of the past. Kosuth formulated this driving force in the following way: “The ‘value’ of particular artists after Duchamp can be weighed according to how much they questioned the nature of art; which is another way of saying ‘what they added to the conception of art’ or what wasn’t there before they started.”4

In practice, artists do not generally deal with their own heritage. They deal with concepts and artworks. Narrowing the scope of Kosuth’s statement, we can reformulate it to apply to partcular artworks rather than to an artist’s entire oeuvre: The value of a particular artwork can be weighed according to how much it questions the nature of art; which is another way of saying “what it adds to the conception of art” or what wasn’t there before it was created.

Kosuth’s criterion is routinely and intuitively used on the scale of concrete artworks. Every time we criticize somebody’s work as being unoriginal, every time we praise somebody’s innovation, we in fact use Kosuth’s criterion. On a larger scale, what was understood implicitly before has now been named. The paradigm has shifted. From an amorphous mass of ever multiplying images, conflicting styles, and incompatible theories, Art is transformed into a discipline consisting of two parts:

1. applied work serving particular public interests; and

2. fundamental research or fundamental inquiries forming the characteristic edge of growth, formerly known as the avant-garde.

Abandoning the long-held preconception that aesthetics is synonymous with art uncovered the true nature of art: art is a discipline connected to but distinct from any other.

In “Art after Philosophy,” Kosuth also identified Conceptual art as an approach to all art—implying that Conceptual art was not a form or a style of art, but rather a meta-discipline concerned with art. This is the second of Kosuth’s groundbreaking ideas that concerns us here. To refer to this meta-discipline, we will use the term “Analytical Conceptualism” instead of “Conceptual art,” noting that Analytical Conceptualism exists on two levels: as a set of meta-art statements, and as a body of supporting artwork. Such a set of meta-art statements together with supporting artwork is called a model.

3. Skersis’s Paradox (Meta-Conceptual Transformations)

Constraining the scope of Kosuth’s statement to the scale of an artwork allows us to concentrate not on the “philosophical” meaning of the statement, but on its implications that are not obvious on a larger scale.

According to Kosuth’s criterion, there are two parts to a work of, for example, Conceptual art:

1. that part of the work that belongs to known art (A); and

2. the innovation (I) of the work—the part that constitutes the “value” of the Conceptual artwork, the part that was “not there” in Art when the artwork was started.

It also can be represented formally as I= (A∪N) - A, in which N represents a new artwork.

To put it simply, we have a paradox:

To put it simply, we have a paradox: The most important part of an artwork is something that is not Art.

There are profound consequences to this paradox:

1. Over a hundred years after Duchamp posed his fundamental question—“Can one make works that are not works of art?”—we now have a partial answer: “Yes. By necessity they will be Conceptual artwork done in accordance with Kosuth’s criterion.”

2. Conceptual art, at least at the time of creation, is not art. It is a meta-discipline existing on two levels: on the level of an artwork, and on the level of a meta-art statement, where an artwork is a manifestation of the meta-art statement.

3. Therefore, what Kosuth called “Theoretical Conceptual Art” should be called Conceptualism, or better yet Analytical Conceptualism.

4. Innovation is identified as a fundamental property, which requires the transgression of art’s boundaries.

Consequence 4 suggests that the transgression of old conceptual boundaries is not unique to art. If we are to develop innovation (not only in art), we need to concentrate on developing mechanisms for transgressing the boundaries of known concepts.

A new discipline concerned with meta-conceptual meaningful transformations is developing, and it is called meta-conceptualism.

4. Meta-Art

Once we assert that the transgression of art’s boundaries is a fundamental property of conceptually new art, we gain a field of view encompassing art, its boundaries, and the surrounding areas of transgression. To describe this new view we need a meta-discipline concerned not only with the history but with the structure of art.

The concept of meta-art is analogous to the concepts of metalanguage and meta-mathematics. A metalanguage is a language in which we discuss other languages. For example, when we discuss the Russian language in English, Russian is the object language, while English is the metalanguage. We can regard meta-mathematics as a metalanguage for mathematics. Regarding mathematics and other deductive disciplines, Alfred Tarski wrote: “From the standpoint of meta-mathematics every deductive discipline is a system of sentences.”5

Art, strictly speaking, is not a deductive discipline, but if we talk about it, we generate a set of sentences. Therefore, just like Tarski before us, we will declare: the set of all sentences about art is called meta-art.

Indeed, because art is only partially deductive, under “all sentences” we mean all—primarily colloquial—sentences stated in plain language: written, spoken, inferred, implied, or possible. Some sentences will form contradictory statements, such as “Art is stupid” and “Art is not stupid.” We will also declare that the set of all such sentences is infinite. Some finite number of sentences can form subsets. If the sentences of the subset are somehow seen or understood to be connected by intent, concept, message, or any other means, then such a subset is called a theory. We need these liberal allowances to accommodate each and every theory, whether we like it or not, including ones not yet formulated.

Judd’s law: If somebody calls it art, it’s art. Kosuth attributed this statement to Donald Judd and, in order to convey its profundity, called it “the philosophic tabula rasa of art.”6 We cannot underestimate the importance of Judd’s statement. If we are to talk about art at large, we need some property that belongs to all forms of art. We cannot and should not, in the course of our inquiries, linger over every artwork and wonder if it is indeed art or not.

We should follow the lead of scientists here. Physicists do not wonder if some phenomenon is the subject of physics. If it is of interest to them, they say so. Even if the subject lacks some physical properties—like mass, for example—it is still physics. Just like any phenomena in the observable universe is the subject of physics, anything can be the subject of art.

Judd’s law has some unsettling consequences. For example, Stockhausen’s comment that the World Trade Center bombing was a “work of art” turns out to be a formally true statement. It caused some uproar at the time, but it should be no more controversial than asserting that the explosion was a “work of physics.”

5. The Fundamental Tautology: Art is Art

Let’s imagine a collection consisting of every and all works of art. We see all kinds of work: big and small, on canvas and in marble, political and erotic, urgent and long forgotten … We see that our collection includes texts, photography, found and appropriated objects, music, movies, actions, concepts … We see that the only universal property they all share is that somebody has called them “art.” Any other property is not universal for our collection. For every case when an artwork has a property (p), there is another with a property (not-p). For example, if one artwork is red, another may be blue. If one is big, another may be small. If one is an object and has a mass, another is a concept or an action and does not have a mass, and so on. Therefore the most fundamental definition of an artwork is a tautology: an artwork is an artwork. This is the only definition that appeals to the immanent criteria defining our collection. On the other hand, any property not contained in what I will call the “Fundamental Tautology” is not an immanent property of an artwork.

Let me put it differently: art today is so diverse that the only property common to all its parts is the name “art.” All other qualities—aesthetic, moral, religious, political, professional—are partial, significant only to some parts of art but not to all. Taken as the criteria to define the collection, they will always define only parts of it. And what is interesting is that the more criteria we apply—that is, the more elaborate description or theory of art we produce—the less art will correspond to our definition. For example, let’s say we declare that true art is aesthetic, moral, religious, political, and professional (assuming of course that we know what is “aesthetic,” “moral,” “religious,” and “professional”). Then to comply with our definition, out of all artworks we’ll have to choose only the ones that are aesthetic, and out of those only the ones that are moral, and out of the remaining group only the religious, and out of these only the ones professionally executed.

The Fundamental Tautology is self-referential and therefore is not a true definition. But we can draw some important lessons from it:

1. Any theory not containing the Fundamental Tautology is a local (partial) theory. If theoreticians— Marxist, formalist, postmodernist, religious, or any other kind—claim that their theory of art is the only correct and all-inclusive theory, we know for certain that these claims are false and the theories are partial.

2. There is an infinite number of partial definitions or theories. A definition is a theory, and in essence every artist judging an artwork, every art critic interpreting art, every viewer of art trying to form an opinion—all build theories (that is, definitions) of art.

3. We cannot give a single finite and all-inclusive definition of art, but we can define the definition of art. The inclusive definition of art is a set of all partial definitions. Such a set is, in theory, infinite.

4. Partial definitions can be formed as statements, questions, or, in some models, even as nonverbal implicators, including artworks themselves.

6. Strata/Scale

Consider a question: When we walk into a museum, do we look at art? Or are we looking at preserved remains of what once was art?

Here is my answer: what we see is a close-up view, one of the scales of the great structure of Art—Ars Profunda. There are many scales of magnification that open different views to us. We will designate them as S1, S2, and so forth, and consider six of them:

S1 Concrete artwork;

S2 The mind of an individual artist, a creator producing artworks;

S3 A cloud (group, collective) of individual artists, creators;

S4 A local art scene, consisting of clouds of individual creators;

S5 An art world, consisting of local art scenes at the current point in time;

S6 Art history.

I chose these scales of magnification because they readily correspond to certain strata of art formed by mutually incommensurable constituents: artifacts, minds, collectives, situations, patterns of situations evolving in time.

The reason for such a classification is not academic. For the past several decades, the conceptual development of art has stagnated. We need to identify possible areas of growth and innovation. For example, the efforts of an artist are normally directed toward the production of an artwork. Artwork (S1) is currently the expected net result of an artist’s activity. Artworks are bought, sold, collected, and criticized. But there is only so much that can be done on the level of an artwork.

We know, however, that a concrete artwork is a manifestation of a concept. In turn, a concept is a verbalized idea, a pattern of neural activity happening in a particular brain. This pattern is always unique. Ideas don’t come from collectives; they come from individuals (S2). By means of communication, we can convey the idea to others, inducing similar patterns of neural activity in other brains (S3). No two brains are identical, and therefore these patterns will be similar but never identical to the original. In fact these similar patterns can be viewed as mutations of the original idea. So if we are to look for innovation in art, we might want to shift our attention to these substrate processes, particularly to strata 2 and 3.

A concrete artwork is a manifestation of deeper substrate processes. If we are to develop conceptually new art, we need to look deeper than the artwork.

7. Levels: The Cardinality of Nature Hypothesis

There are three levels readily discernable in discussions of art: World, Mind, and Language. These realms are not usually recognized as levels, and that fact leads to confusion when attempts are made to define what only can be named.

The very possibility of talking or writing about art is based on the assumption that art, or at least some essential aspects of art, can be verbalized. Consider an art critic writing about a painting. What happens? It seems that information about the painting gets mapped from the realm of reality to the realm of thought to the realm of language. Some information is inevitably lost during the transition. But this loss is not just a distortion caused by imperfections in the translation from one language to another. Instead, there is a distinct loss of information as a result of a decrease in the realm’s cardinality. Consider the difference between the real city of New York, a map of the city, and a verbal description of such a map.

“Cardinality” is an uncommon term in arts and humanities, but it is well established in mathematics and meta-mathematics. It is used to measure the size of a set. For example, a collection of three apples has a cardinality of 3; a collection of five apples has a cardinality of 5. There are also infinite sets. It was proved by Georg Cantor that some infinite sets are infinitely bigger than others.7 The progression of cardinalities can be shown in the following manner:

0, 1, 2, 3, c , n, c; ﬡ0, ﬡ1, ﬡ2, … , ﬡα, …

A set with no elements has the cardinality 0. A set with 1 element has the cardinality 1. A set with n elements has the cardinality n. A set with an infinite number of elements that could be counted—for example, a set of all natural numbers—has the cardinality ﬡ0.

The next larger set with an infinite number of elements that could not be counted—for example, a set of all real numbers—has the cardinality ﬡ1. Cantor hypothesized that there are cardinalities beyond ﬡ1, and each successive cardinality is infinitely bigger than the previous one.

In order to establish that some infinite sets are bigger than others, he used the concept of one-to-one correspondence, meaning that if two sets have the same cardinality, then every element of one set can be translated into a corresponding element of the other. We might consider some phenomena of the real world and the universe itself as infinitely large sets of data. Such large sets we will call realms.

Larger sets hold more information than smaller ones. We cannot translate the information from the higher-cardinality realm to the lower-cardinality realm without a profound loss of information. The loss is infinitely greater than the one occurring during translation from, for example, English to Russian, two natural languages that have the same cardinality.

Reality contains the Mind, and the Mind contains Language, which, we assume, means that the cardinality of Reality is greater than the cardinality of the Mind, which in turn is greater than the cardinality of Language. Our mind can hold a limited amount of information about Reality, and there is only so much that our words can tell us about what is in our mind. The Cardinality hypothesis suggests that the very nature of translation between realms of different cardinality is the fundamental obstacle that prevents us from having a final and all-inclusive definition of art. For this same reason we cannot have an exhaustive description of art either. When we try to give a definition of any real-world phenomenon—not just of art—we designate it with some word and then give a necessarily limited definition to the word, but not to the phenomenon the word designates.

This brings us to an important clarification of terms: There exists <Art> as a phenomenon of the real world. Most of it is unknown to us. The parts we encounter are reflected in our minds as a psychological phenomena [Art]. On this level we cannot define it. There is just too much information. Instead we name [Art] as “Art.” Now we have a proper name, which is still too voluminous to define the phenomenon completely, but we can describe it as an infinite set (we’ll call it “Art L4”) of partial definitions of art (we’ll call it “Art L5”).

In other words, the structure of Ars Profunda looks like this:

Level 1 <Art>—“Art” as a phenomenon of the world.

Level 2 [Art]—“Art” as a phenomenon of the world as it is reflected in our minds.

Level 3 “Art” as a proper name of [Art].

Level 4 “Art” as a set of all finite (partial) definitions of “Art L3.” “Art L4” is meta-art.

Level 5 “Art” as essentially a finite definition of a term, derived from some local theory of what the word “Art” means.

Thus, any verbalized theory aspiring to encompass all of art will be frustrated because the linguistic apparatus we use is fundamentally inadequate. This gnoseological limit applicable to any verbalized inquiry into a real-world phenomenon we will call the “Fundamental Frustration.”

On the brighter side, this also means that there can be an infinite number of theories of any real-world phenomenon, including art.

8. Conclusion

A number of fundamental limits seem to have been reached. This might explain the current stagnation in the development of art. To avoid confusion, it is important to keep in mind which aspect of Ars Profunda is of interest and set expectations accordingly. On the other hand, “fundamental” does not mean omnipresent. Judging from the past, there are always possibilities we do not foresee, yet they will present themselves in the proper time. The possibilities are there, but we lack a fundamental understanding of them. Art as a phenomenon of this world is much bigger and more complex than we think. As our understanding progresses, we will be able to develop new instruments to unlock its potential.