Sunday, May 17, 2009

Definition of Art: Essentialism, Anti-Essentialism and the Problem of Indiscernible Counterparts

Arthur Danto places the problem of indiscernible counterparts at the center of his argument in his book The Transfiguration of the Commonplace, a Philosophy of Art. He begins with a thought experiment which I find useful to lead us through this paper. There is an art exhibition with seven identical red squares framed and hanging on the walls of the museum. Danto establishes several claims about these squares : a) That five of those red squares are artworks, b) that those artworks are not only numerically different, they are also different in genres, such as a landscape, a work of abstract expressionism, an historical painting etc. c) Two of the squares are not artworks at all. These possibilities create a problem of indiscernible counterparts (PIC) which can be given the preliminary formulation:
PIC: What theory of art could adequately explain the possibilities illustrated in this thought experiment?
Finding a theory which would define art and explain all the possibilities of artworks has been the main goal of aesthetics. But first, why is a definition important? A definition is a statement of the necessary and sufficient properties of what is being defined. This statement has to prove its purpose of giving a true or false claim about the nature, or essence of art and what characterizes it from anything else. Many theorists sustain that unless we know what art is, we cannot begin to respond to it adequately or to say why one work is better than the other. So logically, a definition must satisfy the necessary and sufficient properties of the concept it is trying to define. In reality, defining art as a concept is problematic and sometimes even controversial. In this paper I introduce the problem of definition related to Aesthetics. I present Morris Weitz’s anti-essentialist approach to aesthetics with a question in mind; can it solve this thought experiment? I then present Arthur Danto’s essentialist definition of art which presents a solution to PIC as pictured in the though experiment.
I. Why a Definition?
In the past, philosophers have tried defining art by considering the properties of artworks. I summarize some of these theories to point to the problems they have rendered.
a) Mimetic Theories of Art
The first definition of art can be found in Aristotle’s “Rhetoric.” Here Aristotle defines art as mimetic, given that if imitates reality, and also as cathartic, given that it must produce a feeling of catharsis on its audience. Later, Plato in his Republic also states that art must have mimetic properties, because the arts represent or imitate reality. So with these two definitions, artworks become ontologically dependent on physical objects. To Plato, these objects were also ontologically dependent on the non-physical Forms. So it is the real objects which have more reality than the artworks, rendering this conditional (IT)
“If X is art then X is an imitation of reality” But this definition stopped being useful when the camera was invented and photography “captured” reality without having to “imitate” it. This is an example of how a definition becomes too narrow against the dynamics of artistic innovation. So IT becomes insufficient as a theory to define art.

b) Traditional Definitions of Art
Later, traditional definitions of art defined artworks through certain properties such as art being representational (when art imitates reality), expressive (when art expresses something) and formal (when art has a certain form or symmetry.) But if we try to put these conditions together as ones that an artwork must satisfy, it is evident that the definition is deficient.
“If X is representational or formal or expressive then X is art”
Because an instruction manual can also be a representation without being an artwork, and human faces and gestures are expressive without having to necessarily be artworks. Also, both natural objects and artifacts produced for craft or utility purposes have formal properties can even look symmetric, and yet they are not necessarily artworks.

II. Art without a Definition
Many philosophers, skeptic about finding a definition of art, have taken an anti-foundationalist approach based on Wittgenstein’s idea of “family resemblances .” Morris Weitz, in his article “The Role of Theory in Aesthetics” was the first to deny the importance of a definition for art . This anti-essentialist approach to aesthetics derived from Wittgenstein’s anti-essentialist approach to language found in Philosophical Investigations. Referring to language, Wittgenstein raised an illustrative question about the nature of a definition, “What is a game?” He wants to make us aware that although the traditional theoretical answer would be in terms of some exhaustive set of properties common to all games, there may be no properties common to all of these games. Instead, Wittgenstein provides a list of board games, card games, ball games, and asks if there is something common to them all. Despite the assumption that there must be something common to them or else they would not be called “games” what becomes evident is how all of these games have no single property in common. If we look and see weather a ball game, a card game and a board game have something common to them all, whether there are any necessary and sufficient properties to “game,” we realize there are none. All we may find are similarities and relationships between different games. Weitz, like Wittgenstein, points out the difference between describing and defining. He writes:
“Knowing what a game is is not knowing some real definition or theory but being able to recognize and explain games and to decide which among imaginary and new examples would or would not be called ‘games.” (pp.31)

The Wittgensteinian problem about the nature of games is just like the problem about the nature of art. If we look and see what it is that we call art, we will also find no common properties, only similarities. Knowing what art is has nothing to do with being able to define it, but rather with being able to describe it, recognize it and explain it in virtue of those similarities. While a definition would close a concept logically by providing its essential definitions, the characteristic of description is its open texture. We can correctly describe something as art by virtue of its similarities, but no exhaustive definition can be given.
To illustrate how art can be understood as an “open concept” without a definition, I will refer to the example Weitz uses when mentioning Joyce’s novel Finnegan’s Wake. Weitz asks, is Finnegan’s Wake a novel? The traditional way, in search for a definition that would permit us to answer yes or no, would construct this as a factual problem concerning necessary and sufficient properties. The new way, which avoids a definition, would have to decide weather the work is similar in certain respects to other works already called “novels.” As long as Finnegan’s Wake shares some, but not every similarity to other novels, then the concept of art can be extended to cover the new case. So this work is like recognized novels A and B in some respects, but not like them in others. But then, neither was B in some respects like A when a decision to extend the concept was made. Finnegan’s Wake standing as N+1 is similar to A and B in some respects, but not in others so the problem is not factual but rather one of decision making whether the verdict has to do with expanding the conditions as to apply to the new concept. Through Wittgenstein, Weitz notices how an exhaustive definition is not possible because it only closes a concept that should remain open. “Art itself is an open concept” (pp.32) he writes.
I now refer back to the red squares with this question: Would an anti-essentialist theory of art asses all the possibilities in the thought experiment efficiently? If we rely on “family resemblances” as a notion to guide us through the identification of artworks by virtue of their similarities with other works, we can see how this concept becomes deficient. We have seven red squares, all alike visually, and if we approach the thought experiment from this position, then all the squares would have to be considered artworks, given that they all share similar, if not identical properties. But it is the case that two of those red squares are not artworks, they are mere real squares with red paint. So an anti-essentialist approach does not take into account the problem of indiscernible objects (PIC) which would render some red squares to be artworks, such as A) and some such as C) which are squares with red paint, but not artworks. Weitz finds definitions to be problematic in their practicality, empirical validity and lack of inclusiveness to new art works. But his anti-essentialist approach is problematic, I believe, by being too inclusive.
If we base our identification of artworks on the idea of “family resemblances,” then we would logically have to include the squares with red paint which are not artworks into the category of artworks. These non-artworks would have to wrongly be considered as artworks because they share the exact visual properties as their indiscernible counterparts.
III. Art with an essentialist Definition
In relationship to the thought experiment, I explained why an anti-essentialist (AE) approach would not be able to solve PIC. With AE as a theory, we would not be able to say that the squares with red paint are not artworks. AE would assume that if one of those red squares is an artwork, then any square which is similar to a red square, or exactly alike, is also an artwork because they all share the same visual properties. So AE does not solve c) given that we have artworks and non-artworks which are exactly alike, thus, AE is insufficient (and too inclusive) to cover the possibilities of this thought experiment. It is evident then, that an anti-essentialist definition of art cannot adequately explain the possibilities in the thought experiment. What we need is a definition that would help us discern between the red squares considered artworks and the red squares that are not artworks. An essentialist theory of art, on the other hand, would offer a solution to c) and a response to PIC. Danto defines an artwork to have two necessary properties: meaning and embodiment . So x is art only if X has embodied meaning. The point here is that an object such as the red square depends on an essentialist theory for its existence as an artwork. Without essentialism, a reductionist of art would say that red square is just a red square and nothing more. But if the red square is logically dependent, and relies on theories of art, then it is detached as an object from the real world and becomes a part of the world of interpreted things; of an artworld. To Danto, an object o is an artwork only under an interpretation I, where I is a sort of function that transfigures o into a work. So I (o)=W. Then even if o is a perceptual constant, variations in I constitute different works. This form of identification is what Danto calls “the is of artistic identification” and it is closely related to the way we interpret a work of art as opposed to the way we would interpret a real object.
Taking this to the thought experiment, we can now say that there are red squares which have embodied meaning, such as those which have been “transfigured” into artworks and can be interpreted as being more than just objects. The squares in C) are squares painted in red; they are objects reduced to its physical properties and have no meaning as artworks. The squares in A) are artworks because they rely on an essentialist theory that lets us interpret them as such. PIC derives from Leibniz’s law of indiscernibility which states, in one of its versions, that:
“If for every property X, object X has F if and only if object Y has F, then X is identical to Y.”
Danto’s essentialism distinguishes between the manifest, visual properties of the red squares, and the essential, non-visual properties of the red squares considered as artworks to avoid Leibnitzian generality. The PIC that Danto poses can be understood with this formulation:
“X is an indiscernible counterpart (IC) of Y if and only if X and Y share all manifest properties.”
Two objects with the same visual property F can be identical, yet one of them is an artwork while the other is not. So if object X is not identical with object Y, then there must be a non-visual property F, such that X is F and Y is not F. We can see that at one level, the red squares share the same physical properties with their real counterparts. But at another level, some are art while some are not. This solution is similar to those who argue against reductionist accounts of identity for personhood. It would be like saying that a person is a material body and has a whole class of predicates which apply to material bodies. We cannot discover that a person is not a material body, just like we cannot say that these indiscernibles do not have the properties of real objects. They do. But the same way that personhood is more than just a material body (at least to those who are non-reductionists about the self) the red squares are also, more than just physical objects. In this paper I have summarized the most common definitions of art and the problems that these render. I have explained the problem that rise from finding a definition of art solely through the visual properties of artworks. I have also focused on essentialist and anti essentialist definitions of art to present how each theory would work under the thought experiment that pictures indiscernible counterparts (PIC.)


1) Danto, Arthur. “The Transfiguration of the Commonplace, A Philosophy of Art.” Harvard University Press. Cambridge, Massachusetts. 1981.

2) Danto, Arthur. “The Artworld.” The Journal of Philosophy. Vol.61, No. 19, 1964.

3) Mates, Benson. “The Philosophy of Leibniz” Oxford University Press. NY. 1986

4) Stanford Encyclopedia of Philosophy. “The Definition of Art.” Htpp://

5) Weitz, Morris. “The Role of Theory in Aesthetics.” The Journal of Aesthetics and Art Criticism. Vol 15, No.1 (Sep. 1956) pp.27-35

6) Wittgenstein, Ludwing. “Philosophical Investigations.” Translated by G.E.M Anscombe. Macmillian Company. New York. 1958

7) Fisher, John Andrew. “Is there a problem with Indiscernible Counterparts? The Journal of Philosophy. Vol.92. Sept.1995


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Anonymous said...

Wow! I understand Danto a lot better now! Thank you!

Seth Thompson said...

I stumbled on this blog while working on revisions to the first chapter of my dissertation. I'm sorry to be invasive if this is intended as a private journal; however, I really enjoy reading your arguments, and I found them helpful in my thinking about these issues. I'm not sure how active you are on this site (or how welcome my questions are), but I had a question or two for you regarding PIC and the tenability of various definitional theories. I'm also curious as to whether you've published on any of the aesthetics topics you discuss in your blog. In any event, I'll save the questions until you give me the go ahead to bother you. If I don't hear back, then thanks again for your helpful thoughts on these issues.

Carolina Drake said...

Hello Seth.
I wrote this paper when I was an undergrad, and it developed into a series of two papers about the relationship between art and ethics.

At the time I was working with Michael Kelly, who edited the Stanford Encyclopedia of Aesthetics and we where trying to find ways to argue that Danto, despite his claims against this-is regardless, an essentialist, and that such theory brings problems when we start to talk about Aesthetics in relationship to history, politics, ethics etc.

I am currently teaching at a Charter School in NYC and taking a break from the philosophical life, but graduated from Stonybrook University as an MA student last year. All this to say that the conversation is still open, and I would be glad to hear about your work.



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