In his now famous 1956 essay “The Role of Theory is Aesthetics”1, Morris Weitz, having been inspired by some of the arguments in Wittgenstein’s Philosophical Investigations, argued that there is a logical problem with the attempt to formulate a real definition of art, that ‘art’, being an open concept, cannot be given necessary and sufficient conditions. Weitz went on to propose a resemblance theory of art, which says, roughly, that whether something counts as art depends solely on whether members of the artworld decide that it bears a sufficient resemblance to those particulars we already count as art.
Subsequent philosophers of art have dismissed Weitz’s rejection of the possibility of giving a real definition of art. They say that Weitz makes the illegitimate inference that art cannot be defined from the fact that so far, every proposed definition has failed. They say that Weitz holds that the ‘expansive nature’ and possibility of endless innovation that is essential to art would compromised were art subjected to necessary and sufficient conditions, and they are right to say that this is also a non-sequitur. It is true that Weitz does say these things, and the critics are right to reject them. But Weitz suggests another argument that is much more powerful. That is the argument I will put forward in this essay, in defense of the claim that art cannot be defined. The argument for nominalism about art is part of a more thoroughgoing nominalism that includes but is certainly not limited to all artistic concepts, including ‘resemblance’. That is precisely the sense in which it is inspired by Wittgenstein.
Against Real Definitions
First, it is important to clarify what is the ground of disagreement between nominalists (as I’ll call those who reject the possibility of a real definition) and realists. By ‘definition’, I assume that what is needed is a criterion for distinguishing artworks from non-artworks. A real definition assumes that the nature of art, and thus the criterion for something’s being an artwork, is not a matter of human agreement in the sense that, even if a consensus about what counts as art were to emerge among members of the artworld, it would still be possible for us to be mistaken about what is and what is not art. When Plato said that art was mimesis, he was saying that there is a Form or Essence of art in this sense, as was Bell when he said that art is significant form and Tolstoy when he said that art is the expression of emotion. As such, a proper real definition of art could in principle be used as a decision procedure to guide, test, and justify (or not) members of the artworld2 in making and arguing about judgments about what is art. If members of the artworld disagree over whether a pile of stones counts as an artwork, having a real definition will (in principle) give us a means of adjudicating the debate. For realists the philosopher of art’s job is to uncover this principle, so to give a rational basis for the artworld’s decisions about what count as art.
A nominal definition, on the other hand, assumes that whatever art is, and therefore the criterion for what makes something an artwork, depend on human agreement. If and only if, members of the artworld come to agree that a pile of stones is art, is it art. Just as in baseball, it is the umpires’ judgment that determines that is a ball and what is a strike, in art, it is the judgment of members of the artworld that determines whether some thing is a work of art. Given the assumption that art is entirely dependent on our agreement, nominal definitions cannot function as guides, tests, or justificatory grounds in resolving disagreements about whether a particular thing counts as art. Disagreements among members of the artworld can be described, but until some kind of consensus is reached, there is no fact of the matter about whether a pile of stones is, or is not, an artwork. For the neo-Wittgenstinians the philosopher’s job is to simply describe the practice by which we come to call something art. This will not, unfortunately, provide a rational basis for the decisions the artworld makes about what is art; there will be no transcendent principle upon which to base our decisions.
Insofar as arguments against the possibility of giving a real definition of art are supposed to be inspired by Wittgenstein’s general arguments against definitions in the Investigations, it will be helpful to begin just there. In the section of the Investigations to which Weitz appeals, Wittgenstein’s argumentative strategy is to undermine the perceived need for concepts to be bounded by strict necessary and sufficient criteria:
Consider for example the proceedings that we call “games”. I mean board-games, card-games, ball-games, Olympic games, and so on. What is common to them all? Don’t say: “there must be something common, or they would not be called ‘games’”, but look and see whether there is anything common to all. For if you look at them, you will not see something that is common to all, but similarities, relationships, and a whole series of them at that. …the result of this examination is: we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail. 3 When we examine our practice of categorizing different activities as “games”, we find that there is no single criterion we use in making the decision; but it does not follow that the word is meaningless, or that it cannot function to distinguish games from non-games. Rather, in most cases, we are able to make the distinction even though we lack a clear criterion for doing so. And the reason we can do this is because, as Wittgenstein says, we rely on a complicated network of similarities and resemblances by which we decide whether something counts as a game.
Wittgenstein goes on to make the point that the concept is open ended, in the sense that, although we could, for specific purposes, choose to draw a strict boundary, there is no need to do so in order for us to put the word “game” to use. In answer to an imagined interlocutor who suggests that such concepts are defined as the “logical sum” of the individual interrelated concepts, Wittgenstein says:
…It need not be so. For I may give the concept ‘number’ rigid limits in this way, that is, use the word “number” for a rigidly limited concept, but I may also use it so that the extension of the concept is not closed by a frontier. And this is how we do use the word “game”. For how is the concept of a game bounded? What still counts as a game and what no longer does? Can you give the boundary? No. You can draw one; for none has so far been drawn. (But that never troubled you before when you used the word “game”). 4
So the argument is that with regard to concepts such as ‘game’ or ‘number’, it is not the case, as Clive Bell says, that we gibber in using the concept if we do not have a definition. We are perfectly able to function with the word even though we lack a specific definition. We have a series of examples that we agree constitute examples of games, and from there we extend the concept in indefinite and unpredictable ways depending on our finding a resemblance between the agreed upon cases and the new cases. Although we can, for specific purposes, choose to limit the definition, there is no natural limit. ‘Game’ is an open concept in the sense that any activity can come to constitute a game should we decide that it sufficiently resembles other things we recognize as games. It is true that there may be borderline cases about which we disagree. But that disagreement will not, Wittgenstein thinks, be settled by appeal to a real definition. Rather, it will be a matter of our deciding, for a variety of reasons, whether the borderline case sufficiently resembles already-recognized cases. Insofar as ‘game’ is a human construct, it is always open to the possibility of (sometimes radical) change. So we cannot say, once and for all, what constitutes a game, since how we use the criterion today may be radically different than the way in which we use the criterion in the future, or the way in which it was used in the past.
It is easy to see why this argument will not satisfy those philosophers searching for a real definition. The realist can admit that in practice, we do not rely on a strict criterion for deciding which things are artworks, and the realist can accept the observation that the way something comes to be recognized by us is through our seeing a resemblance between it and other things we already recognize to be artworks. But all of this begs the question against the realist. For by urging us to “look and see” how our concepts operate in practice, Wittgenstein implicitly assumes that there is no real definition that transcends those practices. He assumes, that is, that art his a human construction, and that there is no transcendent fact of the matter about what constitutes, for instance, a game. The realist can simply deny that the mere fact that we call something “art” implies that it is art. The fact that we persist in calling it art only shows that we are confused about the nature of art. Thus, the argument begs the question.
What is needed on the part of the nominalist is not an argument to the effect that we do not need a real definition in order to recognize artworks, but rather an argument to the effect that the demand for a real definition is logically incoherent. If it could be shown that we cannot give a real definition of art, then giving the nominal definition will be all that is left open to the art-theorist. That will involve simply describing how something comes to be art. As I said, Weitz gives two admittedly bad arguments for why art cannot be defined. But there is in Weitz’s paper a far more powerful argument that his critics ignore. Let us turn to that argument now.
Weitz points out that a survey of the many theories of art that have put forward definitions of art shows that each of them leave something out of their definition that other theories take to be central to theirs. And when we examine the multifarious art theories up to the point of Weitz’s article, we see that each of them seems to capture one of the important criteria we use in defining art – say, formal balance or emotional power -- while leaving out other aspects that seem equally essential. This wide and deep disagreement among the various theories of art constitutes evidence that there is no one set of criteria we use in calling something art but instead a complex set of criteria that involve many different and sometimes competing aesthetic values.
By itself, as I said, the above argument is not conclusive; it does not follow from the fact that so far, every definition of art has failed, that every definition is logically bound to fail. But it lends support to Weitz’s next point. He says there is another problem with essentialist theories of art:
And then there is a different sort of difficulty. As real definitions, these theories are supposed to be factual reports on art. If they are, may we not ask, Are they empirical and open to verification or falsification? For example, what would confirm or disconfirm the theory that art is significant form or embodiment of emotion or creative synthesis of images? There does not even seem to be a hint of the kind of evidence which might be forthcoming to test these theories; and indeed one wonders if they are perhaps honorific definitions of “art”, that is, proposed redefinitions in terms of some chosen conditions for applying the concept of art, and not true of false reports on the essential properties of art at all.  Weitz’s question -- what would confirm or disconfirm that the theory in question is the correct one? – is devastating. It shows that the attempt at real definition falls prey to Meno’s Paradox and the Problem of the Criterion, both of which would seem to be intractable. In the dialogue that bears his name, Meno is asked by Socrates to define “virtue”. Meno responds by listing the things commonly understood to be virtues. This won’t work, for two reasons. First, Socrates points out that the issue is not what are examples of virtues, but rather, what it is that all the examples have in common such that they are properly called virtues. Secondly, the question arises in the first place because we disagree about what things really do count as virtues. So it will do no good to define virtue by appealing to the examples, because without a definition, we cannot be sure that we do indeed have examples of virtue. Therefore, we must arrive at the definition independently of its examples.
The realist employs this same reasoning with regard to defining art. Given that members of the artworld can – and have – been wrong about what counts as art, it will do us no good, in the search for a real definition of art, to begin with examples of artworks. We must first settle on the proper definition, then determine which things are, and which are not, artworks. But this approach, too, has a serious difficulty, as Meno himself saw:
But how will you look for something when you don’t in the least know what it is? How on earth are you going to set up something you don’t know as the object of your search? To put it another way, even if you come right up against it, how will you know that what you have found is the thing you didn’t know? 
This is another way of asking Weitz’s question: once we have settled on our real definition of art, how will we know we have settled on the right one? What will constitute evidence that we are correct? Tolstoy thought that what made something an artwork was its ability to infect the audience with the emotions of the artist. Then Bell came along and said that no, what makes something an artwork is it’s having significant form. How do we decide which is the correct theory? The only way to do so would be to ask: which one succeeds in picking out all and only artworks? But now we have a quandary. For the test requires that we be able to identify which things are, and which are not, artworks, without, of course, appealing to either theory. Unfortunately, we have broad disagreement over what is to count as an artwork, disagreement that can only be settled by having the right theory.
This is what Weitz means when he says that the theories are untestable. Both sides are free to deny any proposed counterexamples, since they can always argue that the counterexample doesn’t count as a real example at all. The mere fact that Olafur Eliasson’s Your Mobile Expectations: BMW H2R Project—which essentially consists of a stripped BMW frozen in 2 tons of ice – is counted as art despite the fact that it fails to display significant form or infect the audience with the artist’s emotions (let us assume) only shows that members of the artworld are not operating with the correct definition of art. But that argument is equally open to the organicist, the formalist, and the representationalist. So none of the theories can be shown to be the correct one, because none of them can be refuted by counterexamples.
Worse still, it isn’t just that every theory of art so understood is untestable. It’s rather that if we assume that there is a real definition to be had, we have no means of discovering it. On the one hand, we cannot begin with examples, because we cannot be sure we have the correct examples without already having the proper definition. On the other hand, we cannot begin with the definition because there is no way, without appealing to examples, to test which of the various definitions that have been offered is the correct one. And obviously, if we already had examples that could be used as a basis on which to test the theories, we would not need a theory at all. This is the familiar, and vexing, problem of the criterion.
If the above line of reasoning is correct, then we are forced to abandon the idea that ‘art’ can be given a real definition. If there is a Platonic form for art (and notice that we have not proven that there is not), it can be of no help whatsoever to us because we are incapable of recognizing it. So it cannot be our concept. Thus, if we want to know the definition of art, our only option is to simply describe the concept we do in fact use. We appeal to the history and sociology of art. We tell the story, as it were, of how this or that particular thing came to be considered a work of art, what sorts of arguments, dialogues and critical debates were being held about artworks at the time, what the political context was, etc. From there, we may derive some general principles that use in making the decision about what to count as art. But those are always open to change. The criteria used in one period may not be the criteria used in another, and there may not be one criterion at any given time. The point is there is no way to as it were stand apart from the criteria we use in determining what is art in order to judge whether they are the correct ones. Once we recognize that there can be no real definition, all that is left is to describe our actual practice of naming things artworks. Here Wittgenstein’s observation about how our concepts work in practice becomes the basis for the resemblance theory.
Critics of the resemblance theory argue that nominalists cannot give a useful criterion for ‘resemblance’, and that this is fatal to the theory. But the argument against real definitions just given applies not only to the definition of art, but to definitions in general, including the definition of resemblance and most any other term we may use in defining art. Any proposed real definition of ‘resemblance’ will run into the same problems that any proposed definition of ‘art’ runs into. For instance, Noel Carroll and George Dickie argue that since everything resembles everything else, the resemblance theory implies that everything is an artwork. That argument turns on a definition of ‘resemblance’ in which two things resemble one another if they have any properties whatsoever in common. But that is not the sense in which we use the term ‘resembles’ in most ordinary situations; if it were, saying that, for instance, ‘Marsha resembles her sister Jan’ would always be redundant, as would ‘Justice resembles a Studebaker’. Generally, when we say that one thing resembles another we mean that they have important or relevant characteristics in common. And what counts as a relevant difference is itself a matter of negotiation and discussion. So Carroll and Dickie are in the same position as the philosophers of art against whom Weitz argues: the propose a real definition of ‘resembles’ but have no means to test whether theirs is the correct one.
When we look and see how it actually works, we see that all the terms of the language game of art (not to mention others) – shift and slide and are negotiated every day by art-historians, artists, critics, journalists, and other members of the artworld, so that the concept of art and the criteria for what constitutes art are always in the process of being defined. On the nominalist view, we should look at art as an ongoing discussion, wherein the criterion and the examples form a dynamic system that is continually attempting to arrive at what Rawls calls “reflective equilibrium”, sometimes by modifying the definitions, sometimes by rejecting proposed examples. The point is not, as Weitz unfortunately says, that art is creative and adventurous, and that it could not be so if art were not an open concept. It does happen to be creative and adventurous, at least for us here and now; but the point is rather that insofar as art is a human construct, it is always open to (sometimes radical) revision, so that we cannot say, once and for all, what art is in the sense of what it always will be. In this way, art is no different from any of our concepts, insofar as they are, after all our concepts. Thus, the nominalist claim that art cannot be defined is simply part of a more thoroughgoing nominalism based on the argument against real definitions.
1Journal of Aesthetics and Art Criticism 15.1 (1956): 27-35.
2 Here I am using the term “artworld” in the broadest possible sense, to mean anyone who is involved in the discussion about what art is, how art should be judged, etc.
3 Ludwig Wittgenstein, Philosophical Investigations, $66, quoted by Weitz, ibid.