by Daniel A. Kaufman
After a brief hiatus in the last century, the search for a definition of ‘art’ has resumed with great vigour. Wittgensteinians may bemoan this as intellectual atavism, an anachronistic longing for “essences,” but I am inclined to think that the revival of the question of ‘art’ ’s definition is a good thing, for it is often in the search for a definition that one advances one’s understanding of something, a benefit that remains, even if no definition ultimately is found. And while there is much in the Wittgensteinian critique of traditional semantics that I find compelling and which will figure into my analysis here, I must agree with Terry Diffey that to embrace anti-essentialism too strongly is to “run the risk of its cutting us off from important insights…which would otherwise be available to us.” 
It is because the project of defining ‘art’ has undergone such a healthy revival, with some of our best philosophers weighing in on the question, that the time seems right to step back and examine the definitional project itself. I will outline three constraints, which any definition of ‘art’ must satisfy as a basic condition of adequacy, and although I will not discuss which of the current definitions of art satisfy these constraints, some discussion of them will be required, if the constraints are to be effectively presented.
Historicality and Indexicality
Let me begin by suggesting that the philosophy of art is inherently historical, in a way that other areas of philosophy may not be. My point here is only indirectly related to Jerrold Levinson’s notion that “whether something is art now depends…on what has been art in the past,” for while I agree that “historicality,” as Levinson calls it, permeates every artwork, the present idea is that philosophies of art are also constrained by history in a distinctive way.  Rarely do we find in metaphysics and epistemology that philosophical theories stand or fall as a result of historical developments.  Hardnosed dialectic is the arbiter of the truth in these areas, and more often than not it is inconclusive. But a moment’s glance at the course taken by the philosophy of art over the last several hundred years reveals our subject to have been positively driven by the history of its subject-matter, to an extent unprecedented within philosophy, even when one considers those other areas deemed “second order,” such as the philosophy of science or the philosophy of language.
The primary story of the three traditional philosophies of art — of Representationalism, Expressivism, and Formalism — is one of theories being overrun by art-historical developments: the representation theory rendered untenable by the emergence of absolute music; the expression theory collapsing, when confronted with pure abstraction; and formalism meeting its doom in urinals and mock Brillo boxes.  It was not uncommon for partisans to refuse to admit that their favorite theories had been rendered obsolete, but their refusals had little impact on the artworld, for it had been established that the nature of art is such that philosophies and theories of art can never function prescriptively, but at best descriptively. 
Art history’s authority over the philosophy of art was recognised by the followers of Wittgenstein, whose later philosophy was important precisely for its insistence on the priority of practice over theory. Whether one is talking about meaning, epistemic warrant, or other normative philosophical notions, what Wittgenstein opposed was the sort of approach favored by traditional philosophy and by the logical positivism of his own day, according to which such notions are determined in absentia and in abstracto and come into contact with practice, only when being imposed upon it. Wittgenstein’s view was that if philosophical notions like meaning and warrant have any validity at all, it can only lie in practice itself — that all that can be meant by ‘meaning’ or by ‘warrant’ are certain aspects of certain practices, realized in complex and often irregular patterns of behavior — and that consequently, the best that a philosophical account can do is offer a description after the fact; one that must remain open, because human practices are themselves open, in that they are ever evolving.
Diffey, however, has maintained that Wittgensteinianism is as insensible to history as traditional philosophy and that this is why, in his own work in the philosophy of art, he has sought a “midway course…between the extremes of Plato and Wittgenstein,” one that allegedly resides with Hegel.  I must admit to finding this mystifying (not the admiration for Hegel, but the assessment of Wittgenstein), because a significant part of the Wittgensteinian rationale for abandoning traditional semantics, in favor of a semantics based in family resemblances, is precisely the fact that many if not most (true believers might even say all) terms and concepts are shot through with historicality.
The task of the tool-box and other metaphors and language-games that appear in the early sections of the Investigations is to discredit traditional semantic theories like Frege’s, which are constructed around the concept of reference, by demonstrating that terms and expressions have a multiplicity of customary uses, aside from that of denotation.  But it is easy to miss the fact that this account of a multiplicity of uses is not intended simply to describe a current state of affairs — i.e. that there presently are a multiplicity of uses of words like ‘game’ or ‘art’ — but rather to point out that the customary uses of terms and expressions change over time; that the history of even a single term or expression may contain a heterogeneous and sometimes an inconsistent lineage of uses.
It is also easy to forget that the theory of family-resemblances is itself a theory of reference … of sorts. It is an effort to explain by virtue of what terms and expressions that do denote attach to the things within their extension. Specifically, it is intended as a solution to the problem of how terms and expressions refer in the absence of a Fregean sense, which arises not only because there may be, at present, a heterogeneity of possible referents of the expression in question, but because of the ever-present potential for future such heterogeneities of reference. It is because the extensions of terms like ‘game’ or ‘art’ not only presently include a wildly disparate group of objects and activities, but also would appear to be open to unlimited future expansion and contraction, that there can be no intension that will correctly delineate the extension of either term, at present or in the future.
There is a particular irony in Diffey’s charge that Wittgensteinianism is unhistorical because it is in the philosophy of art that the relationship between Wittgensteinian semantics and the historicality of terms and expressions is probably the clearest. Indeed, historicality is explicitly invoked by Wittgensteinians as the primary rationale for a family-resemblance semantics for ‘art’. The aesthetic anti-theory advanced by Morris Weitz, for example, is grounded in the inherently innovative character of art and the unpredictable course of art history; on the idea that because art is always changing, there will never be a single quality or cluster of qualities that will define ‘art’ over time. “What I am arguing,” Weitz writes, “…is that the very expansive, adventurous character of art, its ever-present changes and novel creations, makes it logically impossible to ensure any set of defining properties.”  So, while I agree with Diffey that there is a problem with Wittgensteinianism, I must disagree with his assessment of it. The problem is not that Wittgensteinianism is insensible to the historicality of terms and expressions, but rather that a family-resemblance semantics is the wrong way to account for it. Indeed, a family-resemblance semantics is no better at accounting for the extensions of terms and expressions steeped in historicality than the traditional theories of meaning that it was intended to supplant. 
Maurice Mandelbaum was one of several philosophers (Arthur Danto was another) who saw that more than one lesson might be drawn from the failure of traditional philosophies of art to meet the challenge of historicality. Certainly, the Wittgensteinian view that the very project of defining ‘art’ is misguided is one conclusion that a person might reach, but Mandelbaum wondered whether philosophy’s failure to produce a sound definition of ‘art’ might not simply be a consequence of focusing on the wrong sorts of properties; that rather than concentrating on the exhibited, perceptible qualities of artworks, philosophers should instead attend to the myriad relationships that artworks have had and continue to have to the rest of human life; that the definition of ‘art’ should be relational in character. 
It is not immediately obvious why such a shift in focus should be of any help in our present struggle, for if a definition of ‘art’ that centers upon an exhibited quality can become dated by virtue of a shift in art-historical trends, why should such a shift not also date a definition of ‘art’ that focuses on the relationships that art has had with respect to human life? Does anyone doubt that these relationships have undergone as many changes as have art’s exhibited characteristics? One often gets the impression that those in favor of a relational account of artworks see it as a solution to the problem of historicality — to the inability of philosophers to find exhibited qualities of artworks that will prove to be defining over time — but, taken by itself, this is an insufficient rationale.  Not because such exhibited features will be found (they won’t), but because it is unobvious why anyone should think that trans-historical relationships between art and human life are going to be found either.
The Wittgensteinians’ contention that the historicality of ‘art’ and the heterogeneity of the objects that fall within its extension compel us to embrace a family-resemblance semantics for ‘art’ is based on a false dilemma: that terms and expressions either have intensions (in the manner of Fregean senses) that determine which objects or activities fall within their extensions, or their extensions are determined by way of family-resemblances. Of course, there is a whole class of terms, characterized by the absence of Fregean senses, for which a family-resemblance semantics would seem equally unsuitable, namely the indexicals; i.e. words like ‘it’ and ‘that’. Obviously, indexicals refer, but their extensions are characterized by such extreme heterogeneity that it is as impossible to imagine a family-resemblance semantics for them as it is to conceive of their having Fregean senses. So, it would seem that all that we legitimately can conclude at this stage, with regard to the definition of ‘art’, is that it must be quasi-indexical. Whatever content we assign to the word must enable it to function like words such as ‘it’ and ‘that’, since it will be called upon to pick out radically different sorts of objects, over the course of thousands of years of history. (I say “quasi-indexical,” because, as we will see later, any adequate definition of ‘art’ will have to assign more by way of content than is required for a true indexical such as ‘it’ or ‘that’.) Explicitly formulated as a constraint — I will call it the “indexicality requirement”— what we have is something like this: An adequate definition of ‘art’ must treat the word as quasi-indexical, so that it can accommodate the inherent historicality of art and the potentially infinite heterogeneity of artworks that is a consequence of that historicality. 
Of course, as things turned out, Mandelbaum was right: in addition to being quasi-indexical, ‘art’ must be defined in terms of a relation or set of relations rather than exhibited properties. But, many of us have been confused, I think, as to why he was right. That any adequate definition of ‘art’ must be relational has nothing to do with the historicality of art, per se, and everything to do with the particular course taken by art history in the early to mid-twentieth century. Though Relationalism is a solution to a problem that confronts the philosophy of art, it is not a solution to the historicality problem. And it was Danto, not Mandelbaum, who first identified the real impetus for a relationalist definition of ‘art’, in a series of papers, inspired by the Readymades and Pop Art, to which I turn next.
Relationalism and the Readymades
So long as the story of the philosophy of art’s failure was simply one of the inability of previous philosophers to discover exhibited features of artworks that would retain their definitional status over time, it was not entirely unreasonable to hope that such features might eventually be found, for even as late as the 1940’s and 50’s, the project of searching for a definition of ‘art’ was still a relatively new one, as compared with other essentialist programs in philosophy.  It is likely for this reason that the Weitz’s anti-theory never took hold. It was just too difficult to convince philosophers, after so short a time on the job, that the definitional project had been exhausted. But with the arrival of Pop Art on the scene, all reasonable hope of defining ‘art’ in terms of perceptible qualities was extinguished, and this set the stage for relational theories of art. The grounds for this change were laid down earlier in the century, with Duchamp’s Fountain, but the shift in paradigm only occurred with the advent of Pop and with works like Brillo Boxes. 
What Fountain and works like Brillo Boxes demonstrated was: (a) that anything could be a work of art; and consequently (b), that there is always the possibility that there may be perceptually indistinguishable things, some of which are artworks, the others which are not. These two facts precipitated nothing less than a crisis in the philosophy of art, essentialist and anti-essentialist alike. For traditional essentialists, they revealed the folly of the idea of defining artworks in terms of exhibited characteristics. That things like bathroom fixtures could be artworks foreclosed on the possibility that any perceptible quality could be a necessary condition for being art, since one could always imagine an object that lacked that quality, but was an artwork, nonetheless. Furthermore, that for any artwork there might be a possible perceptually indistinguishable counterpart that is not art (paint flung randomly from a centrifuge that has taken on a pattern perceptually indistinguishable from Rembrandt’s Polish Rider, for instance), revealed that no exhibited quality could ever be a sufficient condition for being an artwork, for one could always imagine an object having quality, but still failing to be an artwork. 
Of course, these facts were equally devastating to the Wittgensteinians, for they demonstrated that providing an account of ‘art’ in terms of family resemblances is as doomed an endeavor as the search for a traditional definition. For, if the idea is supposed to be that one focuses on accepted cases of art and then builds the concept’s extension by adding those things that resemble the accepted cases in relevant ways, then the fact that the set of accepted cases has come to include such items as urinals and Brillo boxes means that nothing will fail to resemble some artwork or other in a relevant way, and consequently, that everything will be art; a clear, if informal, reductio.
Cases involving perceptually indistinguishable twins, one that is F, the other not-F, have long been familiar fixtures in the philosophy of language and the philosophy of mind, so a great deal of thought has gone into the question of what sorts of individuating principles are indicated by such cases. The consensus has been that there are essentially two ways of distinguishing perceptually indistinguishable twins: in terms of microstructural features that are invisible to the unaided eye or in terms of external relations to people, practices, or institutions.  So, if we agree with Jerry Fodor that “whether a twin is an artwork isn’t … a matter of its chemical analysis,” then we are left with the conclusion that something’s being art is a matter of its having a certain relational property, whereupon the key question becomes, “what relational property is it?” ,  Consequently, our second constraint on the philosophy of art — call it the “relationalist requirement” — says: A definition of ‘art’, if it is to be adequate, must be in terms of relational properties, so that we can distinguish those things that are artworks from their perceptually indistinguishable counterparts, which are not.
Any number of relational accounts of art have been proposed since Danto’s early work on the Readymades and Pop and in the wake of his greatest work, The Transfiguration of the Commonplace, which set the standard for Relationalism. Indeed, it is not an exaggeration to say that thanks to Danto, Relationalism is the dominant paradigm in Anglo-American philosophy of art today, with institutionalist and historical definitions of ‘art’ being, perhaps, the most popular versions of it. What this means is that the degree to which we are satisfied or dissatisfied with the theories currently on the scene, will have more to do with how they fare with respect to the first and third constraints than with respect to the second, for the relationalist revolution has virtually insured that the second constraint will be met.
Reference, Performance, and Understanding
Two important insights for which Wittgenstein must be credited are that the meaning of a term or expression cannot be understood in terms of a prior rule that governs its application and other uses and consequently, that understanding a term or expression cannot be not a matter of grasping its meaning. (Putnam has argued, along similar lines, that we must distinguish what determines the extension of a term from what determines linguistic competence, with respect to it.)  Some have seen in Wittgenstein’s arguments a tacit case for linguistic Behaviorism, although this interpretation is controversial.  In fact, the predominant opinion seems to be that not only did Wittgenstein not think himself a behaviorist, but that Behaviorism cannot be reasonably inferred from his writings. 
The first point, as a purely biographical matter, may very well be true, but the second strikes me as unsustainable. Certainly, Wittgenstein’s Behaviorism is not like Ryle’s or Skinner’s, and it is also worth noting that Wittgenstein’s “anti-referentialism” informs a critique that applies to both mentalist and behaviorist ways of interpreting of mental ascriptions (it would appear that Wittgenstein thought that such ascriptions refer neither to mental states nor behavior, but function instead as performatives).  But despite all of these caveats, it is hard to deny that the actual position that emerges in the Investigations is of a behaviorist character. Wittgenstein may not be an eliminativist, inasmuch as he believes that behavior cannot but be identified under intentional description, but he is a behaviorist, inasmuch as he denies that mental states exist separately from and are the causes of behavior.  Wittgenstein’s Behaviorism is also evident in his conception of the intersection of the psychological and the linguistic: both in his rejection of the idea that understanding is a mental act of grasping a meaning and in his performative treatment of linguistic competence. “Don’t you understand the call ‘Slab!’,” he asks, early in the Investigations, “if you act upon it in such-and-such a way?”
The classic demonstration of a Wittgensteinian, performative Behaviorism, with regard to our understanding of the word ‘art’, is William Kennick’s “warehouse test,” in which we are asked to imagine a person who has been instructed to pick out all the artworks in a warehouse, filled with artworks and non-artworks alike, but with no definition of ‘art’ in hand.  Kennick argues that not only would this person be able to perform the task quite adequately, but that had he been provided with a definition of ‘art’ beforehand – say a representationalist or formalist one – he would have done the job less well; i.e. more of the artworks would have been left unselected, than would have been, had the person come to the test unprepared. His point is that what it is to understand the word ‘art’ is to be able to competently perform something like the warehouse-test; more generally, that what it is to understand any term or expression is to be able both to use and to respond to it in ways acceptable to the speaking-community. The search for a definition of ‘art’ is misguided, then, not simply because the term’s extension is characterized by intractable heterogeneity or because there is an insoluble paradox with respect to the idea of following a rule, but because even barring such difficulties, a definition would serve no purpose, since people simply do not consult meanings to determine how they should use and respond to terms and expressions, and such consultation is the only purpose meanings could serve.
Diffey complains that the warehouse test “seems to be a mindless performance” and that “people who did the test but who…could not explain their choices would seem to have a mechanical understanding of the term.”  This is true, of course, but Diffey must recognize that it is hardly an indictment of a behaviorist position in linguistics to point out that it renders understanding and usage “mindless” and “mechanical.” No, the real problem is that Wittgenstein’s linguistic Behaviorism relies too much on traditional conceptions of definition and understanding, for only a person who thought that the sole conceivable purpose a definition could serve is to provide a rule for the application of a term or expression would conclude, on determining that there is no need for such a rule, that there is no need for a definition, and only someone who believed that the only thing that understanding could be is the grasping of such a rule would surmise, on realizing the folly of that view, that what is needed is a behavioristic treatment of understanding.
My contention is that the best reason for seeking a definition of ‘art’ is not so that we can successfully pick out artworks or correctly respond to people, when they utter the word ‘art’. Rather, to search for a definition of ‘art’ satisfies the desire to understand art and art-making better — to put the matter in deliberately Aristotelian terms — which means that we must see the philosophical quest for a definition of ‘art’ as standing alongside art history and criticism, as part of a multi-disciplinary effort to comprehend this quintessentially human activity and its product. Aristotle believed that the desire to understand is inextricably bound up with being human and has both practical and non-practical or “contemplative” dimensions.  This means that while our capacity for certain kinds of performance — our ability to refer to artworks and to otherwise use and respond to the word ‘art’ — may be a part of what underlies our search for a definition, we are also moved by the desire to develop a certain consciousness with respect to art and art-making, one that is entirely separate from any tangible purpose or activity, however such a consciousness is construed. So, while we can accept much of the Wittgensteinian critique of traditional conceptions of definition and understanding, as they apply to ‘art’, we cannot accept his performative account of what it is to understand ‘art’.
What are we trying to accomplish, when we point out paradigmatic cases of artworks and indicate their significant features to untutored people? When we have arguments with peers over the status of works like Fountain and Brillo Boxes? When we try to find characteristics that somehow will bring Greek pots, Raphael frescoes, and color-field paintings together? Behaviorists would have us believe that we are trying to teach ourselves and others how to use and respond to the word ‘art’. Those of a traditional bent claim that the aim of such activities is to determine to what things the word ‘art’ refers. My view, in contrast, is that such behavior indicates a desire on our part to arrive at and to help others arrive at a conscious position — unsettled though it may be — on a set of objects and activities that occupy a central place in our personal, social, and cultural lives.
If I am correct, then the Wittgensteinian view is a non-starter, because it has no place for the contemplative dimension of understanding. Wittgenstein’s conception of wisdom is exhausted by the idea of phronesis and leaves no room for theoria, which means that it cannot make sense of the idea of seeking knowledge for its own sake. On the opposite side of the spectrum, we have definitions like Stecker’s and Levinson’s, which I will call “formal-style,” because of their less-than-substantial character, and which suffer from a different though equally disqualifying malady. “An item is a work of art at time t, where t is a time no earlier than the time at which the item is made,” Stecker says, “if and only if…it is in one of the central art forms at t and is made with the intention of fulfilling a function art has at t or… it is an artefact that achieves excellence in fulfilling such a function, whether or not it is in a central art form and whether or not it was intended to fulfil such a function,”  while Levinson’s view is that “[art is] a thing…that has been seriously intended for regard-as-a-work-of-art; regard that in any way pre-existing artworks are or were correctly regarded.”  The trouble with definitions like these is that while they have the virtue of allowing for a purely contemplative dimension of understanding, they provide so little insight into the character of the things within their extensions, that they are unsuited to making sense of understanding, as I have characterized it. They tell us so little about artworks that the only possible purpose they could serve is to fix the extension of the word ‘art’. But if the Wittgensteinians are correct that meanings are not instructions for correctly applying terms and expressions, and if I am correct that the primary reason that we want a definition of ‘art’ is to expand our understanding of art-making and of artworks, then the raison d’être for formal-style definitions like Stecker’s and Levinson’s is unobvious.
The constraint that emerges from these considerations, which I will call the “substantiality requirement,” says that an adequate definition of ‘art’ must be sufficiently substantial in content, so that it may serve the purpose of advancing our understanding of the character of the activities and objects that fall within its extension. Admittedly, there is some tension between this constraint and the first, for the demands of historicality would seem to point towards a definition of ‘art’ that is generic, i.e. one that does not invoke substantial characteristics of art-making and artworks, while the substantiality requirement points us in the opposite direction; towards a definition that says enough substantive things about the activities and objects within its extension, that we can credibly claim that it advances our understanding of them. Add to this the relationalist requirement, which tells us that any adequate definition of ‘art’ must eschew the perceptible characteristics of artworks, and we see how profoundly difficult the task at hand is. But difficult though it may be, it is not impossible, and both Danto’s philosophy of art and Dickie’s later institutionalism (i.e. the version presented in The Art Circle), succeed to a great degree in meeting all three of the constraints that I have identified. Of course, there remain questions. We may wonder whether Danto’s conception of style is sufficient to distinguish artworks from advertisements, and thus, whether Dantoianism is capable of meeting the relationalist requirement. Or whether the institutionalist’s claim that ‘art’ denotes a status means that institutionalism cannot be applied to those periods of history, in which there was no self-conscious conception of art, which would render it incapable of meeting the historicality requirement. I have some suspicions as to the answers to these questions (“Yes” to the first, “No” to the second), but to pursue them in any detail would take us well beyond the aims of the present endeavor.
 T.J. Diffey, introduction to The Republic of Art and Other Essays (New York: Peter Lang, 1991), p. 1.
 Jerrold Levinson, “The Irreducible Historicality of the Concept of Art,” British Journal of Aesthetics, Vol. 42, No. 4 (October 2002), p. 367.
 There are, of course, exceptions. Kant’s philosophy, for example, is significantly undermined if not falsified, by the relativistic conception of space and time and by non-Euclidean geometry.
 See the outstanding discussion in Peter Kivy’s, Philosophies of Arts: An Essay in Differences (New York: Cambridge University Press, 1997), pp. 1-54.
 Sometimes, the artworld itself experiences a bout of reactionism. In a fascinating anecdote recounted in The Philosophical Disenfranchisement of Art, Arthur Danto recalls the hostility with which the ideas of his article, “The Artworld” (The Journal of Philosophy 61 (October, 1964), pp. 571-584), were received by the elites of the American formalist school of painting, during a presentation at The Club, an Abstract Expressionist stronghold, even though by that point, formalist painting was of marginal importance, its decline having begun some ten years earlier: “As the stubborn resistances of the members of The Club testify, the ideologies of Abstract Expressionism continued to dominate artistic thought…long past the point where the movement it defined was the creative edge of art history.” Arthur Danto, The Philosophical Disenfranchisement of Art (New York: Columbia University Press, 1986), pp. x & xii.
 Diffey, “On Defining Art,” in The Republic of Art and Other Essays, pp. 56 & 57.
 Ludwig Wittgenstein, Philosophical Investigations, tr. G.E.M. Anscombe (New York: The Macmillan Company, 1953). Regarding the view that meaning is reference, Wittgenstein says in §2, “That philosophical concept of meaning has its place in a primitive idea of the way language functions. But one can also say that it is the idea of a language more primitive than ours.” The tool-box metaphor and its implications are discussed in §11-14, while a partial list of the indefinitely many possible uses of language is presented in §23.
 Morris Weitz, “On the Role of Theory in Aesthetics,” reprinted in Joseph Margolis, ed., Philosophy Looks at the Arts: Contemporary Readings in Aesthetics, Revised Edition (Philadelphia: Temple University Press, 1978), pp. 121 & 127.
 The chief problem for a family-resemblance semantics is to identify relevant conditions of resemblance, inasmuch as everything resembles everything else in some way or other. See the discussions in Robert Stecker, Artworks: Definition, Meaning, Value (University Park, PA: 1997), pp. 18-23 and Kivy, Philosophies of Arts: An Essay in Differences, pp. 30-38.
 Ibid., p. 56.
 Maurice Mandelbaum, “Family Resemblances and Generalizations Concerning the Arts,” American Philosophical Quarterly, Vol. 2 (July 1965), pp. 291-228. I say ‘explicitly’, because Danto had already advanced what was, at least, an implicitly relational account of how we see things as art, just a year earlier, in “The Artworld.”
 George Dickie gives precisely this impression, when, in responding to Weitz’s arguments about the open-endedness of ‘art’, he invokes Mandelbaum’s Relationalism. See his Art and the Aesthetic: An Institutional Analysis (Ithaca: Cornell University Press, 1974), pp. 22-24.
 I suggest something along these lines in my paper, “Normative Criticism and the Objective Value of Artworks,” The Journal of Aesthetics and Art Criticism.
 My assumption, here, is that the search for a definition of ‘art’, as we understand it, does not predate the “modern system of the arts,” as defined by Paul Oskar Kristeller, in his “The Modern System of the Arts: A Study in the History of Aesthetics,” Journal of the History of Ideas, Vol. 12 (October 1951), pp. 496-527 & Vol. 13 (January 1952), pp. 17-46.
 I make this qualification, because to assign deep philosophical insights to Fountain and other Dadaist works is to attribute something entirely inconsistent with the deliberately frivolous spirit of that movement. Fountain’s significance as a reason to switch to relationalist accounts of art is one that was only recognised — indeed, was only recognizable — in hindsight, from the vantage point of the late 1950’s and early 1960’s. Ernst Gombrich said, for example, that “…it has always seemed to me a little incongruous to record, analyse and teach such gestures of ‘anti-art’ with the very solemnity, not to say pomposity, they had set out to ridicule and abolish.” The Story of Art, 16th Edition (London: Phaidon Press, Ltd., 1995) p. 601. It would appear that Diffey is thinking along similar lines, when he laments the “nonsense that…philosophers sometimes talk about readymades,” which “trivializes [Duchamp’s] irony and wit.” Diffey, “On Defining Art,” in The Republic of Art and Other Essays, p. 301, fn. 12.
 This example is from Danto’s Transfiguration of the Commonplace (Cambridge, MA: Harvard University Press, 1981), pp. 31-2.
 If, for example, we are convinced, as Hilary Putnam is, that the meaning of the word ‘water’ on earth is different from the meaning of the word ‘water’ on twin-earth, then the chemical compositions of the two substances (the first being H20, the second being the alien compound, XYZ) are the obviously relevant differentiae, inasmuch as Putnam’s thought-experiment stipulates that in terms of their relations to the intentional states and linguistic practices of English and “Twenglish” speakers, the two terms function identically. Conversely, if we were to attempt to explain by virtue of what sorts of facts Joe Biden is the President of the United States, while Frank Jones, his perceptually indistinguishable twin, is not, it would not be their respectively different body chemistries that constituted the relevant differentiae but rather, the fact that the former participated (and participates) in a certain set of external relationships that the latter does not: specifically, that Joe Biden received the requisite number of votes in the Electoral College to qualify for the status of President, whereas Frank Jones did not; Joe Biden is currently commander-in-chief of the United States armed forces, while Frank Jones is not; etc.
 Ibid., p. 42.
 Hilary Putnam, “The Meaning of ‘Meaning’,” in Mind, Language, and Reality: Philosophical Papers, Vol. 2 (New York: Cambridge University Press, 1975), pp. 245-247.
 For a telling glimpse of the intensity of this controversy, consider Stanley Cavell’s somewhat tormented musings in “Notes and Afterthoughts On the Opening of the Investigations,” reprinted in Hans Sluga and David G. Stern, eds., The Cambridge Companion to Wittgenstein (New York: Cambridge University Press, 1996), pp. 279-284.
 See, for example, Robert Fogelin, “Wittgenstein’s Critique of Philosophy,” in The Cambridge Companion to Wittgenstein, pp. 41-45. Hans Sluga refers to the behaviorist interpretation of Wittgenstein as a “misreading,” in “‘Whose House is That?’ Wittgenstein on the Self,” in the same volume, p. 342.
 “When I say ‘I am in pain’,” Hans Sluga explains, on Wittgenstein’s behalf, “I am not describing anything, I am rather expressing pain.” See his, “Whose House is That? Wittgenstein on the Self,” in The Cambridge Companion to Wittgenstein, p. 340. Fogelin says almost exactly the same thing in “Wittgenstein’s Critique of Philosophy,” p. 44.
 In his terrific little introduction to Wittgenstein, P.M.S. Hacker writes:
I]t is the behaviour of a human being that constitutes the logical criteria for saying of him that he is perceiving or feeling something, thinking or recollecting, joyful or sad. Such behaviour is not mere bodily movements, but smiles and scowls, a tender or angry voice…Human behaviour is not a mere physical phenomenon like the … movements of an industrial robot.
P.M.S. Hacker, Wittgenstein (New York: Routledge, 1999), p. 45.
 Wittgenstein, Philosophical Investigations, §6.
 William Kennick, “Does Traditional Aesthetics Rest on a Mistake?” Mind, Vol. 67 (July 1958), pp. 317-334.
 Diffey, “Essentialism and the Definition of ‘Art’,” p. 31.
 Aristotle, Metaphysics A.
 Stecker, Artworks: Definition, Meaning, Value, p. 50.
 Jerrold Levinson, “Refining Art Historically,” The Journal of Aesthetics and Art Criticism, Vol. 47 (1989), p. 21.