Sometimes theories of art are considered in isolation from broader intellectual concerns. One strength of Arthur Danto’s much-discussed aesthetics lies in its intimate relationship with his philosophical system. The definition of art is linked to theories of action, knowledge and historiography. That analysis is summarized in his book Connections to the World: The Basic Concepts of Philosophy, which presents a simple triangular diagram: subject/representation/world. The subject acts on the world, and the world causes representations. The relations are between the world and the subject, between the subject and its representations, and between the representations and the world. The first relation is that of causality, and the third that of truth [1].And to understand the second relation, we need a theory of the self, that is, an explanation of the connection between the representations and the person experiencing them. Danto claims that pretty much every basic philosophical position can be defined in relation to this structure. We are connected to the world; we are aware of the continuity of experience; we act upon the world: These relationships must be described.As it stands, this diagram raises an interesting problem. Danto offers a comprehensive list of everything that exists: the subject, the representations and the world. He refines the analysis in two later versions of this diagram, also in Connections to the World, in which he presents true belief, a relationship between the subject, a proposition and facts, and in the account of action when he describes the triangular relationship between the subject, an idea and an object [2]. In all three diagrams there are subjects, representations and the world. The task of philosophy is to sketch their relationships as revealed in knowledge and action.How then should we understand the place of this diagram itself in this philosophical system? In another book, his treatise on historiography, Danto writes, “It is always a fair question to put, whether a theoretical work on history can apply its theories to self” [3]. The same point can be made about this diagram. Since the diagram shows all that exists, it’s a fair question to ask what its place is in that discussion. The diagram cannot be a representation because it includes also both the world and subject if we accept Danto’s theory; and it cannot be a subject or the world either. Danto wants to diagram a view of the relationship between the world and representations that stands outside of the world. But how is that possible?Danto’s diagram creates an interesting philosophical problem, which he (surprisingly in my judgment) doesn’t consider. What exists according to him are three distinct kinds of things—subject, representations and world. From what point of view, then, are these things presented in his diagram? Thomas Nagel discusses “the view from nowhere” to identify the goal of this search for an impersonal point of view [4]. Without reference to Danto, he identifies a real philosophical problem. A painter must depict a landscape from some particular point of view. Danto wants to diagram a view from nowhere, an illustration of the relationship between the world and its representations, which stand outside the world. But how is that possible? If you are above a city, you can view it as a whole. And if you could stand above the earth, you would see the entire planet from that vantage point. But there’s no way that you can look at the world from outside and describe its structure as the diagram supposes. There is a contradiction in claiming that all that exists are subjects, their ideas and objects, and showing that in a triangular relationship, a diagram with a God’s-eye point of view. We are looking at the world from a viewpoint that is, by hypothesis, outside of that world.Perhaps, then, this diagram is akin to the illustrations of “impossible worlds” discussed by Ernst Gombrich in Art and Illusion, with reference to examples by William Hogarth and M.C. Escher, structures that “cannot exist in our world” [5]. They look like pictures of reality but the elements depicted don’t fit together. There are illogical effects in Hogarth’s engraving False Perspective (1754). The man on the distant hill looks as large as the woman bending out of the window of the inn and can be seen to light his pipe at her candle. The trees on the hill appear to become larger the further their distance from us, and yet some of them overlap the inn sign [6].Maybe, then, Danto could simply have omitted his diagram. Were Connections to the World printed minus these three diagrams, no real loss would be suffered, though the argument might be more difficult to follow. But that doesn’t really resolve this problem, for it would be easy enough for someone else to turn the diagram into an artwork.Imagine that we’re looking at a small artwork—a drawing of a triangle. The three points are labeled subject, representation and world, and are joined by three straight lines. This seems a simple linear drawing. But the reader may ask, Is this artwork not the very diagram by Arthur Danto that you critically analyzed earlier? It is and it isn’t. Danto claimed that after the early period, when he both made artworks and did philosophy, he quit art-making. But in Connections to the World, one finds three potential artworks—the diagrams we have discussed. More exactly, these diagrams are not works of art but, as Danto makes clear, illustrations of his argument. A diagram differs in kind from a work of art. For example, the scale, color of lines and typeface would matter in an artwork but not for a diagram, which needs only to include the words “subject/representation/world” and the three straight lines linking them.Imagine, then, that an artist reads Danto’s books and chooses to make copies of his first diagram. A devoted reader of his accounts of Warhol’s Brillo Box, she takes Danto’s diagram and turns it into an artwork called Diagram—a drawing that is indiscernible from the banal image reproduced in the University of California Press paperback edition of Connections to the World. A midcareer artist who shows at a good gallery, she asks a good price for her image, a product, she says, of years of philosophical study and training as a visual artist; she asks a price considerably higher than what Amazon asks for Danto’s book, $31.95, postage included for Amazon Prime members. Soon enough, the Museum of Modern Art purchases the drawing, puts it on show and sells full-size limited-edition replicas in its shop.And then, taking my story full circle, after visiting the exhibition of Diagram, a graduate student in philosophy at Columbia University sends to The Journal of Philosophy her submission “The Artworld” whose title, she says, is itself a Danto indiscernible, though its contents are very different, she argues, from that found in Danto’s 1964 publication, which it duplicates word-for-word [7]. In her version of that essay, taking up the passage where we read of “the difference between a Brillo box and a work of art,” she writes: “It is the theory that takes it up into the world of art and keeps it from collapsing into the real object, which it is (in a sense of is other than that of artistic identification)” [8]. Here, she says, we see the true difference between the artwork Diagram and the mere diagram in Connections to the World. After all, she observes, we know that “to be a work of art is to be (i) about something and (ii) to embody its meaning” [9]. And here she quotes from her treatise in progress, tentatively titled After the End of Art: Contemporary Art and the Pale of History. “What I have learned from Danto,” she observes, “is how to use visual and verbal indiscernible images and texts whose meaning depends upon the context in which they are presented.”Here I extend the account of my text “Indiscernibles and the Essence of Art: The Hegelian Turn in Arthur Danto’s Aesthetic Theory,” The Library of Living Philosophers. Volume XXXIII. The Philosophy of Arthur C. Danto (Chicago: Open Court, 2013) 215–228. Danto discusses thought examples like Diagram copying “The Artworld” and After the End of Art in The Transfiguration of the Commonplace: A Philosophy of Art (Cambridge, Massachusetts: Harvard University Press, 1981). Thanks are due to Lydia Goehr, Joachim Pissarro and Robert Stecker for comments on earlier drafts.