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Comparing Bearden's jazz-themed canvases with the music to which they are linked on Branford Marsalis's Romare Bearden Revealed CD, this chapter interrogates the presumption of a formal equivalence between music and painting. It argues that such a presumption overlooks the aesthetic experience of listeners and viewers, whose different responses need to be taken into consideration.

This chapter continues the investigation of visual art begun in the introduction, examining the charges lodged against artist Kara Walker in 1997 that her silhouette installations present “negative images” of black people. It conceives those claims about negative black images as a reaction against the principle of abstraction that clearly informs Walker’s figural depictions, and on which abstractionism itself necessarily depends. The chapter then considers the myriad ways in which abstraction has in fact historically been deployed to black people’s detriment, whether in social, political, or aesthetic terms, making it an understandable object of suspicion within African American culture. Maintaining that abstractionism is nevertheless a potentially powerful tool for African Americanist critique, the chapter concludes by outlining some of the historical reasons that visual art in particular is not especially hospitable to abstractionist strategies at this juncture, thereby clearing the way for a consideration of what other art forms promise in this regard.

We offer a general introduction to Abstractionism by outlining its history and by presenting the core philosophical and mathematical tenets of the abstractionist projects. We then locate the 16 contributions to our volume within the current debate of Abstractionism.

The introduction lays out the problem to be addressed and summarizes the argument to be made in the rest of the book, taking as its point of reference a 2011 controversy over a proposed public sculpture for Indianapolis by Fred Wilson, which members of the city’s black community saw as presenting a “negative” African American image. Explicitly appropriating as its primary element the figure of a newly unenslaved black man featured in the city’s existing Soldiers and Sailors Monument of 1902, the sculpture design made racial representation itself an object of critical inquiry, and so perfectly exemplified the aesthetic abstractionism championed in this book, which the introduction characterizes in terms of Bertolt Brecht’s “alienation effect.” Noting that critics of the design nevertheless willfully disregarded its critical engagement with the earlier sculpture, the introduction ultimately suggests that visual art is severely limited in its capacity to mobilize abstractionist critique.

Positing that narrative coherence is the sine qua non of a literary realism that is epitomized specifically in prose, this chapter argues that it is therefore in nonrealist, experimental prose that abstractionism can register its greatest impact. It begins by demonstrating how the resolute realism of writings by Ntozake Shange, Alice Walker, and Gloria Naylor opened them to charges of negative black portrayal throughout the 1980s. It then closely reviews John Keene’s 1995 experimental prose piece Annotations, in order to demonstrate how that work manages to present an African Americanist critique of twentieth-century U.S. racial politics even as it refrains from delineating identifiable characters or elaborating a recognizable story. The chapter thus finally offers up Annotations as a model of abstractionist African American literary practice, and suggests that such work should be understood as definitive of African American literature per se.

This chapter analyzes the argument for idealism sketched in the opening sections of Berkeley’s Principles. It is argued that Berkeley does not find idealism self-evident, does not attempt to base idealism on immaterialism, fails to construct a simple argument from anti-abstractionism to idealism, and does not invoke the likeness principle to fill out his argument for idealism. Berkeley provides two simple arguments for idealism. The first is that sensible objects are perceived by sense, anything that is perceived by sense is an idea, and hence sensible objects are ideas. The second simple argument is that sensible objects are collections of sensible qualities, all sensible qualities are ideas, and hence sensible objects are collections of ideas. Importantly, Berkeley does not argue, as some scholars think, that the ideality of sensible objects follows directly from the fact that it is impossible to conceive such objects existing unconceived.

The abstractionist program of foundations for classical mathematical theories is, like its traditional logicist ancestors, first and foremost an epistemological project. Its official aim is to demonstrate the possibility of a certain uniform mode of a priori knowledge of the basic laws of arithmetic, real and complex analysis, and set theory. Traditional logicism aimed to show that mathematical knowledge could be accomplished using only analytic definitions and theses of pure logic and hence is not merely a priori if logic is but is effectively a proper part of logic. Abstractionism, however, adds abstraction principles to the base materials employed in the traditional logicist project—principles that, at least in the central, interesting cases, are neither pure analytic definitions nor theses of pure logic as conventionally understood. Thus, whatever significance they may carry for the prospects for logicism, the epistemological significance of technically successful abstractionist projects must turn on the epistemological status of the abstraction principles used, with any demonstration of a priority in particular being dependent on whether those principles can themselves rank as knowable a priori. My primary focus here will be on this natural thought.