Research seeking a scientific foundation for the theory of art appreciation has raised controversies at the intersection of the social and cognitive sciences. Though equally relevant to a scientific inquiry into art appreciation, psychological and historical approaches to art developed independently and lack a common core of theoretical principles. Historicists argue that psychological and brain sciences ignore the fact that artworks are artifacts produced and appreciated in the context of unique historical situations and artistic intentions. After revealing flaws in the psychological approach, we introduce a psycho-historical framework for the science of art appreciation. This framework demonstrates that a science of art appreciation must investigate how appreciators process causal and historical information to classify and explain their psychological responses to art. Expanding on research about the cognition of artifacts, we identify three modes of appreciation: basic exposure to an artwork, the artistic design stance, and artistic understanding. The artistic design stance, a requisite for artistic understanding, is an attitude whereby appreciators develop their sensitivity to art-historical contexts by means of inquiries into the making, authorship, and functions of artworks. We defend and illustrate the psycho-historical framework with an analysis of existing studies on art appreciation in empirical aesthetics. Finally, we argue that the fluency theory of aesthetic pleasure can be amended to meet the requirements of the framework. We conclude that scientists can tackle fundamental questions about the nature and appreciation of art within the psycho-historical framework.