In this paper, we first discuss the characteristics of contemporary art and argue that the concept is a key factor of contemporary art. This paper begins with Duchamp’s “Fountain,” which can be regarded as the retrospective origin of contemporary art and emphasizes the importance of the impact of visual materials and the historical background of the artworks. We then discussed the concept of “date painting” by On Kawara as a typical example of conceptual art. In this concept, the unexchangeable unique date and the proper name as On Kawara are connected to human race as a collective of proper names through the activity of making date paintings under the rules of date painting production. Furthermore, by using Rei Naito’s “Matrix,” we discuss how this artwork deeply appeals to the viewer’s emotions through the concept of “water,” which represents the Teshima island where this artwork is placed, and the key word of the “earth,” which Naito has consistently advocated. In the final section, we applied the method presented by Gregory Bateson in the analysis of Bali paintings to Kawara’s and Naito’s works. We discuss that all artworks, including contemporary art, are the presentation of the correspondence between the material of the work and the world outside of the material. We conclude that these correspondences constitute the communication structure between the artist and the viewer.