Continua and clustering processes. The connection between the idea of form and the question of continuity in Peirce’s thought

Peirce’s definition of topology is strictly related to the connection models of the parts of continua. In the last part of his life, Peirce elaborated his topological analysis of continuity in order to answer some important questions which arose in his early works. This paper demonstrates that it is very important to connect the topological analysis of continuity with the questions it tries to answer. If not connected to the basic questions topology tries to answer, topological analysis may appear as the search for a hidden structure that keeps reality together, something to which reality must be traced back to be understood. This hidden structure is the continuum conceived as a precondition that justifies the unity of reality. By contrast, if we reconnect Peirce’s idea of continuum to the questions it attempts to answer, the continuum appears no longer as the condition of possibility for the relations that constitute the unity of reality. On the contrary, it appears as a form whose formation itself is conditioned by relations.