Topologia e Astrazione. La Geometria Senza Punti di A.N. Whitehead

Abstract

Euclidean definition of a point as “that which has no parts” has been a major source of debate regarding the epistemological and ontological assumptions of classical geometry, from the Middle Ages to the full development of point-free geometries and topologies in the 20th century. These theories are based on the general idea that the logical-mathematical and philosophical domain of discourse regarding points as supposedly lowerdimensional entities must be reshaped in terms of appropriate higher-order constructs that address only regions or extended bodies. This article focuses on what is undoubtedly the first comprehensive proposal of this kind – A.N. Whitehead’s theory of “extensive abstraction” – offering a synthetic reconstruction of its formal evolution: from the first purely mereological version, through the revisions presented in the late 1920s, to the final, topological formalization in Process and Reality. Starting from these considerations, in conclusion some considerations will be made on the role of abstraction in Whitehead’s philosophy of process.