Whitehead’s mereotopology and the project of formal ontology

Por • 19 may, 2017 • Sección: Leyes

Sébastien Richard

Mereology is the theory of wholes and parts. The first formal mereology was developed by Husserl in his third Logical Investigation at the beginning of the twentieth century. In 1916 Stanisław Lesniewski gave the first axiomatization of a classical extensional formal mereology. That same year, Alfred North Whitehead also gave a sketch of a mereology in “La théorie relationniste de l’espace”. It was developed in the perspective of a theory of space in which the concept of point is no longer considered as primitive, but is built in terms of the relations between objects. This project was then taken up and amplified in the wider perspective of the method of extensive abstraction presented in An Enquiry Concerning the Principles of Natural Knowledge and The Concept of Nature. Afterwards, Whitehead added to what was first a theory of the part-whole relation some definitions of topological notions such as junction. This would allow a first analysis of the concept of boundary. These topological reflections were then only reduced to mereological ones and it is only in Proces and Reality that Whitehead developed a directly topological theory in which the mereological concepts can be defined. Our purpose in this paper is to study these three mereo-topological theories and to set them out in a formalized way, in order to finally question about their possible axiomatization.

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Vol 54, No 214 (2011) > Richard

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