Whitehead's mereotopology and the project of formal ontology (Q2910358)

The author (F.N.R.S., Université Libre de Bruxelles) questions the specificities of Whitehead's mereotopology. To do so, he explores the differences and complementarity between mereology, topology, and formal ontology.NEWLINENEWLINEHusserl's (1900) and Leśniewski's (1916) contributions are well known: a mereology is a formal theory of the part-whole relation and cognate concepts; a topology is a geometry of sorts that is concerned with the most basic properties of space, such as continuity, connectivity and boundary, abstracting thus from metrical and from projective concepts. Mereotopology was originally a Whiteheadian field: after De Laguna criticized (in 1922) his first mereology, Whitehead reformed it with the help of topological assumptions taking into account his newly adopted ``epochal theory of time'' (according to which there is a minimal event).NEWLINENEWLINEThe author contrasts Vuillemin's and Simons's formalizations of Whitehead (implemented with some of Leśniewski's notations) in order to rework the axiomatization of mereotopology. His argument proceeds in four steps: the mereology of \textit{A. N. Whitehead}'s [``La théorie relationniste de l'espace'', Rev. de métaph. et de mor. 23, 423--454 (1916; JFM 46.1283.01)]; the mereo(-topology) of his [An enquiry concerning the principles of natural knowledge. Cambridge: University Press (1919; JFM 47.0049.02)]; the (mereo-)topology of his [Process and reality. An essay in cosmology. Cambridge: University Press (1929; JFM 55.0035.03)]; some concluding comments on the relation between mereotopology and formal ontology.NEWLINENEWLINEIn 1916, Whitehead uses the concept of extension to sketch a pointless (or point-free) geometry, thereby arguing against the ``absolute theory of space'': space does not come first and the concept of point is no longer a primitive notion, it is a complex entity built in terms of relations of extension. In 1919, Whitehead introduces the more ambitious (because of its process ontological premises) concept of extensive abstraction operating on events: the spatial point and the temporal instant are no longer data of actual experience. By definition, events are extended and every part of any event is itself an event (there is no minimal event). Simons's axiomatization is here commented on. In 1929, Whitehead introduces the (creative) relation of extensive connection operating on regions. Mereological notions are now defined by topological relations. Simons is again very much in demand. In conclusion, the author argues that there is no formal ontology to be found in Whitehead.