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The Marriage of Mereology and Topology: A coherent theory of Ontology

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  1. Introduction
  2. Mereology as an assumption about the relationship between simples
  3. Extensional mereology
  4. Closure mereology
  5. Moving from entity identity to the entity itself
  6. Conclusion

In the study of Ontology some peculiar issue arise out the study of entities and what make them up. The first thing that one notices is that there are parts of things and wholes that are the things which we view ontologically. This ontological status of parthood as relating to what the parts comprise had necessitated philosophers to devise a theory, a sub-theory of ontology, to account for this phenomenon. This sub-theory of the study of the relationship parts to wholes is called Mereology. Mereology goes back to the early Greeks, such as the atomists, who tried to account for how individual entities came together to make a distinct entity from themselves solely from the aggregation of the parts. Although the study of mereology was not coined at this time, it is often viewed as an early attempt to create a coherent theory of mereology, or the study of parts to wholes. What will be done in this paper is an overview of mereology and a mathematical theory called topology (the study of preserving the integrity of a shape even when it loses its original form) which is translated into ontology by two authors, Roberto Casati and Achille Varzi. These two authors contend that mereology, alone, is insufficient to account for the sustained identity of an entity by a mere appeal to the summation of its parts. This thesis of Casati and Varzi will be shown in concert with a background of the issues and debates surrounding mereology.

[...] One can not simply point at the surface of a table and the surface of an apple and say, ?there is the border'. This is because, as soon as one identifies the part of the entity that is supposedly between it and its environment, whether it be a table or an apple, it turns out to merely be a part of the entity. If it is a part of an entity, then it is not some intermediary entity that serves to distinguish one entity from another. [...]

[...] Because the connection between such parts is only possible when identifying the part as a member in a class of things that comprise a particular whole thing, like the top of a bikini is a member of the class of things that comprise a bikini, extensional mereology seems to solve the dilemma of distinguishing ostensibly connected parts and seemingly unconnected parts. Extensional mereology, prima facie, solves the problem of identity, but leaves wide open another problem looming behind the scenes. [...]

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