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. [...]
[...] This could mean that the surface of a table could be the leg of the table, since there are no borders between one part of the entity and the other part of the entity. This is clearly not what Whitehead had in mind, but nevertheless, this is what such a doctrine leads to. This issue of boundaries poses some very troubling situations to mereotopology. At what point, for instance, is there a boundary between one thing and another. Aristotle pointed out the unanswerable question, ‘When a moving thing comes to a stop, is it at motion or at rest?' This is why it is important to see boundaries as non-spatial entities, or more specifically, abstract entities, not literal things in space. [...]
[...] The point that is made with underlapping and overlapping, as seen in the closure mereology model, is that, in the case of the cat losing its tail, a cat needn't be the only whole which a tail is seen in. With closure mereology, the assumption is made that the parts that make up the whole are not solely parts of that entity, rather, the parts (like the tail of the cat) are, as some may say, incidental characteristics of the whole. [...]
[...] So, the amalgam of mereology and topology are, as Casati and Varzi see it, essential to the development of a coherent ontological theory of identifying entities. Another issue that is brought up in view of mereology and topology is that of an entity's identity. How is it that any entity can be identified, in view of part removal, shape changes and the like? One suggestion is that of temporal parts. Accordingly, an entity possesses a part at time to where, even though at time z it loses this part, it still possesses y at that time. [...]
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