Logic and Logical Philosophy 19 (4):309-328 (2010)

Authors
Rafał Gruszczyński
Nicolaus Copernicus University
Abstract
As it is indicated in the title, this paper is devoted to the problem of defining mereological (collective) sets. Starting from basic properties of sets in mathematics and differences between them and so called conglomerates in Section 1, we go on to explicate informally in Section 2 what it means to join many objects into a single entity from point of view of mereology, the theory of part of (parthood) relation. In Section 3 we present and motivate basic axioms for part of relation and we point to their most fundamental consequences. Next three sections are devoted to formal explication of the notion of mereological set (collective set) in terms of sums, fusions and aggregates. We do not give proofs of all theorems. Some of them are complicated and their presentation would divert the reader’s attention from the main topic of the paper. In such cases we indicate where the proofs can be found and analyzed by those who are interested
Keywords formal ontology  mereological sum  set theory  mereological set  mereological fusion  collective set  mereology  mereological aggregate
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DOI 10.12775/LLP.2010.011
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References found in this work BETA

From a Logical Point of View.Richard M. Martin - 1955 - Philosophy and Phenomenological Research 15 (4):574-575.
Pieces of Mereology.Andrzej Pietruszczak - 2005 - Logic and Logical Philosophy 14 (2):211-234.
What is Logic?Hao Wang - 1994 - The Monist 77 (3):261-277.

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Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.

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