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Title: Parts: A Study in Ontology by Peter Simons ISBN: 0-19-924146-5 Publisher: Oxford University Press Pub. Date: 01 October, 2000 Format: Paperback Volumes: 1 List Price(USD): $29.95 |
Average Customer Rating: 4 (1 review)
Rating: 4
Summary: Discover mereology: the mathematics of the future
Comment: Mereology is a theory of the relation of part to whole, one that deviates gently from Boolean algebra and set theory. This is the best book on mereology in existence.
Mereology is Boolean algebra with 1 but no 0, set theory with a universal set but no null set, a semilattice closed under meet but not join. Mereology also has interesting affinities to topology. The mathematical implications of all this have yet to be explored.
Mereology was developed in Poland between the wars. It is also central to Nelson Goodman's (1906-98) "Structure of Appearance."
Woodger at Oxford and Tarski at Berkeley were sympathetic to mereology. David Bostock's brilliant 1970s work on the foundations of numbers has an important mereological component.
The late David Lewis wrote a wonderful book, "Parts of Classes" (1991) in which he derived Zermelo-Fraenkel set theory from a handful of very primitive mereological concepts. Mereology will be part of the mathematics of the future, and "Parts" is an excellent place to begin this journey.
Simons is critical of what he calls "classical extensional mereology" (CEM), but the first 100 pages of his book are by far and away the best survey of CEM ever done. To understand Simons's reservations about CEM, you need to understand some nonclassical logics: free, modal, temporal.
If this book has a flaw, it is that it is more in the nature of a giant survey article than a monograph presenting a coherent body of new knowledge. At the very end of the book, however, the author does commit to an elegant and simple mathematical system. Also, the author claims only to be interested in mereology as a theory of material objects situated in time, disdaining mereology as theory of abstract objects. This would appear to rule out mereology as an alternative foundation for mathematics. I confidently predict that the mental toolbox Simons has created will eventually be applied, very profitably, to abstractions.
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Title: Parts and Places: The Structures of Spatial Representation by Roberto Casati, Achille C. Varzi ISBN: 026203266X Publisher: Bradford Books Pub. Date: 16 July, 1999 List Price(USD): $45.00 |
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Title: Ontology, Identity, and Modality : Essays in Metaphysics (Cambridge Studies in Philosophy) by Peter van Inwagen, Ernest Sosa, Jonathan Dancy, John Haldane, Gilbert Harman, Frank Jackson, William G. Lucan ISBN: 0521795486 Publisher: Cambridge University Press Pub. Date: 22 March, 2001 List Price(USD): $23.00 |
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Title: Four-Dimensionalism: An Ontology of Persistence and Time (Mind Association Occasional Series) by Theodore Sider ISBN: 0199263523 Publisher: Oxford University Press Pub. Date: 01 July, 2003 List Price(USD): $24.95 |
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Title: Universals: An Opinionated Introduction (Focus Series) by D.M. Armstrong ISBN: 0813307724 Publisher: Westview Press Pub. Date: 01 October, 1989 List Price(USD): $29.95 |
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Title: Essays in the Metaphysics of Modality by Alvin Plantinga, Matthew Davidson ISBN: 0195103777 Publisher: Oxford University Press Pub. Date: 01 March, 2003 List Price(USD): $24.95 |
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