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Title: Parts and Places: The Structures of Spatial Representation by Roberto Casati, Achille C. Varzi ISBN: 0-262-03266-X Publisher: MIT Press Pub. Date: 16 July, 1999 Format: Hardcover Volumes: 1 List Price(USD): $42.00 |
Average Customer Rating: 5 (2 reviews)
Rating: 5
Summary: Splendid intro to contemporary mereology
Comment: I like this book very much but cannot say that I have assimilated much of it yet. But it describes a line of thinking which I think is going to come into its own over the course of this new century. The bibliography is excellent.
Mereology all begins with Husserl's Logical Investigations in 1901. These have little impact, and were not translated into English until 1970. Whitehead writes on related subjects, but he made for notoriously hard reading. (In the 1980s, Bowman Clarke splendidly corrects Whitehead's theory.) The American Theodore De Laguna adds his 2 cents worth in 1922. Lesniewski in Poland writes fascinating stuff on this topic, but nobody understands him except his brilliant student Tarski, who writes a nice little introduction but buries it as a technical appendix to a British book on mathematical biology. The USA philosopher Nelson Goodman finally produces a user-friendly version, and calls it the calculus of individuals. Nobody pays much attention, and that's a pity.
The formal theory of part and whole finally takes off in the 1960s and now flourishes. Parts and Places is an excellent university level introduction to this theory, known as mereology.
Mereology is seen as a type of philosophy, and Casati and Varzi are most definitely highly competent philosophers writing in the relaxed manner of contemporary English language philosophy. But I submit that mereology is a form of math, altho' one unlike the chicken tracks that pass for math nowadays. This is math as math should be. Here's a little giveaway. C&S, like Peter Simons, refuse to apply mereology to abstract entities, and focus exclusively on material ones. Result? They are, IMHO, doing a sort of deep geometry. Another giveaway: C&S often mention topology.
Like it or not, contemporary metaphysics has grown ever more mereological in flavor. Mereology is useful for cognitive science, and probably for linguistics. It may find applications in physics, can't say for sure. David Lewis, in his "Parts of Classes" convinced me that a mereological refoundation of ZF set theory was possible. I believe, along with Richard Martin (1916-85) that all of mathematics will eventually be recast on mereological lines. Many of the details have already been worked out; consult any topology text. If mereology displaces set theory, P&P and "Holes" become classics.
Mereology is first order logic with equality and a primitive dyadic predicate interpreted as "is included in" or "is part of".
If you grant the useful fiction of a null individual, then much
of the mathematics of mereology is good old Boolean algebra. Otherwise mereology is a join semilattice.
This book has a close competitor: Peter Simons's "Parts" of 1987.
The first 100 pages of Parts is a better introduction to the formalities of classical mereology than P&P. Sadly, he does not believe in that theory. Simons's bibliography is even more thorough than C&S's for the pre 1986 period. But Simons gets bogged down in philosophical issues. For instance, he thinks that mereology must be done with free logic instead of first order logic. He does not give the impression that mereology is a formal system with a promising future. C&S most definitely do.
Rating: 5
Summary: Nice to see some new ideas...
Comment: Sometimes it seems like philosophy has been caught in amber since the days of Aristotle and Plato with the same tired arguments simply being restated. Or perhaps it is simply the fact that to be anywhere outside of the "box" in philosophy immediately makes one a crank.
Casati and Varzi have bucked the trend to rehash old ideas and have broken a lot of new and very interesting ground in mereotopology. That is, they have put the study of parts and wholes (mereology) on some firm footing by starting with some ideas from topology and creating a first level theory.
Funny as it seems, the area of describing the ontology of wholes and their parts has been very fuzzy since the days of Aristotle. Only in a very literary sense have this "minor" (only kidding, of course) area been explored in the history of philosophy; something the reader realizes very quickly a chapter into this book.
This book is not for the faint of heart or those without some background in formal expressions. I believe the authors have English as a second language and, although the language is proper, it is also somewhat formal. I kept hoping for some breaks for humour or at least some variation in language but this book is a bit relentless.
The authors develop many axioms for mereotopology for everything from "standard" topological relations up to holes and boundaries. Many relations we would consider to be basic (read: boring) and mundane are revealed in a new light when one attempts to formalize them.
The only possible nit I would pick with the book is the fact that many areas have now recieved further treatment from the authors. In other words, I feel this book was released a bit too soon since, if one reads the papers at the author's websites, one sees the interesting developments. Particularly fiat boundaries, which are very interesting for many reasons, recieve only passing treatment in the book. One must read papers for more.
The authors also do not get into any epistemological arguments which I feel would not be out of place. Given that many axioms owe a great deal to how one defines "truth" the authors need a little more included in the book; they also have some very interesting ideas in this area.
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Title: Parts: A Study in Ontology by Peter Simons ISBN: 0199241465 Publisher: Oxford University Press Pub. Date: October, 2000 List Price(USD): $29.95 |
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Title: The Logical Syntax of Language (Open Court Classics) by Rudolf Carnap, Amethe Smeaton ISBN: 0812695240 Publisher: Open Court Publishing Company Pub. Date: January, 2003 List Price(USD): $24.00 |
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Title: Ontology, Identity, and Modality : Essays in Metaphysics 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: Concepts of Space : The History of Theories of Space in Physics: Third, Enlarged Edition by Max Jammer ISBN: 0486271196 Publisher: Dover Pubns Pub. Date: 07 January, 1994 List Price(USD): $12.95 |
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Title: From a Logical Point of View: Nine Logico-Philosophical Essays by Willard V. Quine ISBN: 0674323513 Publisher: Harvard Univ Pr Pub. Date: December, 1980 List Price(USD): $17.50 |
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