Customer Reviews

Parts: A Study in Ontology

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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. Nevertheless, I confidently predict that the mental toolbox Simons has created will eventually be applied, very profitably, to abstractions, including foundational mathematics.

I don't have much to add that the other reviewer hasn't already said, but I want to make a couple of points about this text.

First is that it is still the best survey of mereology to date. There have been some solid additions to the field that are more recent, but most of them spend more time arguing for a particular philosophical or ontological conclusion than discussing mereological theories and their relationships.

The second point is that this text is too often read solely as a survey of theories of mereology. While the early sections of the book do focus on the formal consequences of different systems, most of the latter part of the book is dedicated to ontological/philosophical questions. I would wager to say that if you are interested in the philosophical problems surrounding persistence or composition, you will find the author's discussion of these problems useful.

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.