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While this is a math book, it contains almost no symbolic notation whatsoever (except in an Appendix) and that is its main flaw. First order logic augmented by a bit of mereological notation would have made the argument easier to follow. Anybody who does not understand first order logic and the ZF axioms of set theory has no business attempting this book. Otherwise it is a wonderfully readable contribution to the foundations of mathematics.
Lewis argues that the part-whole relation, not sets should be taken as the foundation of math and abstract reasoning. The formal theory of the part-whole relation is called mereology. Mereology is a mathematical theory, but is entirely the work of philosophers. While part-whole thinking was implicit in a lot of metaphysics from Aristotle onwards, and in math from Euclid onwards, formal mereology begins with Lesniewski (who coined the term) and Whitehead (however Principia Mathematica is innocent of all mererology). Mereology has ever since been a respected part of Polish logic.
Nelson Goodman tried hard to Americanize mereology, starting with his 1940 JSL article with Leonard where he called it the "calculus of individuals." Since 1970, mereology has acquired a bit of a following in the higher reaches of philosophy. But if David Lewis is right, mathematicians, especially set theorists should be paying close attention to mereology. Lesniewski's mereology is forbidding. But the American flavor, of which Lewis's book is an example, is a much gentler thing.
Lewis was not the first person to argue that the Zermelo-Fraenkel axioms for set theory can be derived from simpler mereological axioms. He freely admits that a fellow named Bunt scooped him in 1985. He does not appear to realize that Richard Martin made this point even earlier in "Common Names and Mathematical Scotism" reprinted in his 1980 collection of essays on Peirce.
The book is filled with Lewis's tart wit and gentle humor. Had more math been of this nature, I would have majored in math.
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which offers one of the best dicussions I have ever read on trying to identify these elusive concepts and how they relate to the contemporary world. From there various specialists discuss a sample of about 150 groups and cultures from all six continents. Their text is supplemented by excellent photography of some of these groups/cultures which portrays them not in their traditional pasts but as they live today. The text closes with "Afterword: Cultures in Crisis" by Wade Davis which establishes an interesting concept of the"ethnosphere" and how many of its components (cultures) are imperilled by the onrush of contemporary technological and societal development. The book closes with an extensive list of groups/fcultures and their locations around the world, perhaps one of the largest such list ever published (although not totally complete).
The book offers an excellent summation of the peoples of the world at the dawn of the twentyfirst century. It strikes a good balance by presenting the realities especially of smaller indigenous ethnic groups/cultures around the world but largely avoids the contemporary fashion to patronize them. Although I disagree with some points in the Afterword I highly reccommend this book to anyone who is interested in the nature of mankind.
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