Customer Reviews

Mathematical Logic and the Foundations of Mathematics: An Introductory Survey (Dover Books on Mathematics)

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This is a recently issued Dover reprint of a 1963 Van Nostrand book. It contains a rough coverage of some mathematics, some history, and some philosophy. You need some familiarity with mathematical logic to read the book, but it certainly isnt "graduate-level" as claimed in the editorial review. It's divided into three parts. Part 1 is mostly a shoddy and outdated introduction to symbolic logic. People who dont already know this material will probably be confused by the presentation, and people who have taken a class in mathematical logic will find it dull and clumsy - skim it. Part 2 is a history of the major developments in mathematical logic and foundations from around 1870 to 1940. This coverage is ok but dated, not so much because of the omission of more recent events, but for the lack of critical perspective from the period Kneebone is discussing. He reviews all the historical material you would expect in an introductory survey, without offering anything particularly insightful, and sometimes fails to emphasize the truly important innovations against the background of lesser technical apparatus. Part 3 is a lightweight look at philosophy of mathematics, the longest section focusing on Whitehead's epistemology. Overall the book is routine, broad but not deep, and somewhat outdated.