Mathematical Logic and the Foundations of Mathematics: An Introductory Survey (Dover Books on Mathematics) 0th Edition by G. T. Kneebone (PDF)

Description

Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I agree with the lone reviewer that the book is dated. This has been a field of furious study with applications to robotics and artificial intelligence. But i don’t agree with the reviewer that this book is not, for it’s time, truly wonderful. Even fifty years after its original publication it still got a lot of things right in terms of settled issues from a philosophical perspective. If you want to understand what mathematics is and the impact of the crisis in mathematics in the mid 20th century and its implications how mathematics is understood and practiced today this book could be a revelation for many. I could have wished the author had seen fit to write a 2nd edition that i would gladly purchase. I know he was instrumental in clarifying a lot of my thinking.

⭐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 Part 1 is mostly a shoddy and outdated introduction to symbolic logic.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.

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