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Logic for Mathematicians (Dover Books on Mathematics) Paperback – December 18, 2008


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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 590 pages
  • Publisher: Dover Publications; 2 edition (December 18, 2008)
  • Language: English
  • ISBN-10: 0486468984
  • ISBN-13: 978-0486468983
  • Product Dimensions: 9.1 x 5.9 x 1.2 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #1,353,589 in Books (See Top 100 in Books)

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3 of 3 people found the following review helpful By A.E.V. on August 3, 2013
Format: Paperback
While I think there are better books on first order logic (Quine's, for instance), this one is still quite good. What makes this book truly remarkable, though--unique, even--is its coverage of set theory. It develops the subject matter of a good elementary set theory text, but does it within the framework of Quine's New Foundations (NF) set theory. NF is the chief alternative set theory to Zermelo-Fraenkel and related systems, and no other text that I'm aware of develops NF's theory of cardinals and ordinals in anywhere near as much detail. For those wishing to study NF, or to see mathematics implemented more fully in radically different set theory, this book is an indispensible resource.
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3 of 3 people found the following review helpful By Alan U. Kennington on July 19, 2013
Format: Paperback Verified Purchase
This substantial 1953 book is a modernized presentation of the topics and approach of the Principia Mathematica of Whitehead and Russell (1910, 1912, 1913). So this would be a great companion book to that famous 3-volume work.

In this Logic for Mathematicians Dover book by John Barkley Rosser, the Whitehead/Russell theory of types is replaced by "Quine's New Foundations" (page 206), which is an unfortunate choice, but nowhere near as bad as the Whitehead/Russell theory of types!

Rosser uses the almost unreadable Peano-style dot-notation instead of modern grouping-parentheses, but does use parentheses for logical quantifiers. So the set of non-negative integers is defined like this:

x((β)::0∈β:(y).y∈β⊃y+1∈β.:⊃:.x∈β),

which I think most people would find difficult to parse! (There's actually a hat on the first "x" which I can't type in HTML.) By the way, that definition of the integers (if you do make the effort to parse it), says effectively that the integers are the intersection of all classes which contain zero and all of its successors. That's not the kind of definition which most working mathematicians would prefer to use these days.

Rosser gives an excellent presentation of the possible solutions to Russell's paradox on pages 197-207. There are many fascinating historical discussions, as well as lengthy comments on the application of logic to practical mathematics.
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2 of 6 people found the following review helpful By John-michael Kuczynski on April 14, 2011
Format: Hardcover Verified Purchase
This book is thorough and (so far as the discipline allows) approachable. It's like a sequel to Quine's Mathematical Logic.
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2 of 7 people found the following review helpful By L. Shalla on January 7, 2010
Format: Paperback Verified Purchase
This book is an improved version of the Principia Mathematica by Whitehead & Russel. It is a thorough overview of mathematics.
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