- Paperback: 684 pages
- Publisher: Merchant Books (February 21, 2009)
- Language: English
- ISBN-10: 1603861823
- ISBN-13: 978-1603861823
- Product Dimensions: 7.5 x 1.4 x 9.2 inches
- Shipping Weight: 2.4 pounds
- Average Customer Review: 4.3 out of 5 stars See all reviews (12 customer reviews)
- Amazon Best Sellers Rank: #1,857,051 in Books (See Top 100 in Books)
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Principia Mathematica - Volume One
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Top Customer Reviews
The first volume is the rosetta stone of what might look like some arcane language, but it is actually both a practical and philosphical discussion of how to logically approach mathematics.
While their text is not casual, it is conversational as they talk through the process. Their discussion illustrates common fallacies and serve as instruction to the student. It is by no means pleasure reading, but if you really read the text, you will learn alot. At least I am.
Both Whitehead and Russell are known for their insights into philosophy and mathematics. This book, although a mathematics book, is based upon their philosophy of how the universe works. The basic assumption of this book is that symbolic logic can be used to describe the universe. From that starting point they develop the elements of modern mathematics.
This book is meant for those of us nerds who want to understand why mathematics works and how it relates to a philosophy of the universe. Note that this book is heavy on mathematical symbols (which are explained). It can be slow reading, but Whitehead and Russell's insights are stunning.
It is difficult to think of any other work in the mathematical foundations literature which has been so significant or influential in the development of the modern approach. Although the Whitehead/Russell theory of types has been abandoned in favour of the type-free Zermelo-Fraenkel and Neumann-Bernays-Gödel approaches, most aspects of the Whitehead/Russell approach have been incorporated into the modern literature.
The first half of Volume I presents mathematical logic, both propositional calculus and predicate calculus, and a theory of classes which is essentially equivalent to a set theory. The second half of Volume I presents some introductory concepts which are used in the first half of Volume II for cardinal arithmetic.
The notation of the Principia Mathematica is unfamiliar in some ways, but a large proportion of the modern conventions for notating logic and set theory have their historical origins in this book, which in turn obtained many notations from the works of Peano and Frege. The main obstacle for the modern reader might be the dot-notation. Unfortunately, this annoying dot-notation (which was based on Peano's 1889 dot-notation) was adopted by many authors during the 20th century. With a bit of effort, though, one starts to be able to quickly convert the logical formulas into modern parenthesis-notation.
After the Russell/Whitehead Principia Mathematica, no other work attempted to fully write out a derivation of the foundations of mathematics from the lowest levels of logic up to the theories of real numbers and series. Their bold claim that mathematics can be securely based on pure logic issued a challenge to later authors to continue and develop the logicism research program, which effectively achieved success by about 1970.