This reproduction by Merchant Books of the 1910
Principia Mathematica
(Volume I) by Whitehead and Russell is very nicely printed. It's crisp and clear, with good binding which makes it a delight to turn the pages.
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.
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For true lovers of logic and math
This item met my expectations in that it is a historical peice of mathematics and allowed me to gain a greater appreciation for early 20th century endeavors into the foundations of mathematics. The book, however, is not a pinacle of perfection. There are a couple a corrections to the text in the book, visible as handwritten corrections that were included in the printing, with the earliest correction of this kind found in the first chapter at the discussion of referents and relata. I would recommend this book to any true lover of logic, but would not recommend this book to anyone who firmly dislikes mathematics.
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Came as promised. On time at a very reasonable price. Thank you!
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Reviewed in the United States on February 10, 2012
Reviewed in the United States on October 7, 2016
This item met my expectations in that it is a historical peice of mathematics and allowed me to gain a greater appreciation for early 20th century endeavors into the foundations of mathematics. The book, however, is not a pinacle of perfection. There are a couple a corrections to the text in the book, visible as handwritten corrections that were included in the printing, with the earliest correction of this kind found in the first chapter at the discussion of referents and relata. I would recommend this book to any true lover of logic, but would not recommend this book to anyone who firmly dislikes mathematics.
Images in this review
Reviewed in the United States on February 2, 2015
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Eduardo Ugalde
Principia Mathematica, primera edición 1910-1913
Reviewed in Mexico on July 22, 2016
