Principia Mathematica to *56 (Cambridge Mathematical Library)
Could it be true that Whitehead and Russell's Principia Mathematica is the most influential book written in the 20th century? Ask any mathematician or philosopher--or anyone who understands the impact these fields have had on modern thinking--and you'll get a short answer: yes. Their goal, to set mathematics on a firm logical foundation, was revolutionary, and their tools and rigor continue to influence modern professionals. Using Peano's symbolic logic, they formalized axioms and produced theorems (including the famous "1 + 1 = 2") in orderings, continuous functions, and other areas of mathematics.
|von Alfred North Whitehead|
Although the Principia is far from comprehensive, Whitehead and Russell's method and program captivate their readers. The audacity to hope to formalize all of mathematics logically was inspirational and helped to give great boosts to math and logical philosophy. Though Gödel proved in 1931 that any such program is doomed to incompleteness, the tools found in and developed from the three volumes helped build the atomic bomb and the Internet. It may not be summer vacation reading (for most), but Principia Mathematica will reward the dedicated student with a deeper understanding of how we got here. --Rob Lightner
A Famous Failed Enterprise
The Principia was Russel and Whitehead's famous attempt to axiomise all of mathematics. Godel's famous theorem demolished it, proving that such an enterprise was impossible.
This book is an important step in mathematical history and a brilliant demonstration of the power of logic, but in the end of interest only to logicians for historical reasons.
A monument of mathematical logic
This book is the ultimate attempt to derive all of mathematics from logic while avoiding paradoxes of the sort that Russell himself sprang on Frege--and in passing, it gives in rigorous symbolic form Russell's "theory of descriptions."
Just as Bach took the baroque style of music about as far as it could go, Russell and Whitehead took this attempt to put mathematics on a firm logical footing about as far as it could go (and Goedel's incompleteness theorem killed off the hopes that mathematicians such as Hilbert had for the goal). Nevertheless, like any really good problem, it turned up worthwhile byproducts.
Alas, my exposure to the full three-volume set is confined to time spent at a university library; I could only afford the paperback volume of the first fifty-six chapters. I hope to eventually buy a copy of this classic work in its entirety.
This book is a masterpiece of Mathamatics. Extreamly good.
This is an extreamly good book with more information than you could poke a stick at. I got left behind a few times and had to re-read a chapter, but as long as you love ADVANCED math and like to think logicaly, this book is for you. It goes into many areas of math in general as well as dozens of spacific areas and provides more than enough information. It is a very "deep" book and can sometimes be a bit diffucult to understand, and i recoment this book to people who love deep, deep thought. It is not for everybody, in fact it is probibly for very few, but thouse who read and understand it, will come to love and value it...
Logik > Principia Mathematica to *56 (Cambridge Mathematical Library)|