The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number

Frege, arguably one of the most important theoreticians of logic in the history of philosophy published only 4 major book length works: Begriffsschrift (Conceptual Notation) in 1879; Grundlagen der Arithmetik (Foundations of Arithmetic) in 1884; and two volumes of Grundgesetze der Arithmetik (Basic Laws of Arithmetic)released in 1893 and 1903.The Good and the Bad:This is Austin's translation of Gottlob Frege's second major work, Grundlagen der Arithmetik. As a translation it offers several laudable feats to the reader. The first is its overall fidelity to the author's intentions. The second is its consistency of translation. Important technical terms are translated in the same manner throughout. With the passage of time --some 70 years-- this translation, despite it's qualities, has come to seem dated. Austin was not an accomplished German scholar, and though his English is laudable, as a translation concerned with a highly technical subject, this book sometimes misses the mark. In its original form, presented with German and English pages side by side, the problems of J. L. Austin's translation were of little importance. As a sole text divorced from German text, I fear that it would at times be far too easy to sometimes misconstrue Frege's arguments in either their strengths or weaknesses.I offer 2 lesser criticisms. The first is the quality, or rather lack of quality in this editions printing. The typography has the washed out characters of a copy of a copy, a problem that's most often seen when a publisher, having run out of its initial printings, decides to continue offering the work without resetting the type. With digital technology this needn't happen, but this book has all the visual qualities of yesterday's photocopying.Finally, as one with substantial disabilities I resent the publisher's decision not to digitise the book. Those with either movement or visual limitations find the lack of ebook version a severe impediment.At recent published translation, that of Dale Jacquette for Taylor & Francis, is available as both an ebook and on paper, though the ebook is absurdly priced at more than 11 times the asking of the paper edition.

It's no exaggeration to say Frege was one of the greatest logicians of all time. What's more for the reader these days, he's also one of the greatest and most lucid teachers of this sometimes arcane and difficult science. This book is an excellent introduction to this towering figure's genius.

I have no idea what's going on but I hope one day to be smart enough to understand the foundations of mathematics. Respect

I'm a self-directed learner and had been struggling with generating interest in mathematics for some time. I had bought this book in the hopes that it would bridge my love and interest in logic with a new found interest in mathematics. It did exactly that.

Excellent

If the 'proof is in the pudding', then apparently this book was written by a pompous ass who doesn't wish to be understood.I highly recommend Bertrand Russel's Introduction to Mathematical Philosophy.

You know how _frustrating_ it is, reading a platonic dialog? Some question like "What is virtue?" or "What is justice" is asked, and Socretes goes on for pages showing that the so-called "experts" don't have a clue about what it really is?But what's _really_ frustrating is that you're all expecting, at the end of the dialog, after following a hard line of argument, that you'll be rewarded with THE definitivie definition of 'virtue' or 'justice' or whatever--only to be disapointed. All you get in the end is a new appreciation of your own hopeless ignorance......well, imagine a platonic dialog which started the same as any other platonic dialog, but with the question "What is a number?" Only this time, at the end of the dialog, you actually get an answer to the question?In retrospect, its pretty amazing that Plato didn't write a Socratic dialog concerned with the question "What is number?' After all, Plato considered numbers more real than physical objects, and people like the Pythagorians were going around claiming that everything _was_ made out of numbers. But what the heck _is_ a number, anyways?Perhaps the reason was that everybody thought they already understood what numbers were. But Frege, like Socretes before him, realized that this so-called knowledge was really just a collective ignorance. So Frege starts out this book with a thorough, merciless review of what his coleages and predicessors were saying about what numbers were, showing that they ranged from cocksure to confused, from pompously-wrongheaded to just plain silly.But then Frege does something really amazing--for the first time in history, he goes on give a real answer to the question "what are numbers?" Building on the work of Hume, he gives a sustained argument now known as "Frege's theorem" which shows how numbers can be grounded on an understanding of one-to-one correspondence.Unfortunately, this work had to wait almost a century for the rest of us to really catch up to its significance. Russell found a contradiction in the arguments presented here, and for the next 80 years attention shifted elsewhere. But first Charles Parsons, in 1964, and then Crispen Wright and others in the 80's and 90's begain to realize that Frege's theorem could be reconstructed without the paradox. This sparked a whole flurry of neo-Fregean studies which is one of the most active branches of analytic philosophy today.This revival means that Frege's importance, and the importance of reading and comming to grips with the arguments presented by Frege in this book, are going to continue to grow. Although tragically Frege didn't live to see the day, we now realize that the line of reasoning he followed in this book was one of those signature moments in human history, every bit as profound as the invention of the wheel or the discovery of the pythagorian theorem--it was the moment where, for the first time ever, the question "what the heck _are_ numbers, anyways?" got a real answer.

The publisher: good quality print, didn't like the font for numbers very much, no complaints otherwise.The book: if you study something related to logic and maths, it's a must read but be prepared to reread certain sections multiple times and really think through what's going on. For a casual reader who likes maths, engage at your own risk.