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

Gottlob Frege (Author), J. L. Austin (Translator)

Book Description

ISBN-10: 0810106051 | ISBN-13: 978-0810106055 | Publication Date: December 1, 1980 | Edition: 3

This volume represents the first philosophically sound discussion of the concept of number in Western civilization. (Mathematics)

--This text refers to an alternate Paperback edition.

Editorial Reviews

Language Notes

Text: English (translation)
Original Language: German

Product Details

• Paperback: 144 pages
• Publisher: Northwestern University Press; 3 edition (December 1, 1980)
• Language: English
• ISBN-10: 0810106051
• ISBN-13: 978-0810106055
• Product Dimensions: 8.5 x 5.5 x 0.4 inches
• Shipping Weight: 6.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #152,992 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

20 of 22 people found the following review helpful:

5.0 out of 5 stars A Must for Any Philosopher of Mathematics, September 23, 2000

By 

Pedro Rosario (Río Piedras, PR USA) - See all my reviews
(REAL NAME)   

This review is from: The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number (Paperback)

This book written by Gottlob Frege is one of the most influential books of the 20th century philosophy of mathematics. In here Frege establishes the nature of arithmetics as founded in logic, which is his logicist proposal. For that, he refutes the assertion that logic as such is founded on psychology.

Sometimes he distorts a little bit what others say about logic, so he argues against those thinkers more effectively. In here he establishes the anti-psycology difference between concept and object; though he has not made a difference yet between sense and reference. He also refers to a principle called the contextual principle, in which the word makes reference to something depending on the context. Afterwards after he wrote the book, he would reject this principle, because of his doctrine of sense and reference: the sense of the words determine the sense of the sentence; and the reference of the words determine the reference of the sentence.

This is a great philosophical work, and I would suggest it to anyone who is starting to study Analytic philosophy (philosophy of mathematics, logic and language), and also those who want to consider the platonist proposal.

32 of 38 people found the following review helpful:

5.0 out of 5 stars The first escape from the Elencus..., October 16, 2005

By 

Randall Helzerman (campbell, ca) - See all my reviews
(VINE VOICE)    (REAL NAME)   

This review is from: The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number (Paperback)

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.

12 of 13 people found the following review helpful:

5.0 out of 5 stars great work, November 28, 2001

By A Customer

This review is from: The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number (Paperback)

possibly one of the greatest works in history of philosophy and the founding book of 20th century analytic philosophy... I read it only once and a better appraisal will be coming shortly..I can say right away this is not simply a 'technical' work in philosophy of mathematics but a broad although short philosophical investigation in notions of truth, meaning and identity - although it expressly deals with defining numbers in purely logical terms. continental philosophers who read this work might change some of their negative ideas about where analytic philosophy is coming from.