Qty:1
  • List Price: $54.99
  • Save: $7.43 (14%)
In Stock.
Ships from and sold by Amazon.com.
Gift-wrap available.
The Principles of Mathema... has been added to your Cart
+ $3.99 shipping
Used: Like New | Details
Sold by Wordery USA
Condition: :
Comment: International shipping available. This fine copy is in our depot and should be with you within 11-12 working days via Air Mail. Please note this title is print on demand.
Access codes and supplements are not guaranteed with used items.
Have one to sell? Sell on Amazon
Flip to back Flip to front
Listen Playing... Paused   You're listening to a sample of the Audible audio edition.
Learn more
See this image

The Principles of Mathematics Revisited Paperback – April 28, 1998

ISBN-13: 978-0521624985 ISBN-10: 0521624983 Edition: Reprint

Buy New
Price: $47.56
20 New from $43.56 13 Used from $44.26
Amazon Price New from Used from
Paperback
"Please retry"
$47.56
$43.56 $44.26
Free%20Two-Day%20Shipping%20for%20College%20Students%20with%20Amazon%20Student


"Trust Betrayed: Barack Obama, Hillary Clinton, and the Selling Out of America's National Security"
For eight years, ex-Navy SEAL sniper Scott Taylor served his country in the same region of Iraq as American Sniper author Chris Kyle. After he was injured during Operation Iraqi Freedom, Taylor came home--and discovered the Obama administration was leaking sensitive intelligence information for political gain. Find out more
$47.56 FREE Shipping. In Stock. Ships from and sold by Amazon.com. Gift-wrap available.
NO_CONTENT_IN_FEATURE

Best Books of the Month
Best Books of the Month
Want to know our Editors' picks for the best books of the month? Browse Best Books of the Month, featuring our favorite new books in more than a dozen categories.

Product Details

  • Paperback: 304 pages
  • Publisher: Cambridge University Press; Reprint edition (April 28, 1998)
  • Language: English
  • ISBN-10: 0521624983
  • ISBN-13: 978-0521624985
  • Product Dimensions: 6 x 0.7 x 9 inches
  • Shipping Weight: 14.1 ounces (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #2,081,732 in Books (See Top 100 in Books)

Editorial Reviews

Review

"Every thoughtful mathematician or student of the philosophy of science or mathematics will want to read this book....superbly lucid and well-presented work....highly recommended for upper division undergraduate through professional collections." Choice

"In this engaging, provocative manifesto, Professor Hintikka breaks the ground for what he hopes will be a revolution in logic, in much the same "critical and constructive" spirit as motivted Bertrand Russell...Hintikka claims that present-day logic, with its basis in a beautiful proof theory, is the result of abandoning the idea that logic can have any major role to play in mainstream mathematical...this highly readable, wide-ranging book deserves a great deal of attention and debate." Modern Logic May 2000- Oct 2001

Book Description

This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. Hintikka's new logic is highly original and will prove appealing to logicians, philosophers of mathematics, and mathematicians concerned with the foundations of the discipline.

Customer Reviews

4.4 out of 5 stars
5 star
6
4 star
0
3 star
0
2 star
0
1 star
1
See all 7 customer reviews
Required reading for anyone interested in logic.
David Jefferson
I get the feeling this is one of the most brilliant books that I will ever have the pleasure of reading AGAIN and AGAIN!
David Thompson
While entertaining, the style detracts from the importance of the book.
D. Ghica

Most Helpful Customer Reviews

20 of 20 people found the following review helpful By David Thompson on August 24, 2001
Format: Paperback
I am a working mathematician with a PhD in Differential Geometry who has recently become interested in the foundations of Mathematics. I came to this book circuitously via a pdf by Jaakko called "A revolution in Logic". Jaakko is on the offensive in this book, and he certainly can be polemic, to say the least. Having said that, the book is a tour de force: as a book on first order logic and IF, on the philosophy of mathematics, and the nature of mathematics and its objects and structures---it has gotten me thinking on many different levels. I would guess English is not his first language (due to easily corrected spelling, grammar, Etc), but despite this the writing style is quite smooth, with some interesting turns of phrases. I get the feeling this is one of the most brilliant books that I will ever have the pleasure of reading AGAIN and AGAIN! My 2cents David Thompson Assistant Professor of Mathematics and Computer Science Olivet College, Michigan
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
18 of 18 people found the following review helpful By T. Gwinn on November 5, 2002
Format: Paperback Verified Purchase
This book re-examines first-order logic as it has been applied to the foundations of mathematics. But it is much more than that. If you are interested in the human decisions behind why logics were built as they were, if you want to understand the impact of Godel's Incompleteness Theorem, if you are interested in understanding philosophy of inferential systems in general, then you will find this book quite profound and useful.
Requirements for reading this book are roughly: a general knowledge of syllogistic and first-order predicate logic, an idea of what Godel's theorem is about and the concept of godel-numbering, some philosophy (e.g., ontology vs. epistemology), but mostly a keen interest at learning about logic and it's foibles and potentials.
Chapter 1 begins with the Hilbert program, and the attempt at axiomatization in general. Chapter 5 clears up alot of confusion about the Godel Incompleteness theorem and what it really means. He delineates between descriptive, semantic, deductive and Hilbertian completeness notions, and describes their inter-relatedness and Godel's theorem's role. These chapters alone are useful for gaining deeper understanding of the problems that arise in syntactic axiomatic deductive systems.
Chapter 7 is on the Liar Paradox, and he offers a unique solution to that based not upon Austinian notions, but rather based upon Hintikka's IF ("independence-friendly") first-order logic which avoids resorting to infinities or relying on any semantic re-interpretation (Hintikka uses a simple formal statement "~T[d]" where d is the godel-number of that statement, as the basis of the discussion).
He then goes on to discuss the presumed role of axiomatic set theory and chips away at it's pretense as a secure foundational approach.
Read more ›
1 Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
13 of 13 people found the following review helpful By D. Ghica on May 17, 2001
Format: Paperback
I read this book last year and I found it both entertaining and interesting, but only recently I was struck by how profound it is. I find Mr. Hintikka's insight into the dual use of logic (description vs. inference) and the conflict it caused in the development of logics (expressivity vs. axiomatic completeness) fascinating. He decisively resolves this conflict in favour of expressivity by introducing a brand of logic which is amazingly expressive yet non-axiomatizable. So, instead of proving propositions, we validate them through calculations in the semantic model.
I don't think this book will have the impact it should, only because the philosophical-logical establishment is already entrenched in certain ways of thinking that it can not abandon. And I think Mr. Hintikka is painfully aware of this. His tone is polemical, almost vitriolic at times, and it has a certain voice-of-reason-crying-in-the-wilderness streak to it. While entertaining, the style detracts from the importance of the book.
I consider "The Principles of Mathematics Revisited" one of the most important books on logic ever. Its impact will not be immediate but it should eventually be momentous.
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
18 of 20 people found the following review helpful By David Jefferson on May 17, 1999
Format: Hardcover
Hintikka argues in this book that a novel extension of the predicate calculus, called "independence-friendly" (IF) logic, has a better claim to being the "core" of mathematical logic than the predicate calculus (PC) itself. Besides presenting his formalism, he rethinks the entire history and philosophical foundation of logic based on insights from independence-friendly logic. IF logic is similar to the PC except that variables bound by a new kind of independence-friendly existential quantifier refer to values that need not be functionally dependent on outer universal quantifiers. This is contrary to the PC, in which an inner existentially-quantified variable always depends functionally on all outer universal quantifiers. The definition of truth of a (closed) interpreted formula in IF is based not on Tarski's classic definition, but on the existence of a winning strategy in a formal two-person game associated with the formula. The game associated with a PC formula is always a perfect-information game, and the game-theoretic truth definition is equivalent to Tarski's. But for those IF formulae containing the independence-friendly existential quantifiers the associated game is not generally perfect-information, and truth is not definable by a Tarski-like definition.
IF is a pure extension of the PC in the sense that the PC formulae (those with only standard--not independence-friendly--existential quantifiers) are a subset of IF formulae, and all valid PC formulae are valid as IF formulae. But the resemblance between the two logics ends there. For example, IF, unlike PC, is not recursively axiomatizable, and the law of excluded middle fails. Hintikka argues convincingly that these facts are not defects in IF, but actually liberating.
Read more ›
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again

More About the Author

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

What Other Items Do Customers Buy After Viewing This Item?

Set up an Amazon Giveaway

Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more
The Principles of Mathematics Revisited
This item: The Principles of Mathematics Revisited
Price: $54.99 $47.56
Ships from and sold by Amazon.com