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eBook Mathematical Logic download
Science
Author: Willard Van Orman QUINE
ISBN: 0387910883
Subcategory: Mathematics
Publisher Springer; 1 edition (1940)
Language English
Category: Science
Rating: 4.2
Votes: 397
ePUB size: 1900 kb
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eBook Mathematical Logic download

by Willard Van Orman QUINE


Willard Van Orman Quine (/kwaɪn/; known to intimates as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition.

Willard Van Orman Quine (/kwaɪn/; known to intimates as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century

This book includes nothing about modal logic, deontic logic, etc. This is a good thing. Begin at the beginning, the foundation.

This book includes nothing about modal logic, deontic logic, etc. Then if you want to go off onto one of these tangents you'll have a solid base upon which to evaluate these other logics. Besides all this you'll learn some useful techniques developed by Quine himself such as his Main Method for proving the validity of valid quantificational schema. He'll also teach you alternative methods developed by others.

MATHEMATICAL LOGIC Br Willard J7an Orman Quine. Villard van 'orman quine. This book has been digitally reprinted. The content ren1ains identical to that of previous printings. HARVARD UNIVERSITY PRESS Cambridge, Massachusetts London, England. Library of congress catalog card number ISBN ISBN. 0-674-55450-7 0-674-55451-5. Printed in the united states of america all rights reserved. PREFACE, 1981 When I turned doctor in 1932, I was still wholly under the spell of Principia M atheJllatica.

Willard Van Orman Quine (1908-2000) was an American philosopher and logician who taught at Harvard University, and wrote many books such as Word and Object,The Web of Belief,From a Logical Point of View,Ontological Relativity & Other Essays,Pursuit of Truth,Theories and Things.

Willard Van Orman Quine (1908-2000) was an American philosopher and logician who taught at Harvard University, and wrote many books such as Word and Object,The Web of Belief,From a Logical Point of View,Ontological Relativity & Other Essays,Pursuit of Truth,Theories and Things,Methods of Logic,Quiddities: An Intermittently Philosophical Dictionary, etc.

by. Quine, W. V. (Willard Van Orman). Logic, Symbolic and mathematical. Cambridge, Harvard University Press. inlibrary; printdisabled; ; americana.

W. Quine’s systematic development of mathematical logic has been widely praised for the new material presented and for the clarity of its exposition.

Willard Van Orman Quine (1908–2000) worked in theoretical philosophy and in logic. In practical philosophy-ethics and political philosophy-his contributions are negligible

Willard Van Orman Quine (1908–2000) worked in theoretical philosophy and in logic. In practical philosophy-ethics and political philosophy-his contributions are negligible. He is perhaps best known for his arguments against Logical Empiricism (in particular, against its use of the analytic-synthetic distinction). This argument, however, should be seen as part of a comprehensive world-view which makes no sharp distinction between philosophy and empirical science, and thus requires a wholesale reorientation of the subject.

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Preface, 1981 (Harvard University, January 1981).

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Mave
Quine's approach to logic and set theory was on an evolutionary branch which was doomed to extinction. The Whitehead/Russell style of logic and its clumsy notation were destined to become footnotes in history, although Quine may have only dimly sensed this at the time. So this 1940/1951 book is on an essentially extinct branch of mathematical logic, now known only as fossils in museums.

The "quasi-quotation" notation in pages 33-37 seems to be a Quine innovation, designed to keep deduction lines shorter by using pointers to stretches of text, which you must then look up by number. The dot-notation on pages 37-42 seems to be inherited from Frege via Whitehead/Russell. Various other authors in Quine's time used incompatible variations of this notation. So there is no one single dot-notation convention. Together, these two notational conventions make this book almost as incomprehensible as Frege's diagrams, which I call "quipu notation".

Regarding the substance of this book, it isn't really of great interest any more. The preoccupations of that time have come and gone. Ever since the independence proofs of Paul Joseph Cohen in 1963, concerns about the foundations of mathematical logic have been relegated to the model theory department, where mathematicians don't need to think about them any more. The work of Frege, Whitehead/Russell, Hilbert, Gödel, etc., is now studied in the history and palaeontology departments. Nowadays we have first-order languages, ZF and model theory. Logicism in its original form lost the argument. The new logicism is FOL, model theory, ZF set theory etc.

On the positive side, this book does pay close attention to the linguistic aspects of logic in pages 1-115. In later decades, these were more compactly formulated as FOL rules and axioms. The approach to classes and relations in this book was likewise incorporated into the FOL formalism.

All in all, this book does have some "archaeological" interest, but is unsuitable for the modern world. As always, however, I am grateful to enlightened publishers for keeping the old books alive. In mathematics, semi-abandoned ideas have a habit of resurfacing many decades or centuries later to become the new, modern advanced ways of doing things.
Kanrad
I don't think I can even begin judging the brilliant work by Quine! A student of A. N. Whitehead he wrote this book to summarize what aspects of the Principia he thought remained standing after the attacks by Godel, and the works of Tarski and Hilbert. It is a fantastic book and Quine is a brilliant writer, even if he moves at a fast pace. The first chapter will give you the notation he uses, the truth-tables, and some introduction and then Quine will jump into his theorems, building one on another. This book also has a special Summation-1 proof of the Incompleteness theorem that Quine himself developed.

So I can only really appraise the edition, and the truth is that it could be much, much better. The pages are glued together in a binding which is prone to curling up; there are some pages with some small misprints (nothing that can't be easily picked up), and the ink looks a weirdly shiny way. The book is also rather small to use as a logical textbook, and people trying to write whilst reading (to reproduce the proof) will have some difficulty.

Even then, I cannot more highly recommend this controversial but still brilliant book by Quine. Whether or not you buy into his view of logic (opposed to that of Boolos) no one can claim that he wasn't a beautiful arguer, and more importantly a story-teller. So buy this book and let Quine tell you the story of Maths, Logic, and everything in between!
Zyangup
I have been reading this book off and on for years. It is beautiful. However, I am not well read in mathematical logic, and the comments of a mathematical logician as to whether the proofs are correct and what should be read next would be helpful to readers interested in mathematical logic. I read the book to understand Godel. There are better books for that. However, once I starting reading this book, I appreciated the eloquence of Prof. Quine and the beauty of the axioms, definitions and proofs in the book.
Daiktilar
This book is indeed much shorter than Principia, mainly because it is derived for lecture notes for a 1 semester PhD course. It is also a lot clearer than PM. But the notation is largely the same, which makes for hard reading if your are under 50. Quine's proof format doesn't take up much space, but has always eluded me. This book contains the best treatment of truth functional and quantificational logic prior to natural deduction and truth trees.
I like the set theory of this book, but I warn you that it is very nonstandard. Even ardent lovers of Quine's NF theory hate
the ML theory of this book.
The weakness of this book is its treatment of metatheory:
consistency, completeness, decidability, categoricity. The treatment of Godel's incompleteness is detailed and highly original (altho' it owes more to Tarski than to Godel). But it is very difficult, and Smullyan (1991) is much better.
Quine also had no clue re model theory or recursion.
I respect the historical remarks a lot. Just one big omission: Quine, like nearly everyone of his generation, missed that
math logic as we know and love it does not descend from Frege, but from an 1885 article by C S Peirce.