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Recommended Reading

Timothy
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Posted 04/29/06 - 07:31 PM: Subject: Recommended Reading	#1
Here is a list of recommended books and authors regarding topics in Logic and Mathematics. Many thanks to those who helped with their excellent suggestions, especially to MoeBlee. This list constitutes, as most recommendations, if not all, a somewhat biased selection, and cannot be called completely "objective". As any recommendation, we encourage you to take this one with a grain of salt. New recommendations and suggestions are encouraged to help make this list more complete and objective. - Timothy LOGIC Enderton - A Mathematical Introduction To Logic Van Dalen - Logic And Structure Smullyan - First Order Logic Shoenfield - Mathematical Logic Kleene - Mathematical Logic Quine - Mathematical Logic Quine - Methods of Logic Suppes - Introduction To Logic Mates - Elementary Logic Margaris - First Order Mathematical Logic Grzegorczyk - An Outline Of Mathematical Logic Mendelson - Introduction To Mathematical Logic Ebbinghaus, Flum, & Thomas - Mathematical Logic Church - Introduction To Mathematical Logic Barnes & Mack - An Algebraic Introduction To Mathematical Logic Monk - Mathematical Logic Rosser - Logic For Mathematicians Kalish, Montague, & Mar - Logic Fitch - Symbolic Logic Beziau [ed] - Logica Universalis Bell & Machover - A Course in Mathematical Logic Carnap - Foundations of Logic and Mathematics Carnap - Logical foundations of probability K. Langer - An Introduction to Symbolic Logic. NON-CLASSICAL LOGIC & ALTERNATIVE LOGICS Anderson and Belnap Entailment: The Logic of Relevance and Necessity JC Beall and Bas van Fraassen- Possibilities and Paradox Brady - Universal Logic Bremer - Introduction to Paraconsistent Logic Edwin - Relevant Logic: A Philosophical Interpretation Lambert - Free Logic: Selected Essays Lewis - Counterfactuals Mortensen - Inconsistent Mathematics Priest - In Contradiction ----- Beyond the Limits of Thought ----- Towards Non-Being ----- Doubt Truth to Be a Liar ----- Introduction to Non-Classical Logic Zimmermann - Fuzzy Set Theory and its Applications web resources: Hybrid Logic href="http://plato.stanford.edu/entries/logic-provability/">Provavbility Logic Linear Logic Paraconsistent Logic Connexive Logic Epistemic Logic Many-Valued Logic Relevance Logic Intensional Logic ______ PROOF THEORY Troelstra - Basic Proof Theory Takeuti - Proof Theory Buss [ed] - Handbook Of Proof Theory ______ MODEL THEORY Chang & Keisler - Model Theory Hodges - Model Theory Poizat - A Course In Model Theory ______ COMPUTABILITY Davis - Computability And Unsolvability Boolos, Burgess, & Jeffrey - Computability And Logic Brainerd & Landweber - Theory Of Computation Smullyan - Godel's Incompleteness Theorems Smullyan - Recusion Theory For Metamathematics Smullyan - Theory Of Formal Systems Rogers - Theory Of Recursive Functions And Effective Computability Odifreddi - Classical Recursion Theory Odifreddi - Classical Recursion Theory, Vol. 2 Cutland - Computability ______ SET THEORY Enderton - Elements Of Set Theory Suppes - Axiomatic Set Theory Levy - Basic Set Theory Quine - Set Theory And Its Logic Halmos - Naive Set Theory Kunen - Set Theory Smullyan & Fitting - Set Theory And The Continuum Hypothesis Devlin - The Joy Of Sets Jech - Set Theory Fraenkel, Bar-Hillel, Levy - Foundations Of Set Theory Franekel - Abstract Set Theory Beth - The Foundations Of Mathematics Abian - The Theory Of Sets And Transfinite Arithmetic ______ CONSTRUCTIVISM Troelstra & Van Dalen - Constructivism In Mathematics, Vol. 1 Troelstra & Van Dalen - Constructivism In Mathematics, Vol. 2 Fitting - Intuitionistic Logic, Model Theory And Forcing Beeson - Foundations Of Constructive Mathematics Bishop - Foundations Of Constructive Analysis ______ MODAL LOGIC Hughes & Cresswell - An Introduction To Modal Logic Boolos - The Logic Of Provability Blackburn, Rijke, & Venema - Modal Logic Kripke - Naming and Neccesity ______ NUMBER SYSTEMS Feferman - The Number Systems Mendelson - Number Systems And The Foundations Of Analysis Henkin, Smith, Varineau, & Walsh - Retracing Elementary Mathematics Burrill - Foundations Of Real Numbers Hamilton - Set Theory And The Structure Of Arithmetic Gleason - Foundations Of Abstract Analysis Ebbinghaus, et. al - Numbers ______ ANALYSIS Apostol - Mathematical Analysis Courant - Introduction to Calculus and Analysis Courant - Differential and Integral Calculus Shilov - Elementary Real And Complex Analysis Browder - Mathematical Analysis Royden - Real Analysis Rudin - Principles Of Mathematical Analysis Carothers - Real Analysis Katz - Axiomatic Real Analysis ______ TOPOLOGY Hocking & Young - Topology McCarty - Toplogy Munkres - Topology Janich - Topology Kelley - General Topology ______ ALGEBRA Lang - Algebra Burris & Sankappanavar - A Course in Universal Algebra Warner - Modern Algebra Grove - Algebra MacLane - Algebra Hungerford - Abstract Algebra Hungerford - Algebra Dummit & Foote - Abstract Algebra Deskins - Abstract Algebra Herstein - Topics In Algebra Fraleigh - A First Course In Abstract Algebra Bhattacharya, Jain, & Nabpaul - Basic Abstract Algebra Birkhoff & MacLane - A Survey Of Modern Algebra ______ LINEAR ALGEBRA Schneider & Barker - Matrices And Linear Algebra Smith - Linear Algebra Shilov - Linear Algebra Curtis - Linear Algebra Grech - Linear Algebra Rose - Linear Algebra Fraleigh & Beauregard - Linear Algebra Anton - Elementary Linear Algebra ______ NUMBER THEORY Ireland & Rosen - A Classical Introduction To Modern Number Theory Dense & Dense - Elements Of The Theory Of Numbers LeVeque - Elementary Theory Of Numbers ______ GRAPH THEORY Coming Soon ______ PROBABILITY Jacod & Protter - Probability Essentials ______ STATISTICS Coming Soon ______ GEOMETRY Moise - Elementary Geometry From An Advanced Point Of View Millman & Parker - Geometry Coxeter - Introduction to Geometry ______ REFERENCE Van Heijenoort - From Frege To Godel Barwise [ed] - Handbook Of Mathematical Logic ______ GENERAL READING Franzen - Godel's Theorem Heyting - Intutionism Tiles - The Philosophy Of Set Theory Benacerraf & Putnam - Philosophy Of Mathematics Boolos - Logic, Logic, And Logic Chihara - A Structural Account Of Mathematics Chihara - Contstructibility And Mathematics Chihara - Ontology And The Vicious Circle Principle Corry - Modern Algebra And The Rise Of Mathematical Structures Curry - Formalist Philosophy Of Mathematics Feferman - In The Light Of Logic Franzen - Inexhaustibility Franzen - Provability Hart [ed] - The Philosophy Of Mathematics Hintikka - The Principles Of Mathematics Revisited Hintikka [ed] - The Philosophy Of Mathematics Lavine - Understanding The Infinite Maddy - Realism In Mathematics Potter - Set Theory And Its Philosophy Putnam - Philosophy Of Logic Quine - Philosophy of Logic Shapiro - Foundations Without Foundationalism Shapiro - Philosophy Of Mathematics Shapiro - Thinking About Mathematics Tait - The Provenance Of Pure Reason Wolf - A Tour Through Mathematical Logic HISTORICALLY INTERESTING READINGS Boole - An Investigation on the Laws of Thought Carnap - The Logical Syntax of Language Frege - Begriffschrift Frege - Grundlagen Frege - On Sense and Reference Hilbert & Bernay - Grundlagen Peirce - Grounds of Validity of the Laws of Logic: Further Consequences of Four Incapacities Russell - On Denoting Russell - The Principles of Mathematics Russell & Whitehead - Principia Mathematica (3 vols) Tarski - The Semantic Conception of Truth Wittgenstein - Tractatus Logico-Philosophicus Here are some philosophers to get familiar with: PHILOSOPHERS Alston Benacerraf Bishop Boolos Brouwer Carnap Chihara Curry Dummet Feferman Field Frege Friedman Godel Hilbert Hintikka Kreisel Kripke Lakotas Maddy Poincare Peirce Priest Prior Putnam Quine Resnick Rogers Russell Shapiro Tait Tarski Tennant Wang Weyl Whitehead Wittgenstein WEB RESOURCES http://www.godelbook.net/ http://logic.philosophy.ox.ac.uk/ http://www.cmu.edu/oli/courses/enter_logic.html http://plato.stanford.edu UNREVISED SUGGESTIONS George Pólya - How to solve it JC Beall and Greg Restall - Logical Pluralism Edited by Timothy on 03/19/08 - 02:33 PM. Reason: Update
_____________________ "I think I'll stop here." -- Andrew Wiles immediately after presenting the proof of Fermat's Last Theorem, Cambridge, 23 June 1993

The Bearded Monkey
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Posted 04/30/06 - 07:03 AM:	#2
You should add in the list of analysis the two books by Richard Courant: 1) Introduction to Calculus and Analysis. 2) Differential and Integral Calculus. What has Poincare got to do with philosophy? Edited by hyena in petticoat on 03/24/08 - 12:51 AM. Reason: Capitalization.
_____________________ i shall take the whichpath to quantum catastrophe theory.

MoeBlee
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Posted 05/02/06 - 09:52 AM:	#3
Thanks, Timothy. But the list I posted had some entries that were ones that I just wanted to check out (I wanted other people's opinions on those items) so those entries might not deserve to be in the list. I was pretty informal. And I've made some improvements on the list since I last posted. I think this list can be greatly improved, especially by removing so many overlapping texts on subjects such as linear algebra. Also, another poster pointed out that Bridges's book 'Constructive Analysis' is the revised version of Bishop's book. And since you're including historical texts, I would add Frege's Grundlagen, Hilbert and Ackermann's Grundlagen, and Whitehead and Russell's Principia Mathematica, among many others. I would make the historical text section a separate section from the general reading section. Edited by MoeBlee on 05/02/06 - 10:55 AM

MoeBlee
aka I. Kabruob

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Posted 05/02/06 - 09:54 AM:	#4
The Bearded Monkey wrote: what poincare has got to do with philosophy? http://www.iep.utm.edu/p/poincare.htm

MoeBlee
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Posted 05/03/06 - 05:09 PM:	#5
Oops, I meant Hilbert and Bernays. Anyway, the list needs a lot of work. It's got good books in it, but it needs to be fleshed out and the classifications need to be straightened out. (Originally, I meant for non text-books, or books that you read rather than "work through", to be in separate categories from textbooks and books you work through.) Edited by MoeBlee on 05/03/06 - 05:13 PM

Timothy
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Posted 05/05/06 - 08:10 AM:	#6
MoeBlee, Thanks again for the help. If you consider that there are far too many overlapping texts on certain topic, or wish to simpy suggest the removal of a book in the list, please let me know which ones, for my wide ignorance on those matters doesn't allow me to do it myself. Regarding the historical texts section, it's now separated from General. Principia was added before your post. I just added Hilbert and Bernay Grundlagen, as well as Frege's. Did you noticed Wittgenstein's "Tractatus" on it also? Regards EDIT: BM, thanks for the suggestions. Edited by Timothy on 05/05/06 - 08:26 AM
_____________________ "I think I'll stop here." -- Andrew Wiles immediately after presenting the proof of Fermat's Last Theorem, Cambridge, 23 June 1993

Andreios
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Posted 04/29/07 - 11:10 PM:	#7
Because the list is "biased" towards classical logic, I would like to suggest some non-classical additions to it: Anderson and Belnap Entailment: The Logic of Relevance and Necessity JC Beall and Bas van Fraassen: Possibilities and Paradox JC Beall and Greg Restall: Logical Pluralism Brady, Ross: Universal Logic Bremer, Manuel Eugen: Introduction to Paraconsistent Logic Edwin, Mares Relevant Logic: A Philosophical Interpretation Lambert, Karel: Free Logic: Selected Essays Lewis, David: Counterfactuals Mortensen, Chris: Inconsistent Mathematics Priest, Graham: In Contradiction ----- Beyond the Limits of Thought ----- Towards Non-Being ----- Doubt Truth to Be a Liar ----- Introduction to Non-Classical Logic Read, Stephen: Relevant Logic Restall, Greg: An Introduction to Substructural Logics Zimmermann: Fuzzy Set Theory and its Applications

Timothy
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Posted 03/19/08 - 02:34 PM:	#8
Updates: Added several non-classical logic texts, as well as specific web resources. A comprehensive revision ought to take place anytime soon.
_____________________ "I think I'll stop here." -- Andrew Wiles immediately after presenting the proof of Fermat's Last Theorem, Cambridge, 23 June 1993

7
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Posted 03/24/08 - 12:36 AM:	#9
A few I like that aren't there are: First Order Modal Logic by Fitting and Mendelson (does not cover intensional objects, but exposition of extensional FOML is great and it has a lot on predicate abstraction, which other books seem to ignore) Intro to Godel's Theorems by Peter Smith (beautifully written book, IMO. covers Godel's theorems thoroughly and clearly. also has basic intro to computability, general recursive functions, church-turing thesis, etc. Smith should expand on his text to cover all of the material in the Boolos, Burgess, & Jeffrey. such a book would certainly become the new standard.) Basic Set Theory by Derek Goldrei (best book for in depth intro to set theory that i've seen. designed with self-study in mind, so many exercises with solutions worked out. several exercises and sections assume familiarity with real analysis, but you can skip them if you must without becoming lost. the author makes sure that everything the reader needs to proceed is shown in the text. it's very annoying when you're reading a technical book and the author gives exercises without solutions that are essential for what follows.) Edited by 7 on 03/24/08 - 12:46 AM

7
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Posted 03/29/08 - 04:52 AM:	#10
Does anyone know the Hinman text Fundamentals of Mathematical Logic?

Timothy
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Posted 03/30/08 - 09:01 PM:	#11
I do not. Do you have an input on it? I'll do a quick check of your recommendations before posting them here. Thanks
_____________________ "I think I'll stop here." -- Andrew Wiles immediately after presenting the proof of Fermat's Last Theorem, Cambridge, 23 June 1993

7
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Posted 03/31/08 - 04:35 PM:	#12
I've been reading it since a few days ago. It's the most thorough logic book I have ever seen (900 pages). Mathematical in focus, with little or no attention to philosophy. Still, it reads pretty nicely. I will need to spend more time on it before I comment further. Edited by 7 on 03/31/08 - 04:40 PM

Deus Ith
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Posted 06/12/08 - 02:46 PM:	#13
Hello guys. I'm new to the forums and sadly I haven't got the time to read deep into most of the posts in here, but I noticed you missed some of my favorite books which I think are quite useful for this list * Introduction to Mathematical Statistics - Paul G. Hoel (an introductory book for statistics from a more theoretical than practical approach) * Introduction to Probability Theory - Paul G. Hoel (idem but for probability) * A first course in Probability - Sheldon Ross (instead, this book empathizes a "practice makes the master" point of view - has tons of problems to solve both practical and theorical, but still reviews all theory related to probability) * Infinitesimal Calculus - Michael Spivak (a must read in my school) cheers!

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