Recommended Reading

Recommended Reading
Timothy
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9 of 9 people found this post helpful
Posted Apr 29, 2006 - 7:31 PM:
Subject: Recommended Reading
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

FOR THE ABSOLUTE NOOB

Barwise & Etchemendy - Language, Proof and Logic For the mathematically unsophisticated reader.

van Dalen - Logic and Structure
Enderton - A mathematical introduction to logic (both of these for the mathematically sophisticated reader)

Also see Web Resources for free online web courses on elementary logic.


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.
Hodges - Logic
Hunter - Metalogic

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
Fuzzy Logic
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
______

CATEGORY THEORY

A programmatic reading list
______

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
______

PROBABILITY

Jacod & Protter - Probability Essentials
______

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
Shapiro - Oxford Handbook on the Philosophy of Mathematics and 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
Haack - Philosophy of Logics
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
JC Beall and Greg Restall - Logical Pluralism

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
Haack
Hilbert
Hintikka
Kreisel
Kripke
Lakotas
Maddy
Nagel
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
http://philpapers.org




Edited by Timothy on Jul 24, 2011 - 6:35 PM. Reason: Update: July 2011
MathematicalPhysics Wizard
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#2 - Quote - Permalink
Posted Apr 30, 2006 - 7:03 AM:

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 Mar 24, 2008 - 12:51 AM. Reason: Capitalization.
MoeBlee
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Posted May 2, 2006 - 9:52 AM:

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 May 2, 2006 - 10:55 AM
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Posted May 2, 2006 - 9:54 AM:

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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#5 - Quote - Permalink
Posted May 3, 2006 - 5:09 PM:

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.)
Timothy
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#6 - Quote - Permalink
Posted May 5, 2006 - 8:10 AM:

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 May 5, 2006 - 8:26 AM
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Posted Apr 29, 2007 - 11:10 PM:

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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#8 - Quote - Permalink
Posted Mar 19, 2008 - 2:34 PM:

Updates: Added several non-classical logic texts, as well as specific web resources.

A comprehensive revision ought to take place anytime soon.
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#9 - Quote - Permalink
Posted Mar 24, 2008 - 12:36 AM:

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 Mar 24, 2008 - 12:46 AM
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Posted Mar 29, 2008 - 4:52 AM:

Does anyone know the Hinman text Fundamentals of Mathematical Logic?
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