Keith Douglas' Web Page

About me Find out who I am and what I do.
My resumé A copy of my resumé and other documentation about my education and work experience for employers and the curious.
Reviews, theses, articles, presentations A collection of papers from my work, categorized and annotated.
Current research projects What I am currently working on, including some non-research material.
Interesting people People professionally "connected" to me in some way.
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Intellectual/professional influences Influences on my work, including an organization chart. Here you can also buy many good books on philosophy and other subjects via I have included brief reviews of hundreds of books.
Professional resources Research sources, associates programs, etc.
What is the philosophy of computing? A brief introduction to my primary professional interest.
My intellectual heroes A partial list of important people. Limited to the dead.
My educational philosophy As a sometime teacher I've developed one. Includes book resources.

Book Influences - Logic: Foundations of Mathematics

Purchase / Enjoy Cover
Basic Category Theory for Computer Scientists Pierce A very short book: 100 pages including further reading, bibliography, index and symbol reference. The material is clear but all too brief, especially when it comes to computational applications.
From Frege to Gödel: A Sourcebook in Mathematical Logic 1879-1931 Van Heijenoort See my review. (Correction to it: Davis' collection is back in print.)
Introduction to Logic and to the Methodology of the Deductive Sciences Tarski This one would be only be introductory to someone with a bit more mathematical maturity than most introductory books assume. (When examining logic text books one can make an approximate divide between ones geared towards freshmen general education and philosophy on the one hand and on the other, ones geared toward mathematicians interested in putting their toes in at the sea of "foundations of mathematics".)
Introduction to Metamathematics Kleene This is a reprint of a 1952 classic. Kleene surveys what is now basic set theory, proof theory and recursion theory. Model theory is sort of implicit, as it was less developed at the time. Of historical interest, this work also contains one of the first discussions of Church's thesis. Kleene (unlike Church himself, it seems) does actually take it to be a thesis, rather than a definition. Given that this is how Post took it too, perhaps we should speak of the Kleene-Post thesis? A further interesting feature of the book is Kleene's continued development of an intuitionistic system alongside the classical one, tying it together with the recursion theory with a brief introduction to one of Kleene's own innovations, recursive realizability.
Kurt Gödel Collected Works, Volume I Gödel and a whole team of editors This volume of the collected works of the most important logician since Aristotle contains the first part of his career's published work. Included are the familiar papers about completeness and incompleteness (and many others) all with much in the way of introductory material with detailed extra references, etc. An editorial masterpiece.
Kurt Gödel Collected Works, Volume II Gödel and a whole team of editors This volume of the collected works of the most important logician since Aristotle contains the second part of his career's published work. Included is the familiar papers on the continuum hypotheses (and others) all with much in the way of introductory material with detailed extra references, etc. An editorial masterpiece.
Kurt Gödel Collected Works, Volume III Gödel and a whole team of editors 3rd of 5 volumes of the works of Gödel and translations of the same by a masterful team of scholars. Includes unpublished works and letters. I happen to get vol. 3 because Wilfried Sieg kindly gave this particular volume to me as a gift.
Popular Lectures on Mathematical Logic Wang Wang discusses logic, computability and questions in the foundations of mathematics. He also examines more narrowly philosophhical questions about the nature of machines and human computability. It is also important to realize that the "popular lectures" seem to be mostly addressed to fellow mathematicians, not the public as a whole.
Set Theory, Logic, and their Limitations Machover The text I used at McGill for my second course in logic. Quite mathematically advanced for some philosophers, particularly the set theory material we did not have time to cover.
Sets, Logic and Categories Cameron Another reasonably advanced textbook in logic.
Set Theory and the Continuum Hypothesis Cohen This is sort of a commemoration of a great mathematician and logician as it includes not just an account of forcing from the guy who invented it, but also an introduction by Davis and some remarks by Cohen on Gödel. The latter played an important role on the former's intellectual development and it is interesting to see how they saw one another. Cohen is not nearly as philosophical as Gödel and so the philosophical remarks are almost nil in this little book. However, there are a few, especially after the principle theorems about the continuum hypothesis are proved. Also in the book is a brief survey of the material necessary to understand most of the aforementioned proof.
Set Theory and Logic Stoll A somewhat haphazard (repetitive) text with plenty of exercises of varying difficulties. Probably suitable for a 300 level course or two, depending on how many chapters are selected. Topics include Cantor's concept of set, the natural number sequence, extensions of the natural numbers, propositional (herein: "sentence") and predicate calculus, introduction to axiomatization, boolean algebras, some axiomatic set theory, axiomatization of some algebra, brief metamathematical topics (completeness, etc.). In a way it is very similar to Machover's book (see above) but longer and more "chatty" which is all to the good - in this case - as far as I am concerned.
The Concept of Logical Consequence Etchemendy This is a curious little book, which demonstrates that the usual understanding of (semantic) logical consequence is wrongheaded. Curiously enough (or perhaps not, given how much of it is regarded) there's no reference to vol. 1-2 of Bunge's Treatise which also develops a "nonTarskian" semantics. It would be an interesting project to see how compatible these two are. I've suggested the project to my dear friend and one-time colleague Audrey Yap, who was the one to tell me about Etchemendy's book to me in the first place.
The Undecidable: Basic Papers on Undecidable Problems and Computable Functions Davis, ed. A Dover reprint of a classic collection of classic papers in logic. Picking up where the From Frege to Gödel volume left off (with one item of overlap), this volume includes more papers by Gödel, Turing, Church, Post, Kleene and Rosser. The final paper by Post is quite remarkable and is not available except in this volume (or its Raven Press predecessor). Davis includes brief notes about each paper.
Topoi: The Categorical Analysis of Logic Goldblatt Many more advanced books in logic use a rather ill-specified ambient metatheory; subsequently the main strength of this book is spelling out a rigorous metatheory in the framework of category theory. Unfortunately, this sometimes makes one lose track of the logic. I'm also somewhat worried about the status of one's metatheory generally when things like completeness, etc. are proved: the self-referential aspect is very strange. However, the book does politely start from near first princples. Nice to see reference to some of the workers in the area "from" my native Montreal, too.
Undecidable Theories Tarski (w/ Mostowski and Robinson) A brief introduction (in three papers) to the general approaches to proving various usual mathematical theories (in algebra, for example) undecidable. Very, very elliptical and cursory, but with many important results stated. It is also interesting to note that the book addresses a question I had not seen addressed in any great detail elsewhere, namely the question of what could be called "second order" decidability. As it happens, the general question of whether a theory is undecidable is itself undecidable.


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