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 amazon.com. I have included brief reviews of hundreds of books.
Professional resources Research sources, amazon.com associates programs, etc.
What is the philosophy of computing? A brief introduction to my primary professional interest.
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My educational philosophy As a sometime teacher I've developed one. Includes book resources.

Book Influences - Philosophy of Mathematics

Title
Author
Purchase / Enjoy Cover
Comment
From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s Mancosu English translations (some new to this volume) of key papers from this section of the history of the philosophy of mathematics form the bulk of this volume. In addition to the Brouwer and Hilbert of the title, we also get selections from Weyl, Bernays (in a way the "number two men" of each of the first), Hölder, Kolmorgorov, Borel, Heyting and Glivenko are also all represented in this debate. Beyond the original papers are many pages of introduction and analysis by Macosu and Van Stigt. A good collection and fills in some of the more "philosophical" parts of the history omitted from (e.g.) the otherwise excellent From Frege to Gödel.
Mathematical Experience Davis A curious book, though packed with interesting stuff.
New Directions in the the Philosophy of Mathematics Tymoczko This philosophy book also has some more directly mathematical papers in it, though ones with a foundational flavour.
Reflections on Kurt Gödel Wang Wang discusses the mathematics and philosophy of his sort-of teacher, Kurt Gödel.
Remarks on the Foundations of Mathematics Wittgenstein My own philosophy of mathematics was first articulated in response to this odd and difficult work. It does seem (as many claim) not to fully grasp the Gödelian incompleteness theorems, but this does not affect many of its central concerns. It is, however, odd that W. never uses many examples from mathematics as practiced by mathematicians. That said, it might be rejoined that the foundational works (Russell, etc.) that he's responding to do not either in a different sort of way ...
The Foundations of Arithmetic Frege The first classic defense of logicism in arithmetic. Note that this position in the philosophy of mathematics Frege explicitly says does not generalize to other areas, notably geometry. (It is unclear whether he thinks it extends to analysis, say.)
Thinking about Mathematics: The Philosophy of Mathematics Shapiro A discussion of historical and contemporary views in the philosophy of mathematics, including a chapter on the now fashionable structuralisms. Shapiro's pointing out that there are several different structuralist views is to the good, but I fear he does not adequately address the concern that structuralism is not an answer to ontological concerns: sure, so 1 is a place or role in a structure. What's a structure? He addresses the question, to be fair, but does not seem to completely finish the discussion. For example, one could say that the natural numbers are a role within set theory, but ... roles are concrete, for example, if they are social, so this has to bottom out with all the problems that raises, or ... maybe, an infinite regress looms, not necessarily (and here I am not sure) a vicious one. I guess one could say the view allows, potentially, the structuralist to indefinitely postpone the question of ontology.
Wittgenstein's Lectures on the Foundations of Mathematics Wittgenstein, edited by Diamond I bought this to see what Turing's contribution to the seminar that the book is taken from would be. Shanker has asked why Turing didn't use his "Computable Numbers" work to respond to Wittgenstein here ... I don't see any good reason, myself.

 

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