A Winter of Philosophy and Logic
Winter has passed here in Alexandria and I wanted to reflect on a rich and productive Winter of readings in philosophy and logic. Early this Winter my friend and colleague Ralph Hodgson recommended Sting’s new work If On A Winter’s Night. As if awakening from that long dark night, I have much to share about a time of deep contemplation and thoughtful reflection.
If you follow my tweets, you saw some of it unfolding. Readings from and about Russell’s theory of types provided insight into ramified type hierarchies that remain central to much of the Object Management Group and the World Wide Web Consortium‘s standards development. Proceeding through the development of type theory since Russell, constructive and intuitionistic logic became the central focus of my readings. I am very pleased with the amount of original material I was able to find on this subject. Brouwer’s Intuitionism and Formalism is just one example. My bookmarks are worth browsing for these original materials.
A longer journey into type theory took me through Martin-Lof’s impredicative and predicative type systems, Girard’s Paradox and Coquand’s Calculus of Constructions. These readings brought into focus as sharp as one might get at noon on a hot Summer’s day, the past five years of our team’s work on Model Driven Architecture and the Semantic Web. Following on Coquand’s work, I progressed deeper into algebraic specifications with the EU’s Common Algebraic Specification Language.
Most importantly, I made very good progress with tooling in each of these areas. Proof General is showing itself a very useful proof assistant. Haskell, Isabelle, oCAML and Coq all provide open source licensing that made it possible for me to get my hands dirty. It’s all free. Free as in Freedom !
I’m confident enough with what I was able to accomplish this Winter that I registered the methodeutic.com domain name.
But Winter has passed and it’s a warm Spring morning here in Alexandria. I’ll talk more about this work over the next few months. Right now the Spring weather’s so nice, I’m heading outside !