All in Logic

Gödel, Incomplete

Here's a short movie by Martha Goddard. It features the logician Gödel... one of the most important mathematicians of the 20th century. The title: "Gödel, incomplete." Gödel's most famous results were his "incompleteness" theorems. These theorems demonstrated limits of formal systems. At the same time, Gödel himself, as a person, is incomplete, and defined not only by what he is, but by what he is not... by his empty spaces, his desires. Which include love.

A new approach to understanding why logic works and its applications

My PhD dissertation showed “why logic works,” gave a pattern for creating new techniques for building models of consequence, and developed ways of comparing the relative power of different modeling techniques. It showed how to understand logic as a tool we use for the construction of knowledge, and how design choices in the construction of the semantic model lead to different properties of the resulting system. A new set of techniques, ones more appropriate for modeling the meaning of object-oriented data, were created and analyzed.

My adviser Jon Barwise was a world-famous logician, a founder of the Center for the Study of Language and Information at Stanford, a professor of Mathematics, Philosophy, and Computer Science, and editor of the Handbook of Mathematical Logic. He wrote: “I think what you have done in your dissertation is quite interesting and makes a real contribution to the program of understanding what we mean by logical consequence.”