The Search for Logical Forms

In my dissertation, I defend a new version logical atomism. I first criticize the standard interpretation of Russell’s logical atomism as a search for logical atoms, and then I reinterpret it as a search for logical forms. I argue that logical atomists are term-busters, and they search for logical forms by taking apparent terms and busting them into non-term parts of formulas, just as is done in Principia Mathematica.

I split my dissertation into two parts. In the first part, I support my interpretation of logical atomism using its history. In the second part, I develop my own brand of logical atomism. So in the first part, I reinterpret the logical atomism genus; in the second part, I create my own species of logical atomism.

A dissertation abstract is included in my CV. The chapter titles are as follows:

  1. The Logical Atomism of Russell
  2. The Archetype for Logical Atomism: Principia Mathematica
  3. The Logical Atomism of Wittgenstein
  4. A Philosophy of Logic for Logical Atomism: Pure Logic
  5. A Formal Logic for Pure Logic: Z-Types
  6. A Metaphysics for Z-Types: Logical Concepts and Logical Facts

Coding the Proofs of Principia in Coq

In this ongoing, long-term digital scholarship project, I use the computer proof-assistant Coq to computer check the proofs in Principia under rival interpretations. This has historical interest as a tool to settle longstanding scholarly disputes concerning Principia‘s syntax: scholars debate whether the syntax is ramified or not. This will allow one to automatically verify whether the proofs stand on each rival reading and to survey whether proofs are preserved on the competing interpretations.

This project also bears on the philosophy of mathematics: this coding of Principia will function as a tool for rigorously extending Principia‘s logical framework to areas of mathematics not covered in the original work, like group theory, topology, and geometry.

A Public-Domain Prototractatus

I contributed to The University of Iowa Tractatus Map, a project led by David G. Stern and Phillip Ricks. My main contribution was to convert the text of the Prototractatus into a digital format that allowed us to generate a digital, subway-style map of the Prototractatus and compare it to the Tractatus. The project is described in Daily Nous. Here is a brief summary.

Thanks to Luciano Bazzochi’s work on Wittgenstein’s Tractatus, we have a new and illuminating way to read the Tractatus. We may arrange the Tractatus‘ numbered propositions ‘tree-wise’, as opposed to arranging them in the usual linear manner. This produces a subway-style map of the Tractatus and of the earlier Prototractatus.

So there has been much fruitful activity in producing survey-able, ‘tree-wise’ arrangements of the Tractatus. One thing that is missing is a public-domain, tree-wise arrangement of the Prototractatus. One of my ongoing projects is to produce, in collaboration with Stern and Ricks, such an edition of the Prototractus using LaTeX. Our goal is to produce a readable and illuminating re-arrangement of an important text for both Wittgenstein scholars and students of analytic philosophy.